Climate Feedbacks: Part I

by Judith Curry

Everybody talks about climate feedbacks, but what are they, really?  And where did the expression ΔTs = λRF actually come from?

All of this originated in a loose way from control theory developed in the context of engineered systems.  It is certainly an appealing idea to look at the climate as a control system, where we only need to keep track of the energy entering and leaving the system, and through some basic thermodynamic assumptions, relate changes in the flux of energy in/out of the system to a change in surface temperature.  The application of linear control theory to this problem assumes a very small perturbation to the system.  The following thermodynamic feedbacks are typically separated out in this analysis to be additive: water vapor, lapse rate, cloud, and ice albedo.

Since I don’t have time at the moment to develop extensive new content, here are some resources to kick off the discussion, I will add others as they are suggested in the comments.

Key references

Here are some of the references that I regard to be seminal in framing how to think about climate feedbacks.  AFAIK, Hansen et al. and Schlesinger were the first to frame the problem in this way.   The best overall discussion is given by Roe.

Roe 2009: Feedbacks, timescales, and seeing red

Hansen, J., A. Lacis, et al., 1984: Climate sensitivity: Analysis of feedback mechanisms.

Schlesinger, M 1985, 1986 (unavailable on the web, contact me if you want a copy).

Stephens, 2005:  Cloud feedbacks in the climate system: A critical review.

Aires and Rossow, 2003:  Inferring instantaneous, multivariate and nonlinear sensitivites for the analysis of feedback sensitivities for the analysis of feedback processes in a dynamical system: Lorenz model case study

Bony et al. 2006:  How well do we understand and evaluate climate feedback processes?

Bates 2007: Some considerations of the concept of climate feedback.

The NRC in 2003 published a report “Understanding Climate Change Feedbacks”

In my text Thermodynamics of Atmospheres and Oceans, I have written a chapter on Thermodynamic Feedbacks in the System, which is available online (text, figures).  If you aren’t ok with partial derivatives, you probably won’t get much out of this.

Blogospheric essays

At a simpler level, here are some explanations of climate feedbacks that I’ve spotted in the blogosphere:

JC’s 2003 feedback presentation

Circa 2003, I gave a presentation on feedbacks at a Search meeting, relevant excerpts from the presentation is appended below:

The nature, measurement, and modeling of feedbacks: Some thoughts on framing the feedback issues/strategies for SEARCH

Feedback is an interaction among processes in a system in which a change in one process triggers a secondary process that influences the first one.  A positive feedback intensifies the change in the original process, and a negative change reduces it. A feedback is NOT a forcing (e.g. clouds influencing sea ice is a forcing rather than a feedback).  “Feedback process” is ambiguous; a single arrow is not a feedback process, and a collection of processes is not a feedback unless they contribute to a closed feedback “loop”.

Observing feedbacks: A feedback cannot be observed.  Variables are observed. Correlation between variables says nothing about causality. Direction(s) of causality between variables can (at best) be inferred probabilistically.

Evaluating feedbacks using models: Some causation processes are represented explicitly in models; others are indirect results of nonlinear processes. In a chaotic, nonlinear climate model with 107 –109 degrees of freedom, we do not know how to evaluate the feedbacks.  It is not possible to unambiguously separate individual feedback loops. Estimating feedback through equilibrium simulations of GCMs, linear analysis, or analysis of vastly simplified models can be misleading.  It is not possible to identify the “most important” feedbacks.

Example –  cloud feedback. Cloud feedback is regarded as a very important climate feedback.  This evaluation is tied to the magnitude of “cloud radiative forcing.”   In a complex nonlinear system, a large forcing does not necessarily translate into a large and “important” feedback.  Evaluation of cloud feedback in GCMs using a simple linear analysis shows model disagreement in both magnitude and sign.  If plausible projections can be made with different signs of the cloud feedback, it is possible that cloud feedback is not “important”.  LESSON:  Do not confuse forcing with feedback.

Example – snow/ice albedo feedback. Snow/ice albedo feedback is regarded as a positive feedback. The sign depends on the time scale under consideration. On glacial time scales, there is a period that follows the onset of warming where snow/ice extent increases, owing to an increase in snowfall.  LESSON:  The magnitude and sign of a feedback can be frequency dependent or associated with a substantial time lag.

Example – water vapor feedback. Water vapor feedback is generally regarded as being positive. However, one study of tropical convection suggests a negative water vapor feedback. While this study is very controversial, the relevant point is that we do not know how to unambiguously discriminate between the two opposing theories. LESSON: The sign and strength of a feedback can vary regionally.

How can we productively use the concept of feedback to understand and model climate variations?

1.  Use our understanding of physics, chemistry, biology to construct feedback diagrams or causal graphs.  Such diagrams aid our conceptual understanding of the climate system and its subsystems.

2.  The concept of feedback can help guide effective design of process studies and use of observations to evaluate models

Using observations to evaluate models. Examine the evolution of model processes over short-term modes of variability (e.g. the annual cycle) and compare with a carefully constructed set of observations. Compare model results with observations in the context of the covariance of variables that are related in a feedback loop.  Hypothesis:  current parameterizations of sea ice albedo are too simple to accurately simulate the ice albedo feedback mechanism.  Method to test hypothesis:  conduct model experiments with i) the simple parameterizations; and ii) a more complex parameterization.  Criterion for accepting simple parameterization:  feedback gain ratio for simulations is essentially the same as that for the more complex parameterizations

Conclusions regarding the appropriateness of one parameterization vs another depend on the model that is used to evaluate it.  Investigation of the parameterization in a hierarchy of different models is needed to understand the impact of the parameterization and its role in the modeled feedbacks.  Coupling of two subsystem models will introduce additional nonlinearities into the coupled model.  Nonlinearities arising from the coupling requires additional attention to both the modeling aspects of the coupling and observations with which to evaluate the coupling.

Use the annual cycle and any other short modes of variability to explore interactions and feedbacks. When comparing models with observations, examine the covariance among variables related in feedback loops.  Be patient, the system is complex and the answers won’t fall out easily or unambiguously.

So what are the outstanding issues?

After two decades of wrestling with this issue, I’m not sure  how useful the concept of “feedback” is in the context of the climate system.  We already saw what kind of trouble we can get into on the thread on CO2 no feedback sensitivity, which is supposed to be the easy part of the problem.  The problem flat out isn’t linear, and attempting to do a nonlinear control theory analysis is pretty hopeless, as illustrated by the Aires and Rossow paper.  At best, it seems like the concept is useful as a conceptual aid in thinking about a complex system.  Various metrics like ΔTs = λRF or the partial derivatives may have some use in comparing climate models with each other or with observations, but it may not say much about feedback.  So is this concept useful?  If not, can it be salvaged?  I find the conclusion in the Roe paper to be very insightful.

And finally, are there better ways to try to understand the whole system, something from dynamical systems theory, entropy extremals, etc?

Note: this is a technical thread, comments will be moderated for relevance.

233 responses to “Climate Feedbacks: Part I

  1. I suspect that climate feedbacks in a computer contribute to very large errors in climate predictions.

    With kind regards,
    Oliver K. Manuel
    Former NASA Principal
    Investigator for Apollo

  2. Hasn’t Roy Spencer been fussing a lot about feedback confusion? Might be worth a look.

  3. I don’t understand your issue with ΔTs = λRF ,

    It’s just a way to connect the relationship between the radiative forcing and the final temperature response (e.g., to CO2 increase, solar increase, or whatever). And it’s an equilibrium statement, a fact implied in its very derivation.

    • Chris, here are my problems. For a change in RF, there are many possible distributions of heat in the system and hence many different delta Ts. There is an implicit assumption about lapse rates etc that just dont hold up in any kind of global sense. Also, the system is never in equilibrium, so you need to pick a time scale to average everything and then assume that all the heat stored gets materialized on the surface during this period. The derivation also assumes linearity and hence a very small perturbation, which doubling CO2 and its attendant feedback arguably is not. These are just the main problems i have with the whole formulation; once you start talking about individual feedbacks (e.g. water vapor or whatever), additional inconsistencies arise.

      • Judy – You state re current concepts, “There is an implicit assumption about lapse rates etc that just dont hold up in any kind of global sense… The derivation also assumes linearity and hence a very small perturbation

        It is my impression that current models do not make overgeneralized assumptions about lapse rates or linearity, but rather treat each of these as variable according to latitude, seasonality, and other factors. For the no-feedback scenario, this generates a small difference from the “single linear lapse rate” approximation, yielding a value of 1.2 C/CO2 doubling as opposed to 1 C for the simplifying assumptions. In the case of feedbacks, lapse rates are clearly a variable. Rather than assuming that all heat appears on the surface prior to equilibration, I interpret the models as requiring the pre-equilibrium interval to entail an imbalance between stored heat (particularly in the ocean) and its full manifestation on the surface. I wonder, therefore, whether we are talking about the same things, and if not, whether you can reference the points you are making.

      • Climate models don’t make assumptions about linearity or lapse rates, but trying to relate delta F to delta T in some physically meaningful way invariably involves assumption of connection of the surface to the tropopause temperature, presumably through the saturated adiabatic lapse rate.

  4. An engineered feedback loop can be very explicit and transparent, like a thermostat. The question is whether any such clear-cut sequences exist in climate or weather processes.

    As for the comparison between simple and complex parameterization, this gets you to the point of choosing the most “efficient” modeling of a hypothesis. It says nothing about actual processes.

  5. Note that “forcing” is a concocted concept, unique to climatology. It is not part of physics. It amounts to choosing one step in a hypothetical sequence as primal. In a true feedback loop, all variables are “forcing”.

    • I thought for some time it would be good to throw out the climate science concepts of forcing and feedback and couch the problem in an existing branch(es) of math and science. Also, use proven statistics. I don’t understand why climate scientists have this need to re-create the wheel.

      • Christopher Game

        No, Jim, “they” didn’t re-invent the circular wheel. “They” invented the triangular wheel instead.

        The reason they did it is because it speciously seems to justify their free use of the emotive and propaganda-effective terms “positive feedback” and “amplification”. The existing branches of math and science are too objective and logically transparent for their propaganda needs.

        The article by Roe (2009) has a heading on its page 99 “Feedbacks Are Just Taylor Series in Disguise”. The IPCC “forcings and feedbacks” formalism elegantly parroted in that Roe article may well be as he says “Taylor Series in Disguise”, but the ordinary non-IPCC ideas of feedback are about dynamical structure and are not just Taylor series in disguise. The IPCC use of the term ‘feedback’ is metaphorical and is an effective theft of language for a nefarious purpose; a tried and true propaganda technique; they explicitly cite Bode 1945, but their use of the term is far from his.

      • It seems to me the net feedback should be negative, not positive. Otherwise the system would have already breached the good ole “tipping point.” To make the system hotter, decrease the negative feedback.

      • Jim – It is universally agreed in the climatology literature that net feedback is negative if “feedback” is defined as the total response to a forcing. “Positive feedback” is defined (in climatology) as the sign of the feedback that occurs after excluding the Planck Response – the increased heat shedding by a warmed system as a function of the Stefan-Boltzmann law. The Planck Response is the negative feedback that limits the potential of all the positive feedbacks to mediate a runaway climate. Under current conditions, therefore, the climate continues to operate under negative feedback, and few observers believe an unstable net positive feedback is likely in the foreseeable future, even with continued increases in CO2 and temperature.

      • Christopher Game

        Dear Fred Moolten,
        To judge from your statement “The Planck Response is the negative feedback that limits the potential of all the positive feedbacks to mediate a runaway climate”, you think that the Planck response is a feedback? In my post , I am complaining that the panel a of figure 2 of Roe’s 2009 review does not show the Planck response as part of a feedback loop just as the other feedbacks are shown in panels b and c in that figure 2. I ask again, where is Rf in this figure? So I say that the figure as printed does not make sense and that the referees did not do their job here.

        In terms of the diagram as printed, the result of a CO2 perturbation is not an input as represented in the figure: it is a parameter change that should be shown as a change of λo. This is saying that the “radiative forcing” effect of a CO2 change is a “forcing” only in a metaphorical or handwaving sense, and is not valid physics. The diagrams of figure 2 are therefore nonsense if read as statements of physics. They are only handwaving. But they do represent the IPCC “forcings and feedbacks” formalism, which is likewise nonsense if read as statements of physics. Can anyone provide an account of the IPCC “forcings and feedbacks” formalism that is not vulnerable to this criticism?
        Yours sincerely, Christopher Game

  6. Judith,
    The mistake of climate science is to look for a temperature pattern then create a mathematical formula that will back this. But the unpredictablity of weather has generated failure in this area as temperatures are not solid events. Our planet has an extremely narrow window of temperture changes when the global average is incorparated over many years.
    Many errors in science compond the frustration of accuracy and planetary understanding of events.

    Water in it’s form, is already a forced event from being pressurized from the relaxed state of gases.

  7. Harold H Doiron

    I think it would be helpful for climate scientists to use the same definitions and terminology used in other branches of science that have at least 50 years of computer simulation experience. This would facilitate communication between the climate research community and experienced modelers from other disciplines.

    Whether an item (or process) is considered a feedback forcing function internal to the system, or a forcing function external to the system, depends on where the analyst idealizes the boundary of the system; reflecting completeness of the model. For example, I would take issue with your statement “A feedback is NOT a forcing (e.g. clouds influencing sea ice is a forcing rather than a feedback). ” I agree that internal feedback loops are not external forcing functions. But certainly cloud formation at a specific latitude, longitude and altitude depends on temperature of the air where water vapor was injected into the air, air volume lifting mechanisms in the atmosphere including winds and surface topography, and temperature gradient in the atmosphere. Therefore, I view cloud formation as an internal mechanism of the climate model, and the extent to which existence of clouds at certain x-y-z coordinates reflect the sun’s radiation or re-radiates it and affects the sun’s energy flux retained in the atmosphere; thereby affecting atmospheric temperature vs. altitude, constitutes a feedback loop. If sea ice is considered to be part of the climate model affected by clouds then I view the effects of clouds as a feedback mechanism and not an external forcing function. If we modeled the Physics and Chemistry of the entire universe in climate change simulation models, there would be no external forcing functions. To the extent that external forcing functions must be used because the entire universe is not modeled, the response of a perfectly accurate climate change model is in error by effects of the unknown error in the assumed external forcing functions.

  8. In my view, climate forcings are well defined. Solar input is a forcing, atmospheric constitution (e.g. CO2) can be a forcing if non-naturally varying, and in the case of the ice ages, ice albedo itself is a forcing to the extent that conditions favor polar ice in some orbital and continental configurations. I don’t count ice ages as solar forcing because intrinsic solar irradiance variation is not what drives ice ages, which separates this forcing from the LIA for example, which likely was caused by solar variation.
    Climate feedback is particular in the sense that the feedback loop doesn’t go back to the forcing and hence a positive feedback is not necessarily unstable. A lot of people are confused by this, because they know the climate has never exhibited a runaway effect in the past, but associate all positive feedbacks with a runaway effect, which is incorrect under the climate definition of a positive feedback. Climate feedbacks just produce multiplicative effects on the effects of the original forcing. The most obvious example is how water vapor feedback may amplify the CO2 forcing effect on global temperature. It does this, not by changing CO2 in any way, but by feeding off the temperature effect of the CO2.

    • Multiplicative effects are not feedbacks. A causal chain is not a feedback, even if it branches.

      In the water vapor effect the supposed feedback is on the temperature, not the CO2. CO2 raises the temp which increases water vapor which further raises the temp. The purported feedback is from the first temp increase to the second. One could have a CO2 feedback if the first temp increase increased natural CO2 emissions.

      • Yes, thanks for making that clear. The water vapor feedback can act on other forcings like solar too.

      • “One could have a CO2 feedback if the first temp increase increased natural CO2 emissions.”

        The size of the feedback is somewhat still in question . The lowest estimate I’ve seen is that the oceans will outgas 7ppm CO2 per 1 degree C.

      • There is interesting evidence that CO2 increases more quickly in warmer years than in colder ones. While it is the right sign for the Henry’s Law effect, I have heard it is larger in magnitude than that would predict, and maybe something is going on with the land and biosphere cycles too.

      • Yep, I’ve seen higher estimates as well.

        The whole Boreal Forest/Arctic tundra discussion appears to me to be less then perfectly understood at the current time as well.

  9. randomengineer

    …which separates this forcing from the LIA for example, which likely was caused by solar variation.

    We are told that CO2 must follow temp or vica versa; e.g. CO2 has gone up since the industrial age hence temperature *MUST* go up.

    On the other hand vostok etc purport to show flat CO2 variation hence the MWP is “unknown forcing” and the LIA is “unknown forcing, probably solar” which is a non-answer. “Likely” isn’t good enough. This is especially true in light of constant shooting down of TSI as a factor. We have a new minimum starting and UAH shows 2010 as pretty warm. So much for solar variation. I’d like to see this put to bed. The sun varies and messes with climate or it doesn’t. I really get tired of hearing that the sun of 1650 causes the LIA but the same sun can’t cause warming because it’s constant. Which is it?

    I don’t think any dicsussion of feeback mechanisms can even begin until the MWP and LIA are fully and unambiguously explained to the extent that everyone can understand it (and by everyone that will include me if you use crayons and write slowly.) I mean really, if we can’t accurately describe the last two major climate mini-shifts, how can anyone hope to realistically discuss the role of (e.g.) soot?

    • I would quantify the solar variability as plus or minus 0.5 C at most. This is not expected to be a big factor next to the 3.5 C from CO2, which is why it has taken background role in the 2100 projection.

      • Jim, do you really believe that?

        It is amazing that someone would believe such thing! Simply amazing.

        How would you quantify orbital variabilities? Also 0.5 °C?

      • Orbital variability doesn’t change the global average solar input, only its distribution. I posted above about distinguishing Ice Age forcing from solar variability. It is an important difference because the Ice Ages could happen even with a constant sun, just because of the tilt and orbit.

    • RE,

      Obviously the more information we have about changes to climate in past times the better. But we do know, as you point out, that there were no changes to CO2 levels which could have accounted for the MWP and LIA, and that there has been no increase in solar activity which could account for the current warming, whereas it probably did play a significant part in early 20th century warming.
      So at different times there are different factors in play which will affect the climate – just because CO2 is causing the current warming it doesn’t mean that it had to be responsible for every warming period in the past, and the converse is true with changes to solar activity.

      • Andrew, you make several strong knowledge claims that I think are unsupportable. The basic point is that until we can explain natural variations (which we cannot) we do not know what factors to consider, so we cannot explain recent variations. It is a paradoxical situation, rather than having opposing hypotheses we have one hypothesis (AGW) opposed by known unknowns.

      • randomengineer

        But we do know, as you point out, that there were no changes to CO2 levels which could have accounted for the MWP and LIA… [snip]

        Ahhh, but my point is that we don’t know that at all. Some of the studies re stomata show more variance. I’d think that one could gather enough CO2 data (more studies) and determine that it did vary more, even enough to get a better picture of RF over time such that solar factors are better understood. (i.e. the idea here is that perhaps CO2 really did vary as per RF.)

        I don’t know why there’s such insistence on vostok data showing holocene invariance, but this assumption of invariance seems to cause the invocation (conjuring?) of “unknown” solar variability SWAGs re the MWP and LIA where perhaps these aren’t needed at all, or if they are needed, much better understood. I can’t see how SWAGs are useful.

        A recent article on stomata etc at WUWT had the cynics opining that CO2 variance upsets “the narrative” whereby man can be blamed for CO2 (i.e. a CO2 hockey stick.) While I don’t share the cynicism it does seem to me that the presumption of a stick shape (vostok overreliance) may play a role in not having a better handle on MWP and LIA events.

        As per David Wojick’s summary, he’s right: we need to be able to explain the (recent 2 kyr) past better, and the ability to do this may solve some of the uncertainty re feedback mechanisms.

  10. Check out A. Semczyszak at Jeff Id’s Air Vent on the ‘Historic Variations in CO2’ thread for tundra feedbacks, a great unknown.

  11. David L. Hagen

    Which comes first: The Chicken or Egg?
    Spencer comments on how Dressler’s finds the opposite climate feedback from Spencer, using the same data!
    The Dessler Cloud Feedback Paper in Science: A Step Backward for Climate Research

    The problem is figuring out what the cloud and temperature behaviors we observe in the data mean in terms of cause and effect. . . .Yet we came to a very different conclusion, which was that the only clear evidence of feedback we found in the data was of strongly negative cloud feedback. But how can this be? How can two climate researchers, using the same dataset, come to opposite conclusions? The answer lies in an issue that challenges researchers in most scientific disciplines – separating cause from effect. Because if warming causes fewer clouds, it lets in more sunlight, which then amplifies the warming. That is positive cloud feedback in a nutshell. But what if the warming was caused by fewer clouds, rather than the fewer clouds being caused by warming?

    See: Roy W. Spencer & William D. Braswell On the diagnosis of radiative feedback in the presence of unknown radiative forcing
    JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115, D16109, doi:10.1029/2009JD013371, 2010

    Axel Kleidon Non-equilibrium thermodynamics and maximum entropy production in the Earth system
    Naturwissenschaften. 2009 Jun;96(6):653-77. Epub 2009 Feb 26.
    Erratum Naturwissenschaften. 2009 Jun;96(6):653-77. Epub 2009 Feb 26.
    See especially Kleidon’s discussion on Fig. 7:

    (a) Maximization of entropy production for steady-state conditions implies a negative feedback to perturbations.

    However, when the system changes, then the transition can appear like a positive feedback.

    (b) When external conditions change in such a way that the trade-off between flux and force shifts (. . .new state), a perturbation of the flux would be enhanced until the flux reaches the new optimum value at which entropy production is at a maximum. This could be interpreted as a positive feedback to change.

    So “feedback” depends on distinguishing which is cause and which the effect. In complex systems, moving along a “system” ridge or saddle as the system changes can appear like positive feedback even though locally the system is in stable negative feedback.

      • I have read the originals from Spencer and Dressler. I have read Spencer’s response to what Dressler wrote. I tend to believe Roy is correct. However, what I would like to see is a critique of Spencer’s criticism of the Dressler paper. I hope someone on this blog is prepared to try and show why Roy is wrong. (

      • Jim – As I commented below, neither Spencer not Dessler are very relevant regarding climate sensitivity to CO2 changes. However, in regard to the Spencer and Dessler analyses, Spencer acknowledges that El Nino’s and La Nina’s are responses to changing atmospheric and ocean dynamics and are not caused by cloud changes. Despite his acknowledgement, the logic behind his assertion of negative feedback requires clouds to cause the El Nino’s/La Nina’s. Spencer therefore appears to advance an argument contradicted by his own understanding of climate dynamics. Dessler’s analysis is more robust, at least for short timescales, but still, in my view, difficult to extrapolate to the long term effects of changes in CO2 or other GHGs.

      • … the logic behind his assertion of negative feedback requires clouds to cause the El Nino’s/La Nina’s

        Nonsense. Nowhere does Dr. S say or imply that random clouds are the only cause of internal variation within the climate system; this would obviously be absurd. Lacis is presenting a typical Team “debunking”, armwaving incoherently at strawmen.

      • Craig – It’s not nonsense. Spencer, accurately, doesn’t believe El Nino or La Nina are initiated by clouds, but his analysis requires that logic. The question of whether they are the only factor is largely irrelevant to Spencer’s logic, which requires that the clouds cause the warming or cooling. At this point, it would be worthwhile for interested readers to review the actual papers to see why this is the case.

        My point is that while Dessler is certainly correct in attributing a positive feedback role to clouds in this setting, it is hazardous to extrapolate ENSO responses to long term feedbacks on CO2 forcing. The most cogent case for Dessler here is that his short term positive feedback derived from observations dovetails with long term positive cloud feedback predicted by models. That is persuasive, but not conclusive in my view.

      • My review, having seen Dessler’s paper, and their e-mail exchange.
        Dessler looks at 2000-2010 analyses and finds that clouds have a likely positive feedback on warming because they have a warming effect in the warmer periods.
        Spencer says this could be because clouds cause the warm periods.
        Dessler says no, the warm and cool periods in this analysis are mostly El Nino and La Nina, and clouds don’t cause those which Spencer agrees with, but suggests clouds lead them as part of the process, in which case they would not be a feedback.
        I think they talk at cross purposes because Spencer refers to lags of mid-tropospheric temperature with total forcing, not having separated cloud forcing, while Dessler specifically looked at clouds and surface temperature. To me, the open issue is if there is a lag between cloud forcing and surface temperatures. Neither seem to have a definitive answer on that.

    • David L. Hagen

      See Roy’s post Dec. 31, 2010 on Dec 11-31 on his:

      mini-debate by e-mail during the last 3 weeks between myself and Andy Dessler over the question of whether cloud feedbacks in the climate system are positive or negative.

      Dessler and Spencer Debate Cloud Feedback
      See further references above

  12. Difficulties in deciding what is forcing and what feedback result from vagueness in defining system boundaries.

    One possibility is to choose the wide definition that the whole earth with all internal processes forms our system. Only chances from outside the earth are forcings, all influences within the earth system are then feedback. Changes in GHG concentration influence then these internal feedbacks. From the point of view of a comprehensive earth system model, GHG concentration influences the strengths of internal equations. They are not forcings in the way the concept is used in other fields. Taking an analogy of an electronic amplifier with two control knobs, one influencing the attenuation of input signal and the other influencing the strength of the feedback, changing GHG concentrations can be compared with adjusting these control knobs, not with the changes in the incoming signal itself.

    It is also possible to divide the earth system to various subsystems on spatial basis. Various parts of the atmosphere, oceans and continents are taken as systems with external forcings and internal processes leading to feedbacks within each subsystem. The interactions between these subsystems lead to feedbacks in the wider system created by combining these subsystems. From this point of view all interactions within the earth system contribute to feedbacks. A GCM is then a set of equations which describe feedbacks. There is very little that should not be considered as a part of feedbacks.

    The standard approach in discussing climate change is a bit different. The earth system is not divided to parts using spatial boundaries, but the based on the nature of interactions. In particular the radiative processes are taken separately from the processes involving sensible and latent heat, material flows, biota etc. This division is problematic, because the interactions between radiative heat transfer and other flows of energy are strong and complicated. Increase in GHG concentrations influences radiative heat transfer within the atmosphere, but this influence is immediately compensated by opposite changes in convection and latent heat transfer in keeping the lapse rate almost unchanged in many parts of the atmosphere.

    There is a good reason to ask, what is lapse rate feedback. Is the feedback in limiting the change in lapse rate to be smaller than the radiative changes alone would have caused, or is the lapse rate feedback in the fact that the lapse rate changes a little in spite of the compensating changes in other processes?

    The discussion of feedbacks gets always confusing, when it is approached from a more general point of view. The concepts are not well defined. Their meanings are sometimes clear, when the scope is more limited. The climate modelers may have a common understanding, when they discuss specific feedbacks like water vapor feedback or albedo feedback, but there is certainly a risk that even the active climate scientists get confused by the impossibility of giving unequivocal definitions for feedbacks in the earth system.

    Judith, in my thinking the first part of your Chapter 13 (introductory part, 13.1 and 13.2) are somewhat problematic in the sense i tried to explain above. In control theory most of the interest goes into the dynamics of feedbacks, the steady state amplification is only the first almost trivial step. In the climate system the presently studied problems are different and the analogy is therefore of limited value. The analogy with control theory might be more fruitful when the consideration is extended to the dynamics of the earth system, where everything is dominated by feedback processes. All basic atmospheric circulations are part of feedback chains. Heating of the surface by solar radiation is forcing, nothing else is. The oscillations like ENSO or NAO are particularly interesting examples of feedbacks of this type. (Your equation 13.4 is also incomplete as the forcings have first order effects on the internal variables, I’s. Sun heats directly various parts of the atmosphere and GHG’s have also direct effects in many ways, not only through T0.)

    • Pekka,
      The complexity of the planet and atmosphere is more than our current science understands. The interactiveness of the system and constant changing through our planet rotating around the sun makes it that more challenging.
      Climate science also has to understand space science to fully grasp this complexity.

      An example is why our sun is closer at one point and further at another point rotating around the sun. The suns mass allows it to move through space at a constant speed while our planet rotates around this mass. When our planet is in front of the sun in rotation, the sun is actually moving closer to it and when our plant is at the furthest point away, the sun is moving away from the planet.
      Still has a bearing on the heat distribution on our planet.

      • That the Earth’s orbit around the Sun is an ellipse is not new news. Nor does it come as a surprise to climatologists. Similarly the mechanics of angular rotation and the latent heats of melting and evaporation have long been understood by scientists.

        Why do you persist in making dark hints that there is some cosmic secret about these well studies bits of conventional physics, thermodynamics and astronomy?

        Especially when you cannot back any of these mysterious assertions up with any facts other than to mumble into your metaphorical beard that no conventional scientist can understand your thoughts. Which I call a bigtime CopOut.

      • Thanks Latimer old buddy!

        Physics does not understand how to store and release energy by compression of gases to liquids in a rotational state of centrifugal force. Nor, how it effect mass. There is two areas of centrifugal force. Contained and uncontained.
        Like with your test tubes only with different speeds and gravity added.

      • Well Joe me old pal me old mucker, I think I learnt all about that stuff at about O or A level physics. Where are the conventional descriptions inadequate?

        A concrete example of five of recognised observations that you claim cannot be explained, with a pointer from you to where the errors lie will be a lot more convincing than a handwaving mumble into your metaphorical beard. Physics and chemistry are largely experimental sciences and observations are what count.

      • Sorry – forgot to add – please outline the experimental setup needed for an interested 3rd part (me for instance) to replicate your results and to show conventional physics to be inadequate.

      • Latimer,
        I do wish to apologize for my behaviour.
        I’m not very articulate in trying to show what you are trying to understand. I have tried different ways of showing people mechanically in the past and ususally loose them through the difficulty of the process.
        I have investigated a great deal in the history of our current LAW of science creators to understand what technology was available to them to the current technology today in order to find where they made their mistakes.

        Coil springs and compressing gases in a cylinder is an impossibility in Newtons’ time. Newton was using Picasso’s rotational table to understand circular motion.
        This does not tell how or what energies are inside that circular motion table to the different speeds when applied.
        So, mechanically understanding what centrifugal force was an impossibiltity.

    • Yes, this is a very convincing comment……in theory! However, in practical terms, we can’t model an ‘earth system’ in this way as our knowledge of the different processes and various feedback interdependencies is just not up to scratch. How could we ever hope to extract any meaningful information? Much like the current situation with GCMs, actually.

    • Christopher Game

      Dear Pekka Pirilä,
      You write: “One possibility is to choose the wide definition that the whole earth with all internal processes forms our system. Only chan[g]es from outside the earth are forcings, all influences within the earth system are then feedback. Changes in GHG concentration influence then these internal feedbacks. From the point of view of a comprehensive earth system model, GHG concentration influences the strengths of internal equations. They are not forcings in the way the concept is used in other fields. Taking an analogy of an electronic amplifier with two control knobs, one influencing the attenuation of input signal and the other influencing the strength of the feedback, changing GHG concentrations can be compared with adjusting these control knobs, not with the changes in the incoming signal itself.”

      Hear, hear! I am very happy to see this stated clearly like this. I am tempted to approvingly quote more of your post, but I will content myself with saying ‘Hear, hear!’ to it.

      Yours sincerely, Christopher Game

    • Harold H Doiron

      Pekka thinks about modeling as I do. If climate models don’t model at least the entire Earth system with its important internal feedback loops based on physical processes we must understand confidently and accurately, and let forcings be external to that system, I will always be skeptical of the model output.

      The climate model (in concept) should be exactly like control system models that are used to get the correct, confident answer when public safety is at stake.

      To illustrate, a classic control system problem in rocketry is the thrust vector steering control problem. The rocket’s attitude error (differing from a desired attitude vs. time or altitude, defined by the desired pre-determined trajectory) is continuously measured by a sensor mounted on the rocket’s structure, and the feedback control system gimbals (rotates) the engines slightly in response to the measured error, to rotate the rocket’s attitude with the engine thrust vector lateral thrust component, so that the rocket does not stray too far from the desired trajectory. External to the rocket system and its internal feedback attitude control system, are forcings such as lateral wind gusts that cause the rocket to veer from its desired path. It is straight-forward to model the rigid body dynamics part of the steering process. HOWEVER, if the effects of the structural dynamic bending oscillations of the rocket that affect the measured attitude of the rocket at the measurement station, are not correctly modeled in feedback loops, then the attitude error introduced by the bending vibration (which is also affected by gimballing the engines) is not accounted for, the steering becomes unstable, and any humans onboard die!!!

      Human lives and quality of human lives depend on the output of climate change models, IF you allow politicians to make public policy decisions based on their questionable output results discussed here. Therefore, you can’t leave out any important internal feedback loops, like the bending vibration, in your control system (climate) model if you expect to get an accurate answer for attitude vs. time (or in climate models, temperature vs. time).

      Although climate models are vastly more complicated than the control problem described above, I believe you must take this basic controls systems approach of modeling everything internal to the rocket and its control system behavior that can significantly affect the actual trajectory of attitude vs. time and altitude. For a climate model, this means modeling all atmospheric, oceanic, geophysical, biological, and human mechanisms that can affect global temperatures as well as other expected variations of external forcing functions of energy flux crossing the system model boundary (such as result from orbital dynamics of the Sun and Earth, solar flares, etc.)

      Getting the rocket steering control system model to behave like Mother Nature didn’t happen on the first try. A few rockets had to blow up before the important missing bending dyamics part of the model was recognized, understood, and then correctly incorporated into the system model to get accurate modeling results.

      You could model a perturbation of the climate system modeled like a feedback control system with numerous important internal feedbacks (analagous to the bending dynamics feedback loop) by a sudden injection of CO2 into the system in a specified spatial distribution and then see how the system responds to this perturbation. In this case , the sudden injection of CO2 would be an external forcing function to the climate system modeled. But, all important processes that respond to increased CO2 in the Earth’s atmosphere, and that eventually result in Earth surface temperature changes would need to be modeled, otherwise the model will end up with an inaccurate temperature reading at a later time.

      Once you think you have all of these important climate model internal feedback systems modeled, then I think you need to validate the accuracy of the model by checking its predictions against experimental temperature data in the future (not just the past). Once you are confident the model is right and validated, then it would be ethical to allow the model predictions to be used for public policy decisions.

      Until such time as you can validate models for their intended use, please by all means, continue to do research to improve your models, but be ethical scientists and DO NOT ALLOW public policy to be based on their outputs. As I have written elsewhere on this website, it is the climate research community’s responsibility, not its critics’ or CAGW skeptics’ responsibility, to prevent unauthorized use of very preliminary, incomplete, and unvalidated model results for public policy decisions.

      • Harold,
        While I may think on many issues in the same as you or Christopher, I am not so sure about ultimate conclusions.

        A new control system for a rocket will not be taken into use before it is thoroughly tested and validated. If a new rocket is dependent on this new control system its deployment may be postponed. This is always an alternative.

        The goals of climate modeling are different. We cannot choose, whether we live on this earth or not. We cannot avoid the fact that our decisions, including the decision to postpone all actions, affect the future of our planet. Humanity has reached the power to influence the earth system significantly. Most of this influence is very difficult to control through purposeful decision making by politicians or other leaders, but factors that can be influenced have also reached a level significant for the earth and the future of human race. The climate science has the goal to provide information for wiser decision making. For this purpose we should use the best knowledge available including the best models available even, if they are not fully validated.

        With respect to feedbacks, I am not worried about the use of the concept as it is most commonly used with climate change. By this I mean the use of the concept in openly zero-dimensional way to describe results of analysis, which itself is actually not really using the concept internally at all. I accept the following general steps:

        1. Calculate radiative forcing for a fixed (model) atmosphere summing over the whole globe.

        2. Convert the number obtained for radiative forcing in units W/m^2 (or W for the whole earth) to temperature units. I would prefer that this would be done on the level of effective radiative temperature of earth as seen from outer space, because this conversion involves the smallest number of assumptions.

        3. Call the results of 1 and 2 as non-feedback RF and non-feedback temperature change.

        4. Calculate with full models their results for the change in the surface temperature and repeat this calculation by excluding certain mechanisms from the calculation. Then the results can be expressed as expected climate sensitivity and as various feedbacks, which are explicitly defined as specified differences between various model runs. The differences can be expressed as changes in net forcing at tropopause or as changes in the resulting surface temperature.

        The word “feedback” is not ideal in expressing the results of step 4, but it is difficult to figure out any clearly better word. Therefore I am ready to accept this usage.

        What I was protesting more, was an overextension of the concept and the analogy with control theory. The concept of feedback is so useful in control theory for specific reasons including the smallness of the number of control variables. The concept is in my view not generally useful in describing the very complicated earth system in more details. There are subsystems and interactions between subsystems, where the simple feedback model may apply, but they are an exception.

        In my view the paper of Gerald Roe is evidence on that there is indeed a tendency of trying to use the feedback metaphor in ways that are certainly confusing and possibly outright erroneous.

      • Harold H Doiron


        You make some excellent points in your response. However, the debatable severity of the climate “crisis” we face doesn’t seem to justify the use of unvalidated models for attempting to change climate, especially when important governments with large populations don’t plan to join in the propsed solutions.

        One additional argument I would add to yours about the difficulty climate modelers face, is that we engineers can often build a useful conservative model that biases model results to more severe conditions than should be actually experienced (like dynamic loads used for stress analysis). I can’t figure out how you would do this for climate models. You don’t want to err on the side of either hot or cold…you have to have a model that “threads the needle” of accuracy.

        I don’t have any conclusions other than climate models don’t seem to have the maturity and quality of validation for use in decision making that will be extremely costly, perhaps damaging to the quality of life of many people, and frought with the possibilities of unintended detrimental consequences to many humans. What if a Chinese climate change model of the future can show (in hindsight) if we had just let nature take it course, they wouldn’t have had a such a long drought that resulted in hundreds of thousands of their citizens dying of starvation? Can we assure their scientists using scientific methods, that our attempts to alter the climate will not result in such a scenario?

        The FIRST Shuttle flight was MANNED. Of course the guidance and control system was tested as well as it could be in ground tests. But the first flight (manned) through actual high altitude wind gusts was the first time the system was operated in its intended flight environment . The flight simulation model predictions of the guidance and control system had to have extremely high confidence before committing human lives to this flight…Yes, Bob Crippen and John Young are brave, excellent and experienced test pilots, but they also had faith in the rigor, dedication and successful track record of the control systems modelers (and modelers of many other critical Shuttle sub-systems) who signed their names to the Certification of Flight Readiness (CoFR) for this first flight test.

        Sadly, we aerospace engineers, especially those of us who take pride in the sophistication and accuracy of our computer simulation models, mourn the lost lives, widowed wives and husbands, and orphaned children of the Shuttle Columbia astronauts (also our neighbors whose children go to school with our children) because some less experienced and undersupervised members of our technical community were using an unvalidated “model” of hazards presented by External Tank foam striking the Shuttle Orbiter.

        I believe that climate models need to have more maturity and confidence in their predictions, with a successful track record of predicting the future (at least 10 years into the future of predicting correct trends, certainly we have that much time to delay any overt action) before committing them to decisions that will affect human lives.

        I think the presentation at the following link by a revered aerospace engineer, Burt Rutan, does an excellent job of presenting the engineer’s point of view to the present situation presented by CAGW concerns.

        You might be able to nitpick around the edges of his analysis and interpretation of available data, but taken as a whole, the presentation gives much food for thought about the “crisis requiring action” that the climate research community faces.

        I readily admit that the number of important variables and processes affecting global average temperatures is a daunting task to simulate accurately (personally, I think yearly temperature variability, or yearly rainfall, at a given location are more important metrics), but I think the complexity of successful control systems type models used in the aerospace industry is underestimated in numerous comments made in this overall thread of Climate Feedbacks: Part I

        One of my technical specialties is computer simulation prediction of rocket “pogo” stability (a structural instability nicknamed after the “pogo stick”, and in the class of problems such as wing flutter and flight control/structures interaction, that involves rocket engine random thrust oscillations exciting axial vibrations of the rocket structure, which in turn interact with the liquid propellants in the tanks and feedlines to cause propellant pressure and flow oscillations at the rocket engine inlet, that in turn cause the engines to have a thrust oscillation that re-inforces the structural vibration. An accurate model of all the feedback loops requires modeling of how structural vibrations cause pressure and flow oscillations at the propellant tank outlets, how these oscillations are amplified by the acoustic properties of propellant ducts (like organ pipe air vibration models), how the complex cavitation dynamics of rocket engine turbopumps affect the propellant pressure and flow oscillations arriving at the combustion chamber, and how these propellant flow oscillations into the combustion chamber result in thrust oscillation forces applied back to the vibrating structure. In addition, many (pressure)x(area) forces are applied back to the vibrating structure though propellant feedline bends, structural supports, pump inlets, etc.

        In one new rocket with the first two successful test flights under its belt, SpaceX’s Falcon 9, there are 9 rocket engines, 18 feedlines and two propellant tanks. Certainly the feedback loops in our pogo model are more complex than suggested by you and others like Jim in your comments. Soon, we hope to have our models of the Falcon 9 pogo phenomena, and any required propulsion system design alterations to ensure stability, validated sufficiently to commit human lives for transportation to low Earth Orbit in replacement of the Space Shuttle, whose pogo stability validation I led through a similar process with enough confidence to allow the first flight to be manned.

        Now, after all that, don’t forget the main point of this response is to have readers look over Burt Rutan’s presentation.

      • What I dislike in the climate discussion is the difficulty of getting to the most important open questions.

        For me it is certain that human societies influence climate, but the extent of this influence is uncertain. I do not dismiss the IPCC estimate of the likely range of climate sensitivity although there are definitely some weaknesses in the arguments on which this range is based. For me this is not really the essential problem, because there is so much else that is even more uncertain or that influences the final conclusions more in other ways.

        The precautionary principle is logically correct and it is accepted as basis for risk policies in very many practical applications. It tells that the risks related to climate change should be given serious consideration. It is also easy to conclude that such actions should be taken, which reduce these risks without large costs or risks of some other nature. The problem arises, because such no-regret policies are not likely to change very much. As a result we have the real world controversy where many scientists are convinced that the risks are very large, but the proposed policies are costly and uncertain. Some of them have made estimates telling that the damage to be expected is many times larger than the cost of preventing. Stern report is the best known example. This report does not, however, rest on solid scientific (or other) knowledge or on well understood or generally accepted principles. Many other scientists have been very critical on Stern report. Just to give two examples I mention William Nordhaus from Yale and Richard Tol, whose blog is linked in Judith’s list on the right.

        For me the real problems are related first to the difficulty of deciding, how much we should do and in which directions, and second in knowing, how we can get it done even if can agree, what should be done. These are both very serious problems. In Europe the EU has done many decisions, which are not necessarily all wise as they are not based on good analysis and well-informed discussion of the main issues that I mentioned, but rather on European political realities. In US much less is done based on US political realities. This is again not based on a comprehensive analysis of the situation and wide well-informed discussion.

        There are many different ways of approaching the large open questions. I just mention two very different, in their own way relevant books. One is Mike Hulme’s “Why We Disagree on Climate Change” and another Roger A Pielke, Jr’s “The Honest Broker”. (I have not read his new book, but I think that the thoughts of this older book are very important and relevant.)

      • Harold H Doiron


        You state many reasons why I believe the climate modeling science is not sufficiently mature to justify the economic impacts to our nation implied by the Cap and Trade legislation that has already passed in the US House of Representatives and has a President willing to sign the legislation into law, if he could only get it passed in the US Senate. What insiders from the climate change modeling community are speaking out and against this reckless behavior of politicians that don’t have the scientific credentials to understand the debate regarding uncertainty of climate change models on this website?

        What we need is a high level US government sponsored independent review of climate change model uncertainty and validation status by a commission of independent scientists and engineers with impeccable credentials such as the investigating committee headed up by Richard Feynman after the Shuttle Challenger accident and a similar high level investigation after the Shuttle Columbia accident? Let us see if the climate change models and their proponents can stand-up to the tough questions in an open public forum from the best of the best of US scientists and engineers, including those with experience in use of computer model simulations where decisions based on model output affect public safety. I can’t see any strong evidence that the climate change modeling community is policing itself (other than the dialogue Dr. Curry has graciously hosted on this website) to make sure results of their model predictions are used in a responsible way. There are important national experiences and Lessons Learned from other technical disciplines that need to be brought to bear on this issue of great national importance.

        Surely the economic impact and potential quality of human life impact to our nation from Cap and Trade legislation is vastly greater than either of these Shuttle accidents. Why shouldn’t we have a formal review of climate change model accuracy and validation status before “briskly moving out” on such critical public policy changes based on the dire, but admittedly uncertain, predictions of these models?

      • +1; thanks for the link to Rutan’s presentation

        Pogo is an interesting thing. I was very impressed by the launch ops on Falcon 9’s first flight.

        The criticism that you highlight about model validation is going to continue to be one that climate science struggles with (but that struggle will improve the state of the science).

      • Christopher Game

        Dear Pekka Pirilä,

        You write: “2. Convert the number obtained for radiative forcing in units W/m^2 (or W for the whole earth) to temperature units. I would prefer that this would be done on the level of effective radiative temperature of earth as seen from outer space, because this conversion involves the smallest number of assumptions.”

        This step is the one that puzzles me. Gerard Roe is helpful when he writes: “In practice, the finite absorptivity of the atmosphere in the longwave band means that, in global climate models, the reference climate sensitivity parameter, determined after removing all dynamic feedbacks, is 0.31 to 0.32 K (W m^−2)^−1 (e.g., Hansen et al. 1984, Colman 2003, Soden & Held 2006). For the 4Wm^−2 radiative perturbation that a doubling of carbon dioxide produces, the reference-system climate sensitivity3 is ΔT0 = λ0 ΔRf ∼ 1.2 to 1.3◦C. In general terms, the reference system takes a perturbation in the forcing, ΔRf , and converts it into a response, ΔT0 (Figure 2a).” Does the atmosphere-earth body really reflect infrared radiation as it would need to do to have an apparent “emissivity” less than 1 ?

        If you would feel like further clarifying this for me, I would be very glad.

        By the way, though I agreed above with your thinking about the input of a solar signal, I did not mention that the “amplifier” has not been supplied with a battery and so cannot actually amplify as proposed. In this way of picturing it, the system is like a passive attenuator, not like an amplifier.

        I agree with your comment about “overextension of the concept [of ‘feedback’] and the analogy with control theory”. But I think there might be a use for dynamical systems theory.

        Yours sincerely, Christopher Game

      • Christopher,

        The choice for converting to temperature that I would prefer differs from that one proposed by your references, because they use some simple model for the atmosphere to obtain the temperature at earth surface. Their simple model is by purpose wrong in the sense that there is an attempt to exclude all feedbacks. The choice for defining such a no-feedback model is not unique and slightly different choices could be justified equally well, which would give slightly different answers.

        My preference would exclude all these considerations by being a simple application of Stefan-Boltzmann formula. It requires only changing the total radiative power by the value of the radiative forcing and checking, what is the corresponding change in the effective temperature. This value is unique and very easy to determine given the original effective temperature and the radiative forcing. For the original radiative temperature of 251 K the increase to 252 K corresponds to the radiative forcing of 3.61 W/m^2. The result of same forcing in the other approach is 1.2 – 1.3 K, i.e. somewhat larger, but close enough to allow substitution without major complications.

        The concept of “feedback” and its connection to the surface warming after full calculation would have to be defined a bit differently, but as discussed in this thread, the definition of feedback is not very clear in any approach.

      • Christopher Game

        Dear Pekka Pirilä, Thank you for this. Christopher Game

      • If climate models don’t model at least the entire Earth system with its important internal feedback loops based on physical processes we must understand confidently and accurately, and let forcings be external to that system, I will always be skeptical of the model output.

        It is commonly thought that the further ahead one wants to predict, the more precise the model must be.

        What makes this false is that the “entire Earth system” consists of components with natural time constants over a huge range, from the seconds it takes a drop of rain falling on a hot pavement to evaporate, to the 50 million years it took the climate to drift down to the Holocene, and more.

        If we are interested in the temperature 50 years hence, then every phenomenon with a natural time constant less than 10 years or more than 250 years is irrelevant. This simplifies our task to identifying those components of the entire Earth system with natural time constants on the order of 50 years, give or take a factor of 3-5.

        In particular this rules out diurnal and annual fluctuations, solar cycles, El Nino events and episodes. It also rules out anything to do with Milankovitch cycles. Conceivably a repeat of the Younger Dryas is in our immediate future, but given that the previous one was 11 millennia ago the odds of its circumstances being recreated in the next 50 years is something like one in 200.

        When we look at the last 160 years of temperature as recorded in the HADCRUT3 database, there are no variations in it with natural time constants on the order of 50 years with the following exceptions.

        1. Ocean oscillations, in particular the 56-year component of the Atlantic Multidecadal Oscillation, AMO, and what I believe to be a 75-year component of the Pacific Decadal Oscillation, PDO.

        2. Warming attributable to CO2. This grew negligibly between 1850 and 1930, but then started climbing and is today roaring up at over 2 ppmv per year and is arguably responsible for 0.14 °C per decade of the total 0.165 °C per decade seen in the violet curve here.

        3. Sporadic aerosol incidents, primarily volcanoes, and possibly the Tunguska event and World War II.

        By targeting a specific time frame into the future we can eliminate most of the components of a comprehensive model of global warming and reduce it to sufficiently few that there exists an elementary formula for the model!

        As can be seen from the violet curve in the above graph, which is given by such a formula, it is a good fit to the 12-year-smoothed HADCRUT3 data from 1850 to now. The black curve labeled “Residue” indicates the departures from this model. Although there are short-term departures there is no long-term departure, even over the whole 160-year period.

        This formula was obtained from consideration of the whole 160-year HADCRUT3 database. If the last 30 years are deleted and the model is fitted to, or “trained on” the remaing 130 years from 1850 to 1980, we obtain this graph.

        When we compare the two fits we find that the first 130 years was already good enough to determine the parameters almost as well as with the additional 30 years of data. Hence the predictive power of this method, if available then, would have allowed us to see the sharp temperature rise that was coming.

        Nothing in either the data or the assumptions on which the model is based incorporates a sharp future rise. The manner in which that rise happened is completely transparent and can be understood by consideration of the factors entering into the model.

      • Harold H Doiron


        What you have described to me are some known processes (great that you know them well and know how to deal with them) that you have argued are not important to the end result sought from you model, and therefore you can confidently ignore those processes and eliminate them from your model. Note that I said “the entire Earth system with its IMPORTANT internal feedback loops”. I also believe in the most simple model required to obtain an answer of adequate accuracy. This is one of the most important aspects of modeling that separates the men from the boys. I really have a beef with overly complicated models that are prone to mistakes in results interpretation. However, not being a climate modeler, in my oversight review, I would ask: “Do you know well and completely understand all of the important processes that need to be modeled? How do you know this?” Use empirical curve fits when you have to, to get an answer, but I prefer models based on first priciples…and don’t extrapolate too far out with empirical data fits!! Using them just for interpolation would be a much safer approach. Also see Rutan, a successful airplane and spaceship designer, for guidelines on empirical fits used for extrapolation:

  13. Forcings and feedbacks are weak and inadequate attempts to analyze behavior of a complex distributed dynamical system. These concepts are completely inadequate to the task. The weather system is a field-theoretical problem; all components are fields, vectorfield of velocities and a bunch of intertwined scalar fields. All components are tightly coupled, such that “forcings” and “feedbacks” are inseparable, and therefore the entire idea to divide them does not make any physical sense and is wrong, and thus creates anything but continuing confusion.

    The attempt to apply elements of control theory is nothing but poorly applied formalism. The analysis a la Hansen/Schlesinger/Curry is in fact a static account of position of potential well (that represents equilibrium climate) in response to parameter change. The analysis does not involve any time factor, and all later talk about “slow” and “fast” responses does not formally follow. Yes, the bottom of the well can shift in any direction and far away, and even bifurcate into infinity, but it has nothing to do with real control theory that strives on time dependence and propagation delay of infinitesimally-small perturbations, leading to phase shifts and changes, with all this mathematics of Fourier and Z-transformations, transfer functions, etc. At best the analysis can be carried out for one-dimensional model, because attempts to invoke various speculative “global averaging” schemes are formally indefinable, as Tomas Milanovic have shown.

    And, as Harold Doiron said (and Pekka seconded), engineering systems have clearly separated “boundary” where we can change some “control signal” at will. The climate does not have this. At most, the CO2 infusion should be treated as static “parametric forcing” (see examples from plasma physics) of the system’s boundary condition. Then the weather system must be considered as initial-value problem where all meteorological fields would relax towards new stationary regime, and this relaxation may be not entirely monotonic in time as current models force it to be. As I see it, all this is a big completely undeveloped mess.

    • Al,
      I agree that methods that have helped greatly in control theory are likely to be more or less worthless in the actual analysis of the behavior of the earth system. Using concepts like “feedback” may still have some value in communicating results obtained by other means, but there is at the same time a great risk that their use is more confusing than helpful. Actual experience appears to tell that this confusing aspect is quite essential.

      No simple arguments are sufficient for giving good detailed understanding of the earth system. Sometimes they give useful results, but that has to be verified separately for each case either experimentally or using more comprehensive models, whose validity has been assured sufficiently for that particular need. We are really stuck by the fact that nothing else than large computer models based on finite element method or grid based numerical methods offers any hope for giving reasonably accurate answers – and further by the fact the verification of the sufficient accuracy of these models is an almost hopeless task.

      The dynamical stability properties of very large models are always extremely difficult. If the model becomes totally unstable, it is clearly useless. Making it stable can on the other hand kill very essential processes.

      We know that the atmospheric models tend to be chaotic, i.e. the models are usually deterministic, but extremely sensitive to their initial values. Still they may lead to clear predictions concerning expectation values and variability around these expectation values. My personal view is that it is severely misleading to consider the real atmosphere as deterministically chaotic. My view is that it should be studied as a stochastic system where the deterministic equations are supplemented by some way of introducing stochastic variations. The deterministic equations are still essentially the same that lead to chaotic behavior, but the stochastic inputs may influence significantly the outcome. The presentation of Tim Palmer at AGU about two weeks ago contained good ideas in this direction.

      For a deterministic chaotic system the ergodicity is very important giving both a probability distribution of potential states and assuring that almost all initial conditions lead to the same distribution. For a stochastic process, the existence of a well defined probability distribution of possible outcomes is equally important, but there is no risk that all initial conditions would not give similar results as long as they are within some reasonable limits.

      Even if the real climate system is chaotic, the typical climate models are not. It should be verified that the deterministic nature of these models is not essential for their results. It is not enough to calculate using different initial conditions, as the dynamics of the deterministic model can differ for all initial conditions from a stochastic model which is identical up to the introduction of repeated small stochastic perturbations.

      • Stochastic models assume certain [full] knowledge of the “noise” component superimposed on dynamics. This is exactly where we have no clues about what weather does. Your wishful approach is fundamentally flawed.

      • Your claim may be true for many problems, but it is not true for all problems. May point is that I do not trust the results of climate models at all unless they are insensitive to details of the noise.

        The assumption of validity of average results and distributions from deterministic chaotic models is closely related but not exactly equivalent with the requirement I stated above. Ergodicity is one of the properties required for the usefulness of chaotic models.

      • Pekka, I don’t care about all problems, and we are talking about one particular, weather/climate, where my statement is very likely to be true. Again, you seem to be concerned about structural stability of weather attractors, or if the attractor has well-defined invariant measure. I am quite sure that the weather attractor has all these desired qualities, just as a bathtub half-full of water has all this. I also suspect that the weather and global atmospheric circulation has multitude of [quasi?] isolated attractors, just as a medium Reynolds Number hydrodynamics of similar rotating flow has, as the Couette-Taylor flow for example.

        From what I see in GCMs, they are frequently insensitive to details of noise, except some of them are clearly sensitive to particularities of initial conditions, in which case the model either freezes of blows up. These cases are manually excluded by computer experimentalists as “unphysical” or ” bad physics”, see the experiment for examples of dismissing of about 40% of runs.

        Instead of worrying about fine stuff as ergodicity in models, I would rather worry about ability of models to reproduce major topological properties of the global flow structure first, jet streams, their frequency, major vortex structures as hurricanes and their statistics etc., with correct magnitude and direction of typical velocities (aka seasonal winds). Then we might be able to start talking about sensitivity to parameters of boundary conditions.

      • Al,
        Science proceeds very often through wishful thinking, not directly by wishful thinking of a retired scientist from other field (referring to myself), but by wishful thinking of the active scientists who proceed to do research to either confirm or disprove the idea. In this case I believe that the Oxford group of Tim Palmer is doing exactly that for medium-range forecasts and that somebody will certainly try the same for climate models.

        We seem to agree on many points, but as usual everybody has different views on what might be the best way forward. This is exactly as it should be in scientific issues. It is also very common to disagree on how to simplify the complicated issues in presenting them. Perhaps this is also as it should be, because the audience is also varied and different approaches may work better for different members of the audience.

        When I said that we agree on many points, I meant that I do not have much disagreement with your latest message.

    • Harold H Doiron

      Extremely well said!!! Let me propose Doiron’s Axiom:
      “The more forcings a climate model uses, the greater its output error”.

      Feedbacks in a good climate change model should only reflect how the Laws of Physics, Chemistry, Electro-magnetics, etc. operate on the current state of the system to change the state at a small time increment into the future, AND all important processes that have significant effects on model output need to be modeled……AND, there should be no feedbacks in addition to what is accurately modeled in the model. If climate models don’t obey these basic modeling rules, of what use are their output? How would/could you prove usefulness of the output? Would you bet the lives of your grandchildren on the accuracy of your model predictions?

      It is the responsibility of the climate change research community, not their skeptics, to make sure that the results of their model outputs are used responsibly by others (such as politicians an lobbyists) who don’t understand the numerous sources of uncertainty in their model predictions.

      • Harold H Doiron

        I think my comments here ended up referring to a different comment by Pekka than I intended. I think my above comments are a best fit to Pekka’s comments on Dec 30 2010, 3:53 am that began with “Difficulties in deciding what is forcing and what feedback result from vagueness in defining system boundaries.”

  14. Personally i think the use of terms such as forcing and feedback are quite useful in this context, providing one understands that this is a gross simplification of the real system.

    We KEEP trying to repair this house (climate science) from the roof down, instead of looking at the foundations. It is all well and good (and bloody interesting too mind) discussing the terminology used, the validation processes of the models, the type/characetisation/direction of feedbacks etc; but this all, surely, has to be secondary to the main issue- the basic science and level of understanding.

    Specifically wrt feedbacks and forcings, it is clear that the sun is the driving factor in our climate- yet we still do not understand how it ACTUALLY drives climate. GCR’s are barely understood, sunspot activity and other factors all work at the same time it would seem, to affect our climate- yet we don’t understand this well enough to even say with confidence what will happen during the suns own cycles, let alone the earths.

    The energy in-energy out formula above (ΔTs = λRF ) is a useful tool- but one MUST be mindful of the variables implied and contained within.

    For example, you could have 2 variables in there, 1 being co2, and you could make some decent estimations towards the relative significance of changes in each variable.

    Or, you could have 15 known variables, x unknown AND co2. (with x being 0 to infinity) Where no such estimations are possibe- this is where i think we are currently.

    The use and identification of feedbacks/forcings, to my mind, is VERY important and should be the REAL focus of climate science, as again to my mind until you can understand or at least QUANTIFY ‘x’ above, you cannot assign ANY significance to the other forcings- especially not co2.

    • While I have presented thoughts that bringing the concept “feedback” to discussion leads often to confusion, I agree that the formula ΔTs = λRF is important and useful.

      To me it is certain that RF can be calculated with useful accuracy. Whether the uncertainty is 10% or 20% or even 30% is not really crucial. It seems also clear that a permanent change in the GHG concentrations leads to a change in temperature that is approximately proportional to the original RF (“original” refers here to the fact that RF disappears, when the equilibrium has been reached, the “original RF” is the RF before the temperature has changed at all).

      Furthermore it appears likely from very basic considerations that the coefficient is of the same order of magnitude than required to bring a black body back to radiative equilibrium after the additional RF. In other words, it is natural to expect the climate sensitivity to be between 0.1 and 10 degrees. So far things appear rather obvious to me. Reaching better estimates for the climate sensitivity or for the coefficient λ is the problem for climate science. We know that IPCC and many scientists give much narrower but still wide limits for the climate sensitivity than 0.1 – 10 degrees. My purpose is not to argue now on the validity of those limits. I wanted only to tell, what I would consider very likely even without any of that work that has led to the limit estimates given by IPCC.

      Instead of feedbacks we might use the word amplification to describe the difference between the temperature change calculated from Stefan-Boltzmann law for a black body and the actual change of the temperature of the earth surface. The science does not depend on the words used to communicate its results (or at least it should not depend), but the words make a difference in the general perception. Bad choices confuse and better choices help in reaching understanding. There might be something to improve in choosing words in communicating about climate science.

      • “Whether the uncertainty is 10% or 20% or even 30% is not really crucial.”
        –i disagree, i think this IS crucial. 30% is a huge error.

        ” Reaching better estimates for the climate sensitivity or for the coefficient λ is the problem for climate science.”
        –Which is impossible given our current understanding.

        “In other words, it is natural to expect the climate sensitivity to be between 0.1 and 10 degrees.”
        —Again, i think this is (although on the face of it, sensible – though i’d wager nearer the lower end) based on current understandings and as i outlined above those understandings are incomplete at best. In all likelyhood the effect could just as well be negative- we just don’t know.

        “We know that IPCC and many scientists give much narrower but still wide limits for the climate sensitivity than 0.1 – 10 degrees. My purpose is not to argue now on the validity of those limits. ”
        –Understood, however as the IPCC cannot even give a SIGN on cloud feedbacks (possibly one of the most important) then any estimates are meaningless.

        “Instead of feedbacks we might use the word amplification”
        —the choice of ‘amplification’ would directly imply a positive feedback from such a change. While this is possible (and likely in the lower ranges) it is not a given. To use such a term hamstrings you to one type of SIGN, unconciously eliminating the other. Bad science.

        The terminoligy isn’t the issue here (though climate science has indeed got itself into a mucking fuddle), it is the science itself. Or lack therof.

      • Pekka said: “I agree that the formula ΔTs = λRF is important and useful.”

        It might be useful for a one-dimensional primitive model. As Tomas Milanovic convincingly argued, it is uncomputable nonsense for a distributed field system.

      • I agree that the formula has very limited applicability, but for certain considerations zero-dimensionality makes sense. When only the global total is considered, I am happy with one-dimensional description of the results. Even then the physical analysis that leads to the results is far from being one-dimensional. Thus the concept is useful only as a way of summarizing the results, which have been obtained by other means.

      • I am sorry, but you are completely illogical. It is exactly the “global mean” where the zero-dimensional model was shown to be totally inadequate. The entire concept of “forcing and feedbacks” is wrong and misleading and, as perpetually-evolving discussions show, is far from being useful.

      • Al,
        Tomas Milanovic did not prove anything.

      • Al,
        Concerning the value of the feedbacks, you must have noticed that I am also quite critical of them.

        This does not prove that could no be a useful concept in presenting results. I am not fully convinced that they are the best choice for that either, but it is always a matter of taste to decide, how to simplify when trying to present complicated issues to non-specialists.

        Real feedbacks are by necessity variable in space and time, but there are no strong reasons to say that a summary zero-dimensional presentation would be worthless.

  15. It is, perhaps, worth noting that Carnot’s black-box engine provides an alternative description for which feedback and forcings fall out as distinct black-box parameters. For this box, imagine two surfaces for which we know only their temperatures and energy flux I/O. We specify the flux input to the lower surface and the temperature of the upper surface and let thermodynamics decide the flux output from the upper surface (J) and the temperature of the lower surface (T). Apart from these two measurable quantities, all else we know must be gleaned from fluctuations in these quantities. On the side of our box there is a knob which evidentally controls some internal parameter we’ll call q which alters the state of the box. We presume there are also internal parameters, p, over which we have no control, but may depend on T.

    Assume the output flux, J(q,p(T),T). We assume two constraints: the system is in a thermodynamic steady-state (internal entropy time-independent); output flux deviation from the fixed input flux is minimized although fluctuations are permissable. The variational solution is for a stationary rate of entropy production subject to these constraints. Forcings appear as the partial derivative of J wrt q, feedback by the logarithmic partial of J wrt T, p variable. For values <1, we have positive feedback and, as this derivative approaches zero, CAGW – PROVIDED the flux constraint dominates (no deviations from a constant value). In the alternative limit, things never get worse than they would have been with no positive feedback.

    Carnot's engine shows how the 2nd Law determines the efficiency limits of a thermal engine without any knowledge of its inner workings. Can we, in similar fashion, determine the limits of global warming without fussing about details of radiation, convection, etc?

    • I have a problem with thermodynamics in that it does not acknowledge this planet is under pressure. Gases to liquids are stored energy waiting to be released and relaxed. Centrifugal force from rotation is needed for convection to even occur.
      Solar radiation comes in goes out, absorbed or reflected. Next atmospheric pressure exerts to the planets surface and gravity exerts to the planet surface. What is the counter balance? Convection/evaporation? From solar radiation? The moon gets more solar radiation than us yet their is no convection or evaporation happening there even though in a vacuum their should be some trace gases showing energy release with the current LAWS of thermodynamics.
      Basic physics and science need to be revisted and not by the current “peer-reviewed” boys. They are getting into enough trouble with the current science mistakes.

  16. Dare I suggest that the difference between forcings and feedbacks is largely a matter of semantics. It is also yet another result of the climate science community asking the wrong question – namely how can we show that CO2 is the villain of the piece? The question that they should have asked is ‘how does the climate system work?’ They should have got Dirk Gently on the case as this is clearly an area where the interconnectedness of everything is key.

    • What do you think the climate scientists are doing? A wanted to learn something about that I bought a couple of books. One basic introduction: “Atmospheric Science” by Wallace and Hobbs and one more specialized: “An Introduction to Three-Dimensional Climate Modeling” by Washington and Parkinson. (I do not know, whether I picked the best possible books, but they were readily available.)

      Guess, what they are about. They are about, how the climate system works, how it can be modeled and how the validity of the models can be tested.

      • Pekka writes “What do you think the climate scientists are doing?” I think climate scientists are trying to do two things. They are trying to understand how the climate works, and they are trying to prove that CO2 is a villain. It is the latter objective that Gary is referring to. I too believe that feedbacks and no feedback sensitivity are fictions made up by the proponents of CAGW, to provide some sort of science to back up the idea of CAGW.

      • Pekka

        Table 2.11 from the Fourth Assessment report of the IPCC sets out the uncertainty assessment of forcing agents. Listed below are the agents and the level of scientific understanding
        LLGHGs – high
        Stratospheric ozone – medium
        Tropospheric ozone – medium
        Stratospheric water vapour from CH4 – low
        Direct aerosol – medium to low
        Cloud albedo effect (all aerosols) – low
        Surface albedo (land use) – medium to low
        Surface albedo (BC aerosol on snow) – low
        Persistent linear contrails – low
        Solar irradiance – low
        Volcanic aerosol – low
        Stratospheric water vapour from causes other than CH4 oxidation – very low
        Tropospheric water vapour from irrigation – very low
        Aviation induced cirrus – very low
        Cosmic rays – very low
        Other surface effects – very low

        Does this not tell us where the scientific research has been targetted?

      • Gary,
        I would say that the list tells that the science has so far targeted mainly understanding better the basic mechanisms of climate and its interactions with oceans and that the knowledge on the multitude of additional issues is still very limited. There is evidently very much more to learn also about the basic mechanisms.

        On many of those additional issues even the existing very limited knowledge is sufficient to tell that better knowledge on them will not change substantially our understanding of climate, but clouds and their interaction with aerosols is certainly a very important topic.

        The list is obviously stating relative knowledge. Knowledge is given as “very low” also for factors, which are rather reliably known to be almost insignificant, when this insignificant influence is poorly known on its own scale.

      • That their influence would be very low is utterly insupportable without much better than “low” or “very low” understanding. As many have pointed out, the IPCC has done almost a priori dismissal of many of these factors, despite the fact that numerous scientists not part of the Magic Circle consider them actually dominant.

        Under such conditions, no prediction (or even worthwhile “projection”) is either honest or possible.

  17. Second Coldest December Ever
    Update from:
    Mean Central England Temperature, 2010
    Month CET Anomaly notes
    December -0.6 -5.3 provisional, to the 29th

    • Vukcevic,
      Could the accumulation of H2 18O on the ocean floor change the ocean current pattern?
      Ocean core samples show an accumulation of H2 18O every Ice Age.
      H2 18O being heavier and denser does not seem to bond or mix with saltwater.

      • Hi Mr. Lalonde
        Could the accumulation of H2 18O on the ocean floor …
        No idea but La Niña is moving into Atlantic.
        Could someone (please, please, please!) close Panama Canal’s sluice gates, we are freezing on this side.

        HNY to all.

  18. I just added this reference to the main post, it is very good overview of the subject:

    Roe 2009: Feedbacks, timescales, and seeing red

    • As I already made a remark (in other thread) that Figure2 of the Roe paper is nonsense. First, insert (a) shows “input DeltaR” and “output” with the same DeltaR. Second, in insert (b), in the upper equation (also referred as Eq.[4]), the DeltaT is in fact DIFFERENT: left-side DeltaT comes form current reaction/act of “gain amplifier”, while the DeltaT within feedback brackets is from previous “cycle of amplification”. The Eq.[4] therefore is incorrect, and cannot be “solved for DeltaT”, such that Eq.[5] cannot be opbtained from Eq.[4]. The entire “theory” is mathematically incoherent.

      Also, the root article states that “feedbacks cannot be measured”. This is not true for climate case. As many people noted, all “feedbacks” in climate sensiticity theory are unfolded through changes in DeltaT, and only through DeltaT; therefore, any DeltaT should generate a measurable response that can be attributed to “feedbacks”. This is the core of Lindzen arguments, and Willis Eschenbach’s approach to measure zonal “climate sensitivity” from seasonal temperature changes.

    • I would not go as far as Al and say that the stationary considerations of the paper are nonsense. They have their limitations, but that does not make then nonsense.

      The latter part of the paper that considers time-dependent issues is, however, very weak and not far from being nonsense. There are discussions of power spectra and even regionally visible oscillations like PDO although the paper does not contain any of the physics that could be related to such oscillations. The paper is a good example of the errors that the paper of Bates criticizes as many comments of this chain have also done.

      It is also nonsense to label formula (33) as red noise. Delays related to diffusive processes are definitely not red noise – or any other form of noise. Red noise is discussed erroneously also in connection to PDO. It appears that these concepts are fully unknown to Roe.

  19. Let us imagine a closed system with some critters living in it. These critters, let us say, increase in numbers with a slow rise in temperature. They also emit a certain gas as they increase in number.

    Is the end-result of an increase of the concentration of the gas, a feedback or a forcing?

    • Especially if the gas is their food supply.

    • Harold H Doiron

      The way you describe the process, the process has two outputs: temperature and gas concentration. The gas concentration is neither a forcing or a feedback. However, if there is a known process by which the increased concentration of the critter’s gas emissions affects the end temperature, then the gas concentration constitutes a feedback to the model that predicts temperature.

  20. Judith,

    In my opinion, if you want to know if a radiative imbalance exists on this planet, surface temperature is the wrong metric. There are all kinds of problems with the surface temperature record and unwarranted adjustments to it. In addition to feedback issues, changes in oceanic oscillations can cough up heat into the atmosphere at any time. The amount of heat in the oceans completely swamps heat in the atmosphere. The metric is useless.

    As I understand it, the other choices for a metric changes at the top of the atmosphere and/or changes in ocean heat content. These changes have to be compared to changes in global cloud cover, ice albedo, etc.

    So, the first questions are: Are we measuring the right things? Do we have adequate observation systems to learn what we want to know?

    • Ron

      I agree. I keep banging on about how unscientific the concept of an average surface temperature is. Judith has promised us a post. IMHO this is where the discussion should start because the surface temperature anomaly is used throughout the AGW argument as if it has some meaning! I would really like us (well mostly you scientific types) to nail this.

      • The average surface temperature is certainly not the best possible measure of the warming, but it may well be the best on which we have sufficient data. The heat content of oceans would be much more stable, but there is still too little historical data on it and even in the present data too much uncertainty.

        Ultimately many different measures should be used in parallel to give a more comprehensive picture on changes, but for the moment we are restricted to those timeseries that exist or can be continuously collected. In this respect the estimated average surface temperature is among the best available, if not the best.

      • Judith

        The measurement of the average global temperaure anomaly and the attendant inaccuracies is a common subject of skeptic discussion. Could we have a thread on this please at a convenient moment?

      • will do, i have been waiting on a few things, that don’t seem to be materializing very quickly, so i should just go ahead. will probably be a week or two, tho

      • Pekka

        You say “In this respect the estimated average surface temperature is among the best available, if not the best.”

        The question I would like to have answered please is ok it may be the best that is available but how valuable/useful is it? T his is the topic that I am very much hoping JC will get to in the near future. I realise that this is potentially getting us off topic on this thread but I do hope Judith will get it on topic soon.

        kind regards

      • This is a remarkable way of going about looking at a problem. I can imagine the conversation a while back.

        Young ‘Scientist’ 1: Morning S2. I have been reading some dire warnings about climatology among the advocates. Lets work on it.

        Young ‘Scientist’ 2: OK S1, we haven’t got anything else to do. What is the problem.

        YS1: I don’t know, but of we can find there is a problem we can make our careers out of it. What shall we measure?

        YS2: We could do it properly and look at the big heat sinks like the oceans which are huge and have lots and lots of heat in them. We could set up proper monitoring and really do a proper job and see if there is indeed a problem.

        YS1: But that would take years and years and years and we would be old and wizened before we got any results. and our grants would have run out. Haven’t we got any data lying around that we can do stuff with right now?

        YS2: There’s always the old weather observations. But they were collected for different purposes and may not be very accurate. So they won’t be much real use

        YS1: Perfect. Just what we need. We can get a few bods to do ‘adjustments’ to them so that they show what we want to show. And we can get them from all round the world at no cost. Now how shall we analyse them. What would be a meaningful use of them?

        YS2: I don’t know really. What form are they in?

        YS1; Maxima and minima mostly. I know – we’ll take the average of them!!

        Ys2: But will that actually mean anything (groan)??

        YS1: Probably not, but we can do it without needing to learn any proper statistics and its easy to program in Fortran. And if we adjust them right then we can scare the living bejasus out of people before they notice that the global average temperature is a bit of a meaningless measure. We could even win the Nobel Prize!

        Ys2: Now you are really away with the fairies. But are we agreed? We won’t bother with all that time consuming boring ‘correct science’ stuff, just work with the stuff we have even if it is meaningless?

        Ys1: Yep. That’s the plan. We’ll sweep the world and make a consensus before anybody ever gets to see what we’ve done. Remember that our methods must stay secret. Any other ideas?

        YS2: I’ve got this mate who looks at tree rings. And he needs a job. Can we find him something harmless and useless to do???


      • Judy, how is Latimer’s post “technical”? I thought this thread was reserved for technical discussions, not little dialogues in which the poster’s bigotry is put on full display…

      • Anybody who takes issue with my little playlet is perfectly at liberty to suggest other reasons why ‘global average temperature’ is used as the overriding metric in Climatology.

        But arguing about the format and presentation rather than the substance suggests that the central point is unchallenged.

      • Richard S Courtney

        Latimer Alder:

        Yes. Indeed, I cited your “litte playlet” in my comment below at December 30, 2010 at 1:18 pm where I wrote:
        “Unfortunately, the entire field of climate study has become politicised and is now required to provide simplistic results that cannot possibly be justified (e.g. local and/or global ‘projections’ of climate for decades and centuries into the future). This has induced the adoption of simplistic and unjustifiable procedures and methodologies (as Latimer Alder humorously outlines above at December 30, 2010 at 12:10 pm).”


      • Too kind. HNY! May 2011 be troll and trouble free for us all.

      • No troubles means boring times. But no trolls would be welcome! Shall we make a little list? They never would be missed! (Apologies to G&S).

      • Pekka,
        Other than the fact we have elements of a surface temp record going back 150 years, what is it you like about it?

        You claim there are uncertainties with ARGO (and therefore OHC) data, and there are, but the uncertainties are less than with the surface temp record. The surface temp record has been subject to continuous adjustments until it is unrecognizable. With the right computer code you can get the surface temp record to confess to anything. But even if it was not subject to so much uncertainty and mischief, we are looking at the least desirable metric possible.

        The long surface temp record has value in the sense it tells us our planet goes through cycles of warming and cooling near the surface. But it cannot give us precision and it is helpless in attribution. If on the other hand, we can find proof that the oceans are steadily warming year over year without fail, then that would be proof positive we have a radiative imbalance. Or if we can sample and estimate the different types of energy coming into and leaving from our atmosphere, it would not take long to demonstrate a radiative imbalance if one existed.

        We don’t need a 150 year long data series nearly as much as we need a reliable tool. I don’t care what the tool is as long as it is reliable.

      • Ron,
        I do not like the average surface temperature as a good signal of the changes in the heat balance of the earth system. Even less do I like the actual timeseries of GISS and HadCRU, which are only approximate presentations of the global average.

        Looking at the data summarized and analyzed in the recent Lyman et al paper in Nature (20 May 2010), the data on ocean heat content is unfortunately still too limited and too uncertain to replace global temperature times series as the best existing single indicator for the warming.

      • I, and others, suspect the actual ARGO data is just fine, but is being frantically massaged. Not Climatologically Correct, you know!

  21. I don’t know if this reference has been noted in the various posts and threads:

    J. R. Bates, Some considerations of the concept of climate feedback, QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, 133: 545–560 (2007) DOI: 10.1002/qj.62

    The last sentence of the Abstract:

    These results point to the need for greater precision and explicitness in the definition and use of the term ‘climate feedback’, both to facilitate interdisciplinary dialogue in relation to feedback and to guard against erroneous inferences within the climate field. Explicit definitions of the two prototype categories of climate feedback studied here are proposed. Copyright  2007 Royal Meteorological Society

    Much of what are termed feedback in the climate literature, IMO, are instead sensitivities.

    • thanks dan, i just added this one to the main post.

    • From the article of Bates, the last paragraph of the full article is also interesting.

      In conclusion, the present paper emphasizes that the term ‘climate feedback’ has no universal and obvious meaning. It also stresses that assumptions about feedback concepts that are valid for a zero-dimensional model may not carry over to more complex models. Some existing glossary definitions of feedback fail to describe the dominant usages in the literature, and none appear to recognize that there are common usages that can be in conflict. It is hoped that the definitions suggested here, and the surrounding discussion, will help to clarify some conceptual issues of climate feedback and contribute usefully to the ongoing debate in this area.

      Here Bates emphasizes the point that feedback is well defined and familiar for a zero-dimensional problem, but much more problematic for a complex system based on multiple fields (or functions of both space coordinates and time). A complex model is “all feedbacks”. Giving a special status as control parameter to the global average temperature may easily induce misleading conclusions.

      • Yes, some have noted that the use in climatology of the term “forcing” is arbitrary and incorrect.

      • Words have different meanings, when used in different fields. “Forcing” or “feedback” as used in presenting results on GH effect and warming differs essentially of their use in control theory or electronics. The zero-dimensional mathematics may still be the same.

        In looking at climate as part of earth system and in analyzing the dynamics of this system, the problem is similar to the control theory problem, only much more complicated than any problem solved with control theory. From this point of view the forcing should, indeed, be an external flow, not a change in internal dynamics. In this way of looking at the issue solar radiation is forcing, GHG concentration is not.

        It is, however, possible to take a different view on the problem. In this alternative view adding GHGs to the atmosphere is an external process and can be considered forcing. This original forcing expressed in terms of concentration can be used to calculate “radiative forcing” first as a change in emissivity and from that as a change in radiative balance at TOA or tropopause for an unmodified model atmosphere. The actual calculation of the consequences of the change in GHG concentration is then based on the changes in emissivity of air without further usage of the concepts of “forcing” and “feedback”.

        After getting the results of this complicated calculation, the results can be given in terms of the radiative forcing and change in average global surface temperature. These are just two summary numerical values resulting from the complicated model calculation. It is also possible to calculate on alternative hypothetical change in the surface temperature using a simpler partial model of the warming effect and name this other temperature change as “non-feedback temperature change”.

        Some further understanding can be obtained by calculating, what happens, when the full model is modified by dropping some effects from the calculation. The differences between these model runs and full model runs can be used to define separate “feedbacks”.

        All these calculations and the resulting numbers tell something, when the definitions of concepts used in the calculations are known. The language may be misleading to people from other disciplines, but this is not a big problem.

        The climate science or the model results should not be judged based on the way some words are used. I do not really see much problem in the present way of using the words as long as we do not try to draw unwarranted analogies with control theory where the words have largely different uses.

  22. Judy – I find the forcing/feedback principle conceptually useful, despite the inseparability of the two terms on an Earth-like planet (i.e., one containing water), and despite the complications introduced by non-linearity and non-additive interactions among feedbacks.

    Basically, it permits us to distinguish two different processes. The first is the climate response to an imposed perturbation (“forcing”), and the second is the climate response to a temperature change induced by the perturbation. This distinction may be quite blurry in some circumstances, but it strikes me as reasonable for the evaluation of temperature responses to CO2, other GHGs, solar or aerosol changes, etc. As long as the feedbacks of particular interest, such as water vapor, lapse rate, ice-albedo, and clouds, are not directly impacted by CO2 itself, but only by the temperature changes caused by CO2, they become amenable to evaluation on the basis of temperature changes induced by other perturbations, including those in the realm of paleoclimatology.

    Clearly, caution is required in this regard. For a temperature response to a non-CO2 perturbation to be extrapolated to CO2, for example, we ideally require not only the magnitude to be comparable, but also the global distribution and the response times. This is likely to work well for other GHGs (e.g., methane, at least for a few decades), perhaps fairly well for long term solar changes (which are also global but distributed differently), but rather poorly for short term regional perturbations. Among the latter, ENSO events are additionally problematic because they impose heat originating in the oceans on a previously unwarmed atmosphere – the reverse of a GHG-imposed perturbation. For this reason, recent estimates of “climate sensitivity” based mainly on responses to ENSO cannot justifiably be extrapolated to long term sensitivity to GHG forcing. Examples are recent papers by Lindzen/Choi, Spencer/Braswell, and Dessler.

    The non-linearity issue is also a concern, although as I suggested above, attempts to address it are incorporated into climate models. A typical “classical” expression for sensitivity with feedbacks multiplies the no-feedback parameter lamba-nought (sorry I don’t have the Greek symbols) by 1/(1-f), where the feedback factor f comprises a sum of individual feedbacks (water vapor, lapse rates, etc. – f1 + f2 + f3…and so on). A typical value of f for water vapor is about 0.4 -see, e.g. Water Vapor Feedback . However, as pointed out by the authors (Held and Soden), f is not a constant, but can vary, and in theory can rise to a destabilizing level of 1.0, although there is no reasonable likelihood of this happening in the foreseeable future of our planet.

    In addition to this inconstancy, the interaction among feedbacks requires attention that is addressed in some models. An example is the shielding of the albedo of ice or snow by increased cloud formation over snow-covered regions, thereby diminishing the combined effects of the two processes. Clearly, however, these interactions are sufficiently complicated to elude very precise characterization with current models.

    In all current estimates, the value of f in the term 1/(1-f) is estimated to be <1. "Positive feedbacks" are defined by values of 0 <f <1, whereas "negative feedbacks" involve negative values of f. However, "positive" in this regard simply refers to an amplifying effect on the temperature response to the original forcing. A forcing induces a feedback of its own – the "Planck Response" based on the Stefan-Boltzmann law. When the Planck Response is included within the definition of feedbacks, it becomes clear that net feedbacks in the climate system are negative currently, and with few exceptions (notably James Hansen), are judged almost certainly to remain negative regardless of changes in the level of GHGs.

    Why is this so? The 1/(1-f) term is the value of a series, where the same term can be written as (1 + f + f^2 + f^3…etc.). As long as f has a fractional value – e.g., 0 < f <1 – the series will converge rather than "running away". The value <1 is dictated by the power of the Planck negative feedback response in the context of current climate physics. It tells us, for example, that increased water vapor resulting from a CO2-mediated warming will itself at each individual iteration within the series mediate a warming with a lesser magnitude than the original (although the sum may exceed the original). If the Clausius-Clapeyron equation were different, however, or the greenhouse effect of water vapor more powerful, even the operation of the Planck Response, which limits the effects of both forcings and feedbacks, might fail to maintain the value of f below 1.0 and thus fail to avert an unstable or runaway climate.

    Interestingly, although a runaway climate appears highly improbable simply on the basis of positive feedbacks to increasing CO2, it is not only theoretically possible but in fact likely with sufficient increases in solar irradiance. Fortunately, increases in the solar constant that might trigger this scenario remain millions of years in the future.

    • Fred,

      I partly agree with you that forcing/feedback principle conceptually useful in being as a diagnostic tool of the climate model outputs , but the usefulness is quite limited, esp. when we are seeking the understanding of physical processes.

      The surface temperature changes is just a part of the responses to the external forcing, and it is just a part of outputs, and not necessarily the cause of the changes in water vapor, cloud, hydrological cycle, lapse rate, and general circulation patterns. As we ( Lu and Cai) ‘ve said in our paper, ” Physically speaking, all changes in the climate system, including atmosphere and surface temperatures, water vapor, cloud, precipitation, convections, atmospheric and oceanic circulations, are system responses to an external forcing. “

      • Jianhua – I haven’t claimed that the feedbacks on CO2 forcing were exclusively responses to changes in surface temperature, but I did suggest that they were responses to changes in temperature. If your point is that they are responses to some other variable as well, could you specify what you had in mind? I certainly agree with the last part of your comment- that the changes are “system responses – but I con’t see that as contradicting the principle that water vapor, lapse rate, etc. are responding to temperature changes and not directly to varying CO2 concentrations.

      • Fred,

        In my mind, it may be not right to say that ” they (cloud, water vapor, dynamics, hydrological cycle etc.) were responses to changes in temperature.” They, as the changes in temperature, are parallel responses to external forcing. All these changes are parts of systematic responses of the climate system to external forcing, constrained not only by the planetary radiative balance, but also by the other principles such as mass conservation, PV conservation, etc. Then, maybe the most important is not to identify the “most important” feedbacks, but to seek the most important linkage ( reaction chains in the climate system) of the processes which may contribute the uncertainty in climate change estimate.

    • Fred and Judith,

      About the interaction of climate feedbacks, results (see figure 1, though possible there are some technical errors in the figure)) in Huybers may be of interest.

    • Thank you for this exposition, Fred

      I have been reading and collecting papers on this for a considerable time now, and put up the question of “what happens if f = 1” on an earlier thread

      I might add that within the literature, and even on this and the earlier thread, there IS no consensus yet. Dessler October 2010 claims to have measurements for each of four (4) feedbacks to be summed (and Colose November 2010 states he is unaware of any other feedbacks above four) – but confirmation from other papers is very, very fuzzy

      So I remain sceptical at this stage

  23. Richard S Courtney

    Dr Curry:

    I have a real problem with this discussion. It assumes that ‘feedbacks’ and ‘sensitivities’ are real and/or meaningful concepts when attempting to understand climate behaviour. However, as the above comments demonstrate, it is difficult to define what ‘feedbacks’ and ‘sensitivities’ are and to assess whether some important climate mechanisms should be assigned to one or the other category.

    Hence, whenever this subject is considered the entire discussion rapidly devolves to become an ‘angels-on-a-pin’ debate concerning the categorisations.

    The real subject for consideration is an understanding of how the climate system operates. And that is difficult because the components of the system are not fully known, and the known ones are little understood (e.g. see the above comment of Gary Mirada at December 30, 2010 at 11:06 am ).

    This lack of knowledge has led to adoption of the simplifying assumption that climate behaviour is driven by radiative forcing (at the tropopause or at the TOA). This unproven assumption may or may not be correct, but its adoption has permitted the proper consideration of climate system components to be neglected: instead, system components are categorised as having effects that are ‘feedbacks’ or ‘sensitivities’ relating to radiative forcing.

    Unfortunately, the entire field of climate study has become politicised and is now required to provide simplistic results that cannot possibly be justified (e.g. local and/or global ‘projections’ of climate for decades and centuries into the future). This has induced the adoption of simplistic and unjustifiable procedures and methodologies (as Latimer Alder humorously outlines above at December 30, 2010 at 12:10 pm).

    I remain very doubtful that the radiative forcing assumption is correct. The climate system is extremely extremely complex. Indeed, the climate system is more complex than the human brain (the climate system has more interacting components – e.g. biological organisms – than the human brain has interacting components – e.g. neurones), and nobody claims to be able to construct a reliable predictive model of the human brain.

    Nobody has adopted a single simplifying assumption of brain activity, but the climate system is more complex than the human brain, and the radiative forcing assumption is being asserted to define how the climate system works. To say this assertion is improbable is a very mild response.

    Complex systems do not act in obvious or intuitively anticipated ways. They also throw up unpredictable behaviours.

    An important first step in any scientific study is to acknowledge something we do not know, and the second step is to try to find it out.

    Sadly, ‘climate science’ rejects admitting that we do not know the total system response of climate to any disturbance of any kind. But ‘climate scientists’ do not proclaim that ignorance and, instead, they assert as a fact the unproven simplifying assumption of radiative forcing being the governor of climate behaviour. Radiative forcing may be that governor but nobody can know if it is or not until the climate system’s behavioural responses to disturbances are known and understood.

    ‘Climate scientists’ need to be reminded that science is the joy of knowing we are ignorant. There is an ocean of knowledge that nobody has acquired, but if we are clever enough then we can fashion a ‘teaspoon’ that can be dipped into the ocean then lifted to our lips to taste that part of the ocean. And when we have had the excitement of being the first to swallow that tiny sample of knowledge then we still have the joy of knowing the ocean of unknown information remains.

    We need many more sips of the ocean before we can begin to know and understand the total system response of climate to any disturbance of any kind. Simplifying assumptions help us to gain that knowledge, but they are NOT the knowledge.


  24. Here’s some (vernacular) feedback on (scientific) feedback.

    Feedback appears to have been introduced into climatology by Hansen, (Lacis), et al., 1981. They adopted the “procedures and terminology” from a pioneer text in control system theory. Hendrik W. Bode (1905-1982), Network Analysis and Feedback Amplifier Design, 1945. However, Hansen, (Lacis) et al. jump immediately into discussing feedback without bothering to define it.

    IPCC provides an adequate definition, although qualifying it unnecessarily as “climate feedback”:

    >>Climate feedback An interaction mechanism between processes in the climate system is called a climate feedback when the result of an initial process triggers changes in a second process that in turn influences the initial one. A positive feedback intensifies the original process, and a negative feedback reduces it. 4AR, Glossary, p. 943.


    >> A process is called a feedback when the result of the process affects its origin thereby intensifying (positive feedback) or reducing (negative feedback) the original effect. TAR, ¶1.2.2 Natural Variability of Climate, p. 91.

    The word “mechanism” might suggest a manmade or mechanical system, or as Dr. Curry said in her introduction, an “engineered systems”, but of course that is not the meaning in this application, nor elsewhere in science. Feedback is observed in the natural world of basic science as well as technology. Feedback occurs in biological systems, as in insulin reactions and respiration. Natural feedback couples into electronics, as when microwave ovens sense water vapor patterns to regulate the cooking cycle. Feedback occurs naturally in climate in both the hydrological cycle and the carbon cycle.

    IPCC defines feedback narrowly for climate, identifying the system inputs as “an initial process”. In science, feedback is a signal or information, for example, a displacement, rate, energy, or material, generated within a system in response to its inputs, and which signal has a path to alter the input signal by augmentation or amplification. The input and the returning mechanism have physical connections to the internal structure of the system, “interactions” in IPCC terminology, and the round trip path is the feedback loop. The output of the system may also be some type of signal, or a non-invasive measure of the system’s state.

    The direct connection from the input to the output of the system is the forward path, and it is remarkably different according to whether the feedback path is open or closed. In control system theory, the ratio of the output to the input is the system gain, and it differs according whether the loop is open or closed. Comparing closed loop to open loop, the system output can be mitigated to the point of being benign, regulated, or negligible. Conversely, when the loop gain is greater than one, the system may self-destruct. How a system reacts is determined by its closed loop gain.

    While the IPCC definition would be a start in the right direction, IPCC doesn’t apply the definition in the main body of its Assessment Reports or, apparently, in its GCMs. In climatology, an input signal is a forcing, and to IPCC a feedback is a parameter calculated by the GCM during a run.

    >>A major motivation for the radiative forcing concept is the ease of climate change analysis when radiative forcing, feedback, and climate response are distinguished from one another. Such a separation is possible in the modelling framework where forcing and feedback can be evaluated separately e.g., for the case of CO2 doubling effects. The consideration of forcing, feedback and response as three distinct entities in the modelling framework while originating from the one-dimensional radiative/convective models [1D RC; see Lacis, Hansen, et al., Greenhouse Effect of Trace Gases, 1970-1980, 1984], has made the transition to GCM studies of climate. References deleted, TAR, Appendix 6.1 Elements of Radiative Forcing Concept, p. 405.

    IPCC here suggests it can evaluate the effects of CO2 doubling open loop. Of course it can in the sense of going through the motions. However, the real world is observable only with all its loops closed. Consequently, the model cannot be tuned properly to the real world, and the results are destined not to represent the real world.

    In various places, IPCC struggles to decide whether a process is a forcing or a feedback. For example, it explains

    >>[N]o quantitative metric separating forcing from feedback and response has yet been implemented for climatic perturbation processes that do not act directly on the radiation budget … . AR4, ¶2.5 Anthropogenic Changes in Surface Albedo and the Surface Energy Budget, p. 181.

    >>Some aviation effects might be more appropriately considered feedback processes rather than an RF. However, the low understanding of the processes involved and the lack of quantitative approaches preclude reliably making the forcing/feedback distinction for all aviation effects in this assessment. Citation deleted, AR4, ¶2.6.3 Radiative Forcing Estimates for Aviation Induced Cloudiness, p. 187.


    >>[C]hanges in water vapour in the troposphere are viewed as a feedback variable rather than a forcing agent. However, in the case of the second indirect aerosol forcing, the separation is less distinct. … Changes in the condensed liquid and solid phases of water (i.e., clouds) are also considered as part of the climate feedback. The strict requirement of no feedbacks in the surface and troposphere demands that no secondary effects such as changes in troposphere motions or its thermodynamic state, or dynamically-induced changes in water substance in the surface and atmosphere, be included in the evaluation of the net irradiance change at the tropopause. TAR, Appendix 6.1, p. 406.

    IPCC has departed from its own paraphrasing of feedback, to redefine it in practice to mean a parameter computed during a computer run, distinct from a forcing given at the start of the run. To cap off its confusion, IPCC defines feedback loop to mean connections between parameters and their inclusive processes, all with neither inputs nor outputs, and speculates that a loop instability may arise out of positive correlation, and not from a loop gain. See TAR, Figure 7.4, where pluses and minuses have different meanings, SST and Salinity are disembodied from the THC, and SST decreases the THC (p. 439); Figure 7.6, where Open Ocean and Surface T are disconnected boxes, and decreasing Surface T seems to decrease Sea Ice (p. 445); Figure 7.7, Atlantic THC and SST boxes are duplicated, and THC increases SST (p. 448); and Figure 7.8, where the negative loop comprises four plus connections and one minus connection, while the positive loop has two pluses and two minuses (p. 454).

    None of this resembles the teachings of control system theory, nor of Hansen, Lacis, et al. (1981), developed from Bode. The principles of feedback arise from control system theory and are universal. They are applicable to climate science, and are the foundation of the well-developed and extensive linear control system theory. But to the extent discussed here, feedback is not restricted to linear systems, as Dr. Curry suggested in her introduction, and its application is not limited to small climate changes.

    Meanwhile, the GCMs omit entirely the temperature feedback of ocean CO2 outgassing through the greenhouse effect, and they omit the dual albedo feedbacks, one to temperature that mitigates warming, and the other to solar activity feedback that amplifies insolation. Because IPCC elected to use the radiative forcing paradigm instead of heat modeling, it lacks flow variables, it is unable to form closed loops, and it cannot calculate the critical closed loop gains required to assess the extent of these feedbacks and real climate responses.

    Of course, science does not dictate that scientific models emulate real world processes at all. For example, an accurate model for Earth is that its climate varies in a pattern between -9ºC ± 1ºC and +3ºC ± 1ºC, with a period of roughly 100 kyears, and currently is near its maximum. That model can be built on a portion of the Vostok ice core reductions, reserving the remainder for validation.

    However, to the extent that a model relies on natural processes, those processes may require faithful representation of the real world less the model fail validation. This is especially true with regard to climate sensitivity, the temperature rise for a doubling of CO2, and alternatively to the equation ΔT_s = λRF, which concerned Dr. Curry. IPCC models run open loop with respect to albedo, the strongest feedback in all of climate. The real climate response will be therefore be less, mitigated by the negative feedback of cloud albedo. Furthermore, solar variations will have a greater impact than modeled because of the positive feedback again of cloud albedo. This causes IPCC to underestimate solar forcing, to attribute its effects wrongly to humans during the industrial era, and consequently to overestimate climate sensitivity.

    • BlueIce2HotSea


      The allegory of the climate as a complex network is still very interesting.

      Some of Bode’s most useful work looked at finding poles, those points where infinite gain is demanded of an amplifier at certain frequencies – thus resulting in system instability. Also phase shift (time delay) as a function of frequency has a potential parallel in climate.

      Could deliberate manipulation of the frequency of anthropogenic forcings be one day be useful in damping a potential runaway climate? Don’t know but fun to explore this anyway.

      • BlueIce2HotSea 12/31/10 at 6:18 pm

        >>The allegory of the climate as a complex network is still very interesting.

        When you speak of allegory and a complex network, are you thinking perhaps of chaos theory or the Gaia hypothesis, a pair of misnamed conjectures, one from mathematics and another from Greek mythology? The first leads to the butterfly effect, a infinitesimal initial condition upsetting a conditionally stable system on the ragged edge of a transition. See IPCC, AR4, FAQ 1.2, p. 105. For the other, consider “Interaction of climate factors and emission of dimethylsulphide should be studied to prove or refute one of Lovelock’s Gaia hypotheses.” IPCC, First Assessment Report, Chapter 5, section 7, Summary of likely impacts of global warming and stratospheric ozone depletion on air quality, ¶7.4 Tasks for the Near Future, p. 5-33. IPCC has not been asleep at the switch.

        >>Some of Bode’s most useful work looked at finding poles, those points where infinite gain is demanded of an amplifier at certain frequencies – thus resulting in system instability. Also phase shift (time delay) as a function of frequency has a potential parallel in climate.

        You’ve stepped away from the broad scientific principle of feedback that is the foundation of control system theory, a robust, essential, and dominating phenomena in complex natural systems, and prematurely into the narrow field of linear control system theory.

        A scientist contemplating the mysteries of Earth’s climate would wonder what makes the secular climate as stable as it is, tending to lodge in either a warm state like the present, or a cold state like the ice age minima. He would be led to a search for feedback mechanisms that could lock Earth into a snowball state for a few hundred million years, and otherwise keep Earth for millennia in a state dominated by the properties of liquid water that store heat and reflect solar radiation. He would be led to albedo.

        Climatologists, by contrast, unclear about feedback and cavalier about equilibrium (a fine topic for Dr. Curry), have built an unstable, anthropogenic CO2-based climate modeled from the greenhouse effect, and modeled open loop in both the hydrological and the carbon cycles.

        Poles, and in a sense certain zeros, are singularities in the frequency domain of transforms of linear transfer functions. Those transfer functions approximate the modulation of flow variables in models. Flow variables, and hence transfer functions, are notably absent in GCMs.

        >>Could deliberate manipulation of the frequency of anthropogenic forcings be one day be useful in damping a potential runaway climate? Don’t know but fun to explore this anyway.

        All the chemical and potential energy converted by man is one 24,000th the energy impinging on Earth from the Sun. Man’s carbon emissions are only about 6% of the ocean’s by IPCC’s own estimates, and has an effect only by the fantastic assumption that anthropogenic CO2 accumulates in the atmosphere while natural CO2 mysteriously remains in a Gaia-like homeostasis. Man is impotent to change the weather or the climate, for good or for bad. Anthropogenic forcings are mythical beasts, existing only in the untrained mind or in GCMs.

        Those GCMs, being based on the radiative forcing paradigm, have neither flow variables nor heat capacities. Heat models have both, but at this first level, heat lacks inertia, also modeled as an inductive mechanism. Frequency and a phase arise in complex solutions to a quadratic equation, which is a model for the exchange between induction, or inertial, energy, and capacitance, or potential, energy. Consequently, harmonic motion cannot occur in heat, and phase and frequency do not arise, nor would poles and zeros in a linear, frequency domain model. Heat does not oscillate absent an oscillating driving force.

        On the other hand, and at the next level, the ocean acts as a heat pipe or a tapped delay line, absorbing thermal energy at various locations, and by virtue of Earth’s rotation coupled with latitude dependent heat transfer, releasing heat at other, distant locations. Warm currents caused by mechanical gyres are examples. So too are the effects of the THC, combined with the Ekman pump created by Coriolis forces. Thanks to those oscillatory, mechanical forces, the ocean has the potential to provide tuned responses, features with phase and frequency. Even at that, the results are damped oscillations, not runaway effects. So while in theory natural climatic forces can have tuned response where phase and frequency parameters, nothing like that is in the cards for anthropogenic forcings.

        I remember a cartoon — Tom & Jerry, as I recall — where ants are marching in lock step across a lawn, up a tree, and across a hammock to another tree. The hammock soon goes into resonance with the marching ants, and chaos! All the humans and flatulating cows, trained to emit in synchronism, are not going to alter Earth’s delicate blue climate.

  25. Lindzen and Choi also proposed a good introduction to climate’s feedbacks problem, mainly showing, based on ERBE satellite data, that the sign of feedbacks used in models is wrong and opposed to the one provided by measurements.

    Spencer & Braswell also pointed out potential biases in feedback diagnosis based on observational data ( especially with regards to clouds aspects.

    See also the good paper form Knutti & Hegerl ( that Scafetta also refers to in his own SPPI paper (

  26. I suggest that the question is wrongly posed. Forcing and feedback are not intrinsic properties of the climate system: they are concepts, and like other concepts they exist in our minds, not in nature. We can define them in any way that is useful, that lets us think more clearly about what is going on.
    Can I suggest that the most useful definition should focus on which things climate scientists are responsible for explaining? For example, solar irradiance, industrial CO2 production, and volcanic activity all affect global climate, but for the purposes of climate science they are givens (that is, forcings). Cloud formation and albedo, various forms of heat transport, changes in the polar ice caps, and the rest, are all matters that climate scientists should eventually be able to understand in detail. Many of these interact with one another in circular chains of influence (that is, feedbacks), but both direct and feedback effects need to be understood together (why is why the concept of no-feedback sensitivity gives so much trouble).
    But which items are forcings and which are feedbacks is determined by the question we are asking: how comprehensive our explanation should be, if you like. And this is a matter of judgment.
    Consider an example: increased CO2 production from industrialization has caused climate to begin changing, which has caused some scientists to warn of the consequences, which has caused national and international policy responses, which have caused a demand for new biofuels, which has caused additional tropical deforestation for palm-oil plantations, which has caused additional release of CO2 and albedo-related changes to climate. According to Judith’s definition, this is clearly a causal feedback mechanism (“an interaction among processes in a system in which a change in one process triggers a secondary process that influences the first one”). However, climate modelers have their hands full without expecting them to model sociological, political and economic mechanisms. So as a practical matter we will treat palm-oil plantations as a forcing rather than a feedback mechanism. Brian H says that “forcing” is a concocted concept, unique to climatology, but it may still be very useful as a way of delimiting what is to be part of the explanation and what is somebody else’s problem.
    But a search for something fundamental in the physics to distinguish forcings from feedbacks is not going to find anything.

    • Richard S Courtney

      Paul Dunmore:

      You say;
      “But a search for something fundamental in the physics to distinguish forcings from feedbacks is not going to find anything.”

      Yes! And that neatly summarises the problem.

      A concept that cannot be clearly defined may have a poetic truth, but for science it has no use, no meaning and no value. And no amount of rhetoric can change that.


  27. Just curious. Does anyone know how much CO2 is converted to calcium carbonate by ocean creatures and then how much of that sinks to the bottom when they die? That would be a negative feedback from rising CO2, I guess?

    • The so called ocean acidification is a substantive negative feedback on atmospheric pCO2 Eg Zondervan et al 2001 Ridgewell et al 2006

      Analysis of available plankton manipulation experiments demonstrates a previously unrecognized wide range of sensitivities of biogenic calcification to simulated anthropogenic acidification of the ocean, with the “lab rat” of planktic calcifiers, Emiliania huxleyi not representative of calcification generally. We assess the implications of the experimental uncertainty in plankton calcification response by creating an ensemble of
      realizations of an Earth system model that encapsulates a comparable range of uncertainty in calcification response. We predict a substantial future reduction in marine carbonate production, with ocean CO2 sequestration across the model ensemble enhanced by between 62 and 199 PgC by the year 3000, equivalent to a reduction in the atmospheric fossil fuel CO2 burden at that time of up to 13%. Concurrent changes in
      ocean circulation and surface temperatures contribute about one third to the overall importance of reduced plankton calcification.

      • This seems to be saying that one species(?) of plankton will calcify less CO2 with increasing CO2 absorbed by the ocean. And you call this a negative feedback? Seems it would be positive as the ocean couldn’t absorb as much. Of course that assumes only this one species exists in the ocean, which isn’t true.

      • How will this INCREASE the rate of CO2 absorption by the ocean?

    • Jim,
      I guess, the book Ocean biochemical dynamics by Sarmiento & Gruber is a good source for that kind of information that you ask.

      My own knowledge is limited to knowing that the issue has been studied, that one important factor is the resolubility of calcium carbonate while sinking through deeper layers of the ocean where the chemical balance allows for that and to the numbers given in Figure 7.3 of IPCC, AR4, WG1 page 515.

      In that picture the sedimentation rate is given as 0.2 GtC/y, while the whole carbon flux due to biota from surface ocean to deep ocean is given as 11 GtC/y indicating that resolubility is a very important factor.

      • So that includes dead animals with no CaCO3 shell. Is it that they rot and the CO2 bubbles back up to the surface or is it that the shell re-dissolve or both?

      • The CO2 remains for a long time in those layers where the re-dissolving occurs. This mechanism is therefore an important part of transport of carbon from upper ocean to deeper layers. The stronger such mechanisms are the shorter is the lifetime of additional CO2-concentration in the atmosphere and surface layers of the oceans and the lower is increase in CO2-concentration caused by additional emissions.

  28. I distantly recall when feedback was covered in my Physics course that the amplifier had a power source.
    Not only that, but the input and output quantities were the same.
    The units used for input and output were the same.
    It might seem attractive to some in the Climate Science community to “borrow” the concept of amplifier feedback.
    Are the input and output quantities and units for the proposed formula the same.
    Is there a credible power source rather than just a vague hint in that direction?
    The last thing Climate Science needs is a feedback theory that is not the same as the conventional feedback theory.
    They have a busy enough time with the climate Greenhouse Effect which has nothing in common with the real Greenhouse (glasshouse ) Effect.

    • I think the power source is incoming Solar radiation. The “ground” line is outgoing radiation. I was actually thinking about this in terms of an operational amplifier yesterday. So the TOA equilibrium is certainly important, but so is everything else on Earth.

      • Christopher Game

        Bryan, you are not so far out of date, and on this one I think you never will be. Amplifiers still today have a power source, and I think they always will. A power source may be modeled as a circuit element that contains an ideal voltage or current source; such a source can supply arbitrary power at a prescribed voltage or current, though it has a Thévenin or Norton equivalent wasting immittance attached. You are right to imply that there is, in the ‘amplifier’ analogy, with the sun as signal source, no such auxiliary power source in the earth’s energy transport process: the use of the ‘amplifier’ analogy is thus a scam.

        Jim, you propose a different analogy, with the sun as the battery; it is apparently drifing a leaky passive device; there is no apparent signal to be ‘amplified’ in this case; a signal comes from a source of energy that is not controllable or predictable, again to be modeled as an ideal voltage or current source with a wastage immitance attached; and again, in this analogy, not to be found in the earth’s energy transport process; so again the ‘amplifier’ story collapses. Operational amplifiers need a power supply, just like any amplifier. Changing the CO2 level is modeled as a change in the leakage of you device, not as a signal.

        But the ‘device under test’ can be well pictured as a a variable attenuator, with loss, as contrasted with the “gain” beloved of the IPCC. No auxiliary power supply needed for an attenuator, which is thus the natural way to picture the earth’s energy transport process. But this is no use to the IPCC because it lacks the emotive propaganda benefits of “positive feeback” and “amplification”.

      • If you want to include solar variation and external magnetic effects, you would have to include the sun and external magnetic fields in part of the circuit, not just as a power supply. But it could be done if one could either figure out what chaotic attractor to match and in how many dimensions or just knew how the climate worked well enough to model it outright, it could be done in an analog circuit. An op am or op amps have a power supply but so does a digital computer. Same difference.

    • If the climate is chaotic, one could turn to chaotic operational amplifier circuits for inspiration. If we could determine the shape of the climate attractor, we could create circuits that mimic that attractor and perhaps gain some insight into climate.

      • You don’t need chaotic oscillators to generate chaos in a spatially distributed liquid system. A lattice of simple self-sustaining oscillators can produce rich chaotic dynamics even with simple linear coupling. Google for “coupled oscillator model” or “Kuramoto-Sivashinsky Equation” or “Complex Landau-Ginzburg Model”. See also “vacillations in shallow water”.

    • Here is another interesting circuit. The output graph looks a little, but only a little, like the long term climate.

      Abstract—An improved implementation of Chua’s chaotic oscillator is
      proposed. The new realization combines attractive features of the current
      feedback op amp (CFOA) operating in both voltage and current modes to
      construct the active three-segment voltage-controlled nonlinear resistor.
      Several enhancements are achieved: The component count is reduced and
      the chaotic spectrum is extended to higher frequencies. In addition, a
      buffered and isolated voltage output directly representing a state variable
      is made available. Based on a linearized model of Chua’s circuit, the useful
      tuning range of the major bifurcation parameter ( ) and the expected
      frequency of oscillation, are estimated.

    • Consider each component of the circuit a dimension, ignoring the fact that the op amp is composed of multiple components, and the fact that climate has many more dimensions than these circuits. Then look at the graphs of the output of one point in the circuit over time. The big argument is over three dimensions, CO2, time, and temperature. This three dimensions out of hundreds or thousands? More even than that? I’m reminded of the 6 blind men and the elephant only on a ginormous scale.

    • Christopher Game

      Brian, you write: “Not only that, but the input and output quantities were the same. The units used for input and output were the same.” This is not required of an amplifier. Some amplifiers are used to change the impedance properties in the signal path as well as to increase signal power. Besides voltage amplifiers and current amplifiers, there are also uses for transadmittance and transimpedance amplifiers. There are sixteen basic types, lucidly expounded in E.H. Nordholt, ‘Design of High-Performance Negative-Feedback Amplifiers’, Elsevier, Amsterdam, 1983, ISBN 0-444-42140-8 (Vol. 7).

  29. Two recent papers by Yi Huang et al at Harvard are relevant to this thread because they propose a method to disentangle CO2-mediated forcing from feedback responses based on differences in their spectral fingerprints. The first is
    Separation of Climate Feedbacks – an excerpt from which states:

    “based on a GCM simulation of climate
    change forced by doubling of CO2 in the atmosphere, we
    have theoretically investigated the separation of longwave
    climate feedbacks from spectral OLR observations in the
    all‐sky condition. Spectral fingerprints of greenhouse‐gas
    forcing and different feedbacks, namely atmospheric temperature,
    water vapor, and cloud feedbacks, are shown to
    exhibit different radiance spectral features that allow the
    detection and separation of individual signals from the
    overall change in the OLR spectrum.”

    The second describes an additional method for resolving ambiguities in the spectral signatures: Longwave Forcing and Feedback

  30. For a quantitative analysis of climate feedbacks, it is necessary to first clearly identify and define the climate system forcings. By the way that climate GCMs are structured to study climate perturbations relative to current climate, these climate system forcings are radiative in nature. Solar forcing is the easiest to visualize. Solar radiation is directly measurable in W/m2, and has been precisely monitored for over 30 years (exhibiting a characteristic 11-year variability, with no discernible long-term trend). Diurnal and seasonal changes in solar insolation are precisely known, and are fully accounted for in climate GCMs. The difference in solar insolation between two different points in time ( a directly measurable quantity) constitutes “solar radiative forcing”.

    Climate forcing by greenhouse gases is similarly defined by the difference in (non-condensing) GHG concentration between two different points in time (this is a directly measurable quantity that is being accurately monitored), and constitutes the “GHG forcing” in climate GCMs. The radiative model of the climate GCM then expresses (converts) the GHG concentration change into W/m2 heating or cooling, calculated for the given atmospheric temperature and absorber distribution.

    For off-line comparisons, GHG forcings are typically expressed as W/m2 flux changes (at the tropopause) relative to some reference atmosphere. (This involves two radiative calculations – once for the reference atmosphere, then for the reference atmosphere with the GHG perturbation included.) And, as noted by Fred Moolten, as the climate system responds to the applied GHG forcing, the flux difference diminishes and goes to zero as the climate system approaches its new equilibrium. Thus, the GHG “radiative forcing” in terms of W/m2 is not a directly observable quantity. It is the GHG change in ppm that is the directly observable quantity.

    There are other climate forcings that are included in climate GCMs. The most important of these are aerosols (tropospheric and volcanic). Also, more typically than not, changes in ozone, vegetation surface albedo, and cloud-aerosol indirect effect, are prescribed rather than predicted in GCM climate simulations. In GCM operation, anything that is prescribed should be considered as an “applied radiative forcing”, while the radiative effect due to changes in water vapor, clouds, or temperature lapse rate are “feedback effects”.

    Climate feedbacks (including the direct Planck temperature re-adjustment to the direct GHG radiative forcing) are the result of the climate system response to the applied climate forcing. In view of the inability to directly measure the GHG forcing (from space in terms of W/m2), so too, it is not possible to measure climate system feedbacks directly from space. (What can be measured are spectral radiance changes, but interpretation of what the spectral radiance changes mean requires major assumption as to what part of the climate system remains fixed, and what part is assumed to be changing.)

    Given also the points raised by Aires and Rossow (2003) that climate system interactions are highly non-linear, and that there are substantial advective energy transport changes that are not being reflected in TOA observed spectral radiances, appropriate caution should be exercised in associating and interpreting spectral radiance changes in terms of climate feedback changes. Satellite measured spectral radiances are best applied to retrieving detailed information on cloud and atmospheric radiative properties, and how these radiative properties change with time. Detailed climate modeling analyses are needed to back out and infer the nature of climate system feedback interactions.

    The linearized feedback representation that we derived in Hansen et al. (1984), was: ΔTs = 1/(1 – g) ΔTo
    where g = g.wv + g.cld +, and
    g.wv = ΔT.wv / ΔTs, g.cld = ΔT.cld / ΔTs, = Δ / ΔTs,

    (for doubled CO2, we then got: g.wv =0.4, g.cld = 0.2, = 0.1, which makes g = 0.7, so that ΔTs = 1/0.3 ΔTo. For ΔTo = 1.2, this gives ΔTs = 4).

    This is a useful concept to help understand the nature of climate system feedback interactions. Note that this is an “empirical” relationship that was derived from climate model output data, and not a prescription for the physical processes under which the climate GCM operates.

    The doubled CO2 experiment (control and doubled CO2 equilibrium runs) described in Hansen et al (1984) provides full definition for all of the above quantities, which can be obtained via radiative model evaluation of the GCM produced output data – changes in water vapor amount and vertical distribution, cloud cover and height distribution, temperature lapse rate, and surface albedo between the control and doubled CO2 equilibrium.

    The feedback efficiency factors ΔT.wv, ΔT.cld, and Δ are the temperature equivalents computed with the GCM radiation model operated in 1-D radiative/convective equilibrium mode, of water vapor, cloud, and surface albedo changes changes that resulted from the total ΔTs change in equilibrium surface temperature for doubled CO2. Note also that these are global-mean values. When globally averaged, horizontal advective flux transports must average out to zero.

    Climate feedback sensitivity is anything but some sort of a constant of the climate system physics. Climate feedbacks are functions of latitude as I described earlier, and in my recent posting on Roger Pielke Sr blog

    Not only are climate feedbacks functions of latitude, they are also likely to be functions of longitude as well as season, and non-linear, as noted by Aires and Rossow. It is only in the context of where the radiative forcings and the corresponding climate system response are fully defined, that it is possible to define linearized relationships between the different participating components that are applicable to the specific climate experiment analyzed. The fact that similar relationships are also obtained for the 2% solar forcing experiment, suggests that the linearized feedback relationships are useful for comparing and interpreting climate system response to different radiative forcings.

    There are of course limitations to the above simplified analysis of climate system response. The conundrum is that the climate system (including also GCMs) exhibit natural (unforced) variability. For a climate system that is in radiative equilibrium, the TOA radiative flux shows inter-annual variability (real world and GCMs) up to 1 W/m2 in global annual mean TOA radiative flux balance. The TOA flux difference between a high-flux and a low-flux year must be explainable in terms of water vapor, cloud, and/or temperature lapse rate changes. But if the radiative forcing between the two reference years in question is zero, how do you define a “radiative forcing-feedback” relationship if there is a “feedback” response of the climate system for zero radiative forcing?

    Here is where it may useful to look to quantum mechanics and particle physics for an applicable analogy. In classical physics, the vacuum consists precisely of “nothing”. But this concept applies only to time and energy situations that do not impact the Heisenberg uncertainty principle. The instantaneous picture of the vacuum conjures up virtual particles and anti-particles that flash into existence and disappearance within the confines that are allowed by the uncertainty principle.

    Similarly, there appear to be “virtual” radiative forcings in the climate system (and GCMs) that arise from fluctuations in water vapor, clouds, or temperature lapse rate. After all, any change in water vapor, clouds, and temperature lapse rate due to whatever causes will produce a radiative heating or cooling effect (that is indistinguishable from the radiative heating or cooling produced by the applied radiative forcing).

    In order to minimize the “noisiness” effects of this natural (unforced) variability, it makes sense to average climate modeling results over several decades, or to make use of ensemble averages. There is an implicit time and spatial scale over which climate system result need to be averaged over for the linearized radiative forcing-feedback relationships to be properly applicable.

    Given the above climate system complexities of natural (unforced) variability, advective transports of latent, sensible, and geopotential energy, caution needs to be kept in mind in attempting to characterize climate system feedbacks based on short-term observations of spectral radiance variations. A capable climate GCM, along with the relevant observational data, is needed to fully disentangle radiative forcings from climate feedback response.

    • A Lacis:

      Your comments are very nice and insightful. ” Climate feedbacks are functions of latitude” I’d add that climate feedbacks are also functions of altitude, i.e., both climate forcing and climate feedbacks have vertical structures.

      I totally agree with your opinion about “advective transports of latent, sensible, and geopotential energy “, which in fact should be considered as dynamic feedbacks as part of climate feedbacks. We have tried to incorporate the dynamic feedbacks into a newly developed framework (see the link in Judith’s former post )

      • Analogies should not be overextended. The atmospheric physics involves many different interactions between spatially separate subsystems and between different degrees of freedom at each location. Trying to use the concept of feedback in a system, which is in a sense all feedbacks in an infinite number of ways gets easily more confusing than clarifying.

        As described by A Lacis, a lot of partially arbitrary definitions are needed for global feedbacks. Going to more limited subsystems requires many additional defining choices. Perhaps it would be better to discuss the effects directly using the variables used in the models without the extra layer of definitions needed to discuss in terms of feedbacks.

        I do not particularly like the analogy with quantum field theory and its virtual particles either. I admit that a similar analogy has been extremely useful in quantum theory of non-relativistic many particle physics, where phonons and other excitations are virtual particles, but I think that the analogy with atmospheric fluctuations is too far-fetched to be anything but confusing.

    • You assume the only solar forcing is solar radiation.

  31. On reading through the thread there are some reasonably agreed conclusions.

    First, what is being done here is to model the real world. Thus while the modeling can aid understanding it is always contingent upon the fit to the assumptions, and as system complexity increases so it becomes more difficult to to guarantee this. Model complexity may have diminishing returns.

    Second, the system under study needs to be well defined including what’s going on at the boundary, what’s going on within the system and between systems and subsystems. This does presuppose that the real world can be simplified by disaggregation and mapping onto a model without significant loss of information about the critical structures and relationships.

    Much of the discussion has centered on control theory vis a vis GCMs, but the above are more general issues.

    In the case of GHGs it does sound as though modeling the impact of surface temperatures by considering physical process on the land, sea and air is beyond our current capability, but that it might be possible to model some of these subsystems under simplifying assumptions and that feedback etc could be useful in formulating models of those subsystems (some I know would argue with that, but so be it).

    One quick comment and a question.

    I do think the question raised by Quondam @ December 30, 2010 at 7:32 am about Carnot’s heat engine is worth thinking about. If we treat it all like a black box how does it behave and is it in any way predictable?

    And a question that follows what evidence do we have outside GCMs that a CO2 impulse does have a material impact on surface temperatures in a real world? (I mean this as a genuine request for information, not a skeptical wind up).

    • Limiting studies to those that eschew GCMs and rely directly on observations seems to reduce the number of studies significantly as a browse through WG1 contribution to IPPC shows.

      “Exploring Granger causality between global average observed time series of carbon dioxide and temperature” (2010) Kodra et al is a very recent example that cites some earlier papers that had difficulty identifying links between CO2 and global temperature but argues for the ability to detect Granger causality log CO2 ppm to global temperature (but with caveats).

      Ironically over at WUWT there is a post today about “Warming Power of CO2 and H2O: Correlations with Temperature Changes” (2010) Soares, that argues the reverse but using a much shorter time frame.

  32. I don’t see any discussion of this newish paper slipped out without fanfare from researchers at NASA and NOAA. Apart from Lewis Page at, it has slipped past everyones radar. Yet it has some important findings for climate sensitivity and modeling.,bounoua

    Basically, adding a real-world negative feedback; leaf response, to a climate model reduces the CO2 sensitivity to 1.6C. If the sensitivity had doubled it would be front page news. But since it halves the sensitivity, let’s just all ignore it shall we?

  33. Alexander Harvey

    The equation ΔTs = λRF or rather λ = ΔTs/RF is related to a statistic (a value emerging from data [some modelled] without further assumptions) which for convenience I will name λ^(ta,tb)

    This is in turn related to the data statistic G(ta,tb) defined by a regression of the difference between a function of forcings minus global heat storage flux, against a function of the temperature series. The (ta,tb) merely represents the period over which the statistic is calculated. G is the reciprocal of λ^ and hence has the units of a thermal conductance per unit area.

    The statistic λ^ could calculated against any temperature series, HadCRUT3, GISS, satellites data, etc., and over various time periods, and against any forcing data series, and against any GHC (global heat storage) series.

    It is the last one that is the most pressing issue as we do not seem to have any GHC series. We do have the OHC(700m) series from NCDC/NOAA and some means of putting some bounds on what the GHC series should be. The forcing series is also becoming a bit of an issue as the staple GISS series terminates in 2003 and much has happened since then.

    Now there is no good reason why the Ts (surface temperature series) should be the one used. One could just as easily regress against a function of lower troposphere temperatures. Each will give a different statistic and they should each be judged on their statistical merits.

    Fundamentally G and hence λ^ are statistics, real values that can be determined from appropriate data, not theoretical concepts. They do not rely on whether ΔTs = λRF holds but inform us as to the likelihood that such a relationship may hold, for whatever reason. They are evidence on which theory could be based, they are not the theory they are the evidence.

    I gave an illustration of how one can determing the statist G and hence also λ^ here:

    The same posting also includes some argument over the need for rather high values of unquantified heat storage (GHC minus OHC) in order to square the statistic G with the IPCC central value for equilibrium climatic sensitivity. Not just in the post 2005 period but since the start of the OHC record (1955).

    Now my λ^ is a statistic so it suffers no argument about it being a groundless value, it is grounded in its definition not in theory. However being a statistic derived from actual data, it may inform us as to whether there are grounds to suspect that the relationship ΔTs = λRF is of some value. Personally I think that the statistic does add weight to the argument in that on the timescale 1955-2003 the statistic explains enough of the variance in the data to be of merit in itself and hence may lend merit to the theoretical equation. It is not a matter of why or how, it is a data relationship.

    Also being a statistic it has no fixed value. If we had a GHC record we could give it as a time series. Sadly we lack a GHC record but we can make some progress using the data at hand. Currently and since ~2001 it is likely that λ^ is dropping, this is related to the worry over “missing” heat. My estimates for λ^ are that it is falling and I am finding it difficult to square the IPCC central 3ºC sensitivity figure with the data statistic. I doubt I am the only one having this problem. On the other hand we have some satellite evidence that the heat really is missing, but the satellite data is the difference between contemperaneous meaurements which perhaps may be systematically out by a fraction (only a few parts of flux per thousand is required) such a bias once integrated could lead to large errors in the heat storage requirement, whereas the OHC data relies on the difference between temperatures taken at times spanning decades and are used to determine the heat storage directly so are not prone to accumulative error in the same way but they are not perfect either.

    So to recap whatever one might think about the theory, I think that λ^ is a useful statistic and one that can inform us as to the likelihood of estimates for the climatic sensitivity. If nothing else my values for λ^ seem to correlate somewhat well with the AGW poll ratings. Rising strongly from ~1990 to 2001, wobbling a litle before heading south ever since 2004. The values are consistent with AGW theory (and they are based on it through the use of forcings) but the values of λ^ (impaired as they are due to failure to collect the necessary oceanic data 700m-2000m) do not seem to provide strong evidence for high end values of λ.


    • Alexander Harvey

      A note for anyone that has access to radiative satellite data.

      λ^ could be calculated in a way that would remove the worry of a persistent (in-out) flux bias. Integrate the flux series to give a running integral and remove its mean and linear trend (which removes a persistent constant flux bias) and regress against the series of the running definite integral of your choice of temperature series for the same period after removing its mean and linear trend. The reciprocal of the regression coefficient is a λ^ statistic. Could be fun to see if this also indicates missing heat.


      • Alexander Harvey

        I have looked at the seal level pages you suggested.

        Unfortunately there deosn’t seem to be a steric level time series. One would need this and going back 40 or hopefully more years.

        Due to our not knowing the equilibrium values that would have applied for the GISS 0 forcing (1880), which this is not the same thing as the temperatures back then as we do not know how far away from equilibrium they were, we cannot use the slope of any GHC record we must look for the signal in detrended data. The general sea level signal is almost all slope (the AGW signal is not as marked as in the OHC series), this general slope extends back to around 1910 and then more gentle further back.

        Basically the AGW signal in detrended data is mostly in the last 60 years and looks like a soup bowel with a shallow but wiggly bottom and steep sides particulary the recent side (1995-2010). There is nothing as marked as that in the sea level record I think.

        The apparent (according to my λ^ statistic) deficit that is not a recent thing, it seems to be structural. I have thrown in all the “known” missing heat (about a 23% OHC equivalent as done by Hansen) and assumed that it also contains the signal (which it may not), I have thrown in a few metres of water equivalent for the atmosphere and a good few more for the land surface. I have down graded the 3ºC figure ot 2.4ºC on the assumption that there is a longterm positive feedback factor of 0.1 that is scale separated. The statistic still needs about 18% OHC equivalent more and for it all to have the AGW signal (just a general linear rise in heat will not statisfy demands for signal). Now the statistic is just that a statistic, it does not mean anything in itself. But to satisfy the energy budget a sizable signal of retained heat due to the AGW forcings is required. I can’t find it. I will repeat, that it is the signal that seem to be lacking, there can be little doubt that GHC is still rising but that in itself does not allow a signal to be attributed as a regression will not pick it out as being signal, because it isn’t a discernable signal. Slopes won’t be counted, only wiggles will do.


      • Alexander Harvey

        In the above, where I have referred to AGW siganl that should read GISS forcing signal which includes solar, volcanoes, etc. The world cares little as to the origin, just the quantity suffices.

        Sorry for the error.


    • Alex – Your comments on estimates of global heat storage (GHC) are reminiscent of Kevin Trenberth’s lament about the disparity between the apparent increase in GHC derivable from CERES measurements and the absence of a total accounting in terms of temperature change and observable OHC data. One can only speculate, and mine is that the CERES observational data are probably reasonably accurate, and so the “missing heat” is somewhere, and most likely in the deep ocean inaccessible to accurate measurements.

      On the other hand, I think it important to recognize the uncertainties regarding OHC measurements. The Argo data are invaluable, but still plagued by technical issues, sampling inadequacies, and a restriction mainly to the upper 700 meters (although this is changing).

      That said, I believe that current evidence suggests that OHC is continuing its long term upward trend, despite some Argo data challenging this conclusion. Over the long term, possibly the best metrics for OHC changes entail changes in sea level, which can be measured more accurately than OHC heat content at our current level of technology. Without doubt, sea level has been rising for many decades, and probably at an increasing rate, although with periodic bumps and dips. Part of the rise reflects melting of land ice (the “eustatic” rise), which itself appears to have accelerated over the past century in response to a warming climate. However, it is difficult to ascertain the temporal relationships between warming and ice melting, because once a temperature imbalance exists, ice can continue melting despite further temperature changes (albeit at a declining rate).

      A more reliable component to the sea level metric is therefore the “steric” sea level rise, reflecting the expansion of sea water as a function of temperature. This has its own problems. For one, steric sea levels are typically calculated by subtracting the estimated eustatic component from total sea level rise, and are subject to uncertainties regarding the extent of ice melting. Second, the thermal coefficient of expansion of sea water is not a constant, but varies with pressure, temperature, and salinity. Nevertheless, over the long term, steric sea level rise can be interpreted as a good indicator of increased OHC.

      Both total and steric sea levels have been rising over the decades – again with periodic ups and downs. A good source for both is at Sea Level – visit both the “time series” and “steric” pages for relevant data.

      Note that the steric data on that page end at 2003, but it’s clear that total sea level has continued its upward trend up to the present. Has the recent rise been due exclusively to ice melting, reflecting a marked acceleration of this phenomenon, or is a steric component still present, confirming a continued increase in OHC? I’m unaware of data for the past two years, but a 2009 paper by Leuliette and Miller provides data up to 2008. It appears as though a shallow steric rise continued until about the end of 2006, which saw a slight decline.

      The authors speculate that the decline might have reflected the 2007-2008 La Nina, but I find it easier to attribute it to the 2006-2007 El Nino (probably slightly out of phase), given that the latter entails a transfer of heat from the ocean into the atmosphere. If this is correct, we might expect new data to show resumption of a steric increase subsequent to the 2007-2008 La Nina, a later decline with the 2008 El Nino, and a rise again after the recent shift between El Nino and La Nina conditions, but that is conjectural. These interannual variations aside, the data are most consistent with a continuation of a long term increase in OHC until the present. Whether the steric changes adequately explain the total changes in GHC estimated from observational data remains to be seen.

      • Calculating the effect of the transfer of heat from ocean to atmosphere during a El Nino event, its influence to the sea level is certainly not large. A rapid calculation indicates that 1 degree change for the whole atmosphere would correspond to approx. 0.6 mm in sea level or less depending on the temperature of the water loosing the heat. The El Nino variation is certainly much less an not large compared to the average annual rate of 3.1 mm/yr.

      • Pekka – I agree. What is at issue is the source of a very slight decline in the steric sea level shortly after the middle or end of 2006, and whether that has reversed subsequently. There is no question that total sea level has continued to rise (see the U. Colorado time series).

        My speculation is that an El Nino could account for a small negative influence on steric sea level via a small loss of OHC. I would add that once atmospheric temperatures have risen, theymight begin to elicit positive feedbacks that then act to put more heat back into the oceans than was oriignally lost. This would lag the initial OHC loss, however. I will be interested to see the newest post-2008 data on steric sea levels and OHC.

      • Alexander Harvey

        Fred my response has not gone where I intended, it is here:


      • Alex – I’ll try to respond there. To help dispel my own ignorance or confusion regarding points you were making, I’ll ask a few questions, hoping that they may address those points – but perhaps they don’t.

        Would you clarify what trends you need to detrend and why? Is there reason why the CERES measurements should exhibit a systematic bias? If the heat is really in the system, must it not manifest itself eventually, presumably at least in part as an increase in temperature? Recent data (I think in GRL but I can’t immediately reference the source) suggests that transfer of heat to the deep ocean occurs at a faster rate than previously estimated – to what extent can this resolve perceived discrepancies? Since CO2 has continued to rise in at least a quasi-linear fashion, its contribution to forcing (defined as a change in radiative balance since some specified historical baseline) will also be rising – shouldn’t this increase in forcing manifest itself as a trend in Ts, OHC, etc.?

        All of this will help me to understand exactly what signal you wish to disentangle from observed trends.

      • Alex – In case you haven’t responded yet, I have another question. I’ve now looked at your Open Thread post, which addresses some of my earlier questions, but I also notice that your equations have a zero on the left hand side. How valid is that for data far from their equilibrium value?

      • Alexander Harvey


        They are balance equations, they sum to zero by defintion. I write them that way to emphasise that point. They must balance wherever they are with respect to an equilibrium. If you like you can include an error term on that side, not to alter the data balance but to balance data errors.

        Like I say it is just a statistic because it is based on the data, but it should home in on λ, if λ is meaniful. I post with respect to the indroduction of this thread, if the relationship of forcings to equilibrium temperatures doesn’t hold then the statistic remains a statistic but not support the relationship which it might show by never converging to a value. But that in itself could be meaningful in that it would support the notion that the world can cool itself and warm itself in ways that are not temperature driven. That is not necessarily a good thing. Oc course it will never converge if the forcings data fails to converge on the real world forcings. The record is long enough for sub decadal fluctuations to be minimise at scale of the record, which is a consequence of the summation process. If there are significant fluctations that are not scale separated that would prevent closing the energy budget. Again that would be significant in its own way. Obviously anything that has been acting against warming, might cease to act as a drag or become a push. That might be such sum either. Basically the GISS forcings should imply a signigficant and ongoing acceleration in heat storage if the sensitivities are central to the IPCC range. So either they are wrong or there has been offsetting that may or may not continue. That the λ^ doesn’t seem to wish to converge is not a for or against point. It is generally bad news alround. It means that λ could be almost any value, or not related to the system in any meaningful way.

        If it had converged to a value around 2.4 +/- 0.3ºC then it would have informed us as to the medium run sensitivity, which would not, in itself mean that long term values double that would be out of the question but they would be long run effects.

        Now one thing that is not much considered but is a possibility is that the models may work in the same way in that they have a low value on the medium < 50-100 year scale, this would be consistent with a low λ^ statistic as it is a value that can be dependent on its scale. That is a reason why the work that has been done on feedbacks in the models (not the real world) is so important. If low values of λ^ are compatable with high values of λ, i.e. λ^ will eventually converge on λ from below, then navigating the world through the 212 st century with any finesse may be virtually an impossibility, as it will be just a series of false horizons.


      • Alex – I think one of the reasons I have trouble following your logic is that it is not illustrated with examples or specified quantities. For example, you state, “Basically the GISS forcings should imply a signigficant and ongoing acceleration in heat storage if the sensitivities are central to the IPCC range. ”

        Why should heat storage necessarily be accelerating? The current radiative imbalance of about 0.9 W/m^2 is only about half the IPCC-estimated forcing of 1.6 W/m^2 since 1750. Presumably the ~0.7 W/m^2 difference represents heat emitted to space from a warming climate, principally involving oceans warmed by an increase in OHC. Is the imbalance increasing or diminishing? Either could be consistent with an increase in forcing, depending on the rate of increase (which in turn reflects balances between positive and negative forcings). Since OHC changes at any time point occur in response to the magnitude of the imbalance at that point and not to the magnitude of the forcing, couldn’t they be decelerating or flat?

        All this might become clearer with some quantitative examples.

      • Alexander Harvey

        Sorry missed your post.

        I think taht I have to emphasise what the statistic needs to find and why, but it is in the post on the other thread as linked to in this chain somewhere.

        We do not know the baseline temperature, the one equivilent to what a millenium consisting of just the 1880 forcings would give as a long term average temperature. The decades around 1880 may have been a little cooler or warmer than that temperature. Short of guessing, which is somewhat objective but much indulged in, it is best to remove refernce to it from the balance equation. This is done if one integrates the temperatures and the forcings (the GHC or OHC is essential an integration of the storage flux) so they can be related to the stored heat. The reliance on a refence temperature is removed if one removes the linear trend form all three data sets. The GHC is also not referenced to an equilibrium value so its mean has to go, and hence the mean from the intregrated data sets. This is sufficient and necessary to remove the unknown equilibrium values form the balance equation in its integrated (acually summated) form. Not to do this would be not to have a data statistic as it would be entirely subjective in the light that we have no evidence to support a choice of value. We may have some idea of a prior distribution (some notion that the 19th century is unlikely to have been several degrees out of kilter).

        This process has some good and bad points, on the bad side much of the variance is removed at that step. On the plus side, when regressing series which all have a marked slope it prevents on getting carried away with the strength of variance attirbuted to the match, e.g. you might get >80% attribution to a linear slope or to almost any similar curve. Also it will discriminate between real signal in the post war period from warming that was “in the pipeline” as part of the pre WWII warming or even the end of the LIA if one considered that necessary. So it comes down to regressing of the forcings since 1955 less the GHC or OHC to the integral of the temperature record during the same period, after mean and linear trends are removed. It is a deliberately discerning statistic, it is not confused by just some warming it has to have the correct signal. Obviously that means that even if it is given the signal it will still be rather sensitive to noise, this can be evaluated from the residuals and probably a +/- 0.3ºC margin is called for on that basis alone. After that it may be down to data errors, the obvious choice is the GHC but the statistic is much more sensitive to the GISS forcing data (it is much the bigger component and it is sensitive just according to its scale, they are the same on a percentage basis). It is not known how accurate the forcing data is, so issues like sulphate uncertainties are still there.

        I hope that this helps, I apologise if I am unable to spend as much time on this point from here on, as up to now, but that will probably be the case. From my point of view getting a result, any result, would be a fine thing. It would put a peg in the ground.


      • Alexander Harvey


        my understanding, which is limited, is that to to derive the energy balance from using satelites, one very large and flip-flopping value, the solar flux, has to have another large and varying value, reflected and emitted radiation subtracted from it and come to a value good to a fraction of a watt. Missing apart or two in 10000 of the solar would put it out of whack. I know that it is clever technology but a risk of bais is always there. That is why I suggested performing the analysis after removing the mean, that would remove such a bias at a stroke. If the record is to short to allow this then perhaps we should have started earlier. The issue of unknown base lines is I think a common one and it is one that can be dealt with provided that there are sufficent wiggles in the data to be able to use them to find a scaling (regression) coefficient between the data sets, that is scale separated from confounding processes.


  34. Christopher Game

    Good post, Alex. Christopher Game

  35. Forcing is very easy to define in GCMs, so I suspect that the language has carried across from there. In a GCM, a forcing is an imposed quantity, such as solar irradiance, volcanoes, aerosols, CO2 and trace gases. The temperature change is from the response of the oceans, sea-ice, snow-cover, water vapor, clouds etc. Some models may also predict vegetation, so land-cover turns from a forcing to a response. Others may predict the carbon cycle, so instead of atmospheric CO2 as a forcing, it is just the anthropogenic emission distribution. Feedback mechanisms apply to much simpler systems with one input and one output, and are just tools to help understand the response.

  36. Christopher Game

    Dear Judith Curry,

    You write:
    “So is this concept useful? If not, can it be salvaged? I find the conclusion in the Roe paper to be very insightful.
    And finally, are there better ways to try to understand the whole system, something from dynamical systems theory, entropy extremals, etc?”

    Roe’s final comment on his page 112 reads:
    “In these cases, the most important implication is that, rather than trying to solve for the specific system response to a given forcing, it may be that characterizing the feedbacks and their uncertainties is the better and more tractable goal.”

    As I read it, this final comment of Roe is a polite statement that the IPCC “forcings and feedbacks” formalism is a failure.

    Control systems theory is unsuitable for this task. What about, as you suggest, trying dynamical systems theory (for example, G.D. Birkhoff (1927/1991), Dynamical Systems, American Mathematical Society Colloquium Publications, volume 9, Providence, RI, ISBN0-8218-1009-X) ? We are trying to make simplified models that will lucidly exhibit the skeleton of the physics. The usual scientific way to write such models is as a system of ordinary differential equations. To make this work, one must first actually understand the skeleton of the physics. Procrustes will not supply a mathematical procedure to do it without this; surely we can accept that Theseus did him in? One must by experience find out some external driver variables and internal state variables and parameters that sufficiently capture the skeleton of the physics, so as to describe the dynamical structure that governs the time evolution of the system under investigation. One will seek to write some ordinary differential equations in canonical form, with the time derivatives of the dynamical variables on the left-hand side, and functions of the external drivers and the internal state variables, with some time-independent parameters, on the right hand side. This is the ordinary way. I have difficulty understanding why Aires and Rossow (2003) are about the only people in this debate to say so. It looks as if people are hypnotized by the IPCC doctrine? In the theory of dynamical systems, feedback is not a specifically defined quantity; it is just a general implicit background idea; the dynamical structure is described with other more specifically defined terms.

    Reading Roe’s initial exposition (on page 96, headed ‘Basics of feedback analysis’) of the IPCC “forcings and feedbacks” formalism, I can’t help feeling that only someone who has been thoroughly brainwashed could regard it as a rational scientific presentation. The misprint in his Figure 2, that labels both the output as ΔR, seems to epitomize the situation: did the referees really not read this paper? In panel a of this figure, where is ΔRf ? Surely this paper of Roe is telling us that after a quarter of a century, they really can’t do any better than the ludicrous presentation by Schlesinger (1985) at DOE/E-0237, IRN13397400 ? If they can do better, why doesn’t Roe tell us where? But instead on page 104 he writes: “Equation 29 is arguably one of the most important equations in climate dynamics (and system dynamics in general), …” It seems as if he really means it! Is that the best they have?

    Yours sincerely, Christopher Game

    • Harold H Doiron

      In my posts herein I haven’t tried to distinguish between controls systems models or Dynamical Systems models, the latter is the more general of which the former is a subset. Using a simple 2nd order differential equation for dynamics of a spring-mass-damper system to illustrate why I like the control systems analogy for climate models, we can write:

      m*xddt(t) + c*xdt(t) + k*x(t) = f(t) + g(t)

      where we call the dynamical model on the left hand side the system and f(t) and g(t) the external forcing functions. But what if we can show that,

      f(t) = a*xdt(t) + b*x(t) ?

      That is, f(t) is really not an external forcing function, but actually a force acting on the system that is a function of the state of the system defined by
      x(t) and xdt(t). Then we can write,

      m*xddt + (c – a)*xdt + (k-b)*x = g(t)

      From this form of the model, we can recognize that g(t) is the only external forcing function and that force feedback mechanisms ( f(x,xdt) ) within the more completely and accurately modeled system, cause the actual system to have a different frequency and damping in its response to g(t), than originally defined by the spring constant, k, and visous damping coefficient, c , assigned to the model.

      This is a type of feedback controls system formulation, but it is also a dynamical system model with internal feedback mechanisms that more precisely define system behavior.

      • Christopher Game

        Dear Harold H Doiron,
        Thank you for your reply. I do not like what you propose because it conflicts with the view that I put in my post:
        “To make this work, one must first actually understand the skeleton of the physics. Procrustes will not supply a mathematical procedure to do it without this”.
        Yours sincerely, Christopher Game

      • Harold H Doiron

        We should not call them models if what is in them doesn’t represent even “the skelton of the physics”. I didn’t realize this was actually the case. This similar misuse of the term “model” for a database of past history of foam impacts on the Shuttle Orbiter, used for the basis of Shuttle flight operations decisions that ignored the impending disaster of the Shuttle Columbia accident, and ignored requests of concerned engineers to perform a structural inspection prior to re-entry, was a major finding of the post-flight accident investigation board.

        What kind of accurate predictive tool for long term climate change can be used that isn’t based on at least the skeleton of the known and well-understood physics? Is this really the case? If so, the climate change model uncertainty issue is much worse than I feared. I would not trust any predictive model that isn’t based on how the known Laws of Physics, Chemistry, etc. act on the current state of the system, and external inputs to the system, to create known rates of change of all important system variables required to predict a future state. If current climate change models can’t do this, then they should be kept locked behind closed doors until such time as they can. Why are the results of such “less than models” even worth publishing? To make critical decisions using such things can’t be much better than coin tossing.

    • “The misprint in his Figure 2, that labels both the output as ΔR, seems to epitomize the situation: did the referees really not read this paper?”

      Christopher – I’m not sure what you mean by “both the output as ΔR”. I think you may have misinterpreted Figure 2, because I believe it was printed as intended and not a careless mistake. In the figure, ΔR is the flux adjustment needed to restore equilibrium. It is therefore both input into the climate system capable of mediating a feedback, and the output that restores balance. The point of the figure is to illustrate how the changing flux (the input) can result in different temperatures despite the same final output when feedbacks are evoked. Perhaps the text could have made this clearer, but I don’t think the figure is wrongly drawn.

      • Christopher Game

        Dear Fred Moolten,
        Thank you for your thoughtful reply.
        As for typos, who am I to complain, having written, besides the one already noted above, “both the output as ΔR” when I should have written “both the input and output as ΔR ? And you politely didn’t jump on that.

        Perhaps I am the brainwashed one, expecting to find ΔT at the output, as in Schlesinger (1985), Schlesinger (1986, Climate Dynamics 1: 35-51), Peixoto and Oort (1993), and Stephens (2005).

        Perhaps you may be right that the figure is intended to illustrate that ΔR is the flux adjustment needed to restore equilibrium.

        But if so, then surely Roe is using an eccentric diagrammatic syntax, and should let the reader in on it? He was careful about such a thing in his footnote 4 on page 97.

        The panel a may perhaps illustrate that ΔR is the flux adjustment needed to restore equilibrium ; but I don’t think it illustrates how it does so. For the how, I may ask where is ΔRf ? I would like to see both ΔR and ΔRf in the same diagram to illustrate Roe’s equation (2). It is not apparent to me how the panel a could show that. Surely a feedback loop is needed to show how? The usual job of referees is to make sure that such things are clear, especially in a didactic article like this one.

        You write that ” perhaps the text could have made this clearer”. I am complaining initially about the labelling and now about the structure of the diagram. I think we have to make these complaints about unclarity because the basic thinking of the formalism is muddled when it tries to make out that the Planck response should not be regarded as a feedback like any other.

        If Gerard Roe or Andy Lacis have time to read this, perhaps they will very kindly clarify it?

        Yours sincerely, Christopher Game

      • Christopher Game

        Another typo; it’s getting bad; it should read:

        Perhaps I am the brainwashed one, expecting to find ΔT at the output, as in Schlesinger (1985), Schlesinger (1986, Climate Dynamics 1: 35-51), Peixoto and Oort (1993), and Stephens (2005).

        Perhaps you may be right that the figure is intended to illustrate that ΔR is the flux adjustment needed to restore equilibrium.

  37. Christopher Game

    Sorry, typo, Schlesinger 1985 at DOE/ER-0237.

  38. Alexander Harvey | January 3, 2011 at 12:51 pm | Reply
    I have looked at the seal level pages you suggested.

    An excellent comment and observation — where’s the signal? Where’s the beef?

    But I couldn’t find any further mention of the seal population. Did you neglect to follow-up on it?


  39. Here’s a brain teaser for feedback enthusiasts:

    Theorem: The influence of positive feedback is greatly enhanced by the presumption that steady-state perturbations are equivalent to those for equilibrium systems.

    By definition, equilibrium refers to a system with time-independent entropy. A steady state system has a time-independent internal entropy and a constant rate of entropy generation due to fluxes of energy and mass entering and leaving the system. I’ve previously suggested a black-box description with well-defined boundary conditions as a model for analysis. Forum limitations require some reference to external equations, so

    Eq. 6 describes the basic perturbation of a steady-state system (high temperature approximation) with an external flux dependent on some internal parameter, q, e.g. a GHG, and the temperature difference of the I/O surfaces. Lambda is a Lagrange multiplier adding a constant-flux constraint.

    Eq. 8 follows directly. The LHS is a forcing, the logarithmic partial represents feedback, with linearity, a unit value, taken as zero feedback.

    Were we to repeat this calculation assuming J rather than dSn/dt the stationary function, the result would be almost identical except that the term in brackets involving lambda would be absent (limit of infinite lambda). As the partial decreases, the temperature perturbation may become quite large. With a finite lambda, however, positive feedbacks are capped. I’ll propose that lambda represents internal degrees of thermodynamic freedom and lambda=0 is a thermodynamic limit for the minimum possible temperature changes adding or removing GHGs.

    With lambda very large, fluctuations of J from Jo will be very small. As the degrees of internal freedom increase, larger fluctuations occur. We can, with our black box, actually determine the partial by changing the temperature and tracing out the variation of J. Lindzen and Spencer have tested this hypothesis, seeking a correlation of temperature noise and flux noise. The most significant result seems to be a shotgun pattern from which one might infer that other degrees of freedom are overwhelming detection of the feedback signal

  40. Tomas Milanovic


    I found it amusing that you would write in a post about assymetry of time you take to write a post and the time that some poster take to react on your post.
    I wonder how much time you took to write this one because I took a bit more than 2 hours to write this comment.

    I appreciate also the focus on the “sensibility” questions and equations because in my opinion these questions concentrate most if not all misconceptions and arbitrary assumptions that one can find in climate science.

    1) 0 dimensional model

    The equation ΔTs = λRF can only make a limited sense in a 0 dimensional model.
    Physically we deal with a homogeneous isothermal body in radiative equilibrium with an isotropic radiation field – imagine a metallic Earth in the center of a thin shell Sun .
    Every single assumption mentionned above is wrong and can’t even remotely approximate the real Earth which is a heterogeneous non isothermal body out of equilibrium within an anisotropic radiation field.
    There is no reason why such an accumulation of unrealistic or flat out wrong assumptions would give any information whatsoever about the behaviour of the real Earth.

    2) The real 3 dimensional Earth and the functionals

    To take in account at least the spatial heterogeneity and radiation anisotropy while still maintaining only 1 variable , people choose to spatially average the fields.
    This defines AV(T) = 1/S . ∫ T(R,θ,φ).dS with R fixed at the surface of the sphere.
    AV(T) is a functional.
    It maps a function in some function set to a real number.
    Operations on functionals are notoriously difficult and specifically a functional can NOT be differentiated.
    In other words d[AV(T)] is not well defined what should not be surprising because the variables of AV are functions and not numbers.
    A functional derivative can be defined but is not unique.

    The most prominent use of functionals (it earned a Nobel) was Feynman’s observation that the probability of transition from a quantum state q1 to a quantum state q2 could be written as a functional which had to be integrated for all paths going from q1 to q2.
    This gave rise to the third consistent formulation of quantum mechanics (after Schrodinger and Heisenberg) in terms of path integrals.

    The difference between Feynman’s functional and the AV functional above being of course that there is no way to compute 1/S . ∫ T(R,θ,φ).dS for all paths between 2 states.
    Not mentioning the fact that Feynman wrote a dynamical functional with a relevant function (Lagrangian) while the “climatic” AV functional is completely arbitrary and contains no relevant dynamical information.

    Of course everything said above applies mutatis mutandis to the functional RF.
    Now before coming to Δ , one has to integrate the infinitesimals d.
    But as we have seen, neither dAV nor dRF is well and uniquely defined so there is no way to integrate – the relation is just mathematical non sense.
    One could elaborate more but I already did so on another thread where I choose a particular formulation of the functional derivative.

    Statistical interpretation and temporal chaos

    Al Thekaski very rightly said that the climat problem is a field theoretical problem.
    As such it should be treated by field theoretical tools. More specifically one should ban confusing and misleading terms like “feedback” which come from the linear control theory. Unfortunately this is not the case sofar.
    There are also many misconception concerning the use of chaos theory and one sees sometimes terms like attractor or orbit thrown around.
    The chaos theory, also unfortunately, is of limited help with the climate problem for the simple reason that it deals with dynamical systems in a finite dimensional phase space with variables depending ONLY on time.
    It makes no sense to talk about “climate attractors” because these are topological beings in the phase space of the chaos theory and the space becomes uncountably infinite dimensional for weather/climate.
    For the same reason, ergodic theory can’t be easily extended to the spatio-temporal domain.
    And as it cannot be extended, it doesn’t make sense to talk about statistical interpretations in the sense that there would be an invariant probability distribution of future states. This is due to the fact that there is no natural metrics for the spatio temporal dynamical states – what does it mean that the state A = state B ?
    In chaos theory this meaning is obvious – 2 states are equal if all their coordinates in the phase space are equal.
    In weather/climate the “number” of coordinates is uncountably infinite what just reflects the already mentioned indetermination of the variation of the functionals.
    So even if a statistical analysis of a time series gave a correlation between AV and RF, one could not conclude that this correlation still holds for another time scale and/or another initial/boundary conditions.

    4) Equilibrium
    There will probably be a specific post on this issue one day because it is quite central.
    Clearly the Earth is in no kind of equilibrium what should automatically lead to the dynamical field theoretical treatment.
    Strangely this did not happen and what we have instead is this unnatural and mathematically horrible notion of “things balance over long period”.

    An equilibrium is not “anything goes”, it is a precisely defined local concept.
    Substituting time averages to the instantaneous values is an extremely hazardous exercice that never works for non linear equations. Aditionally, like this is the case for N-S Reynolds averaging, this has always for consequence that a closed problem becomes open and additional more or less arbitrary assumptions must be taken.
    So even if we had “integral radiative energy in = integral radiative energy out” over some time scale (what time scale and why?) this absolutely would not mean that we have equilibrium of any sort at any instant and there would be an infinity of different states obeying this condition. Besides this condition is not realised anyway.
    Time averaging spatial averages means taking a functional of a functional what makes the already difficult problem completely untractable.

    As a conclusion, outside of 0 dimensional model which is irrelevant to the real Earth, the relation ΔTs = λRF with λ constant is arbitrary, unjustified, misleading and certainly mathematical non sense.

    • Tomas, thanks for your post, I probably agree with it including your conclusion. note, next post up (hopefully later today) is one on synchronized chaos, related to tsonis papers.

      • Tomas Milanovic

        That’s great . I have read almost everything by Tsonis . It is not exactly chaos theory it is more like a “Taylor development” or a “principal component analysis ” of a chaotic solution if you see what I mean.
        Very interested to read what you have to say about it.

      • Tomas Milanovic

        Btw you will see why Tsonis does this Taylor development like treatment.
        It is precisely the way (he sees) to tackle the uncountably infinite dimensional phase space that I have already been talking about.
        By selecting N (N finite) most “important” spatially extended objects considered as being only time dependent (temporal chaos) and by coupling them among themselves with different coupling constants, he achieves both spatial extension AND finite phase space dimension what would be impossible in the “full” theory.

        This is what the coupled map lattices models in spatio temporal chaos do too – transform infinite dimensional in finite.
        Only CML do that with classical grid (like GCMs) while Tsonis uses real observed physical systems (ENSO etc).

      • i need to understand this better, i look forward to your further comments on this. a brief post on this will be up later this a.m. I am in the middle of trying to figure out ways to do a decent decadal scale forecast for my weekend job, this makes more sense to me than anything else i’ve seen

      • Christopher Game

        Trying to revert the font to Roman.

      • Christopher Game

        It didn’t work.

      • Might be an open blockquote
        an open italic

      • Nope

      • If you note the faint greyed-out description of acceptable tags below the comment box, it does not include any font settings. Linking, quoting, timestamp, italics, bold (em, strong), and strikeout. That’s all she wrote.

      • Christopher Game

        open angle bracket i close angle bracket text open angle bracket slash i close angle bracket puts the text in italics when this system is working aright. So also for b for bold.
        Let me try it here to italicize ‘text’: text
        and here to bold ‘text’: text.

    • Tomas,

      “A functional derivative can be defined but is not unique.”

      Doesn’t the Gateaux derivative address issues about derivatives of functionals? My ‘engineering math’ expertise runs out of gas well before we get to these nitty-gritty aspects.

      Thanks for any info.

      As an off-topic aside. I had a pure-math kind of professor for one course. He would deduct points if you didn’t explicitly state that whatever functions were the subject of the problems must be continuous to the necessary degree in order for unique solutions to exist.

      I always wanted to state that the functions were not continuous so there are no solutions and then leave that problem. Especially for those problems that were giving me grief. And as a pure-math person, he gave us many problems like that.

      In my experience in engineering, deep considerations about continuous-ness, existence, and uniqueness get short shift. Maybe we’ll get around to those issues some day, but right now we’re way busy cranking out numbers. [ Except in the case of numerical solution methods and algebraic parameterizations. Lack of continuity can set off aphysical ringing at the drop of a digit. Oh, and conservation of mass, momentum, and energy easily get zapped, too. ]

      • Dan,
        Nothing like that is needed here. The claim of Tomas is completely misplaced here. Some functionals have well defined derivatives with respect to a parameter and this applies here. The derivative of the functional defined by the integral and related differentials are in the present case uniquely defined and matter of rather elementary courses of calculus.

      • Thanks. That is more in line with my rough experiences.

    • Richard S Courtney

      Tomas Milanovic:

      Thankyou for your superb post.

      I agree much of it including your final paragraph that says;

      “As a conclusion, outside of 0 dimensional model which is irrelevant to the real Earth, the relation ΔTs = λRF with λ constant is arbitrary, unjustified, misleading and certainly mathematical non sense.”

      But I would welcome some clarifications because I was especially interested in your statements saying;

      “The chaos theory, also unfortunately, is of limited help with the climate problem for the simple reason that it deals with dynamical systems in a finite dimensional phase space with variables depending ONLY on time.
      It makes no sense to talk about “climate attractors” because these are topological beings in the phase space of the chaos theory and the space becomes uncountably infinite dimensional for weather/climate.”

      Perhaps so, but if the system behaves chaotically then our (at present) inability to describe it mathematically is a purely practical problem that has potential to be resolved. Or do you have a proof that such a solution is not possible? I have not seen such a proof and, as you say, Tsonis adopts an approximation which attempts to overcome it.

      I agree your point that says;

      “In weather/climate the “number” of coordinates is uncountably infinite what just reflects the already mentioned indetermination of the variation of the functionals.
      So even if a statistical analysis of a time series gave a correlation between AV and RF, one could not conclude that this correlation still holds for another time scale and/or another initial/boundary conditions.”

      However, as I see it, this is also a purely practical problem that has potential to be resolved. Again, am I wrong?

      Indeed, as you say, Tsonis adopts an approximation which attempts to ‘get around’ these practical limitations which you state. As you say of Tsonis;

      “By selecting N (N finite) most “important” spatially extended objects considered as being only time dependent (temporal chaos) and by coupling them among themselves with different coupling constants, he achieves both spatial extension AND finite phase space dimension what would be impossible in the “full” theory.”

      It seems to me that Tsonis’ approximation is a useful contribution to the problems. If so, then the problems’ affects may only provide inaccuracies concerning the positions of the attractors (which Tsonis call “climate states”) because the Tsonis ‘solution’ is an approximation, and the only real problem is a determination of those inaccuracies.

      But I may be misunderstanding you because you say the existing mathematical theory;
      “deals with dynamical systems in a finite dimensional phase space with variables depending ONLY on time”.

      Hence, for clarification, I ask if you are suggesting that variable inputs (e.g. altered radiative forcing) alter the system so require a different model if a chaotic model of the climate system is adopted. If so, then that is not how I interpret Lorenz 2005 paper
      (ref. Lorenz EN, Designing Chaotic Models. Journal of the Atmospheric Sciences: Vol. 62, No. 5, pp. 1574–1587 (2005) ).

      So, I would be grateful for a clarification.


  41. Christopher Game

    The main font seems to be stuck with italics. Here follows a couple of unitalic strings:

    • Christopher Game

      Now a test string. I think it will come out as italic.

      • You can display the angle brackets if you want: < >
        Use ampersand lt semicolon, and ampersand gt semicolon, as I did above.
        Italics: italics
        bold: bold
        emphasis: emphasis
        strong: strong
        strikeout: strike

        And that’s it.

      • The problem is in the following string of letters separated here by commas:

        This appears in the message of Christoffer Game on January 3, 2011 at 3:59 pm.

        Exactly the same series of letters caused earlier similar problems in another chain. The were supposed to end a section of italics, but the slash was erroneously after the i. Perhaps the blanko is also somehow influencing the outcome. It is also possible that WordPress software has added the blanko.

        In any case it appears to be important that the slash is not mis-located.

      • WordPress software was clever enough to remove the letters that I wrote they are: <,i,blanko,/,>

        The are the ending sequence of italics except that i and slash are in wrong order and there is a blanko between them. This is at least the way they come out, which may differ from the way they were typed.

  42. Harold H Doiron

    Dr. Curry,

    I am getting dizzy from the confusion, lack of agreement, and uncertainty regarding the Earth’s climate change processes discussed in this thread of Climate Feedbacks: Part I. We can all be thankful that designers and manufacturers of commercial airplanes with similarly complex structural, control, navigation, electronic, pressurization, fuel management, jet engines, mechanisms, etc. don’t have this much uncertainty before they recommend that it is safe for the general public (that does not understand this scientific and engineering complexity) to ride in these airplanes.

    Apparently, because of the faith that so many learned people have placed in these climate change “models”, I have naively assumed that these models (which I really don’t know any details about) used a vector, X, of Earth System variables such as temperature at different locations, CO2 spatial distribution around the atmosphere, CO2 absorbed in the oceans, rate of CO2 emissions resulting from economic activity, earth’s surface albedo distribution, Earth’s water vapor distribution, rate of CO2 release into the atmosphere from CO2 contained in the Earth’s oceans, rate of growth of biologic mass due to increased CO2 and longer temperate growing seasons due to increased temperatures, CO2 release due to decomposition of biologal mass, rate of cloud formation within the atmosphere due to water vapor distribution and temperature distribution in the atmosphere, etc., etc. in a simulation model of the form,

    Xdot = f(X,t) + g(t)

    where g(t) are the external forcings of energy flux from the sun based on historical data (stochastic?) and deterministic orbital mechanics effects.

    If we can’t confidently write the vector of functions f(X,t), describing how the known Laws of Physics, Chemistry, etc. act on the state of the system to create rates of change of all IMPORTANT system variables for the simulation time of interest, X, how can one possibly predict what some of the variables contained in X, (such as temperature distribution around the earth’s surface that can be used to form a scalar metric such as “average global temperature”) will be at a later point in time? We are talking about this temperature metric at some future point in time aren’t we? This implies to me that we must integrate rates of change of all quantities required to make the calculation at some future state. Without being able to confidently write these equations, at least the most important ones, where does confidence in current climate change (dare I call them “models”?) come from?

    The task of defining the functions f(x,t) is daunting, but not impossible. Are there not known Laws of Science that could be used to define these functions at some stable spatial gridwork granularity, such as finite element methods (FEM) used in complex structures stress and vibration dynamics analysis, or Computational Fluid Dynamics (CFD) for fluid systems? Modern structural dynamic models have hundreds of thousands of such state variables, and CFD models solving the Navier-Stokes equations have similar or greater order of magnitude number of state variables. Is it impossible to get a measurement of the necessary state of the system X at some point to confidently initialize the model? I think the answers to some of these questions is a matter of priority regarding where climate change research funds are being expended. It may be an impossible task for one researcher, but certainly a dedicated team of researchers could do it if they organized around the goal of an accurate climate change model.

    If you don’t flow chart this process, to define all of the interacting sub-models, then eliminate the unimportant ones by some documented logical process and arguments that can be re-visited by other researchers at a later time, and and get folks working on the different pieces of these numerous processes to define the important functions f(X,t), of what practical use are climate change models?

    I suggest the climate change research community must use the available research funds to began taking bites out of the above outlined tasks (the list of tasks wasn’t meant to be complete) as opposed to making numerous garbage-in/garbage-out computer simulation runs with current models and then publishing the garbage results. I hate to be so rude, … is not my basic nature, but I have found that sometimes straight, blunt, sobering talk is needed to shake-up herd mentality when it is so deep into the weeds, it loses sight of what must be done to resolve the current confusion. Clearly, the climate change research community needs to do some sobering, reflective thought about uncertainty in climate change models that I have observed starting to happen on this thread you have started….and what they must eventually do to get rid of this uncertainty.

    Does the climate change research community not have confidence in the known Laws of Science needed to attack the Climate Change (read rates of change defined by f(X,t) ) problem with the same confidence used to to send humans on space flights to the moon and back?

    • Harold – The person(s) most qualified to answer your questions are those who design GCMs for a living. Perhaps Andy Lacis will see your comments and respond.

      Not being a climate modeler, I can only state tentatively that most of the variables you list are incorporated into the models, admittedly with some parametrization for details of a sub-grid size nature. I believe all of them are incorporated into models if we include those focusing on particular phenomena rather than the comprehensive realms of the GCMs.

      One point deserves mention, however, and I believe it also addresses a misconception inherent in Tomas Milanovic’s earlier comments. Climate science in general, and models in particular, do not try to compute average global temperature or its change over time – to do so would be a far more daunting challenge than what they actually attempt. Rather, they compute changes at multiple individual grid locations that are homogeneous enough for reasonably accurate output – output that can be checked against observational data. Interactions between grids are also estimated, but this is a less formidalble undertaking than an averaging of global temperature. It is these changes with time, that are averaged, and not a hypothetical “mean global temperature”.

      The limitations of current climate models are well understood (at least by the modelers). The latter do not pretend that their estimates are accurate within the very narrow tolerances required for some engineering applications, but the claim that the models have no value in assessing the projected effects of changes in important variables such as CO2 is refuted by the empirical evidence. To appreciate that, however, requires some familiarity with the literature in the climate science journals. Unfortunately, information with the requisite detail and objectivity is unavailable on the Internet, which is why it is hazardous to rely on assertions there that may be misinformed or biased by the use of data selected to represent a predetermined opinion.

      • Harold – In case you wondered why I made my last statement about the Internet, it was motivated by your citation elsewhere of claims by Rutan. Although others may disagree, I believe that with the aid of 5 or 6 hours’ time, and several dozen literature references, it would be possible to persuade an objective observer that almost all his claims were invalid. Probably none of us here is willing to take that effort, and so my simpler recourse was merely to warn against Internet claims in general – by any of us or anyone else – when it is possible to visit original data sources instead.

    • Christopher Game

      Dear Harold H Doiron,

      You seem to me to have too much faith in ‘brute force’ computability, to the neglect of the development of new and more powerful physical principles. I think the path of ‘brute force’ computation is already being pushed as hard as people can. I think it can’t be expected to work in a reasonable time frame for this problem.

      New principles of physics are hard to come by. But they do come over time. Prigogine’s theorem of minimum rate of production of entropy came in 1945. It holds only in a very narrlowly restricted range of processes, but it is a new principle for them. For the cases in which it applies, it must be very carefully applied. Newton seems not to have known the law of conservation of energy, but eventually it was discovered. I think this is the necessary way.

      Yours sincerely, Christopher Game

  43. Christopher Game

    Back at, before my typo, for which I am sorry, I wrote: “In terms of the diagram as printed, the result of a CO2 perturbation is not an input as represented in the figure: it is a parameter change that should be shown as a change of λo. This is saying that the “radiative forcing” effect of a CO2 change is a “forcing” only in a metaphorical or handwaving sense, and is not valid physics. The diagrams of figure 2 are therefore nonsense if read as statements of physics.” Expanding this thought a little, it means that the citing ( Hansen et al. 1984 at IRN1263184X, and by Bony et al. 2006) of Bode 1945 is a false lead to the meaning of the IPCC “forcings and feedbacks” formalism. The picture that one is led to by that citing, of a device that transmits and transforms a signal, is not an appropriate interpretation of the formalism. The Bode-like feedback circuit diagram pioneered in the climate literature by Schlesinger 1985, and followed by Schlesinger 1986 and 1988, Peixoto and Oort 1993, and by Stephens 2005, and now by Gerard Roe 2009, is does not fit the formalism. The formalism is about the change of location of a dynamically fixed point when the parameters of a dynamical system are changed; it is not directly about propagation of a signal. The language of “amplification” and “gain” are about propagation of a signal, when used with a citation of Bode 1945. But they are not appropriate to the IPCC formalism, and use of them as interpretations of that formalism is misleading.

    Let me re-word my criticism: the result of a CO2 perturbation is not an input to a signal path as represented in the figure: it is a parameter change that should be shown as a change of λo.

    I would like to repeat my question, “Can anyone provide an account of the IPCC “forcings and feedbacks” formalism that is not vulnerable to this criticism?”

    Perhaps I should be more polite and ask would anyone be so kind as to provide an account of the IPCC “forcings and feedbacks” formalism that is not vulnerable to this criticism?

    I think that perhaps the CFRAM accounting procedure of Cai and Lu may be a suitable vehicle for this purpose?

    Christopher Game

    • No reply. It seems I am whistling in the wind. Does this mean that no one read my post, that you think I am talking nonsense, that my post is so boring that it doesn’t deserve a reply, that you think my post is so obviously right that no reply is called for, other things?

      • This issue has been discussed so many times that there is nothing to add. Rephrasing the earlier comments:

        There are similarities and differences between the uses of the concept “feedback” in control theory and in climate science.

        The basic idea applies to both: The system considered is influenced by some external factor through some chain described by a set of variables. The internal processes lead to changes in some variables that were also affected directly by the external factor. These additional changes due to the internal processes are the feedback. Defined in this way the external influence can be of any nature including both levels of input like the voltage at the input to amplifier or flux of solar radiation, and controlling factors like the setting of (non-feedback) amplification of the amplifier or GHG concentration.

        The big difference is in the fact that for a typical control system the actual analysis of the system includes a direct consideration of the feedback factor, but in climate science the actual analysis is done by methods unaware of the values of feedbacks. In climate science the actual system is continuous in space and can be described in terms of fields (or functions of both space and time), not in terms of a finite number of discreet variables. For the climate system the feedbacks are defined for presentational purposes from the results of the full analysis.

        Although the feedbacks are not used in a full analysis of the climate system, they can be used in demonstrative calculations, but this kind of use should not be overextended. All climate models based explicitly on feedbacks are extremely aggregated and therefore not suitable for any serious research. Attempts to build better models by adding new details to these models are not likely to add much to the understanding as the standard feedbacks are really only summary numbers without any other obvious meaning. The summary numbers need not, and usually do not, follow the same equations as the detailed data they are summarizing. (Just to give a very simple example: the product of average values of variables Xi and Yi is in general not the same as the average of the products Xi*Yi.)

        To conclude: There is nothing wrong in presenting summary results of climate research using the concept of feedback, but the concept of feedback does not have much other use in climate science than this presentation of summary results. Attempts of using the concept further may easily lead to erroneous conclusions.

        There may be exceptions to my last claim, but I have not seen evidence of that.

      • Christopher Game

        Dear Pekka Pirilä,
        Thank you for your careful and patient reply.

        The heavy work of climate research is said to be done with AOGCMs. These are so elaborate that only the most expert can usefully criticize them. Sooner or later, before they can expect the plebs to act on their concluions, the most expert must tell their conclusions to the plebs in more or less ordinary language. The experts (e.g. Bony et al. 2006, Roe 2009) currently tell their stories in terms of the IPCC “forcings and feedbacks” formalism, which is in effect the ordinary language they use for this. If the experts can do no better than choose a formalism that is vulnerable to obvious criticism, such as yours, that it is “not suitable for any serious research”, and mine, “that it is nonsensical”, the plebs will ask “if they cannot express themselves rationally in ordinary language, why would we trust them to do their heavy research rationally?” This matter is too important to simply trust to the uncriticized authority of experts. Perhaps in authoritarian societies, that can be done, but in non-authoritarian societies, experts have to do better.

        My criticism, that the ideas of “amplification” and “gain” are nonsensical in terms of the cited Bode theory, and that the natural interpretation of the formalism is to think instead of a change in λo, is not intended to try to replace AOGCMs. It is intended to move towards a way for the experts to present their conclusions rationally, which in a non-authoritarian society they need to do.

        While I agree that “There is nothing wrong in presenting summary results of climate research using the concept of feedback”, provided that such presentation is rational and intelligible, I would say that it is not good enough in a non-authoritarian society for experts to be unable to present their conclusions to the plebs except in terms of a “concept [that if used] further may easily lead to erroneous conclusions”. Therefore I think some effort needs to be put into finding rational ways for the experts to present their conclusions to the plebs.

        My criticism is intended to serve this purpose. So I think it deserves a direct answer. I think that Cai and Lu have perhaps developed an accounting procedure that is capable of providing a rational framework for assessing such criticisms.

        Personally, I don’t think that AOGCMs, as brute force computational exercises, can be expected to provide the answers that a non-authoritarian society can demand of the experts whom it supports. I think that new principles and phenomenological laws of physics are needed. When they come, of course they will inform the construction of new AOGCMs which will be far more trustworthy than present-day ones, which rely very heavily on “parametrizations” which are not thoroughly founded in the basic laws of physics. You have previously told me that you expect proper work to be so founded, and I agree with you on that.

        Yours sincerely, Christopher Game

      • Excellent comment and summary. You are starting to seriously impress me!

        It should be noted that the alternative “authoritarian society” is actually far more exposed to the risk of going very far down dead end implementation streets using flawed research. Naive, common-sense, democratic demands for Reasonableness Tests and jargon-free justification is a feature, not a fault.

      • Christopher Game

        Dear Brian H, Thank you. But I think it would be going too far to rely solely on naive, common-sense, democratic demands for Reasonableness tests; we need also valid arguments that are well defensible against reasonable criticism. Yours sincerely, Christopher Game

      • Yes, and I didn’t say or imply “solely”. But to exclude them is too dangerous. Especially when matters of vital and sweeping import are being discussed, and the “findings” are being turned into very expensive public policy initiatives on the fly.

      • Christopher Game

        Brian H, yes I agree. Christopher Game

      • Pekka Pirilä 1/8/11 at 4:09 am,

        You wrote,

        >> There are similarities and differences between the uses of the concept “feedback” in control theory and in climate science.

        >>The basic idea applies to both: The system considered is influenced by some external factor through some chain described by a set of variables. The internal processes lead to changes in some variables that were also affected directly by the external factor. These additional changes due to the internal processes are the feedback. Defined in this way …

        The principles of science, founded in language, logic, and rational argument, transcend any of its fields of specialization, including climatology. Now science is quite permissive, tolerant of different fields using the same words defined in different ways. However, neither science nor principles of argumentation permit the same word used in nakedly different ways within one field.

        Popper declared, “definitions do not matter”. Popper, K, “Objective Knowledge, a Realistic View of Logic, Physics, and History (1966)”, in Objective Knowledge (1972). He was quite wrong. But some people believe that Popper defined the scientific method.

        The way you have defined feedback matches the sense of that word in the main bodies of IPCC reports, well-described by Andy Lacis on 12/31/10 at 6:34 pm. It is the method they attribute to the GCMs. However, that is not the way feedback is defined in control system theory, or when Lacis along with Hansen introduced the concept into climatology, or when IPCC defined feedback in its Glossary. See my post on 12/30/10 at 1:54 pm for complete references and quotations.

        Your definition, and as used by IPCC and Lacis, a parameter merely has to be different than a forcing and be affected by forcings. This divides modeling parameters in two: {forcing and not forcing}. At least it’s logically complete. However, the essential ingredient in control system theory, in Hansen, Lacis, et al., and in IPCC’s formal definition, is that response to a forcing ALTERS one of the forcings. It may amplify it (including attenuating it) or augment it (by addition or subtraction). Clouds modify insolation; surface temperature alters ocean emissions.

        In the formal scheme, modeling parameters comprise {forcings, feedbacks, and neither}.

        The climatology you and Lacis describe is incomplete, and two-valued in the definition of feedback. It violates science.

        You continue, >> The big difference is in the fact that for a typical control system the actual analysis of the system includes a direct consideration of the feedback factor, but in climate science the actual analysis is done by methods unaware of the values of feedbacks.

        You might have written accurately: A model for a typical control system accounts for feedbacks within its flow variables, from which descriptive parameters can be evaluated, such as a feedback factor, stability, dynamics, margin, and gain. In climate science as practiced by IPCC, meaning using its radiative forcing paradigm, the climate models have no flow variables by which feedback can be represented, quantified, and assessed.

        Cloudiness responds quickly to solar activity (a positive feedback) and slowly to surface temperature (a negative feedback). The ocean outgasses CO2 in response to the global average surface temperature (a positive feedback). These, among others, are not modeled in the GCMs. The loop gain of these phenomena cannot be calculated from the GCMs. As a result, the GCMs run open loop in the hydrological cycle and in the carbon cycle. The results of the modeling is unlikely to match the closed-loop real world except at the point to which investigators tuned their models, plus perhaps an accidental point or two, in the continuum of climate.

    • Christopher Game

      On one point I have had some clarification. Reading Andy Lacis at, I find: “Climate feedbacks (including the direct Planck temperature re-adjustment to the direct GHG radiative forcing) are the result of the climate system response to the applied climate forcing.” I read this as a clear statement by Lacis that the “Planck response” as labeled by others is a “feedback” as labelled by Lacis. Anyone disagree with this reading?

      Also I note that Andy refers to Aires and Rossow 2003 and that he refers to some ideas of quantum mechanics.

      • Christopher,
        The reference two quantum mechanics is presented as an analog and seems to refer actually to vacuum fluctuations of quantum field theory rather than ordinary quantum mechanics. I do not think that it is an useful analog in this case.

      • Christopher Game

        Pekka Pirila, Yes, indeed. Christopher Game

  44. Dr. Curry

    We are all spending a lot of time on this thread (climate feedbacks) discussing such topics as whether or not clouds act as a climate forcing in themselves as postulated by Spencer or are simply a feedback to another forcing, such as from GHGs as postulated by IPCC.

    The recent Dessler/Spencer exchange touched on this topic, but it appears that the two talked past each other rather than directly debating the same issue.

    I am looking forward to the thread on the impact of clouds on climate you promised for sometime early in this year. It should be interesting.


  45. Albedo is in charge of the temperature control of the earth.
    Not solar cycles and not orbit cycles and not CO2.
    From whatever source, the more heat you add the harder it snows.
    The less heat you add, the less it snows.

  46. Alexander Harvey

    Roe 2009 makes several references to “memory” when refering to red noise processes and slab ocean type thermal inertia.

    This puzzles me a little. What may be memory to the author is not memory as I know it. The ongoing development of of systems characterised by red noise and slab type thermal masses are completely defined by the current state and perturbation. They are totally oblivious to past events, they contain no information from which it is possible to deduce any aspect of the previous history of the system. For instance it is impossible to know from which direction the current state was attained, all information as to whether the signal (commonly temperature) was increasing or decreasing prior to the immediate present is lost.

    It is this oblivious nature that makes them such popular candidates for simplistic modelling, despite indications that real systems are seldom characterised by red noise processs or slab like thermal masses.

    I would suggest that this choice is urged by the desire to derive time constants (tau values) for the purpose of making some mathematical manipulations to produce a few tidy looking equations, despite the possibility that such time constants lack physical meaning.

    More generally I find the treatment of feedbacks by this author, and many others, to be dissapointingly trivial. In general, simple feedback factors (scalars to subtract from 1 in the denominator) do not occur when working in the time domain although they do occur in the frequency domain.

    Feedback networks are much richer than is indicated in the text. They embody system aspects represented by differential equations and in combinations these may be more or less intractable mathematically but easily reproduced by the network. Many complex causal behaviours can be represented by feedback networks, including oscilatory, and if non-linear elements are included, chaotic (continuous chaotic development not the simple iterative kind). One might be forgiven for being unaware of the ability for feedback networks to embody complex aspects of system behaviour and to perform analogue computation, given the limited exposition given in climate texts.

    One paticular trivialisation that does irk me is the overhelming tendency to describe the network as asasymetric with regard to its elements with some characterised as pure feedbacks and hence a single input and output. I cannot see where this is applicable with repsect to climate. For example, if one takes a proposed Temperature-CO2 network, to regard one component as a control and the other as a feedback is both subjective and to largely miss the point. The point being that if a feedback loop exists the network is best described as dual ported and the possibility that one or other or both are acted upon by external agents and in turn can act on them is explicitedly catered for.

    When expressed as multiported networks a interesing distinction between positive and negative feedback loops is revealed that must otherwise remain hidden. Positive feedback ensures that the relationships are always of the same sign irrespective of which component is driven, negative feedback ensures that the relationship always differs in sign between at least one pair of inputs. This is a telltale behaviour that can be useful.


  47. Alexander Harvey


    Thank you for recalling me to Vonegut. I read him when we both are very much alive. Some fourty and more years passed perhaps. I shun to read his again now. I can recollect little but being much influence by his words hence should not wish to undo all that. I fear the slow creep of infestation by asynchronous metaphor that is so commonly the fate of great writing. More than that the befogment of original inference and the invasive blight of alien richness in books once bereft of author.

    Many thanks, I could perhaps have never thought of him again, and perhaps shall not.


  48. There is a relatively simple method to analyse a signal series to see if it is subject to positive or negative feedback because both have quite different characteristics. Negative feedback ‘subdues’ change while positive feedback ‘amplifies’ change.

    Therefore if some noise deviates the signal from the average equilibrium value, negative feedback tends to steer the signal right back, while positive feedback tends to increase the deviation from the average, so other factors like the forcing functions and random noise will have to restore the balance. This means that a signal under negative feedback statistically shows more than average reversals back to the average (antipersistent), whereas a signal under positive feedback shows less than average reversals back to the equilibrium (persistent).

    Olavi Karner et al have investigated many climate signals this way and found basically antipersistent behavior just about everywhere.