Climate, control theory, feedback: does it make sense?

by Richard Saumarez

You may wonder why a medic is writing a post on control theory in climate.

As Professor Curry asked me to give some biographical detail, I should explain that after medical school, I did a PhD in biomedical engineering, which before BME became an academic heavy industry, was in an electrical engineering department.  My clinical research interest developed around the study of sudden cardiac death – people with genetic heart diseases who drop dead from a fatal rhythm disturbance of the heart.  I soon realised that a purely clinical approach had to be augmented by quantitative understanding how basic cellular and physiological abnormalities in disease create the conditions for a fatal arrhythmia to develop; the problem being that measurements in an animal model may be very difficult to reproduce safely in humans. In clinical cardiac electrophysiology, we routinely stimulate the heart and make recordings from within it (it is surprisingly safe) and signal processing applied to intra-cardiac signals showed there was much more information in them than had been previously recognised. This allowed deductions about the mechanisms that precipitate ventricular fibrillation and prediction of sudden death in some patient groups. The link between basic physiology and man was established through mathematical models of the relevant cardiac electrophysiology so one can investigate the influence of basic pathological effects, reducing intercellular connectivity, changing ionic currents in cardiac cell membranes etc. on the measurements that one can make in man.

The use of engineering techniques in a clinical problem –sudden death – has taught me some of the pitfalls (by falling into them regularly) in interpreting data from one system in another and that carelessness in representing the basic physical nature of the system could lead to major conceptual problems.  In physiology and medicine, the devil is the detail and a mathematical approach that fails to recognise these details may produce absurd results.  Following the debate on climate feedback, I realised that there were similar problems: the physical concepts of climate and a formal approach to control and systems theory didn’t quite mesh.

Remembering AP Herbert’s famous dictum: “If nobody were to open their mouths without knowing exactly what they were talking about, a Deadly Hush would fall upon the World”, I have written a review of signal/control theory that is relevant to dynamic climate feedback. It is in two sections.  This is a verbal, qualitative description of the problem, and my conclusions, of the argument that is developed at a simple mathematical level in the attached PDF [climate_feedback].

Physical assumptions in SB2011

I start with the equation used by Spencer & Braswell and Dessler to describe feedback.  This is a first order differential equation.  When you write a differential equation to describe something, in this case feedback, you have made a definite statement about how you think the systems works physically.  In this case, the equation describes a simple physical system that contains an energy storage element and an energy dissipation element.  Examples of this are: a resistor capacitor network, a spring/damper system reacting to a force or the concentration of injected dye passing through a mixing vessel.  All these systems are described by the same equation and are said to be analogous.

There is no feedback in any of these systems.

I then discuss the process of “Convolution” and “deconvolution”.  We are trying to identify the behaviour of a system, short-term climate feedback, by looking at goes in (net Flux) and what comes out (Temperature).  A system can be defined in a number of ways, one of which is the impulse response (IR).  This is the output of the system when its input is an impulse (an abstraction of an infinite magnitude, infinitely short pulse).  If one knows the IR, because one can calculate it theoretically, it is straightforward to calculate the output from the IR and any input signal.  This is called convolution and represents a laborious process of treating the input signal as a set of impulses, at infinitely small time steps, weighted by the amplitude at that instant, applying the impulse to each one and integrating them. Although convolution is a central analytical concept in systems and control theory, it is rarely calculated in this way because there are better ways of analysing it. The process of working out the shape of the IR from the input and output signals is called deconvolution and is generally more difficult.  Therefore we are faced with a problem of deconvolution.

 A very simple model of cloud feedback

Using this idea, one can construct a very simple model in which radiative flux heats the oceans, water vapour is generated and after some delay become clouds which modify the flux heating the oceans.  This contains a number of simplifying assumptions, and is not intended to be an accurate model of the climate system but an illustration of how to go about using systems theory to model the climate system.

Assumptions:

1)    There is no set point in this system.  Control theory usually assumes some sort of demand and the system makes the output conform to that demand.  This isn’t the case in climate.

2)     The oceans are a perfect heat sink and, for simplicity they are well mixed within a very short time frame.

3)    The cloud formation is described as a linear process; proportional to temperature and the clouds themselves have a linear effect on flux.

4)    The heat required to produce a cloud in negligible compared to the heat in the oceans.  This is a very important assumption from the systems theory point of view because the feedback, should not “load” the output.

One of the key words in these assumptions is linear.  Most things in real life aren’t linear, but a widely used technique is to “linearise” a system.  This assumes that for small change in an input, the output can be written as a series (Taylor’s) and that if the change is small, the output is proportional to the input because the other terms in the series are negligible.  How far you can push this in any particular situation needs to be thought out carefully.

Given these assumptions, the model is consistent with the “thermodynamic” definition of feedback and the convolutions in the forwards and feedback paths can be analysed using a powerful technique called the Laplace transform, which is widely used in systems and control theory.  Using this technique, the equation that describes the IR can be derived and is shown to be a second order differential equation (which from basic theory must be true).

Since any system with feedback must be described by, at least, a second order differential equation, the first order equation used by Spencer & Braswell and by Dessler cannot contain a term related to feedback.

Two quite interesting things come out of thinking about this very simple model. The first is that clouds could have both a positive and a negative feedback and the negative feedback has to be within certain limits to keep the system stable.

The second is that feedback systems may be prone to overshoot.  A poorly damped system in response to a sudden step input will perform a series of exponentially damped sine wave oscillations above and below the level at which it eventually settles.  Spectacular degrees of overshoot are unlikely, but small degrees are possible.  It is important to recognise this effect because overshoot might be misinterpreted as “positive feedback”.

What does delay mean in a system?

Following this, how does one work out what is going on the system?  A very important issue is delay.  Although the static gain of a feedback system (i.e.: the climate sensitivity) is important, the dynamic behaviour of a system such as cloud feedback is determined by the patterns of delays imposed by the forwards and backwards components of the system.  If there were a sine wave disturbance in a feedback system so that it was added to the output, negative feedback will cause a –ve sine wave to be summed at the input.  However a negative sine wave is one that can either be thought of as phase shifted by 180 degrees or being delayed by half its period, so the negative feedback can be interpreted as a delay.  If the delay were increased still further, the –ve sine wave feedback would become positive and the system would become unstable (or blow up). Suppose this system has perfect negative feedback at a particular frequency.  What happens if we double the frequency of the disturbance?  The feedback will be delayed by a whole cycle, rather than half a cycle, and the system is unstable.   In practice, feedback is created by physical systems that store or dissipate energy, an in doing so, create a phase shift, or delay that depends on frequency. and so:

In any realisable feedback system the delays are related to frequency.

The impulse response of a system is related to phase shift because Laplace transform or (when calculable) the Fourier Transform of the IR is the system transfer function. This is a function of frequency, which describes how a signal at a particular frequency is attenuated and how it is shifted in phase.  The Transfer function is an alternative definition of the system and is useful because it may be easier to calculate than the impulse response.  Finally, convolution in the frequency domain is simply multiplication of the transform of the input signal by the transfer function and the output is the inverse transform of the result.  This can be computed very efficiently.

Calculation of the phase spectrum of the impulse response of the model described above shows that it does not remotely approximate a pure time delay.  While a time delay can be calculated for a particular signal, this will depend on the form of the input.  Hence:

Delay imposed by a system is not a useful way to characterise that system since it depends on the input.  The correct measure of delay is the phase spectrum of the transfer function.  A single value of gain is also incorrect. It is the amplitude spectrum of the transfer function

Both Spencer & Braswell, and Dessler use correlations to determine system parameters.  A lagged correlation is simply a correlation between two signals, one of which has been shifted in time and is therefore a function of delay.  This is a well-known signal processing operation, more formally expressed in the cross-correlation function, which is in theory incorporates all possible delays.  An autocorrelation function is a signal correlated with itself, shifted by all possible delays.  If one has an input signal passing through a system to produce an output signal:

The cross-correlation between the input and output signals is the convolution of the input auto-correlation function and the impulse response of the system.  Any analysis technique using correlation to determine a property of the system should reflect this basic relationship.

It is not entirely clear to me what is being measured in the analysis by SB2011 and D2010, D2011 but when these methods are applied to the simple model discussed here, it is immediately clear that the parameters (gain and “feedback”) are a function of input signal bandwidth and so are not parameters at all.

How to measure the system parameters

One has to be very clear in what one is trying to achieve with an analysis of highly variable data and should start with a formal statistical hypothesis.

Hypothesis:  The means of the distributions of the system feedback parameters are zero and the system cannot be distinguished from a system without feedback.

Having raised this hypothesis, one can explore the difficulties in testing it.  A very common problem is that one can have an elegant mathematical model of a process but the data in too restricted to distinguish one’s model from a simpler one, in this case a model with feedback and the null hypothesis, one without feedback. This problem crops up in virtually every branch of science and generally results in an ill conditioned set of equations used to calculate the parameters of the model.

As a simple example, one has data of washout of a radioactive tracer in the body (appearing in breath or urine).  This is of the form e-kt. One might say that actually there are two different processes causing the washout, one fast and one slow, so the decay curve could be 0.5.e-(k+a)t+ 0.5e-(k-a)t, ie.: two exponentials.  These two models can be distinguished with “perfect” data but, with errors in sparsely sampled data, it is notoriously difficult to distinguish between them.

Another major problem is that if the model has an incorrectly modelled component, the real response of this component can “contaminate” the representation of another part of the system.  In the model presented here, the ocean is represented as an integrator, simply because that is how SB2011 and D2011, D2010 choose to represent it.  In practice, I bet it isn’t and it should really be represented as a multi-compartment system with flows and diffusion between different compartments.  However, using real data to perform a deconvolution, the real behaviour of the ocean cannot be represented in the model and it will turn up spuriously in the “feedback”.  This effect has been a huge problem in system identification in biology and medicine.

In climate because there is only one record of temperature, fluxes etc. and so one is dealing with essentially one observation, unlike classical systems analysis where one can “interrogate” a system using multiple input sequences and obtain a robust estimate of the system parameters. This may lead to formidable statistical problems in testing the hypothesis.

In practice, this depends on the length of the record, which determines the fundamental frequency of the discrete Fourier transform of the record and the length of the impulse response.  In the time domain, this means that if the impulse response of the system is much longer than the record, one can’t characterise it.  A further problem is that the Flux signals are band limited and may not fully cover the range of the impulse response.

Alternatively, if the impulse response is relative short, say a month, one will not be able to detect it with a record in monthly samples because it will be aliased[1]. ( For some reason, filtering a signal with a rectangular impulse response and then decimating the signal is commonly used in climate “to reduce noise”.  This is highly undesirable because it may force aliasing on previously correctly sampled signal).

If we are lucky and the impulse response is relatively short compared with the length of the record, the record can be segmented into lengths that contain the impulse response and the parameters estimated from each record, allowing a better statistical estimate of the system response to be obtained.

An alternative approach, which I would use, is a parameter fitting technique.  Although there are many schemes, the simplest is to use the model to create an output as function of the parameters and determine the integral squared error between the predicted and actual outputs.  Minimisation of this integral with respect to the parameters of two competing models may determine whether the “best fit” model is one with or without feedback and allow the hypothesis to be tested.

The thesis I have advanced is that if one is to model a process, great care should be taken to ensure that the model actual conforms to the physical hypothesis, which should be stated explicitly and the assumptions underlying the model should be scrutinised. The data analysis methods should reflect the mathematics of the model and lead directly to estimation of its parameters. The use of multiple stages of analysis can become blind alleys and so one should ask what each processing step means in physical terms.  I am somewhat sceptical that a systems approach of using deconvolution to imply feedback would yield an unambiguous answer, although it may be possible with better models of ocean temperature dynamics and cloud formation, coupled with a careful error analysis.  I am, however, in no doubt that analysis of flux and temperature data, even at the modelling level presented here, is a formidable problem and requires a substantial amount of critical thought.


[1] Aliasing means that the sampling frequency is too low to capture the full frequency content of a signal.  In this case, the signal is irretrievably corrupted and cannot be analysed.  This is an error that has bitten many uncritical researchers in the hindquarters and given a sampled signal, the first question should be “is it aliased?”.

JC note:  I have long been very interesting in getting perspectives from control theory experts on how climate science interprets the issue of feedback.  I find this essay to be be very thought provoking and I look forward to your response. This is a technical thread and comments will be moderated for relevance.

275 responses to “Climate, control theory, feedback: does it make sense?

  1. JC, please feel free to moderate this out.
    I’d just like to say thank you to Dr. Suamarez, for such a beautifully written piece. Clear and comprehensible.

  2. Two quotes:

    (1) I will take the basic equation used by
    Spencer and Braswell [1] and Dessler [2] as a starting point and try to see whether it implies feedback and discuss what constraints exist on determining if a system has, or does not have, feedback.

    (2) The thesis I have advanced is that if one is to model a process, great care should be taken to ensure that the model actual conforms to the physical hypothesis, which should be stated explicitly and the assumptions underlying the model should be scrutinised.

    In between, your mathematics assume that the process is stationary.

    It seems to me that (2) rather contradicts (1), unless you think that the role of clouds, cloud response to temperature increase, cloud response to CO2 increase, differential effects of clouds on lower and upper atmosphere are all understood well enough.

    Since solar input varies by time (annually, daily) and location (latitude effects, effect of the tilt of Earth’s axis), is stationarity a reasonable hypothesis? I don’t think so, but I do think that an explicit statement (your (2)) should be made.

    • Richard Saumarez

      Linear systems analysis asumes stationarity. The question is whether the non-stationarities are linearisable over the frequency range that the control system is operating? In the case of cloud feedback, I don’t know but that is surely the starting point for an analysis. If the data doesn’t fit the analysis and is genuinely non-stationary, the analysis doesn’t describe the system properly.

      • Linear systems analysis asumes stationarity.

        If the data doesn’t fit the analysis and is genuinely non-stationary, the analysis doesn’t describe the system properly.

        Something fundamental is missing here. If you have a non-stationary process, you can’t really do things like Laplace transforms as easily because the integral transform assumes a stationary time series (i.e. it operates from time=0 to time=infinity). That does not mean however that we can’t stay in the time domain and work the problem that way. For example, we can use a convolution to account for some arbitrary behavioral change in mid-stream.

        In the end, we should be able to solve any problem before us, we just have to use the right mathematical formulation.

      • Richard Saumarez

        I don’t think so. If there is major non-stationarities, naive transforms are not applicable. However, if one is studying some thing over a short time scale, one may be able to treat the system as approximately stationary. For eample, if the mean temperature was slowly rising, this would suggest a non-stationary system, but if the parameters of a feedback system operating over the short term were constant, one could probably get away with using a Transform approach.

        Let me make one thing clear. I don’t think that one can reduce the “control” problem to a couple of boxes and I have stated this clearly by saying that the model is an illustration. What I saying is that if one has a model of a particular mathematical form, one has made an assumption about the physics of the system. Taking this further, if one states that there is feedback, one is making another statement about the way the system operates. The model used by SB2011 and D2011 does not allow feedback and any model containing feedback has to be of a different mathematical form. Following on from this, one questions the method of analysis to see how one can measure feedback using a model that, mathematically, doesn’t have feedback. In my view the analysis leaves something to be desired.
        The moral being is that one should stive for clarity in the assumptions and the analysis.

      • I said “In the end, we should be able to solve any problem before us, we just have to use the right mathematical formulation.” with regards to using a convolution instead of a Laplace transform approach if the problem has non-stationary behaviors.

        You said:

        I don’t think so. If there is major non-stationarities, naive transforms are not applicable.

        So I think we basically agree, because naively using a Laplace transform would be wrong in this case.

      • In the end, we should be able to solve any _prediction problem _ problem before us, we just have to use the right mathematical formulation.

        Fixed that for you. You are kidding me, right?
        Leave it to WHT to trumpet the simplistic thinking.

      • Leave it to WHT to trumpet the simplistic thinking.

        Yes, I have a knack for taking complex problems and breaking them down into simple foundational building blocks. Thanks for noticing.

  3. Good read, Thank you

  4. As a licensed electrical, control systems, and chemical engineer, I have to say that to the best of my knowledge, this is the most complete application of control dynamics theory to climate science that I’ve seen anywhere. And it’s obvious that there’s much more to be done.

    Congratulations, Dr. Suamarez. Let’s hope some other people pick this ball up and run with it. And let me note something else in passing: over the past thirty years or so, the fields of digital signal processing and statistics have grown to overlap enormously. A lot of these techniques have counterparts by other names in the field of statistics. So the statisticians have a lot to offer in this as well.

    My intuition tells me that there should be a robust way to do what S&B were trying to do, using a method along the lines of what you outlined, but it’s going to have to be a multidisciplinary effort. In the end, I thing that S&B made the same mistake all the people arguing with them made – they tried to do it all themselves. You can’t do this kind if business that way.

  5. Before CO2 started upwards, was there positive feedbacks making the earth warmer and warmer each year?

    Or was it the Little Ice Age?

  6. Well written, clearly written, professionally presented.
    Thank you, Dr. Suamarez, for taking the time to write this. Thank, you. Dr. Curry for hosting this work. There are many implications in this post, and I look forward to exploring them.
    The cloud conditions you list raise some questions which I hope to be able to ask later, due to a busy work day.

  7. Sorry, not a technical comment as I’m not qualified, but I can’t help contrasting the wry, humble tone of Dr. Suamarez to the nasty arrogance of yesterday’s guest poster. A welcome breath of fresh air.

    • Stirling English

      +1

      The difference is that Dr Saumarez is trying to educate and guide us. The regrettable Lacis was trying to browbeat us into subsmission.

      It is probably not a coincidence that Dr Saumarez does not claim to be a ‘Climate Scientist’ so does not feel the nee to be Right About Everyhing and to Crush The Opposition.

  8. Wonderful essay on control systems concepts.

    This essay strongly suggests a need for much greater interdisciplinary involvement in climate modeling and understanding.

  9. I have followed recent blog discussions of control theory applied to the cloud feedback analyses of Spencer and Dessler, and to climate science generally. And I think, as here, that they miss the point by imposing inappropriate dynamics considerations.

    The climate notion of feedback is very old. Arrhenius was well aware of it. It is set out rather explicitly in this paper by Zhang et al, for example. It defines an equilibrium sensitivity – corresponding to the elec concept of static or dc gain. That doesn’t involve an assertion that there are no dynamics – only that they are analysing what happens on a lomger timescale when the dynamic effcets have settled down.

    The simple arithmetic is illustrated by water vapor feedback. If TOA flux were to increase, then there would be a flux imbalance and the surface would warm. This would continue until the outward radiation increased to balance the TOA increase. Calculations based on this say that an imposed 3 W/m2 flux increase would be balanced by a rise of 1 °C. For present purposes, the exactness of this figure doesn’t matter.

    That is called the no-feedback sensitivity. But the warmer surface leads to higher humidity which hinders outgoing IR. This is interpreted as an effective extra downflux of about 1.5 W/m2. Again, for this argument, there’s no point in debating whether some other figure is right.

    So that subtracts from the IR radiation that is produced by the temp rise, and means that the 1C rise only increased outgoing IR by 1.5 W/m2. It takes a 2C rise to balance the initial TOA increase, after evap etc has settled down.

    If the WV effect had been 3 W/m2 instead of 1.5, then the temp would just go on rising indefinitely without achieving balance. That is the runaway scenario.

    Then there are other feedbacks, which add, and may be positive or negative. I’ve spelt out this traditional climate analysis, known to Arrhenius, to show that no time scale was mentioned. There are no dynamics. In RC’s terms, a zero order differential equation.

    That feedback relation is present in the right side of the first order de discussed here. The λ is not a factor relative to the time derivative – it is the static relation between ΔF and ΔT. The time derivative merely adds a delay, like the dashpot or whatever, which has to be taken into account for system identification.

    • You’re assuming that you have a system that can come to a state of equilibrium. The earth doesn’t work that way. There are oscillations of various types and periods, and you don’t get to know ahead of time what those periods are, and what those lags are. This offers a way to back those parameters out of a dynamic system that will, I repeat, never come to an equilibrium. You have any better ideas?

      • No, the equilibrium feedback notion assumes that the short-time responses will fade, leading to longterm effects that have to balance. If you can identify the oscillations, they can be allowed for. But this control theory analysis does not do that.

        In fact, the big non-equilibrium issue is heating the ocean. The objective of a quasi-steady analysis as is involved in equilibrium sensitivity is to get to a stage where the responses can be represented by constants, and then to balance those. But the ocean goes on gradually heating.

        That’s the real issue with the C_p dT/dt term in SB/Dessler. They are trying to take account of the heat flux into the ocean as if, for the purposes of flux balance, it is steady. It’s not intended to be a dynamic term for which you solve, and which determines the feedback status. That’s where Richard S goes wrong. It’s a flux which is actually time-varying, but they are approximating as steady over the period of analysis (about 10 years). And that is where the argument about the thickness of the ocean layer is important. SB say 25 meters. D doesn’t say exactly, but Spencer says what he does is equivalent to 700m. I’m not convinced of that figure, but anyway, the depth is rlelvant to how good the necessarily rough approx is.

        But all this is a refinement. Whatever the flux is, it isn’t particularly large. It’s a small term that has been ignored in the past, and being roughly approximated here

      • You’re jumbling several things together. Let’s forget about the flux into the oceans, because, as you said, it behaves like a DC signal. Now what are we left with? A lot of signals that if not oscillatory, are at least dynamic.

        We have two choices. We can try to back out parameters from a dynamic system, or we can collect data for a few hundred or thousand years, and not worry about dynamics. Or we can jump into the paleo swamp, and argue over whether that produces numbers that are any better than a pair of dice.

        I say we we check this out. It might be a blind alley, but the other ones aren’t looking super-fantastic right now, and this is the first fresh, new idea to hit climate science since Mann-o-matic. And it might actually pan out, if done right.

      • “or we can collect data for a few hundred or thousand years”

        No, that’s not a choice – unless you suspend the putting of carbon into the atmosphere until the measurements have been taken. The purpose of all this analysis is to determine what will happen if we burn, say, 3000 Gtons of carbon. Not much use finding out the answer after it’s done.

        We have ten years of cloud observations. We’d like more, but at least there is some evidence of the multi-year timescale. Oscillations, like MJO and ENSO, do confound the issue. Dessler was very clear on this:
        “Obviously, the correlation between ΔR_cloud and ΔT_s is weak (r2 = 2%), meaning that factors other than T_s are important in regulating ΔR_cloud. An example is the Madden-Julian Oscillation (7), which has a strong impact on ΔR_cloud but no effect on ΔT_s. This does not mean that ΔTs exerts no control on ΔR_cloud, but rather that the influence is hard to quantify because of the influence of other factors. As a result, it may require several more decades of data to significantly reduce the uncertainty in the inferred relationship.”

        But that doesn’t mean there’s nothing to be learnt.

      • Nick,
        Why are AGW believers stuck on the false precautionary principal you demonstrate in your post?

      • Why do you insist on using the term ‘equilibrium’? You know it is absolutely wrong thermodynamically to describe the Earth:Sun system as an equilibrium, yet you use it. You KNOW the term steady state is appropriate, and yet you use it anyway. Using the term ‘equilibrium’ makes as much sense as using the term multiplication in stead of addition.
        I suspect you use it, knowingly, as it gives you free reign to apply equilibrium thermodynamics to non-equilibrium systems.

      • “Why do you insist on using the term ‘equilibrium’?”

        I’m following convention. Equilibrium climate sensitivity is the standard term. But is you prefer steady state, then fine – it may be more exact. Quasi-steady might be even better. The point is that you have a time scale at which some effects can be regarded as short-term and have settled, and some are very long term and can be regarded as constant, or perhaps with some approx based on very slow variation.

        In Richard’s Laplace domain, we’re talking about very near s=0.

      • Jinx. I wrote that a couple of comments down, and then saw this comment. Of course, we’re both right.

      • How are you so certain that there’s nothing between “short’ and “long”?

      • There is no such certainty. As I said, ten years is an unfortunately short period of measurement. What you’d like to think of as transient hasn’t settled properly, and it isn’t long enough to fully characterize long-term effects. But it’s what we have.

        Actually, the ten years is a limitation for the cloud observations – for temp, say, there is much more. And I think that is why D and SB here take account of the ocean uptake. They allow a thin well-mixed layer, instead of just assuming that the flux has gone to zero. Not ideal, but possibly an improvement.

      • Nick, a quick and short response to your comments, which hopefully given the other discussion that you linked, you’ll see the issue: If the system is in self-oscillation (as the coupled atmospheric-ocean system seems to be, e.g., the ENSO or the large-scale ocean circulation), the assumption of static equilibrium is violated.

        It is true the oscillations of a system in dynamic equilibrium can be controlled for, but you don’t do this by invoking the assumption of static equilibrium.

        If you look at the time scales of the oscillations, they are equal to and larger to the time scales assumed by S&B. Were we to have multiple centuries of observations, static equilibrium may have a chance of working. I think this is P.E.s comment to, which it does not appear you followed.

      • I’m not making an “assumption of static equilibrium”. I tried to make that distinction (responding to P.E.) here. There’s an equation of heat flux balance, and it’s just a question of whether, on a certain timescale, terms are small, and if not, are slowly varying eneough that they can be sensibly equated (to an approximation).

        And yes, oscillations interfere. I tried to make that clear with the Dessler quote here. It actually doesn’t matter whether it’s a self-sustained oscillation, just that it affects either F or T.

      • Both S&B and Dessler effectively are making the assumption of static equilibrium, and you used it yourself in dismissing the “dynamic” aspects of the system pointed out by Richard.

        The relative time scales are important for allowing their assumptions to be valid (observation time >> period of oscillation), that is clearly violated here. As to your comment:

        It actually doesn’t matter whether it’s a self-sustained oscillation, just that it affects either F or T.

        I think this shows some confusion or lack of understanding on your part.

        It certainly can matter. I gave an example here. You might argue whether it does matter, but showing that it doesn’t matter is not a proof left to the reader:

        It needs to be included in the argument for justifying the method.

      • Richard Saumarez

        I do not agree. If you write an ODE as a function of time, you are making a statement about the behaviour of the system in question. S&B try to analyse the dynamics of the system and assume that there is lag. They then measure feedback, which using their basic equation doesn’t exist – at least not in the sense understood by the majority of the civilised world.

      • Richard,
        You are wrong about what the rest of the world thinks is feedback. And in particular this statement, which you highlighted, is untrue:

        “Since any system with feedback must be described by, at least, a second order differential equation, the first order equation used by Spencer & Braswell and by Dessler cannot contain a term related to feedback.”

        See these standard Elec notes from Stanford. They define conventional static feedback. Nothing varies in time. There is no differential equation (zero order). This is what climate scientists are talking about.

        SB choose to relate one of the fluxes to a time derivative. This does not change anything.

      • Richard Saumarez

        @Nick Stokes – Don’t seem to be able to reply directly.

        There is no such thing as a static control system because any physical system will have delays in the forward and feedback loops. It is abstraction that gives you steady state gain, i.e.: it is a limit as s or jw tends to zero. Since, in practice, we cannot observe the system from +- infinity, we cannot in theory determine the static gain. Of course in real control systems we can because they respond quickly.

        If SB2011 attempt to measure a delay in the response to changes in flux, they are stating that the system responds dynamically. If they are claiming that this is due to feedback, there must be phase lag in the system. Their basic equation does not allow for this.

        I have have no idea whether there is feedback of the type claimed by SB2011. I am quite sure that one cannot represent feedback in climate as simplistically as I have, which is purely an illustration. What I am saying is that if you want to introduce well known systems/control/engineering concepts into an analysis, it is probably better to analyse them in way that reflects these concepts.

        Most of the control points you have raised, rather aggressively in my view, seem to stem from not following the mathematics I have presented.

      • “There is no such thing as a static control system because any physical system will have delays in the forward and feedback loops.”
        There certainly static control systems that work as such in practice. In fact they are very common. Your mouse/screen pointer is one. The notes that I linked to show a number of DC feedback circuits. The fact that you can’t get perfect knowledge of them in a finite time, or that some lag is unavoidable, could be said of any system. It’s irrelevant to the use of such an abstraction as a model for climate systems.

        I have followed your mathematics well; I am very familiar with the theory. You have not done the same with what climate scientists are doing, and your mathematics is quite irrelevant to that. If I sound aggressive, it is because you have based a rather large amount of disparagement of climate science (“rest of civilized world” etc) on that wilful ignorance.

        The review by Gerald Roe, which Dan Hughes linked, gives a very good introduction to the static feedback concepts used by earth scientists.

      • Richard Saumarez

        Static feedback as defined in climate is a control system in which s=0. As I pointed out in the text, this is the climate sensitivity and I have no problem with the idea of DC gain. The systems you refer to are in fact dynamic. When you refer to the mouse, I presume that you are talking about a loop of hand, mouse, screen, eye, brain, hand. Do you really believe that this is a static system?

        How does one climate go from one static state to another?

        You seem to be missing the point, which is really very simple. Spencer and Braswell talk about feedback as a dynamic issue. The postulate that there is feedback, but their maths doesn’t show that. They talk about delay and attempt to measure it, In otherwords they have a physical concept of a system with delays. This implies a “control” model. If one is going to talk about control, it should be analysed correctly.

      • With the mouse, I mean the electronics that senses the movement of the mouse and adjusts the pointer accordingly. It is intended to be instantaneous – a dc feedback with no delays. Of course,if you move the mouse rapidly across the screen, the lag is noticeable. But for normal use, it works as a DC circuit. But your hand is moving.

        This is a quasi-steady state. It is not constant, but the responses of the system are so much faster than the rate at which the supplied signals vary that delay can be ignored. That is the situation with climate. It is what S&B are talking about.

        The real electronic DC amplifiers shown and analysed in the Stanford notes are of this kind. Of course the inputs are not invariant. They simply amplify the signals submitted to them with negligible delay.

        The point when it comes to analysis is that there is nothing that you can put into your Laplace transforms or convolutions. There is no relevant timescale. As you say, it comes down to s=0, and a 0 dim range is just not a useful transform.

      • Richard Saumarez

        I am beginning to think that we are at completely cross purposes. (The mouse isn’t a control system – it is open loop)

        As regards delay, phase and construction of control systems, I should refer you to
        Modern Control Systems – Dorf
        Mathematical Control theory – Sontag
        Modern Control Theory – Bubnicki

        If you are saying that the climate goes from one static point to another and the dynamics of the “feedback” is instantaneous, you are correct. If you believe that SB2011 is describing a static system with feedback, the flux and temperature should follow each other precisely with a static gain. As I understand it Spencer’s thesis is that they are not precisely aligned temporally and that therefore there are delays in the system.

        If, on the other hand you postulate that there are delays in the system, the time it takes for clouds to form, the time it takes for ice to form, the time it takes for currents to transfer heat, etc you have to consider these effects. You may argue that they are negligible in the overall dynamics of the climate, but I am not certain that this has been demonstrated. The GCMs are written with time as one variable, from which one presumes that there are delays. It might be interesting to try to deduce which variables can in fact feedback, although this would be formidable problem.

        I have simply pointed out that if there are delays, which seems entirely possible, and some elements act as a feedback, then this takes us logically throgh certain steps that involves simple system/control theory, given a large number of simplifying assumptions. I have presented a very simple and unrealsitic model to demonstrate some of the concepts that could be used in going from a purely static perspective to a dynamic perspective and I have tried to state that you can’t push the analogy too far. This argument however has very important implications as regards how one analyses data. Whether this modifies transitions between different steady states, I’ve no idea.

        At the start of my piece, I discuss the problem briefly of using one system as analagous to another, because I’ve run into huge difficulties trying to apply engineering ideas to a medical problem and have many mistakes along the way. I would simply ask you if you really believe that the climate can be be treated as a set of steady states or is it possible that you are falling into the same trap?

      • The mouse is certainly a feedback control system. It is a servo system. Nothing else could reliably convert movement over a pad into proportional movements on a screen.

        But probably the example I should have given of an ubiquitous DC feedback system is the normal circuitry of an operational amplifier. The analysis given corresponds to the feedback analysis of climate science.

        The feedbacks of clouds etc are not instantaneous. Ignoring delays is an approximation. But it is what climate scientists do, and part of the reason is that they do not have the information to resolve whatever delays may exist. They use the best model that our present measurement capabilities can support. They do not have the luxury of signals that travel down a wire and can be sampled at microsecond intervals. They have a heterogeneous 3D system where their best instrument is a satellite that transits on a scale of hours.

        So it comes back to my basic objection to your analysis – you talk of transforms and convolutions of time varying functions that are simply not part of their model. In terms of analysing the feedback process, there are no functions of time to transform.

      • Feedback is frequency dependent. In an oversimplified model, it appears that there are no functions of time to transform

      • Static feedback is not frequency dependent. And it is certainly feedback, as I have tried to show with many examples, of which the op-amp is the most mainstream. It is the most reasonable feedback model for climate science to use, given the information available.

        Again, I would commend the review article by Gerald Roe of feedback as used in earth sciences.

      • Richard Saumarez

        We are simply going round in circles.

        Try running a “DC” amplifier at 100 MHz and see what happens. If you were to do this, you might be surprised.

        I think that we just have to agree to disagree on this point.

      • DC, frequency-independent response is the concept that people use to understand the operation of op-amps. It works very well in the (very wide) ranges where they are used.

        Yes, at 100 MHz it doesn’t work any longer. The response is frequency dependent. That is where an analysis of your kind would have something to work with.

        But almost no-one does it for an op-amp, except the manufacturer. It would not help with the successful use of DC response as an explanatory concept for the device. The DC concept for an op-amp is used within its intended range. The usefulness of that is not impaired by a lack of frequency response information outside that range.

      • Richard Saumarez

        Ok.
        I will reply to this.
        I have made amplifiers! In my PhD I made video amplifiers. They didn’t work until I was rescued by a practical engineer. This was in the days when you couldn’t buy a video amplifier chip,

        I have extensive experience in making bio-electric amplifiers. You may regard this as a trivial exercise in control theory, but they are not! They have to work under a large range of conditions. They have to work under the conditions of a high and variable source impedance, with poor connections, fluorescent lights, an x-ray set close by and withstand a 5KV discharge, while maintaining a low source impedance to allow reliable stimulation of the heart.

        I have been told by theoreticians: “ that if that is what the equations sat, that is what is happening”. Having followed your comments, I am convinced that you understand very little about the role of amplifiers in the real world.

        I would have to say that your comments are typical of modellers. You grab an equation without understanding what it means, and you attempt to browbeat people who have worked with these equations in a practical situation., thereby highlighting the difference between those of us who have learnt our trade in the real physical world as opposed to a mathematical bubble.

        If you doubt what I am I saying, I suggest that you attempt building some practical amplifiers. I would suggest that you start with a “DC” amplifier circuit driving a low impedance, but reactive load. Consider what happens at different frequencies. After hubris comes nemesis, and I suggest you contemplate on the disconnect between mathematical modellers and those who have done experiments.

      • No, I have also built audio amplifiers. And lots of oscillators. Electronic music was my thing, in the days just before op amps were becoming available.

        However, none of this answers the basic issue with your analysis. Climate scientists use a widely and well understood concept of DC or static feedback. There is no place in it for your time-varying analysis. It’s true that frequency-based analysis could be used to analyse deviations from that model, if the data could be obtained. But it can’t. That doesn’t mean static feedback is a useless concept.

      • Dear P.E.:
        Unlike conventional thermodynamic systems, surface temperature is not a measurement of sensible heat transfer between earth and sun. The later is constant and the earth is thermodynamically stable and in equilibrium. Surface temperature oscillations are not indications of earth system’s instability. Surface water temperature rises a result of heat transfer from the upper atmosphere to surface. Please research the simultaneous cooling of the upper atmosphere with surface warming. The cooling of the upper atmosphere is equal to surface warming, and the net change in sensible heat exchanged with the earth as a whole is zero. The earth as a whole is thermodynamically in equilibrium.

      • It may be in approximate steady state. That’s a different argument. It’s not in equilibrium. Pretty much nothing in the real world is at equilibrium. Equilibrium is more of a concept than a reality.

      • In process, steady state is a state where variables are constant with time. But for the earth, surface temperature is never steady. It is constantly changing and will continue to be so. However, what counts is the sensible heat exchanged between sun and earth, and this heat is constant with time, which I call it equilibrium. It can change slightly during events like ENSO, but in the long run its average is constant. I would say, using the term steady-state is better than equilibrium say for a decade or two. For one thousand years, equilibrium, I believe is a better term.

      • But it remains unproven that there aren’t other process going out into the thousands of years. We can’t assume anything. It’s dynamics all the way down.

      • But one thing that did not happen in the last several billions of years is that surface temperature never went a stray. The geological record and continuity of life are a proof. This may give a hint of earth’s thermodynamic stability.

      • I never suggested that things can run away. Dynamics simply means that things are bouncing around like a car with bad shocks on a bumpy road. That’s all. If you want to know where the road is, you can drive a long distance and then average the position of the body of the car, and hope you weren’t on a hill all the time, or you can try to understand the bumps in the road and the resonant frequencie(s) of the suspension, and get the same information from a shorter distance.

        One thing you can’t do is stop the car.

      • P.E., A picture is worth a thousand words…

        reality can bite, real quick. This was over a few days time.

      • Leonard Weinstein

        Dear Nabil,
        You are wrong on your basic issues. Surface water temperature is by far mainly due to direct absorption of solar energy, and transfer to depth (storage) or to the atmosphere. Atmospheric temperatures are mainly heated by transfer of this heat by evaporation/condensation, and convection of surface conducted heat up. There is a small air to water heat transfer when air is warmer than water, but this is unimportant to the average. Back radiation is also of no consequence on the average. The cooling of the upper atmosphere is only related to the warming at the surface during non-equilibrium condition, and to the atmospheric window effect, both of which may be present (so you can’t distinguish them on short time scales).

      • Dear Leonard,
        Of course you are right. The absolute value of surface water temperature is due to solar radiations absorbed. Please note that we are talking about changed in this surface water temperature, and these changes are due to sensible heat transfer between upper atmosphere and surface. No changes in the total sensible heat exchanged between sun and earth, which is what counts for equilibrium considerations. The Earth is thermodynamically stable at all times, and has no feed backs of any sort.

      • Nabil;
        I think much or most of the feedback S&B were referencing was on the order of minutes, or hours at most. The implicit point, for me, was that this kind of virtually instantaneous radiative response to warming is a very plausible reason for abandoning the search for ‘missing heat’. It left on the first train off-planet, and isn’t coming home.

    • You’re forgetting the negative feedbacks – convection and latent heat of evaporation.

      • No, I said:
        “Then there are other feedbacks, which add, and may be positive or negative. “
        However, you’d have to establish that the ones you mention are feedbacks.

      • Sorry, didn’t read your last two paragraphs.

        Anyway, if the surface warms, both evaporation and convection must increase. Not only does this remove energy from the surface, but also aids in transporting the energy towards the upper atmosphere – in effect cooling the surface as well as making it unnecessary for the surface to warm as much to restore radiative balance at TOA.

        This makes (latent heat of) evaporation and convection negative feedbacks in my book.

    • There is no evidence CO2 has warmed the planet in the past or present. Co2 is a follower of temperature.

      During the 20th century, bright sunshine has increased. As well, Albedo darkened considerably in the 1990s. CO2 is irrelevant.

      http://www.arm.ac.uk/slides/epb/

  10. From what I understand of what he is saying here, the only response I have is:

    Didn’t the climate modelers think all this through right from the beginning? If they did, wouldn’t they have listed all of their intent, their bases for their models, in black and white? As I understand it, every non-academic program written has to be reviewed in the first draft stage and every stage thereafter, in order that they not spin their wheels and waste a lot of everybody’s time.

    Had this been done 20 years ago (and more), it seems they would have determined that:

    1.) They did not know enough about several varying factors to model them
    2.) They did not then know enough about some of the values to model them
    3.) They needed to begin some basic evidence gathering in order to fill in the gaps.

    When, for example, the Pacific Decadal Oscillation was discovered, there should have been a huge redness on the modeling community’s face, knowing that they had built a tower of cards without a major factor being even know about, and thus any prior outputs had to be total crap and self-delusional.

    The modeling community should have been their own toughest critics, but somehow their inability to correctly model recent past climate was ignored, and so was their inability to get even short-term results correct – how were they able to look at themselves in the mirror every morning? Didn’t they know they were scamming themselves as well as the policy makers and the world?

    All of that could have been avoided if they had begun properly. In engineering we have long had a maxim: “Well begun is half done.” It all begins with making sure of the formulas. It is not so much as garbage in garbage out, as much as it is garbage formulas that can take good input data and do nothing useful with it.

    • “Didn’t the climate modelers think all this through right from the beginning? If they did, wouldn’t they have listed all of their intent, their bases for their models, in black and white?”

      Yes, of course they did. The notion of climate equilibrium feedback is old and sound, and what is said in this post is of no relevance to it. And modellers do list their intent in black and white. Here is just one example. You might like to say in more detail what you find in it that is unsatisfactory.

      You won’t find anything there about feedback. The reason is that, as opposed to equilibrium feedback arguments, they are indeed solving the nonlinear dynamics of fluid flow with radiative transfer. There is feedback in the system, but it is a consequence of the fundamental equations.

      • Why is it you cannot state why you do not get a correlation vs [CO2] and the temperature record?
        If
        “As I said, ten years is an unfortunately short period of measurement. What you’d like to think of as transient hasn’t settled properly, and it isn’t long enough to fully characterize long-term effects. But it’s what we have”

        You know only [CO2] is a forcing, you know how well you can measure the ‘equilibrium’ temperature, given the error bars are smaller than Obamas c.v., so why don’t you know the oscillation time of this ‘ transient’?

      • “You know only [CO2] is a forcing”

        I don’t really know what you mean by that. But SB and Dessler are talking about cloud and temp, not [CO2].

      • Lacis, Schmidt, Rind and Ruedy in Science 2010 state there is only constant solar flux, CO2 and other green house gasses that can raise the Earths temperature, FIGURE 1.
        Don’t you keep up with the literature Nick?

        Or is it going to be another one of those ‘conventions’ in climate science where by ‘feedback’ and ‘forcing’ can mean different things at different times?

        “Dessler are talking about cloud and temp, not [CO2]”

        Yet the while the ‘equilibrium constant’ depends on the ‘amplification’ effect that water vapor has, modulated by CO2.
        You do remember that bit don’t you Nick?
        CO2 goes up, more water vapor, and so more ‘green house gas’.
        This is how the ‘equilibrium’ constant is calculated.
        This is a positive ‘feedback’, but can’t be called a ‘feedback’, so is also part of the ‘forcing’, but not really a ‘forcing’. Atmospheric water isn’t a ‘forcing’, it only becomes a ‘forcing’ if it magically gets there via [CO2].
        Simple really.

        ‘But “equilibrium” doesn’t mean “a non-equilibrium pseudo-steady state”,’ Alice objected.

        ‘When I use a word,’ Humpty Dumpty said, in rather a scornful tone, ‘it means just what I choose it to mean — neither more nor less.’

        ‘The question is,’ said Alice, ‘whether you can make words mean so many different things.’

        ‘The question is,’ said Humpty Dumpty, ‘which is to be master — that’s all.’

      • Well, Fig 1 has a fairly large orange box called “Other”. But we’re actually talking here about that big green box (maybe bigger than CO2) labelled clouds.

        But you’re getting way off topic.

      • “Lacis, Schmidt, Rind and Ruedy in Science 2010 state there is only constant solar flux, CO2 and other green house gasses that can raise the Earths temperature”

        Lacis et al were addressing the components that make up the greenhouse effect, not the components that make up Earth’s temperature as a whole. You don’t understand the paper, your criticisms of it are worthless.

        You cite figure 1. Yet figure 1 doesn’t even mention solar flux. What to make of that? Did you just include it to make your complaint sound more credible?

      • “”“(Me) You know only [CO2] is a forcing”

        (NS) I don’t really know what you mean by that.””

        Let me lay it out very simply:-

        Lacis et al explicitly state:-

        “Noncondensing greenhouse gases, which account for 25% of the total terrestrial greenhouse effect, thus serve to provide the stable
        temperature structure that sustains the current levels of atmospheric water vapor and clouds via feedback processes that account for the remaining 75% of the greenhouse effect.”

        In Figure 1 they show that ‘noncondensing greenhouse gases’ are the horses and that water vapour and clouds are the carts. The ‘noncondensing greenhouse gas’ are forcings (an energy flux) and water vapour and clouds are manifestations of this forcings, and so are thus ‘feedbacks’

        They then remove all the CO2 from the atmosphere, which causes the water content of the atmosphere to crash and the Earth to arrive at a steady state temperature of minus 22, Figure 2.

        Thus, is as of itself water vapor is not a greenhouse gas. Water vapor can only act a a GHG when lofted by a ‘forcing’. As solar flux is invariant, this ‘forcing’ cannot be solar and so must be CO2 or another ‘noncondensing greenhouse gas’.

        The only forcings are solar flux (invariant) and ‘noncondensing greenhouse gases’, explicitly CO2. Water is a ‘feedback’, not a forcing, and does not in anyway, shape or form, independently affect temperature. All the effects that water has are a direct result of ‘noncondensing greenhouse gases’.

        The use of ‘forcings’ and ‘feedbacks’ could be used to describe a mercury barometer. The two ‘forcings’ are ‘invarient’ atmospheric pressure and vacuum hardness, whilst the ‘feedback’ is Hg column height.

  11. Dr. Suamarez your post is going to make me go back to my library (which seems to happen to me a lot here at Climate, Etc.) to get a bit of a refresher on Systems Thinking. Thank you for your post! If you can recommend anything newer then my Systems Thinking Systems Practice by Checkland (1981) I would appreciate a newer reference.

    • Richard Saumarez

      Thanks.
      Actuqally I used an referred to all my ols texts, you will see that the references are all for books published ages ago. Signals and systems by Oppenheim is a good start.

  12. In climate because there is only one record of temperature, fluxes etc. and so one is dealing with essentially one observation, unlike classical systems analysis where one can “interrogate” a system using multiple input sequences and obtain a robust estimate of the system parameters. This may lead to formidable statistical problems in testing the hypothesis.

    Sadly, close enough to true (especially before satellites) to reflect extremely poorly on the lacadaisical approach to data collection globally.

    Happily, gives much better information on one type of uncertainty faced, which is of a very limited sort. Infinite, but still limited.

    The data analysis methods should reflect the mathematics of the model
    and lead directly to estimation of its parameters. The use of multiple stages of analysis can become blind alleys and so one should ask what each processing step means in physical terms. I am slightly sceptical that a systems approach of using deconvolution to imply feedback would give an unambiguous answer, although it may be possible given some more accurate models of ocean temperature dynamics and cloud formation, coupled with a careful error analysis. I am, however, in no doubt that analysis of flux and temperature data, even at the level presented here, is a formidable problem and requires a substantial body of highly critical thought.

    Nicely said. Gallops along at quite a pace in the reasoning, has some gaps, but very worth considering, especially where results are not separately confirmed by alternate analyses.

    • To clarify..

      Only one planet available with an Earthlike climate, ergo not possible to do multiple test runs of the actual system and we’re left with simulation methods based on only one data record; however, the data we could have had also has not been well-treated. Where you can’t test multiple climates, you can at least record and analyze multiple flavors of information, and with more granularity.

  13. S.G. wrote: “When, for example, the Pacific Decadal Oscillation was discovered, there should have been a huge redness on the modeling community’s face, knowing that they had built a tower of cards without a major factor being even know about, and thus any prior outputs had to be total crap and self-delusional.”

    Imagine how they felt when they remembered the sun. Oops. Talk about red faces. Hah!

  14. I must admit I cannot contribute to the technical discussion here apart from expressing interest in the fact that real climate science has become increasingly dependent on numerous, well established scientific/engineering disciplines which have much to offer. I suspect that the complexities in climate have been grossly underestimated hitherto and render IPCC’s “………very likley……..” very questionable.

  15. The point about aliasing is spot on. I think much insight can be gained by looking at data in the Fourier domain. Alasing is concerned with the question “Is the data sampled often enough (temporally and/or spatially) so that system responses are caught in the signal? For cloud feedbacks, you must be in the domain of hours, not days or months.

    Aliasing deals with the maximum frequency of the spectrum. What is just as important, perhaps more so, is the lowest frequency that exists in the data, which is solely based upon length of the time-series data. The lowest Frequency is key to the question of what is the warming per decade, warming per century. In a WUWT comment (link below) I wrote up my concerns about analyzing temperature records in short intervals and stitching them back together. From a Fourier Analysis, point of view, the low frequency component is thrown in the bit bucket and replaced by manufactured low frequency which can only come from the suture mechanism –hypothesis replacing real data.

    http://wattsupwiththat.com/2011/03/31/expect-the-best-plan-for-the-worst/#comment-634734

    Stephen Rasey says:
    April 2, 2011 at 11:58 am
    Re the Scalpel and Low-Cut Filter.

  16. A very nice presentation, I however think that this sentence is not completely true;

    “In climate because there is only one record of temperature, fluxes etc. and so one is dealing with essentially one observation, unlike classical systems analysis where one can “interrogate” a system using multiple input sequences and obtain a robust estimate of the system parameters. ”

    Now we are rather lucky in that there is a 6.9% difference in the solar light flux between Jan 3rd and July 4th. We also have the equinox’s where the light flux is matched, but flux falling on the two hemispheres is different.

    Looking at 15 days either side of aphelion/perihelion and when we have equal solar flux, along the equinox line.
    We have four planets; a pair where one with 6.9% more influx and a pair where one hemisphere has more light flux than the other.

  17. He says we can’t have feedback in a first-order system of equations, which makes me think his terminology is different. If the temperature change is written as
    dT = F + f*dT
    where F is the forcing and f is a feedback factor, we have a first-order system with a feedback in the sense used in climate.

    • Yes, I think that’s exactly right. D and SB are doing a static feedback analysis. It’s quasi-static, because one of their terms is the flux that goes into and heats the ocean. This is represented as C_p dT/dt.

      The control theory people have seized on the time derivative to treat it as if they were solving an ode over time. They aren’t. They are simply trying to identify and balance the flux terms.

      • I am also with you on this viewpoint. The data I am currently analyzing is change in atmospheric CO2 concentration with temperature change, which is in addition to the significant fossil fuel fraction.

        So the premise is that we know that the major change in [CO2] is due to fossil fuel emissions, yet there also is a fractional change due to the global temperature anomaly. This is basically explained by outgassing of the oceans as they get warmer. In other words, for a change in temperature due to the convolution with the initial fossil fuel impulse, then the increased temperature will draw out more CO2 from the ocean. If this isn’t a positive feedback scenario, I don’t know what is.

        In any case, this is actually a pretty good test case for applying these techniques to. We have a fluctuating pulse train of monthly global temperature variations along with a sequence of CO2 measurements from Mauna Loa since 1960. The cross-correlation of T with d[CO2]/dt shows a 1 PPM/month differential change for every degree change. We can use this to construct a lagged response of CO2 to temperature changes which might look like:
        [CO2] = k*T *(1-exp(-t/t0))
        which is a first-order approximation to the total outgassing that would occur over a period of time. The initial outgassing is largest and then it slows down as the ocean temperature tries to equilibriate with the air temperature.

        I am phrasing this like an analysis yet to be done, but in fact I tried to do it a few days ago.

        http://theoilconundrum.blogspot.com/2011/10/temperature-induced-co2-release-adds-to.html

        This will in fact only turn into a positive feedback situation if the CO2 is actively forcing the temperature anomaly to increase. If not the case, then we have a way of figuring out what the contribution of fossil fuel emissions to the CO2 increase is, with the rest due to Henry’s law.

        This analysis ought to be done and I think there might be enough data to do it. As was just mentioned, how about this site:http://www.pmel.noaa.gov/tao/data_deliv/deliv.html? Air temperature, surface temperature, subsurface temperature is all there and we may be able to do a cross-correlation on these numbers to get a thermal response out of it to complement the CO2 / Temperature cross-correlation.

        So let’s get to work and try out some of Richard Suamarez’s ideas.
        I had just made a comment earlier today that no one on this blog likes to talk about convolutions and impulse responses (not to mention cross-correlations). And here we have somebody that is talking about it and he is getting praise for discussing it.
        The question is : will this enthusiasm continue when it gets down to lifting a finger and actually doing the convolutions and cross-correlations? Or is everyone besides Nick and Mosher just all talk and no bite here?

        I know, I know, honey and bees, and all that, but come on, isn’t anyone interested in getting their hands dirty?

      • Richard Saumarez

        The reason I haven’t done the computations is, beause as I clearly state, this is a very difficult problem and requires a lot of thought and statistical modelling to get a reliable answer. Fools rush in …….

      • The reason I haven’t done the computations is, beause as I clearly state, this is a very difficult problem and requires a lot of thought and statistical modelling to get a reliable answer. Fools rush in …….

        Well, start from a more foundational basis then. Like I suggested, let’s look at modeling the CO2 alone. This clearly has elements of the control problem, as I have already done the following steps:
        (1) Use a convolution approach to generate the CO2 atmospheric concentration from the fossil fuel emissions forcing function.
        (2) The impulse response function also comes from control theory.
        (3) Do cross-correlation on the data (CO2 with T) to establish the lag relationship
        (4) Use a simple form of system identification (PD autoregression) to try to find the positive feedback of CO2 increase from the data
        (5) Add (3) to (1) to incorporate the feedback element to the main convolution

        This is not “fools rush in” but actually working out a real problem.

        Perhaps its is pPredictable that no one wants to get their toes wet on this one, as the commenters here are pretty much all talk and no action.

        I did this kind of analysis to work out a comprehensive oil depletion analysis the past few years and got just enough input from interested parties to overcome the occasional misstep that I would run into. So far, it’s all here:
        http://theoilconundrum.blogspot.com/2011/10/temperature-induced-co2-release-adds-to.html and click through to follow the arguments.

      • Leonard Weinstein

        Web,
        While it may appear that the CO2 from the oceans should increase due to higher temperatures, it also would enter the ocean due to higher atmospheric concentration from burning fossil fuel. Since the claim is made that the pH is decreasing, it might be that CO2 entering the oceans might be the dominate factor. I don’t think it matters much either way, but a simple assumption may be wrong.

      • Web,
        While it may appear that the CO2 from the oceans should increase due to higher temperatures, it also would enter the ocean due to higher atmospheric concentration from burning fossil fuel. Since the claim is made that the pH is decreasing, it might be that CO2 entering the oceans might be the dominate factor. I don’t think it matters much either way, but a simple assumption may be wrong.

        It’s going the wrong way. If pH decreases, it is getting more acidic, and that means the net for CO2 is decreasing. Of course some is going into the oceans and that is the basis of the long-tail diffusional model.

      • In general, that simply does not work. It is like trying to approximate a quadratic function with a linear one over a range in which the quadratic curvature is very pronounced. It will not give you any insight into the quadratic function. It will not allow you to make reasonable predictions of the function into the future or to back-propagate it into the past.

        As Einstein said, a system should be made as simple as possible, but not simpler.

    • For most of the past millennium the climate has been subject to slow forcing changes mostly from the sun that are detectable in the Little Ice Age, so it has been close to equilibrium. However, now with the forcing changing quickly we are in a transient climate until some time after CO2 stops changing. Equilibrium sensitivity is still a useful and more tractable concept as it does not depend on time scales and lags which complicate the solution procedure and make transient sensitivity depend on a lot of internal processes like ocean mixing and the carbon cycle.

  18. Two quite interesting things come out of thinking about this very simple model. The first is that clouds could have both a positive and a negative feedback and the negative feedback has to be within certain limits to keep the system stable.

    I can see that we have some nomenclature issues. That’s an unconventional sign for the feedback. Most of the world uses positive and negative feedback in such a way as to make all positive feedback unstable beyond a certain gain.

    • Richard Saumarez

      Actually it it isn’t unconventional. Climate science has redefined negative feedback, as it is widely understood, as positive feedback and vice versa. While one can call it anything one like, if you reverse the sign in a mathematical description of control, you will end up with some rather challenging results.

      • I don’t believe that is true. Could you substantiate it?

      • Richard Saumarez

        I ma not sure what you want me to substantiate. If you are taking issue with positive and negative feedback existing in the same system. In the mathematical section I have rather careful to define this:

        1) A system with positive feedback is unbounded. Therefore if the clouds increase temperature, we have positive feedback.
        2) If there is an unbounded element in a system, the system can be stabilised by negative feedback.
        3) I have avoided using poles in s plane because most people, myself included, find them mystifying when they first encounter the concept.
        4)However all one is doing in control terms, is shifting a pole from the right hand side of the jw axis to the left hand side. In its simplest form it called proportional control.

        As regards the nomenclature of feedback, both Tremberth and Santer refer to feedback in way that I would not immediately recognise. However, my main point is that one should be explicit in definitions \nd you will find in the mathematical section I have been explicit, and I hope consistent.

      • There’s no difference in the sign convention used in climate science and elsewhere. Both consider positive that feedback, which strengthens the change, and negative that, which act to reduce the change. That applies to cloud feedback as it does to every other component of the feedback.

        One special concerns concerns the role of the Planck feedback, which is included in some considerations and excluded in others. It’s natural to include it, when the feedback is considered at in terms of net flux at TOA, and exclude it, when temperature changes are considered.

      • Richard Saumarez

        I wouldn’t call Planck, or Stefan-Boltzmann, a feedback. It is a property of the system.

        Without hair splitting, many of us would regard feedback as a loop that is determined bt the output and is summed with an input.

      • What I would like you to substantiate is your claim that “Climate science has redefined negative feedback, as it is widely understood, as positive feedback and vice versa.” You offer no evidence and I believe it is false.

      • Richard Saumarez

        Okay I admit, that I may have made a mistake here. Reading some of the literature I got this impression, and if I’m wrong, I’ve made a mistake. It shows a lack of diligence on my part and a misunderstanding.

        However, I would like to expand, if I may, on your comments about feedback being described as functions not involving time, having thought about it over supper.

        We often think of feedback in terms of electronics. I agree that if you take a modern amplifier, at low frequencies, its will appear to be perfect and you can treat its performance as a time independent system. This is because it notionally has an infinite input impedence and zero output impedence with a very high gain. In reality, this isn’t true. If you take a modern amplifier and pass a square wave through it, in a virtual earth configuration, you will find that what comes out isn’t a square wave and you will see non-ideal behaviour. If you are dealing with high frequencies and you ignore the capacitance of tracks and in the inductance of resistors you will come unstuck.

        However, I am am not sure what the “gain” of the climate system is (and I think it’s a false analogy to compare it electronic systems). However, the effects that you can ignore in an amplifier circuit are certainly not neglible in a system that has very little gain. Amplifier circuits are very useful because one can arrange that simple networks behave ideally.

        The point is that real feedback systems don’t behave ideally and if you are dealing with systems with low amplification, they really do not behave ideally. One assumption, which I have stated explicitly, is that the feedback loop does not load the output. Electronically, one would say that this because the forward system has zero source impedence and and the feedback loop has a high imput impedence. In climate terms, if you want to discuss feedback, it means that the latent heat of evaporation is negligible compared to the total amount of heat in the heat sink (I think).

      • Richard,
        If climate science is using novel definitions of positive and negative feedbacks, does this have impacts on the quality of work they can perform?

      • Nick, you stated it as so yourself.
        Earth Sciences Use, as against what the rest of Science and industry do.
        “Static feedback is not frequency dependent. And it is certainly feedback, as I have tried to show with many examples, of which the op-amp is the most mainstream. It is the most reasonable feedback model for climate science to use, given the information available. ”
        “The review by Gerald Roe, which Dan Hughes linked, gives a very good introduction to the static feedback concepts used by earth scientists.”

      • Nonsense. I simply said that earth scientists use static feedback concepts. I didn’t say they were different from what the rest of Science and industry do.

        If you think they are, then please explain in what way.

    • In discussing “positive” and “negative” feedback in climate science, they are generally talking about internal feedback. The overall system is negative feedback (in particular, it is difficult to overcome the quartic negative feedback of radiation, which increases in local linear slope as the cube of temperature). But, internally, there can be both positive and negative feedbacks. The former tend to amplify and unsettle the response, the latter to attenuate and smooth it.

  19. I have been following some of the Climate Science blogs for a quite while without commenting. However, I am simply appalled by the lack of mathematical and statistical rigor associated with Climate Science. Can’t stand it anymore!!!

    Cross-correlation analysis of non-stationary data using simple OLS regressions makes me want to scream. Climate feedback analyses that lacks a basic understanding of Control Theory makes me want to scream louder. Using ‘calibarated’ parameters when modeling data is the work of a grifter not a scientist.

    From what my very limited understanding of the Climate Science suggests, the climate is a non-stationary process with non-linear feedback.
    These problems are very hard to understand, are very hard to measure, are very hard to model, require a tremendous amount of data (in-sample fit) to properly estimate the parameters, and require even more data (out-of-sample performance) to validate the model. I have never seen a properly conducted out-of-sample analysis.

    I applaud Richard Suamarez for educating people on Control Theory. However, I think his wonderful discussion needs to consider non-stationarity. Many engineers only consider stationary processes because engineers typically face these types of problems. Thank you Richard! Wonderful article!

    My biggest applause goes to Judith Curry for educating people on uncertainty. There is not enough accurate information to understand, model, estimate, and validate. Thank you Judith for being the only ‘real’ scientist on the various Climate Science blogs.

    I think that Ross McKitrick’s ideas of using Vector Autoregression – VAR (possibly Cointegrated Models) is likely the best approach in my opinion. Again, such analyses require a tremendous amount of data. VAR is probably inadequate for the obvious non-linear relationships; but, VAR is a better linear approximation than approaches have been previously posed. There are non-linear forms of VAR; but, unfortunately, these models would require even more data. Back to Judith’s concerns!

    Finally, the various climate models rely heavily on computer simulations. Simulations assume that you have a rich history of accurate data. You can simulate with ever large super computers for years and years; but, the data will not present you with any new information. This foolishness must be a con-game to simply impress the politicians and public. They bought a really big computer. Big deal!

    Given enough clever computer simulations, I can prove that I am smart, handsome, witty, and very debonair. Judith, would you marry me based on the results of my computer simulations?

    We need to hear not only from the Time Series Analysts, Control Theorists, but also the Information Theorists. Climate Science gets failing grades in these areas.

    • Old Navy: From what my very limited understanding of the Climate Science suggests, the climate is a non-stationary process with non-linear feedback.

      I believe that there is a swelling chorus in agreement with you.

      Padilla et al, linked here a few weeks ago, had a non-linear ensemble Kalman filter.

      There is no lack of data. NOAA and other agencies have posted gigabytes of data on the web. It has hardly been examined. Here is one set: http://www.pmel.noaa.gov/tao/data_deliv/deliv.html. Willis Eschenbach at WUWT has a current post on another data set.

    • Now, now, ON, Nick Stokes as already laid out why why Control theory is a waste of time.

      ‘The control theory people have seized on the time derivative to treat it as if they were solving an ode over time. ‘

      • I don’t think it’s a waste of time. It’s what I did my PhD on. But I don’t think a frequency (or Laplace) analysis is relevant to steady-state feedback.

      • Nick, do you believe that that there is a cyclical change in the light flux in a 24 hour and 365.25 day periodicity?
        Do you think that the distribution of the ocean/land in the Norther and Southern hemispheres is homogeneous or heterogeneous?
        Why does the ‘equilibrium’ temperature of the Earth go up and down, over the last 100 years, rather than being a smooth curve?
        If the up and down in the ‘equilibrium’ is noise, where are the ‘heat’ hide and emerge?

      • Yes, there is a daily scale, and an annual scale. And even a time scale where gas atoms collide with a sueface and we call the resulting average of impulses pressure. All this has been known for a long time.

      • Nick, you may have done your Ph.D. on control theory, but it’s may not be the case that you’ve been exposed to systems that are in dynamic equilibrium (or quasi-equilibrium). Just consider the response of this system:

        x”(t) + (-1 + x(t)^2 + x'(t)^2) x'(t) + x(t) = E(t)

        when x = x’ = 0,

        versus when x = sin(t), x'(t) = cos(t). (This is an exact solution by the way to the steady-state when E(t) = 0.)

        The response of self-sustained oscillators to external stimuli has a fairly rich literature, but I don’t know of any examples where assuming x=x’=0 ever worked.

      • Well, if you could demonstrate that such a system actually existed here, could be properly characterized, and that it’s effect was dominant, then indeed it would have to be analysed in those terms. But we’re a very long way from that, and Richard’s approach won’t get us there.

      • Nick:

        Well, if you could demonstrate that such a system actually existed here, could be properly characterized, and that it’s effect was dominant, then indeed it would have to be analysed in those terms

        The fact that you have ocean currents, an ENSO, a PDO etc isn’t evidence that the system is in oscillation? I’m not involved in your argument over whether Richard’s approach would work.

      • Well, I was referring to your specific ode. But let’s just stick to “could be characterized” then. Given what we know, how would you do it?

      • By the way, when you said this,

        Well, if you could demonstrate that such a system actually existed here, could be properly characterized, and that it’s effect was dominant, then indeed it would have to be analysed in those terms.

        You’ve simply described what would be needed to analyze the system properly. It isn’t my or any other reader’s responsibility to demonstrate any of this for S&B and/or Dessler to be in error in their approach.

      • Nick:

        Well, I was referring to your specific ode

        Hopefully you understand I chose that ODE because it is a particularly simple system to examine the characteristics of systems in self-sustained oscillation, and not because I thought it was the exact ODE representing climate.

        As you may know, we an use simple limit-cycle oscillator models to describe aspects of the response of much more complex systems to external stimuli. This is a generally known result (I even have peer-reviewed papers doing exactly that and comparing the results from the limit-cycle equation to measurements from physical systems that are governed by much more complex dynamics).

        Given what we know, how would you do it?

        I wouldn’t try. To me, it doesn’t seem like a very tractable problem without a longer observation period.

      • When you analyze the dynamics of an airplane, you take into account thrust, mass, lift etc. It’s true that there is a subsystem of sloshing in the fuel tanks, which probably obeys an ode something like you describe (And OK, modern planes probably have tanls full of baffles). But that doesn’t mean that an analysis that doesn’t resolve this is useless.

      • Nick:

        When you analyze the dynamics of an airplane, you take into account thrust, mass, lift etc.

        I’d suggest going back and thinking of about it works in that case, and what you need in terms of measurements to make it work. Then applying that mutatis mutandis to this problem.

        But that doesn’t mean that an analysis that doesn’t resolve this is useless

        I would think the fact the system is in approximate dynamical stability rather than static probably does make S&B/Dessler’s analysis useless. That’s my opinion and YMMV.

      • Oscillations are not necessarily self-sustaining. The ones we are concerned with are not. Take away the Sun, and it will all damp out to a given level of insignificance over a finite time interval.

        What we are dealing with is a distributed parameter system with oscillatory modes which are excited by the inputs. The general method of solution for such a system is a finite element or similar method, whereby the oscillatory mode shapes which exist at particular frequencies are determined, and their amplitude functions are the outputs of second order linear systems. These amplitude functions are often very lightly damped, giving the appearance of self-sustained oscillation over a finite time interval.

      • Why not Nick, Steady state is just a special case. The full form of the equation would be roughly, {4A(T)^3+B(T)^2+C(T)}/T. Normally, you can assume the first term is most significant (or insignificant depending on the case)and consider just one order of the equation. In the atmosphere, conductive, latent (with sensible component) and radiative would be ~ linear at the surface for a small range. But you have three boxes, surface, lower atmosphere and tropopause. It can be simplified to a RCI circuit for a reasonable approximation. Regional boxes would provide better accuracy. Come on guys it’s not rocket science, it’s just Earth sciences.

    • Not to mention the fact that much of the modeling does not assume a day-night model. Nick Stokes at 7:38pm points this out.

      The footnote about aliasing is key. If you want to study clouding forcing, a monthly averaged temperature dataset is undersampled in time by at least two orders of magnitude. It might also be understampled by a factor of 100 in X,Y.

      • Monthly averages are not aliased in the important low frequency range. The transfer function of a continuous average (discrete averages have the same zeros) of time T is sin(w*T/2)/(w*T/2), where w is radial frequency. The zeroes of the response are at k*2*pi/T, i.e., when you alias the copies of the frequency response, there is zero aliasing to dc, and negligible aliasing in a region around dc. This is precisely why boxcar averages are used so extensively in applications – it’s not generally an optimal response (except for purely white noise), but it prevents aliasing to dc.

    • David L. Hagen

      OldNavy
      Thanks for mentioning a few of the real life control problems.
      For further details see my post under: Severe Tests
      “See chemical engineer Pierre LaTour who is a world specialist on the issue of controlling nonlinear multivariable systems.
      See: Pierre LaTour “Engineering Earth’s Thermostat with CO2?” and Letters between Latour & Temple
      Committing
      to “control” climate when we do not even know all the physics – particularly on cloud feedbacks – cannot accurately measure the temperature signal – have large delays between forcing and feedback – have numerous uncontrolled variables – have nonlinear relationships with chaotic interactions – etc – is incredible hubris and ignorance. When a world premier expert raises warnings over control terms most are not familiar with, it is worth taking notice!”
      Dr. LaTour clearly lays out numerous issues, each of which shows it impossible to “control” climate using the CO2 signal in a closed loop.

      (Obviously you can “control” CO2 in an open loop by getting rid of fossil fuels).

    • ON, I have a draft post on nonequilibrium theory, including nonequilibrium steady state. I’ve identified a relevant paper, talked to the author, trying to coax a guest post out of him, but I am not to optimistic. I may just go ahead with the post anyways (after i have a few hours to further digest)

  20. Pehr Bjornbom

    This is an interesting discussion by Dr. Suamarez and it is thought provoking indeed.

    As I understand the energy balance model used by Spencer and Braswell (SB11) their conceptual model is based on the following assumptions:

    1. The climate system consists of the troposphere and the mixed layer of the ocean. The system is well mixed in such a way that the global temperature changes may be represented with one global temperature anomaly.

    2. The radiative flux from the top of the atmosphere may, by using Taylor expansion, be represented by the expression N(t) – λΔT where N(t) W/m2 is called radiative forcing and λ W/(m2 K) is the feedback parameter.

    3. The non-radiative heat flux between the mixed ocean layer and the deep ocean is S(t) W/m2.

    4. The overwhelming heat capacity of this conceptual climate system is the heat capacity of the mixed layer C W/(m2 K).

    5. The energy balance over this climate system gives the following equation:

    C dΔT/dt = S(t) + N(t) – λΔT

    Note that what is measured is the temperature anomaly ΔT and the radiative flux N(t) – λΔT while the heat flux S(t) is unknown.

    If there would be no change in radiative forcing, ie if N(t) would not be changing (after suitable smoothing to cancel out short term random fluctuations) then the radiative flux would be a linear function of the temperature anomaly. The change in radiative flux would be proportional to the change in temperature anomaly.

    This is what Dessler has claimed while Spencer and Braswell claims that there is indeed a radiative forcing part in the radiative flux. By the way this radiative forcing may be seen in the phase plane diagrams that were introduced by Spencer and Braswell (2010) in their JGR paper. In SB11 they claim that this radiative forcing is causing a lag between radiative flux and temperature changes that is found in the observations.

    However, Dr. Suamarez seems to have used a somewhat different conceptual model with other assumptions since his derivation results in a second order differential equation. This is based on a control system concept, but how do we know that he really has derived a model conserving energy as required by the climate system?

    • I hope your realize that at different circumferences of the planet and atmosphere, you have different speeds due to size difference in the planet rotating.
      A single mathematical equation will always fail and need adjusting due to the planet slowing down and changes with the suns output of energy along with surprise changes we still do not understand that interact with the atmosphere.

      • Pehr Bjornbom

        A single mathematical equation will always fail and
        need adjusting due to the planet slowing down and changes
        with the suns output of energy along with surprise changes
        we still do not understand that interact with the atmosphere.

        The energy balance model is not using temperature but temperature anomalies as the dependent variable. The usage of temperature anomalies may be seen as a method of eliminating much of those effects. There are different temperatures in different locations, in different parts of the ocean and in different times of day and night and year. But by using temperature anomalies those differences disappear to a large extent.

    • David L. Hagen

      Pehr
      Speaking of phase plots, see
      David Stockwell: Phase Plots of Global Temperature after Eruptions

      On diffusion into the ocean, see Global Warming Temperature Trends

    • Richard Saumarez

      It will conserve energy as formulated.

  21. MattStat forgive me.

    It is not the amount of data – gobs of data for one time period. It is the length of the historical record. For example, VAR models require very long histories.

    In addition, there are many cycles in the historical record which requires even longer histories.

    • It would be nice to have analyses actually performed, to quantify the inadequacies. We may not have to have eons of data at all sampling rates in order to make a reasonably accurate prediction for the next 40-80 years. Padilla et al might be right, and the data available in 20 years may dramatically reduce uncertainty.

      It’s better to fit an appropriate model to insufficient data than to ignore the data totally. IMO.

      • Richard Saumarez

        I would simply comment that if you model something with insufficient data you don’t know what the results mean. If the “stat” in your cognomen refers to statistics why not think about the Neyman-Pearson Lemma?

      • Two good comments. I am assuming that your reference to N-P refers to the notion of power, not to the likelihood ratio test.

        Are you better off with insufficient data or an inadequate model?

        Tukey said “It is better to have an approximate answer to the right question, … , than an exact answer to the wrong question, … .” But it’s always a matter of debate which question is the “right” question and which answer is “accurate enough”.

        Are you asserting that there are in fact adequate data to estimate the parameters in your model? If your model omits clouds completely, what can that possibly mean? If your model assumes stationarity, can it possibly be accurate enough to assess even the sign of the hypothetical CO2 effect? Assuming stationarity for a non-stationary system isn’t necessarily bad, as you wrote above, but for this purpose it is bad enough to get the wrong answer with non-negligible probability. Isn’t it?

      • Richard Saumarez

        No I’m not!
        I am not even saying that the model that I am proposing is realistic, it is simply an illustration of a model that does contain feedback and its parameters are, in principle, calculable through a deconvolution type operation. Having said that, I think the whole thing is fraught with difficulty and likely to be ill-conditioned.
        As I say in my piece, there should be a formal statistical hypothesis and then one can explore the difficulties in testing it.

    • From a pragmatic point of view (but not necessarily a mathematical point of view), we probably don’t need to understand climate responses and oscillations on a multi-century scale. If we knew for certain that the LIA were part of a multi-century oscillation, what would we do differently today because of that knowledge? Imagine the hubris of people in 1910 making investments and policy recommendations based on what they thought would be best for the world today and then ask how much foresight for 2010 we should give ourselves credit for today. Is there really any point looking hundreds of years in the future? Yes, people several hundreds of years from now may be cursing our generation as the ocean submerges Bangladesh, South Florida, and all of today’s major coastal cities. Equally likely, they will be laughing at our ignorance.

  22. Question Dr. Suamarez:

    Is there a medical name for the type of feedback such as is involved in the HOT of a pepper… like a habanero pepper.

    And, there are much hotter peppers than habanero. Even so, the HOT is due to capsaicin. It is my understanding that no matter how HOT the pepper may be, it is not actually ‘hot’ on the flesh in the sense in is damaging like a hot skillet or a drop of acid.

    With the hot pepper, nothing is actually damaging the tissue. The ‘hot’ of the pepper is transmitted information as nerves ordinarly would due if there really was something HOT-HOT-HOT that was burning your tongue. And, the body acts as if it really is hot–and your tongue feels like it really is burning. But, it’s not really hot and your tongue is not really burning at all.

  23. MattStat is correct in my opinion.

    State-Space Modeling (Kalman Filtering) is the correct mathematical tool for Climate Science. VAR (ARIMA) are just examples of state-space modeling. State-space modeling estimation and prediction and also folds well into Control Theory.

    I would recommend that Andrew Harvey’s textbooks on non-stationaty statespace modeling be considered. It advances Box-Jenkin’s style ARIMA models.

    Additionally, I have become a big fan of ‘Singular Spectrum Analysis’ by Nina Golyandina, Vladimir Viktorovich Nekrutkin, Anatoliĭ Aleksandrovich Zhigli︠a︡vskiĭ.

    SSA lets the data do the talking. SSA can help you decompose signals.

  24. In my opinion, the ‘energy balance’ ideas are highly deceptive. Energy balances are very hard to measure and even harder to explain. Having work in nuclear fusion in a past life, ‘Cold Fusion’ is based on an energy balance. The ‘Cold Fusion’ ideas make me even crazier than some of the arguments of related to Climate Science.

    If scientists cannot properly measure the ‘energy balance’ in an ‘experimental chamber’, can they be expected to be able to measure the ‘energy balance’ on a ‘planetary scale’?

    This arrogance alone scares the hell out of me.

    These ‘energy balances’ are assumed to be easily measured and explained. (And they are even more easily sensationalized.) The real problem is understanding non-stationarity in the both inputs and outputs.

    Non-stationarity is foolishly ignored in Climate Science.
    Standards of scientific proof must be far higher. Back to Judith’s concerns about uncertainty.

    Nothing there. Go home!

    Sorry, I am getting weird tonight!

  25. For clarity, I’d suggest changing:

    “For some reason, filtering a signal with a rectangular impulse response and then decimating the signal is commonly used in climate “to reduce noise”

    to

    For some reason, filtering a signal by averaging over a rectangular window function and then decimating the signal is commonly used in climate “to reduce noise.

    What they’re really doing (in plain English) is using an unweighted mean to average e.g. measurements for each day of the month to yield a monthly series. I’m not sure aliasing is much of an issue here, but it’d be worth looking at to at least eliminate as a concern.

  26. Dr. Suamarez,

    Very good thought provoking analysis.

    The area of climate science is so complex that multiple interacting models must be the way to go to try and cover all parameters. The single calculation is too general to cover multiple points on this planet. The short time frame currently being used by models is a major hindrance to the 4.5 billion year planet and misses a vast number of changes the planet has taken.

    I hope to read more and possibly interact with some of your research in this area.

  27. Alexander Harvey

    Much of this I like, but there are difficulties in the attempt to apply control theory to the climate. These are not major issues, the mathematics are correct but the identification of the key climate variables needs more care. Mind you this is likely due to the baffling way they are dealt with by S&B and D.

    In the pdf, it is pointed out that the climate issue is not a control system one, which is correct and well worth remembering. One can borrow the mathematics but not some of the notions, including the concept of control. There is no input to the climate system that represents an intention that the system obeys.

    The simple feedback model that is described is best seen as an illustrative example but one that fails to capture either of the S&B or Dessler representations. Too rigid an adherence to control theory is not helpful. In this case it is the notion of an input and an output. Much of the S&B vs D divergence is an argument about which is the input and which is the output and the relative degrees in between. The model needs to be symmetrical in terms of inputs and outputs. This does have knock on effects particularly when it comes to forming lagged covariance (or correlation) matrices as their is no obvious choice for the input/output pair so one would do both combinations.

    Also the issue of scale separation is needs to be more usefully addressed, by this I refer to the transfer function from temperature to flux being shorter than the sampling interval and the transfer function from flux to temperature much longer than the sampling interval. Given that this is the case in the cliamte feedback example, and that progress is required, the second order component cannot be distinquished from zero so the system is indistinquishable from the first order one that both S&B and D have used. The large scale separation with respect to time between the two transfer functions makes this not unreasonable.

    Lastly the question of observables needs to be addressed, the obvious assumptions would be that the inputs and outputs are observables. This is not necessarily the case and borrowing thinking too literally from control theory might lead one astray. In the S&B and D case one observable is the integrable flux, which is the value after summation with the fedback flux not the input flux prior to summation. As best as I can understance the Dessler argument it is the fedback flux that is the observable, the input being considered to be effectively zero in keeping with the notion that the is no natural radiative forcing.

    In general, and I have said this before on other threads, the concepts inherited from a simple application of control theory are not sufficiently generalised for an application to climate problems. In particular the notions of input and output encourages bad results. Commonly the choice of input repesents a bias that can prejudice the remaining analysis. The notion of the feedback loop and the correct indentificaiton of the observables are the essential elements of the analysis.

    It would be good if Richard or someone else would look again at the S&B and D case and try to analysis their model more faithfully. In my view all these authors made a bit of a hash of it so it still needs doing.

    Alex

    • The author made the same point – that the earth has no setpoint, and the control analogy doesn’t fit for that reason. Mathematically, it’s a distinction without a difference; when you perform a dynamic analysis on a system with a setpoint, the setpoint, being a constant, essentially drops out. The dynamics remain.

      • Hmmm. Not quite true as magnitude correcting feedback increases with divergence from setpoint. With no setpoint, neither proportional nor integral control is definable. That is to say, negative feedback is a null concept if there is no setpoint for that feedback to correct to. That is not to say that there are no negative feedbacks in the climate system. It means that analysis of climate as a control system is invalid. Borrow concepts from control theory if it helps but don’t thereby claim the climate can be modeled as a control system.

      • Richard Saumarez

        I think this stems from whether you consider T0 to be a set point or whether it is just the the temprature at the time.
        You can recast the statement “magnitude correcting feedback” as simply a signal path that involves feedback without having to postulate a control system.
        If you read what I have actually written, I have said that you cannot assume that there is a control system but you can borrow the mathematical tools of feedback to analyse such a system. The results are are similar whether you regard it as a control system or not.

      • Perhaps we are in agreement on this. I suppose I was reacting to “The results are are similar whether you regard it as a control system or not.” I believe assuming a control system as an appropriate model can mislead folks. Positive and negative feedback concepts are not limited to control system theory. Electronic amplifiers, oscillators, filters, and signal processors all use feedback in various ways. The concept of setpoint and control are not part of the necessary for that kind of analysis though simple control theory may be employed to maintain dynamic range.

        I would prefer a model of signal processing instead of control systems. It may seem a subtle difference at some theoretical level but it is not at the engineering level.

      • Richard Saumarez

        I wouldn’t have a problem with that. I’m regretting mentioning control at at all. I should have said that we have a system/network with a particular characteristic that is or isn’t governed by feedback.

      • Alexander Harvey

        Richard,

        You could have used LTI system theory which gives access to the same mathematics but fewer people would be familiar with the term.

        LTI systems theory is more generalised and (linear) control theory is an application, as is electical circuit theory, signal processing, etc..

        Anyone interested should go to wikipedia for their LTI system theory summary.

        The good news is that choosing a control theory banner will pull a bigger audience precisely because the term is more familiar. The bad news is that is has baggage and it inspires a metaphor that misleads.

        Googling: “control system” climate

        I got ~30 million hits

        Googling: “control system” climate

        I got 30 thousand hits

        I think that it is unfortunate that climate science has latched on to control as opposed to LTI (Linear Time Invariant) system theory.

        You noted in your article that the “control” part was just a means of accessing appropriate mathematics yet it is unfortunate that the control metaphor once conjured imposes a too narrow view and certain biases of interpretation that are difficult to correct for.

        Alex

      • Alexander Harvey

        Oops:

        Googling: “control system” climate

        I got ~30 million hits

        Googling: “LTI system” climate

        I got 30 thousand hits

  28. David L. Hagen

    Suamarez gives important control specialist perspective on climate.

    For further control analysis, see <a href=http://landshape.org/enm/category/solar-accumulation-theory/.David Stockwell’s Solar accumulation theory, especially his phase lag showing a Pi/2 (25% of cycle) lag of surface temperatures behind solar forcing.

    Stockwell also found that phase shift in Spencer’s data.

    Such control systems analysis with the lags fitting is an important critical evaluation of climate systems.

    Fred Haynie’s Future climate change where he has a wealth of fascinating CO2 variations and analyses. Fred Haynie Future climate change

    http://www.kidswincom.net/climate.pdf

    See thread on CO2 under Torturing the data and
    CO2 under detecting CO2 fluctuations

    While not being a control specialist, CO2 and Temperature lagging the annual solar insolation cycle at both Arctic & Antarctic by about 90 degrees (3 months) and being 180 degrees apart suggest to me that there are strong primary solar driven cycles with temperature and CO2 lagging together.

    • please stop spaming the conversation with links to OT material.

      • David L. Hagen

        steven
        Sorry for not explaining the context. Suamarez stated:

        In practice, feedback is created by physical systems that store or dissipate energy, an in doing so, create a phase shift, or delay that depends on frequency.

        I was showing reports of evidence and models of phase lags of temperature behind solar as shown by Stockwell. etc. identifying the presence / absence of phase lags can provide significant input into the feedbacks involved.
        These examples provide some data and models to further explore what Suamarez observed:

        I am, however, in no doubt that analysis of flux and temperature data, even at the modelling level presented here, is a formidable problem and requires a substantial amount of critical thought.

        Suamarez is focusing on cloud feedback. Today:
        Willis Eschenbach observes on clouds:

        . . . . the temperature changes lag the insolation changes by about two months in the Southern Hemisphere, and by one month in the Northern Hemisphere. This is because of the thermal inertia of the planet . . .along with the greater thermal inertia of the greater percentage of ocean in the south. . . . the phase diagram shows that there is no lag at all for the changes in the clouds. They change right in step with the insolation, in both the Northern and Southern Hemispheres.

  29. Richard,
    As a physicist and electrical engineer your arguments make a great deal of sense. I have been giving the likes of Spencer, Braswell & Dessler way too much respect. When it comes to feedbacks none of them have a clue compared to electrical engineers.

    What this tells me is that the “Models” created by “Climate Scientists” are very primitive which may explain why they have trouble explaining the past and why they totally lack predictive skills.

    • Stirling English

      @gallopingcamel

      ‘the “Models” created by “Climate Scientists” are very primitive which may explain why they have trouble explaining the past and why they totally lack predictive skills’

      An IT salesman’s dream project.. doomed to eternal failure, but consuming ever-more resources in the hope of success. When I was in sales, having the Met Office as your client was considered to be a passport to commission-led riches out of the grasp of mortal box-shifters…a bottomless moneypit that never ran out.

      In IT Technical, we have another phrase for the models.

      We call them ‘Total Crap’. This is based on their complete inability to provide any useful results for the real world.

  30. Ian Blanchard

    To this humble Earth Scientist, the maths and stats is getting a bit over my head, but one thing I do like in this presentation is the explicit statement of assumptions, particularly where these are ‘hidden’ within the mathematical processes. Also well done on saying that these assumptions are not strictly correct and highlighting where this difference is likely to be negligible and where it might be serious.

    This seems to be one of the areas where climate modellers have much to learn in their communication of the science and I suspect in some cases even in their understanding of their models which are obviously developed with a range of both explicit and implicit assumptions – my suspicion is that in several cases, models that have evolved over time have had so many extra routines and calculations added to their basic shell (by different programmers at the behest of different scientists) that no-one really knows all the functions embedded in the programme and hence the implicit assumptions therein.

    • Ian, I suspect that you are right about the content of the GCM code. These programs are huge and, from what I have heard, have been driving the computer makers to make bigger and better computers for a long time. Call it a spin-off of climate research.

      That said, climate research evolved over time. There was no moment where someone said “we need a model of the earth” and set out to design it. As computers were able to do more, so did the models. When the output did not match the data, there was always a debate between the “model needs to be better” and “we need more data” . This has driven the satellite observation network which we have now as well.

      When the output of the models started showing huge temperature increases, there was some alarm. And here we are.
      Rose

      • Stirling English

        You amaze me that anybody even bothered to compare the output with observations at all. The First Law of Climate Modeling is:

        ‘If the real world data and the model disagree, the data is wrong’

        and the Oath of All Climate Modellers

        ‘Under no circumstances whatsoever will I use models to make quantifiable testable predictions in the real world. I will restrict myself to ‘is consistent with…’ and ‘simulations suggest …..’ And I promise faithfully to call model runs ‘experiments’

      • Ian Blanchard

        rmdpbservations
        Your post is factually correct. I do wonder however what would happen if a genuinely multidisciplinary group was to go back to first principals and construct an entirely new GCM-type ‘model earth’ using well documented techniques optimal to current computer technologies, rather than the rather more ad hoc developments that have occurred.

        Stirling English
        It’s back to a comment from one of my PhD supervisors – ‘You can’t prove anything with computer models’. I had some tweaking of the wording of my thesis regarding how certain model outputs appeared to be consistent with the patterns seen in the real world. This was about the strongest phrasing I was allowed to get away with

      • Latimer Alder

        In the case of my MSc, the numbers modelled from the theory we were testing did not at all match the observations that my colleague in the same research group was making.

        And guess what? We junked the theory rather than junked the observations!!!!

        How quaint and old-fashioned can you get? Just like those old fuddyduddies used to….Newton, Einsten, Feynman, Maxwell etc. They obviously had not the benefit of today’s computers to tell them what the results should be and so were reduced to just looking at how nature presented itself. Poor primitive fools!

        And think of the opportunity missed with Aristotle – the very old ago guy who just used to sit and think about how he thought the real world was and then told everybody what the Truth is. That was good stuff….no pesky ‘observations’ to worry about. Just pure rational thought. Think how many more Great Thoughts he culd have had with today’s technology to guide him!

      • WisconsinitesForGlobalWarming

        In my first job (Chemical Engineering research) we had a great new process for creating isoprene, one of the key monomers that are polymerized to make raw materials for tires and other rubber products.

        We modeled the reaction kinetics based on the chemists’ test-tube scale experiments. We did thorough V&V on the model including predicting the composition of the reactor effluent given unique operating conditions (temperature, feed rate, catalyst, etc.).

        We then used the model to design, specify, and build a larger scale reactor to start scaling up the process. We paid $250k for reactor (a large sum in 1983) and when it came in we loaded it up, cranked it up, and waited for the effluent to hit the gas chromatograph.

        Nothing ever came out. This is where we learned a valuable lesson about modeling: no model ever includes what you don’t know.

        In our case, we created the isoprene quite nicely. It then went on to polymerize quite nicely, burn, and create a godawful gunk in the entire reactor system. We hadn’t realized, until that point, with REAL EXPERIMENTS, that our catalyst not only cracked the starting material, it also was great at speeding up the polymerization of isoprene.

        Why it so hard for climate “scientists” to admit there might be something they really don’t know?

      • In a similar tale to Wisconsin’s, I was working with a group of people who were developing code to control a robot. Using the virtual environment their code worked amazingly well. The robot zoomed around, responding to its sensors appropriately and everyone was happy.

        Night before the demo it was moved to the robot and of course the thing just sat there. The indicators all suggested that the code was running, but the robot didn’t budge.

        It turns out that a glitch in the code was causing the motor to reverse hundreds of times a second. In the simulation, the net movement was still in the forward direction because the simulated motor was represented as a simple formula that translated input into motion without considering all that messy physical stuff like inertia, magnetic fields and so on.

  31. Richard Saumarez

    Thanks for the compliments!

    “A word means what I want it to mean” – Humpty Dumpty.
    As an outsider, I have always been impressed that some climates scientists have inverted the meaning of feedback (and the sign) as understood by the rest of the civilised world.

    I am definitely not an expert on control theory. Just a jobbing biomedical engineer with “a spanner in his pocket”.

    Stationarity. Linear systems theory assumes stationarity, otherwise you get non-linear ODEs. This can be accomodated by local linearisations, or more complex techniques. I am not suggeting for one moment that I think the climate is stationary, or even in a steady state. I am simply saying from a short term control statndpoint, you may be able to ignore the non-stationarity.

    Assumptions.
    I read Lacis’ paper again. It is riddled with assumptions.
    Personally, I would like to see a GCM guru write a post that states every physical assumption in his model. I have always wondered whether World.6.2.ver3 is an improvement on World.6.2.ver2!

    Actually, my name is SAUmarez, not SUAmarez. My family originates from an island off the south coast of England, Guernsey. I am not spanish – I am a Brit!

    • Dr Saumarez, if you or anyone else could get a list of the full assumptions used in a gcm i reckon we’d need a bigger blog to post them all….

      In all seriousness though, it would be very interesting to get the full list- they must have put it up somewhere. I’ll have a looksie when i have a chance.

    • Dr Saumarez,

      Your right!
      A great many assumptions in many areas of science has generated the current mess of incorrect modeling.
      We have to dissect the planet first to understand it before making assumptions as to how it will react.
      Understanding the planet first is highly complex before even adding in the tilting for changes of heat to different regions that change everyday.

      So, how can a single formula cover the whole planet, when regionally they are vastly different due to land heights, circumference differences, distance differences of solar heat. gravity differences, etc.

    • “I have always been impressed that some climates scientists have inverted the meaning of feedback (and the sign) as understood by the rest of the civilised world.”

      It is the same with the term ‘sink’. Where one would use ‘reservoir’ they use sink, quite often the efflux from a ‘sink’ is greater than the influx.

      I also like:-
      (sigma*(Tmax)^4 + sigma*(Tmin)^4)/2 = sigma*(Tmean)^4

  32. I have much doubt about if control theory is applicable to climate which have thousands of variables if not millions of them. Mathematical representation of climate is beautiful and attractive to some but the reality of nature is not that simple and too big to control.

    P.E. said ” In the end, I thing(k) that S&B made the same mistake all the people arguing with them made – they tried to do it all themselves. You can’t do this kind if(of) business that way”

    Very true indeed, applicable to the author of this article. He tried to do it all himself.

    • Richard Saumarez

      Actually, I haven’t.

      All I am saying is that if you are going to use a control/systems approach to energy balance, one has to very careful about definitions and shopuld take care that the stated mathematics conforms to your statements about the model. The “model” is very simple and is only used to illustrate some general features of the approach and to illustrate that I think that what has been done in this field is probably wrong.

      I conclude that this is a very non-trivial problem. If I were going it alone because I thought it was simple, I would have grabbed some data, done a deconvolution and said “That’s the answer”. The reason I haven’t done this is because I recognise the difficulty of the problem, I have no climate background and do not have much insight into the meaning of the data.

    • Richard Saumarez

      On reflection, this statement is nonsense logically. The whole idea of systems analysis is reduce the order of the mathematics to a simpler form. The fact that we can use control theory successfully in medicine, where there thousands, if not millions, of variables, argues against your apprroach. Furthermore, any model of the climate as in GCMs is representing millions of variables, some of them successfully.
      If you argue that it is philosophically impossible to represent climate mathematically because of its complexity, that is a predjudice.

      • Dr Saumarez,

        I definitely like your approach to the field of climate science.
        I found the generalized theories on how this planet operates is vastly different and fails when changing time frames to the past and understands little to a circular planet that rotates.

      • “On reflection, this statement is nonsense logically”. Your article so far does not convince me its not one of them. Control theory on Nature!

        “The whole idea of systems analysis is reduce the order of the mathematics to a simpler form.” Indeed if back up by a good theory and observed in reality. Your presentation appears to be in a confused form.

        ” The fact that we can use control theory successfully in medicine, where there thousands, if not millions, of variables, argues against your apprroach.” I don’t know much about medicine control variables but if you said millions, it must be hot air or gas in reality.

        “Furthermore, any model of the climate as in GCMs is representing millions of variables, some of them successfully.” What are they?

        “If you argue that it is philosophically impossible to represent climate mathematically because of its complexity, that is a predjudice.” You might be correct it is a prejudice. Did you ever think that this statement is a prejudice by itself!

      • Richard Saumarez

        My presentation is in a confused form. I’m sure it is, but what bits of it precisely?

        As regards millions of variables, the human heart contains something in the order of 3×10^8 cells. They beat in sequence depending on their connectivity and local ionic current. Each cell membrane current can be described using ~30 ODEs and ~50 parameters, depending on the model and their characteristics change spatially in the myocardium.
        Explaining how the heart goes into VF is a matter of describing how they interact. I do believe this is hot air or gas in reality.

        A predjudice is making statement that one cannot logically challenge. I have no idea whether one can model the climate successfully, but I am prepared toentertain the idea that it is possible.

      • “My presentation is in a confused form. I’m sure it is, but what bits of it precisely?”

        Medicine might be controllable but not climate. What part of the climate that you think can be controlled? I would say, none. Your article confused the readers without substantiation of a control theory on climate. You went to the mathematics to show off you are capable of mathematics and thats all.

      • Richard Saumarez

        If you read what I actually said, I stated very clearly that one should not assume that there is a setpoint in climate, but one could use the mathematics of control theory to analyse what would happen in the presence of feedback.

        Therefore, I do not accept that this post is confused, although it is entirely possible that you are confused. I suggest that you read the mathematical section again, and you might understand the point.

      • Richard Saumarez

        I am sure my presentation is confused, what parts of it specifically?

        The human heart contains ~3×10^8 cells which fire (or have action potential) in a sequence determined by their connectivity and local membrane ionic currents. One can represent the ionic currents by a set ~30 highly non-linear coupled ODEs with ~50 parameters whose values vary spatially through the heart. Further complexity is introduced by structural abnormalies in disease. They way each cell interects with its neighbour is represented by two partial DEs decribing current flow in the intracellular and extracellular domains. Solution of these equations will involve more than 1 million variables.

        As regards whether the solutions make any sense, I can only say that under some circumstances it is possible to reproduce the broad form of experimental results obtained in human investigation and these seem tto be consistent with the risk of ventricular fibrillation. A key step is simplification to make the models soluble in a way that makes sense physiologically.

      • “If you read what I actually said, I stated very clearly that one should not assume that there is a setpoint in climate, but one could use the mathematics of control theory to analyse what would happen in the presence of feedback.” Where did I mention setpoint? None of the climate paramters are controllable <- if you can understand this sentence! Therefore, feedback control as your article indicated was non-sense.

        "Therefore, I do not accept that this post is confused, although it is entirely possible that you are confused. I suggest that you read the mathematical section again, and you might understand the point." You confused most of the readers who sing with you not me. Your little world medicine control might be valid but unfortunately it does not apply to real climate at all as no parameter is controllable.

      • Richard Saumarez

        @ Sam NC.
        I’ve been waiting for a comment along these lines – I’ve had enough of them from so-called intellectuals. I am discussing control, as o[[osed to climate. I have never implied that this is a control problem and stated this very clearly. I suggest you read my “mathematical” post.

        However, since you have brought the subject up, there is a widely used clinical description of your posts. ” Excreta Tauri”!

      • You dig too deep a hole or paid too much attention to the tip of a leaf and forget the forest around it. Too bad for a doctor too sick to realize his own symptom when someone like me point you to the right direction – climate control is not your area of expertise. If you believe in religion, even your god cannot handle/control the climate on the Earth. Your article is non-sense.

  33. I worry about
    “3) The cloud formation is described as a linear process; proportional to temperature and the clouds themselves have a linear effect on flux”.
    since it is the case that cloud cover is inversely proportional to temperature:

    http://greenerblog.blogspot.com/2011/09/cloud-cover-decreases-in-warming-planet.html

    • Richard Saumarez

      No. Not correct. See the mathematical description.

      If you are worried about the linear part, I discuss the principles of linearisation and its use in engineering maths, numerical analysis etc. I point out that you have to be very careful with this assumption.

      • Right, because the assumption is at very least an oversimplification, because as temperature rises evaporation increases which may lead to more clouds but relative humidy decreases which may lead to fewer clouds.

        You may need to use partial diffential equations instead of ordinary differential equations.

        And as the data Richard cited shows, with more temperature there is less clouds, which is a bit of a problem for the cloud iris control theory, but supports the idea that there is no climate temperature setpoint.

      • Richard Saumarez

        I would have to say that, as a medic, I don’t have a great deal of insight into clouds (unless they are pink). One could write an over determined model of fast and slow phases of cloud formation, some of which would reflect flux and some would trap it.
        My feeling is that one has no chance of unravelling such a model with the available data.

  34. I posted this message first in a wrong thread. What comes below is exactly the same text.

    Feedback is a difficult concept in relation to climate, because feedback is really a working concept only, when it’s possible to look at a small number of variables.

    Thus it’s applicable to global climate on timescales that are long compared to the time scales needed to spread the influence of a strong local effect to global dimensions. In practice this means decades rather than years.

    It may be applicable locally, if the local feedback is strong in comparison with the interaction with other parts of the Earth system.

    Most reaction to any impulse don’t satisfy at all either of those requirements. There will be a reaction to the original impulse, but that leads to interaction with other subsystems as much as it may lead to feedback that influences the phenomenon of the original impulse. I.e., we don’t have a system of a few variables and well defined delays in the responses. Rather we have a genuinely complex system, where the reaction to the impulse spreads to the whole Earth system with a very wide range of time scales. Separating the reaction to one impulse is impossible as an essentially infinite number of other disturbances affect the behavior as the system has also many characteristics of (spatio-temporal) chaos and a lot of stochasticity.

    My impression is that there is very little that can be transferred from the handling of feedbacks in system theory to the climate science. The Earth system is far too complex to allow such transfer to produce much insight. What I have read of such attempts has always confirmed this conclusion.

    • Pekka,

      The theory of chaos is the lack of understanding the complexity.
      Dissecting the planet from equator to the poles and then interacting each individual region would give a slightly better understanding without including tilting. Tilting adds another complexity of region receiving more energy than others and angles of distance to other areas.

    • Richard Saumarez

      I do not agree. If you are going to describe a system by a set of linear ODEs, relating an input (Flux) and an output (temperature) the system will be described by its impulse response, irrespective of its internal structure and will be analysable.
      Whether the system is linearisable or not is open to debate but, given sufficient data can be tested rigorously.

      However, comments about things being to complex to analyse appear to be pseudo-academic obfuscation as opposed to argument. We routinely describe very complex systems succesfully and the key is to analyse them in such a way that we can describe their behaviour realistically.

      • You are referring to internal structure and stating that it doesn’t matter. This is a valid point for the whole Earth system on the time scale of decades, because for that we can define summary variables and look at the feedbacks. This is the approach that’s common in climate science. That’s fine, but that cannot be extended without new problems to more local phenomena or so short time scales that the summary variables are seriously incapable of describing, what’s going on.

        When the considerations are brought to more local phenomena, the problem is not with the internal variables of the system considered, but wit the excessively strong interactions with the external system.

        Trying to use global summary variables on shorter timescales is a bad approach, because the system is internally far off from any quasiequilibrium that could be described by the summary variables. This is the case, because the same summary variables could describe an infinity if off-equilibrium systems, but the different off-equilibrium systems would have a very different dynamical behavior. Trying to describe such systems by the summary variables alone would likely lead to totally misleading conclusions.

        Unfortunately the only way that we have any hope of describing the dynamic behavior at an useful level is often with the help of more complex models of the type of GCM’s. This is unfortunate, because it means that very many analyses remain hopelessly model-dependent. Attempts to describe them more directly without models leads to erroneous conclusions, while describing them with models means that the results may be artifacts created by the models. The models are absolutely necessary, but even they offer a unsatisfactory solutions.

        There has been some discussion on the value of model experiments. Working with models making alternative calculations – experiments – tells, how the particular phenomena appear in the model. That may be useful in two ways. First of all it tells often new things about the model. That may either confirm or discorfirm that the model is reproducing similar behavior that what’s observed in reality. In the former case we may gain understanding on, how the real Earth system operates under such conditions, and we get some more confidence in the model. In the latter case we learn about the limitations of the model and we may get useful ideas on, how to improve it.

      • Richard Saumarez

        I completely agree that if you leave out major internal variables that would act as inputs to he model in question, you will not get sensible answers because you have not formulated the model correctly.

        This post is centered around the question: “Can you deduce the presence of feedback from measuring radiative fluxes and temperature?” Let us assume that we had ideal data, and tons of it so we could segment it into shorter epochs, and tried to perform an analysis along the lines that this question suggests.
        If one was dealing with a perfect system with no other inputs, the coherence spectrum would be notionally one across the entire frequency range. It almost certainly wouldn’t be and this could tell you one of three things. One, there was noise, (which can be resolved), 2 the system was non-linear or 3) one had not characterised the inputs correctly. In these cases one has to back to the drawing board.

        I am not suggesting that we should represent climate as a set of “systems” boxes. What I am saying is that if you simplify one aspect of climate by using a linear ODE, you are making an assumption about how the system works. In this case, the system as stated does not permit the presence of feedback and in my view the analysis is not correct.

        At a more general level, I am highly sceptical that an overall systems analysis is the right approach and in this post I have “flown a kite”. It may be useful to answer a specific question in a relatively high frequency, linearisable aspect of climate, but I agree that the modelling should reflect the physics.

        The question to my mind is should one consider climate sensitivity as a “feedback question” at all. However, if one is going to postulate feedback, I think one should at least try and analyse to see what it implies.

      • We seem to be mostly in agreement with some differences in judging issues, where judgmental differences are natural.

        One point that I had is, that the feedbacks are most easily defined on long (multidecadal) time scales. We have had discussion on the concepts of equilibrium and transient (where transient refers to something like 50-100 years) climate sensitivity and there are global level feedbacks in both. There are questions on the value of these concepts as well, but the dynamics of the Earth system may well be such that these concepts are rather well defined, but there is also the possibility that chaotic dynamics makes even them badly defined.

        The resent interest in feedbacks on much shorter time scale leads to additional problems. I would consider it clear that no global level feedbacks can be reasonably defined on timescales of less than a few decades, but there may be local feedbacks, which are better defined. That requires, however, that we can find phenomena, which are controlled on some specific spatial and temporal range. To make sense out of that the local processes must dominate over variable external couplings. Whether that happens to anything that’s really climatic rather than meteorological, is not at all obvious.

      • This aspect of the discussion gets to the heart of the matter as summarized by Pekka and Dr. Saumarez. This is why we have GCMs. Linking back to Andy Lacis post, the degree of confidence seems to be reasonable w/r/t the basic radiative transfer equations and too high with respect to other variables. I think the problems are generally twofold: 1) getting the parameters right for the necessary paramaterizations of physical processes occurring at scales below the model resolution and 2) the inclusion or neglect of important variables such as the biosphere, ocean dynamics etc.

      • Richard Saumarez: However, comments about things being to complex to analyse appear to be pseudo-academic obfuscation as opposed to argument. We routinely describe very complex systems succesfully and the key is to analyse them in such a way that we can describe their behaviour realistically.

        I am glad that you wrote that.

        However, before applying the results of the modeling or claiming to have achieved understanding from them, you do have to demonstrate that the model is sufficiently accurate for the purpose.

        Your post was in fact a nice introduction to the topic. I just think that more information about the actual mechanisms is necessary.

        Someone up above provided a link to Willis Eschenbach’s current post at WUWT. I’ll repeat it:http://wattsupwiththat.com/2011/10/11/wrong-again/

        It directly addresses whether the forcings are in fact well-enough known for a differential equation model based on them to yield accurate results. It is worth your while to read it, though I can’t say the same for the comment thread — that’s much more uncertain.

      • Richard Saumarez

        I wouldn’t argue with that!

  35. Dr Saumarez,

    I have found areas of science fluffed off as having no meaning.
    Meanwhile when you do analyze the areas very carefully through massive researching, you find that they do have a vast amount of play in the areas of the past and future of what this planet will be.
    Meaning following the salt residue trail.

  36. This article by Gerard Roe presents a recent detailed review of Feedbacks, Timescales, and Seeing Red. Footnote 4 on page 97 might be of interest.

    • A list of recent texts is here.

    • That is a very helpful rwview.

      • That is a very helpful rwview.

        The calculus derivations are very straightforward indeed.

      • Thank you for the link to Gerard Roe’s review. Really useful supplementary context & discussion to help with Dr. Saumarez’s excellent read.

        Note Gerard Roe’s acknowledgments:
        “I have had more fun than anyone has a right to in talking over these ideas with Marcia Baker, who gently pointed out my errors in thought and math, and I am indebted to Richard Lindzen for teaching me the method. Feedback from Mark Brandon, David Battisti, CarlWunsch, and Chris
        Brierly was also extremely insightful.”

    • There is a very interesting discussion in that review article by Gerald Roe of the very differential equation, with static feedback, that was the subject of this thread. It comes at around his Eq 29.

      The first derivative does indeed imply an RC response, but this is not part of the feedback. Instead, what the feedback does will be familiar to circuit designers. Positive feedback raises the effective R; negative feedback lowers it.

      The result is that positive feedback extends the time constant of the resulting exponential decay, and again, negative feedback lowers it.

      • The result is that positive feedback extends the time constant of the resulting exponential decay, and again, negative feedback lowers it.

        That is interesting and the implications it has for explaining what we think are multi-decadal oscillations are provocative, to say the least. Noise forced into that response function can generate what appear to be quasiperiodic behavior with sporadic cycles, very random-walk like.
        Fred Moolten has also been referencing an article that says that the PDO may be more due to climate change than natural variability.

      • On PDO, see:

        Evidences for a quasi 60-year North Atlantic Oscillation
        since 1700 and its meaning for global climate change

        Nicola Scafetta, Theor Appl Climatol DOI 10.1007/s00704-011-0499-4
        That evidence appears to be more than “climate change”.

    • that’s good. thanks for the link.

      Besides the uncertainty in the parameter estimates and the initial state of the system, there is the problem of unknown unknowns. Are there important feedbacks that are not in the model? Are known feedbacks nonlinear rather than linear, that is, nonlinear enough that the linear approximation is sufficiently inaccurate not to get the right answer to the most important question (whatever that is)?

  37. @Prof. Curry… The footnote link doesn’t work (#_ftn1 vs. #_ftnref1).

    A great article, which puts some experienced detail behind my own intuition that 0-dimensional and 1-dimensional models are of little value besides as hints, possibly pointing the way for more sophisticated models to follow. Thank you for posting it.

  38. Richard

    Thanks very much for your time and effort to bring your model for discussion to this forum in a very open way. I wish other did the same, instead of just claims and obfuscations while hiding methods and data.

  39. I am struck by the similarities of frequency analysis discussed here with the tools I use in my field: music.

    Take a look at this:

    This is indistinguishable from magic.

    The process used here is extremely advanced fourier analysis which allows the musician to analyse the principle components of a complex signal, manipulate them and then reconstruct them.

    Convolution is also a form of signal analysis with which I am extremely familiar. We use this to recreate the reverberation characteristics of physical spaces and apply them to a raw sound source. Typically we would play back a recording of the sine wave sweep within the space to create an IR (impulse response) and then deconvolve them by reversing the phase of the raw audio, thus cancelling out the sine sweep and leaving us with the characteristics of the space.

    Much of the sense of space depth you get on modern film and TV recordings are used using this sort of technology.

    It would be interesting for a climate scientist to collaborate with other disciplines say audio developers like Nuenbacker who are geniuses with decoding complex signals.

    • Heh. A practical demonstration that the suggestions of linkage between musical and mathematical neural processing are likely quite valid!

    • That’s a really nice video. There are many new ways of looking at data and model output that can give insight into understanding the climate. Current researchers might not have the time or knowledge to delve into these other areas, as you suggest. As an example, I would love to run “Moodle” on the GCM code. Just for fun. Or some sort of netwerk diagram to visually show what is happening. I think it is possible.
      Rose

  40. –> “I am somewhat sceptical that a systems approach of using deconvolution to imply feedback would yield an unambiguous answer, although it may be possible with better models of ocean temperature dynamics and cloud formation, coupled with a careful error analysis.“

    Translation: In as much as the statistics of McShane and Weiner has shown that there is absolutely no signal in the data underlying MBH98/99/08 – let us all bow our heads and look to a deconvoluted signal from the God of Mann to guide us.

    Does this make any sense to anyone? Why don’t we simply abandon linear thought altogether and throw a little more white noise at scientists like Wegman, McIntyre, McKitrick, McShane, and Weiner.

    “More to the point, the shortcomings in many science papers used by the IPCC are not usually specialty-related but rather result from ignorance or misuse of advanced (and even standard) statistical methods, computer programming, basic scientific procedures and simple common sense.” (Holland D. Bias and concealment in the IPCC process)

    • Indeed, and the errors in applying the other specialties are so numerous and serious that they almost overwhelm any attempt to “de-convolute” them.

      Which is apparently relied on to keep the show on the road.

  41. I’m grateful to Richard Saumarez for describing control theory in a way that allows my previously superficial understanding of the subject to improve a bit. I have a number of questions about the climate relevance of his explanation, but since my level of control theory understanding is still below that of several of the other participants, I would like the following analysis to be considered tentative, with hopes that Richard and others who know control theory better will correct my misconceptions.

    As I understand his description, a first order differential equation as in SB-11 and D-10 and D-11 will lack an explicit feedback term, and so a second order equation would be necessary to distentangle the time evolution of initial system change from the consequent feedback response. This principle seems plausible to me, although its application to efforts such as those by SB-11 strikes me as problematic, given the uncertainties in determining the temporal order of causes and effects – e.g., is an observed flux change an initiating event arising in the atmosphere or a feedback on a preceding event arising in the oceans during alternating El Nino and La Nina phenomena? The difficulties are compounded by the existence of multiple feedbacks on different timescales and by uncertainties cited by Richard regarding underlying assumptions about ocean behavior. One wonders whether the problem they address is tractable – it may be, but is certainly formidable.

    On the other hand, much climate interest is focused on what is probably a different phenomenon, at least quantitatively – feedback responses to long term climate forcings such as imposed by increases in atmospheric CO2, with an eye toward estimating the climate sensitivity to such forcings. Here, I see the control system analogy as less useful for a number of reasons. First, the flux imbalances at the top of the atmosphere vary slowly over the course of years and decades, with feedbacks operating in parallel over these same intervals, so that there is essentially no time separation in the real world (although lead-lag intervals can of course can be evaluated in model simulations). Second, although feedback is not explicit in the equations used to estimate climate sensitivity, it is included implicitly due to the fact that it describes deviation from a no-feedback climate behavior that can be well approximated by differentiating the Stefan-Boltzmann (SB)equation to yield ΔT/ΔF = 1/4 σT^3 , adjusted (slightly) via modeling to account for spatial and temporal heterogeneity. One can thus describe climate sensitivity in terms of forcings (imposed flux perturbations at the TOA), a parameter λ, and a temperature response, as ΔT = λΔF, where the no-feedback response is λoΔF, and λo for our climate system is ~0.3 K/Wm-2 based on the SB calculation described above. The relationship between the actual temperature response, λΔF, and the no-feedback response, λoΔF is given by a feedback parameter f where λ = λo (1/1 – f). The term in parentheses is the sum of a Taylor series in which f is the fractional feedback response to a forcing, f^2 the response of the feedback to its own effects , f^3 the response to that response, and so on – i.e (1 + f + f^2….+ f^n). The climate is stable – it won’t become a “runaway” – as long as f0 (also see below).

    For energy balance formulations, a different parameter is often described, as in Gregory and Forster 2008, who were interested in estimating transient climate responses rather than equilibrium sensitivity, and used the parameter α to describe the radiative response to a temperature change (other authors have used λ for similar types of calculations, which unfortunately can be confused with a different use described above). In GF-08, during a persistent climate forcing, ΔF, and before radiative equilibrium is reached, the climate system is gaining heat to raise surface temperature, but this surface heat gain is reduced by radiative heat loss to space in proportion to the temperature change, with a proportionality that can be expressed as αΔT, and also heat loss to the ocean at a rate given by N, the net heat influx into the climate system after subtracting loss to space (N = ΔF – αΔT). At equilibrium, N is zero by definition, and so equilibrium sensitivity could be written simply as ΔF/α, although that was not the purpose of their paper. As in the previous example, feedback can be inferred from the deviation from the no-feedback temperature response described above.

    Finally, control theory and climate feedback estimates have often suffered from a semantic problem involving the definition of feedback that has led to misconceptions. In climate discussions, it is universally understood that the Earth’s response to a temperature change includes the Planck Response (based on the SB law) which dictates that a warmer body will shed more heat, thereby tending to restore a radiative balance. However, this is often not referred to as a “feedback”, and so one often reads that net feedbacks are positive because they will amplify a temperature change beyond the level expected from the Planck Response alone. Once the latter is considered, it becomes clear that this amplification, while important, is not unlimited and will eventually be constrained by the Planck Response to temperatures that once again reflect a balance between incoming and outgoing radiation. Whatever one wants to call this, it is the control theory equivalent of a net negative feedback. Conditions on Earth have never departed from this scenario, and similarly, in the foreseeable future, there appears to be almost no prospect of a runaway climate until millions of years in the future, when the sun heats up enough to make this possible, and the oceans evaporate into a hot, water-saturated atmosphere.

    I have tried above not to suggest that control theory is entirely irrelevant to our interest in long term climate change and the attendant feedbacks, although I don’t see the detailed application of the theory as central. I will be interested in additional “feedback” on how it can be usefully applied.

    • My sentence above, “The climate is stable – it won’t become a “runaway” – as long as f0 (also see below).” ran into HTML truncation. My intended statement was that the there would be no runaway as long as f is less than one, but that the temperature effect of a forcing will be amplified if f is greater than zero.

      • Richard Saumarez

        I absolutely agree that systems analysis may be marginally relevent to long term climate science. My basic point is that if you are trying to analyse short term dynamics, it may be applicable, in which case, it’sprobably better to use a conventional mathematical framework.

        As regards terminology, equations may suggest a better way to express oneself. Were one French, which I’m not, one would simply say:
        “As I speak the most beautiful language in the World, why should I learn English?” (!)

      • I think another implication of your article, which is fairly explicit, is that if you’re going to use the terminology and concepts of a formally developed field, at least use them coherently, and understand the definitions.

        Both constraints seem to have been widely violated wrt control systems.

  42. Arcs_n_Sparks

    I greatly appreciate the article by Dr. Saumarez. As an Electrical Engineer I’ve thought about many processes in terms of control theory. Note: you do not actually have to have a variable you control in order to analyze a system using control theory (although that helps greatly; in the case of the Earth, we have a lot of moving parts and trying to isolate them is difficult). I do not subscribe to the notion that the Earth is too complicated to apply control theory (put another way, simplifying models to the point of computational tractability is probably garbage-in/garbage-out, especially with specious assumptions). I think these cross-disciplinary discussions and collaborations are sorely needed.

  43. I’ve been wondering why, if the 1 deg warming caused by CO2 increase, is amplified, by positive feedback, to 3 degrees of warming due to changes in the Earth’s albedo, increased water vapour content etc, those extra 2 degrees themselves don’t get amplified leading to runaway warming?

    How great is the danger of this occurring?

    • There is no danger of a runaway. I discussed some of this in my earlier comment – see the part about the feedback factor f, but the comment was so long that probably few people read the whole thing.

    • “I’ve been wondering why, if the 1 deg warming caused by CO2 increase, is amplified, by positive feedback, to 3 degrees of warming due to changes in the Earth’s albedo, increased water vapour content etc, those extra 2 degrees themselves don’t get amplified leading to runaway warming?”

      The 2C includes all the warming from feedbacks, which includes feedbacks acting on warming from the feedbacks themselves. It’s the finished result so there’s no more feedback on top of it.

      For example if every 1 deg C warming causes another 0.66C warming then, that extra 0.66C warming will cause 0.44C more warming (0.66C x 0.66) and the extra 0.44C warming in turn causes another 0.29C warming (0.44C x 0.6), which causes another 0.19C, causes another 0.13C, another 0.08C, another 0.05C, another 0.03C…

      If you add all the warming up (1 + 0.66 + 0.44 + 0.29 + 0.19 + 0.13…..) then it is sort of roughly 3C in total.

      So what gets said is that 1 degree C initial warming results in 2C more warming from feedbacks, 2C being that total from feedbacks.

    • The next time you see the term “runaway”, run away. It has been empirically shown to be non-operative over a huge range of the postulated inputs over the last few billion years.

    • Thanks Fred and Lolwot,

      I think these are good answers. My experience, many years ago, of playing with regenerative amplifiers , controlled positive feedback, wasn’t particularly good. They were just so touchy and nearly always took off into oscillation.

      I hope you’re right! Incidentally, Stephen Hawking has said that he worries about the possibility of thermal runaway too.

      • tt,
        Not to be snarky, but Hawking has been wrong before.
        Thermal runaway from CO2 is not going to happen.

  44. Cloud feedback is certainly real enough. However, the present analysis has precious little relevance to either assessing cloud feedback in climate models, or deriving cloud feedback from observational measurements.

    First, it’s not just ‘cloud’ feedback. There are at least a dozen different kinds of cloud feedbacks. Basically, any change in cloud morphology that will have some effect on cloud interaction with radiation can be considered to be a separate cloud feedback type. Thus: cloud cover, cloud-top height, cloud optical depth, cloud particle size, cloud water/ice phase are some of the more obvious cloud changes that affect how clouds interact with radiation. Also there are changes in cloud bottom, cloud heterogeneity, cloud longevity, as well as changes in cloud diurnal, seasonal, and geographic variability (clouds shifting from daytime to night time occurrence will have a profound impact on their effect on SW and LW radiation).

    Furthermore, all climate feedbacks (not just clouds) are highly non-linear. This has been discussed in some detail by Aires and Rossow (2003) http://pubs.giss.nasa.gov/abs/ai09000a.html Moreover, the climate feedbacks are atmospheric state dependent – that is, they are not ‘constants’ of the climate system.

    Frankly, I don’t believe that it is really possible to measure climate (or cloud) feedbacks directly because you will never have simultaneous measurements of all the other climate variables that define that particular state of the climate system.

    The formulas that are used by Spencer & Braswell and by Dessler are useful as analysis tools (helpful and necessary) in order to extract some estimate of cloud feedback, and in the process, by making a whole bunch of assumptions regarding the local state of the climate system. When you make different assumptions about the state of the atmosphere and the measurements you are making, you will also get different estimates for the cloud feedback that you infer.

    It is, perhaps, easier using a climate model to get a handle on cloud (or other) feedbacks. This requires differencing two states of the atmosphere, say, the control run and a doubled CO2 run. There will be found differences in clouds, temperature, water vapor, etc. between the two GCM runs. Using an off-line radiative transfer model, the observed cloud changes (cloud over, cloud height, cloud optical depth, etc.) can then be evaluated for their effect on the SW and LW radiative fluxes, and the resulting planetary energy balance – all in the context of the reference atmospheric structure. The radiative forcing of the doubled CO2 experiment can also be evaluated by the same radiative modeling. This gives a ‘feedback’ determination for the observed cloud change in response to the applied radiative forcing of doubled CO2. As per the Aires and Rossow study, such a cloud feedback evaluation will only be valid for that particular GCM, and that particular climate forcing experiment. In principle, the cloud feedback might be different is you did a further doubling of CO2 on the doubled CO2 run. (But you would expect physical continuity.)

    This type of cloud feedback evaluation is very tedious and time consuming, and therefore is not frequently performed. One example of such cloud feedback evaluation is described in the paper by Hansen et al. (1984) http://pubs.giss.nasa.gov/abs/ha07600n.html Similar formulations such as Spencer & Braswell and Dessler can also be applied to GCM data, but that approach will yield more approximate results.

    How then are clouds computed in climate GCMs?

    There are no simple formulas, Taylor expansions, or the solution of differential equations to calculate GCM clouds. There is instead the use of theoretical and empirical relationships that are applied to the local atmospheric temperature, humidity, stability, and wind profiles. A description of how clouds are calculated (or as they were parameterized in 1996) in the GISS GCM is given by Del Genio and Yao (1996) http://pubs.giss.nasa.gov/abs/de06000k.html

    How do we know if the GCM clouds are any good?

    You compare the model generated cloud fields and compare them with observational data (say, ISCCP cloud climatology) in terms of global and geographic cloud cover, cloud height distribution, cloud optical depth, liquid water/ ice phase, particle size, seasonal and diurnal dependence, and whatever other cloud information that may be available. Any adjustable parameters in the theoretical and empirical relationships are tuned to match the observed cloud distribution as closely as possible. The ‘critical relative humidity of cloud formation’ is the one major tuning knob that is adjusted to match the observed global cloud cover and planetary albedo.

    OK, so your GCM cloud parameterization is able to match the current climate cloud distribution. How do we know if the model is going to get the right cloud feedback for a climate perturbation relative to current climate such as doubled CO2?

    You don’t. Cloud feedback will not depend on the CO2 amount per se, only on the local atmospheric temperature, humidity, stability, and wind environment. At best, you can hope that if the GCM clouds respond reasonably to seasonal changes in temperature, humidity, and wind, there is reasonable expectation that the model will respond with ‘reasonable’ cloud feedback to small perturbations relative to current climate.

    Current best estimates of cloud feedback suggest that the overall cloud feedback for perturbations relative to current climate, is small, and very likely, slightly positive. (Note that for doubled CO2, an increase in cirrus cloud cover or cirrus optical depth will produce a positive cloud feedback, while an increase in low cloud cover or low cloud optical depth will produce a negative cloud feedback.)

    This is why determination of cloud feedback is difficult task. It also means that there is no real hope for direct verification or validation of cloud feedback sensitivity from any foreseeable set of observational measurements.

    There is one further complication to getting clouds right. And that is the cloud-aerosol indirect effect. This is also difficult of observe and quantify. But there is ample evidence that the cloud-aerosol indirect effect has a substantial impact on cloud radiative properties, which is why this is a very hot topic in cloud/aerosol research.

    The only thing that can be said with certitude, is that cloud feedback is definitely a climate feedback effect (and not a forcing). I think we can also say that the cloud feedback will not do something crazy within the climate system for no apparent reason. The reasonable range for cloud feedback must necessarily be bracketed by how clouds respond to seasonal and latitudinal variations in temperature, humidity, atmospheric stability, and winds.

    • If cloud feedbacks are highly nonlinear one would think they are capable of doing unexpected, and large, things. You do not seem to allow for that.

    • Richard Saumarez

      I agree that simplistic models are unhelpful in determining the overall effects on climate.

      What I am saying is that if you choose to represent a system by a differential equation, you should think about the physical meaning of that equation. If the effects of cloud are a short term linearisable feedback, as proposed by Spencer, one should analyse data in such a way that it reflects the mathematics that one is proposing. In my view, Both Spencer & Braswell and Dessler don’t do this.

      The goal of most engineering mathematics is to write equations in a lineariasable form. This is how one solves partial differential equations using finite difference methods. The numerical solution of ODEs, generally uses linearisation (See Williams’ seminar at the institure of Mathematics on the effect of step length in climate models ). Having looked at some GCMs they certainly contain implicit linearisations.

      I should say emphatically that I do not believe that one can write a generalised systems model of the atmosphere and solve it neatly using transforms. In this article, I was “flying a kite”. However, If one is going to try to determine the presence of short term feedbacks by observing radiation and temperature, then an initial systems approach is not unreasonable, although one would have to consider other “inputs” such as ENSO etc. My guess if that the data isn’t good enough to allow the distinction of an open-loop and a feedback model. However, if one did have good enough data, one could in principle determine if the system were linear or non-linear. In the latter case, a simple systems approach would obviously fall flat on its face. If there was a high degree of coherence between the inputs and outputs of the model and reality, one could say that the climate BEHAVES in a manner that is consistent with short-term feedbacks. This does not imply that they actually exist. A reductionist approach may determine the real mechanism(s).

      The difficulty in my view with the reductionist GCM approach, and I am arguing by analogy from a far simpler system – cardiac electrophysiology which is spectactularly non-linear, is that the system becomes exquisitely sensitive to its parameterisation. The ODEs representing ionic currents are basically fitted empirical equations that appear to fit the data obtained from experiments performed in rather artifical situations. Although the 3D molecular structure of ion channels are now being determined, I don’t think anyone can say with confidence that they know how to write truly deterministic equations describing their behaviour.
      The difficulty is that small variations in some of these parameters (~1%) will determine whether one’s model develops an arrhythmia or not. One can compare model predictions in what one can measure in patients with heart disease and occasionally this produces real insights but it is very difficult to do. What I question is whether GCMs, although they naturally are underpinned by many experimental observations, have all the physical processes been sufficiently well determined to be certain that the overall behaviour of the model is robust?

      • Richard Saumarez

        One thing I forgot to add about cardiac models, is that incorrectly formulated models with wildy incorrect parameterisations, lead to results that are obviously wrong. However, there is a wide body of mathematical thought that ventricular fibrillation is due to a “spiral wave”, because “If this is what the equations say- that’s what’s happening”. This has found its way into textbooks (See Keener Mathematical Physiology).
        The difficulty is that many of the mathematical physiologists I have encountered know remarkably little about the heart (an afternoon is all you need to know about it). One points out that numerous multielectrode and optical voltage fluoresence studies have never revealed a spiral wave. One points out that a spiral wave will exist in very small volume of heart muscle, but it is well known that fibrillation can only exist in a relatively large volume of tissue. One points out that spiral waves imply a pattern of conduction velocities that simply doesn’t doesn’t exist in heart. (How do I know? Because I’ve made about 10000 measurements of CV in normal and diseased hearts in patients). And so on and so on.

        I have to say that I became increasingly diusenchanted with mathematical physiologists, not because of their charm, but their lack of intellectual rigour and total disregard for proper experimental evidence. Whether these attitudes exist within the climate community, I couldn’t say.

    • Moreover, the climate feedbacks are atmospheric state dependent – that is, they are not ‘constants’ of the climate system.

      Isn’t that true of CO2 effects, and all other “forcings”?

    • Oops, the following belongs here, not below:

      Current best estimates of cloud feedback suggest that the overall cloud feedback for perturbations relative to current climate, is small, and very likely, slightly positive.

      “Small” compared to what? Could be large compared to the CO2 effect, couldn’t it?

      Why “very” likely slightly positive? To what perturbation is the feedback positive (surface temperature?), and what is the evidence?

    • “Current best estimates of cloud feedback suggest that the overall cloud feedback for perturbations relative to current climate, is small, and very likely, slightly positive.”

      Those estimates are worthless. They are using inappropriate tools (linear regressions on phase plane plots). Proper analysis shows that the feedback is substantial, and negative.

      • Long term data from HIRS and ISCCP are most consistent with a positive cloud feedback and exclude a strong negative feedback, and so I would have to say that a claim of substantial negative feedback is wrong – at least for long term forcings such as those due to CO2. Short term flucutations due to ENSO are more problematic, and the issue probably isn’t settled by any available data. One of the reasons is that the concept of time lag is uninterpretable in a circumstance of alternating El Nino and La Nina events, and with temperature effects that are redistributed from their point of origin to other oceans and land masses over different intervals. Under these circumstances, global averages are uninformative and the data don’t permit us the determine whether a flux change is initiating a temperature change or is itself a response to a previous temperature change. I’m not sure there is any simple mathematical or statistical escape from these uncertainties. Definitive claims are not justified at this point.

      • “Under these circumstances, global averages are uninformative and the data don’t permit us the determine whether a flux change is initiating a temperature change or is itself a response to a previous temperature change. I’m not sure there is any simple mathematical or statistical escape from these uncertainties.”

        Phase relationships allow causality to be inferred. You are talking about things which have been done in control systems design and analysis for decades. One of the things that irks me about the whole debate is this presumption of arrogance on the part of the climate science community that they are somehow doing this kind of analysis for the first time, and they have no apparent inclination to investigate whether their conceit is true or not.

  45. “Frankly, I don’t believe that it is really possible to measure climate (or cloud) feedbacks directly because you will never have simultaneous measurements of all the other climate variables that define that particular state of the climate system.

    How do we know if the GCM clouds are any good?

    You compare the model generated cloud fields and compare them with observational data”

    Sounds like something a skeptic might write. If only this limited acknowledgment of uncertainty were applied to the GCMs in toto – “How do you know the GCM[s]…are any good?”

    They are attempting to model something which is extremely complex and chaotic, so the only way to know if the models are any good is to compare them to observational data. Until that is done, we just don’t know how accurate they are, and should not base large scale public policy decisions on their claims.

    • Do you ever look to see what is being done? The AR4 has a whole chapter on evaluation of models. Just one extract on clouds:
      “Data from field experiments such as the Global Atmospheric Research Program (GARP) Atlantic Tropical Experiment (GATE, 1974), the Monsoon Experiment (MONEX, 1979), ARM (1993) and the Tropical Ocean Global Atmosphere (TOGA) Coupled Ocean-Atmosphere Response Experiment (COARE, 1993) have been used to test and improve parametrizations of clouds and convection (e.g., Emanuel and Zivkovic-Rothmann, 1999; Sud and Walker, 1999; Bony and Emanuel, 2001). Systematic research such as that conducted by the GCSS (Randall et al., 2003) has been organised to test parametrizations by comparing results with both observations and the results of a cloud-resolving model. These efforts have influenced the development of many of the recent models. For example, the boundary-layer cloud parametrization of Lock et al. (2000) and Lock (2001) was tested via the GCSS. Parametrizations of radiative processes have been improved and tested by comparing results of radiation parametrizations used in AOGCMs with those of much more detailed ‘line-by-line’ radiation codes (Collins et al., 2006). Since the TAR, improvements have been made in several models to the physical coupling between cloud and convection parametrizations, for example, in the Max Planck Institute (MPI) AOGCM using Tompkins (2002), in the IPSL-CM4 AOGCM using Bony and Emanuel (2001) and in the GFDL model using Tiedtke (1993). These are examples of component-level testing. “

      • Yes, I look at what is being done. What is being done here is that Andrew Lacis wrote a guest post ranting about how the AR4 used weasly words in grossly overstating uncertainty, and thus the need for mitigation now. Then several days later, he posts a comment patiently explaining how complicated it is to model just one factor influencing climate, clouds.

        My comment was not on the skill with which the GCMs model clouds, or whether they are trying to improve their models. It was about the disconnect CAGW advocates have about uncertainty.

        They will admit that any particular element of their models is extremely complex, and the only way we can be sure they have it right is by comparing it to actual observations. But the complete models themselves should be accepted as sufficiently accurate regarding the future climate as a whole to justify massive public policy changes, without being so verified.

        Did you read Andrew Lacis guest post?

        Do you believe after reading that that he thinks we should wait until the GCMs as a whole are tested against observational data, before enacting decarbonization policies?

        To paraphrase his comment again:

        “How do we know if the GCM[s] are any good?

        [We} compare the model generated [predictions of warming] and compare them with observational data. [And we don’t enact massive public policy changes until we do.]”

      • Nick, all that long piece you quote really says is that the models have been improved. This in no way implies that they are any good. Nor is there really any discussion of the issues Lacis raises in his comment. Simply saying “we are getting better” dodges all the important issues.

  46. Richard Saumarez

    My final comment is that have “flown a kite” with a rediculously simple model to make some points about whether “control” / systems think can be applied to climate.

    In restricted situations, I think it can be, although it is difficult and requires some clarity of thinking about the basic ideas.

    If one is going to make a post such as this, I think it it is only right that one should attempt to answer one’s critics, even if one does not necessarily agree with them. If you make an argument, you should be prepared to defend it.

    That’s it! I off to the Pub!

    • And I hope you enjoyed you drinks, you certainly earned them. I would just like to convey my thanks to you for preparing this article, and Judith Curry for publishing it here.

      The article and the discussion have been most interesting and instructive. They have reinforced my opinion that control theory cannot be successfully applied to modelling much of the climate systems, an opinion which evolved from an engineering background and reading the publications of Roe. The structure of the functions in an engineering control system and the behaviour of most of the phenomena in the climate system are not synonymous.

  47. The rigorous analysis of linear feedback control systems, wherein the system output produced by components with fixed (time-invariant) response characteristics is sensed and a control signal is looped back to the input, is a well-developed discipline. It has little to do, however, with the climate system, whose response characteristics are time-varying and often nonlinear.

    Although changes in response characteristics are commonly called “feedbacks” by climate scientists, they are not a return loop between system output (SW and LW radiation to space) and input (TOA solar irradiance). Changes in albedo produced by snow cover, ice and clouds act as a variable shutter that modulates the effective insolation available to thermalize system components, but reflectivity and thermal capacitace are different mechanisms than bona fide physical feedback of the output signal.

    In that light, positing a “feedback system” whose input is the total radiative flux anomaly and the output is the global mean temperature anomaly becomes a computational exercise that is devoid of physical significance. What does it mean when output Kelvins are fed back for algebraic addition to Joules or Watts? And what sort of physics governs the presumed deterministic relationship between the statistical abstractions embodied in those climatic anomalies, especially when they are virtually uncorrelated?

    If progress is to be made in physically understanding the climate system, the signal of diurnal and seasonal variability–which is suppressed in climatic anomalies–will have to be analyzed rigorously by appropriate methods. Misapplied blackbox models of “climate feedback” simply don’t provide meaningful measures of the sensitivity of surface temperature to changes in system reponse characteristics.

    • Richard Saumarez

      If you read what S&B and D have written, they assume linearity and that it is analysable. In this case, one can very easily draw conclusions about the way to analyse data.

      I think you are mistaking linearity and linearisability. If there are short term feedbacks, in the sense that clouds form in response to changes in radiative fluxes and these modify the fluxes, this is feedback in the more restricted meaning of the word and it may be sufficiently linearisable to permit a simple model to be constructed that gives a framework in which to analyse the data.

      Again, while the system proposed by S&B and D is short term, the non-stationarity may be ignorable because its frequency range is entirely different from other non-stationarities.

      If you feel that blackbox models have been misapplied, can you demonstrate that within the narrow confines of the subject of this post that they have been misapplied rather than stating that they have?

      • Having spent the better part of my career in analyzing various geophysical systems both linear and nonlinear, I can assure you that I’m not “mistaking linearity and linearisabilty” in my indictment of the “feedback” presumption that is endemic in climate science. My objection is much more fundamental: there simply is no physical loop that feeds the output signal back to the input without putting a load on the latter. And the idea of a feedback system whose supposed output is differently dimensioned than the input violates the fundamental rule of physically meaningful system modeling. Temperature being an intensive variable that characterizes the state of a particular parcel of matter cannot be “fed back” meaningfully to any extensive variable.

        Your sense of physics seems to be misplaced. While clouds certainly modify both the insolation and LW fluxes, they are the product not of radiative fluxes but of condensation of water vapor convected aloft. It is these fluxes of latent heat that set the surface temperature much lower than it would be with radiative transfer alone. These abrupt, chaotic phase changes are not susceptible to linearization.

        Blackbox modeling that blithely ignores all these physical matters, which result in the lack of strong coherence between radiative fluxes and surface temperature, leads to nonsensical results. A demo of that was recently seen on a Dessler-related post at CA, where Bart derived an “impulse response function” for the “cloud-temperature” system. If you believe that physical sense can be made of a purported linear system whose presumed input and output are not strongly coherent, you’re welcome to explain this to a professional audience.
        By ignoring these physical matters as well as the

      • Correction: In my objection, it should read “without putting a load on the FORMER.”

      • Please scratch the last incomplete sentence in my reply.

      • “And the idea of a feedback system whose supposed output is differently dimensioned than the input violates the fundamental rule of physically meaningful system modeling.”

        I’ve read this more than once here. But it makes no sense. It’s very common in analysing electrical circuit feedback, for example, to think of on output voltage fed back as an input current. It’s often fed back through a resistor, and you can switch to whatever description you find convenient.

        Here is a typical negative feedback where the output appears as a voltage but, as they do here, you consider the feedback as an input current (because you have a good handle on current gain).

        And all feedbacks put a load on the output. How much depends on the gain of the device.

      • With an electrical circuit, you can take either a voltage or a current point-of-view. In the determination of the dimensionless system transfer function , however, these descriptions cannot be mixed. It’s a question of which one is the independently varying input signal. The output signal must be identically dimensioned. Even in your quaint example of an amplifier the voltage is passed through a resistor to obtain feedback current. In the realistic climatic case, there is no analogous determinstic relationship that allows one to convert surface temperaure to radiative flux when the surface is evaporative.

        It is not true that all feedback systems put a load on the output. Many use a sensor on the output and an independently-powered control signal is fed back to the input.

      • “The output signal must be identically dimensioned.”

        These systems are infinite dimensional. They can be expanded in terms of discrete, finite dimensional systems. Do some studies in functional analysis before making more inane comments.

      • Richard Saumarez

        I you read what I actually said in the post, one assumption is that the latent heat of cloud/water vapour formation is small compared to the heat capacity of the oceans. Hence, the assumption that the feedback does not load the output.

        Whether this is strictly true, i’ve no idea but it certainly can be handled if it is.

        Thank you – I am a professional in signal processing (highly trained) and have dealt with highly non-linear systems with demanding experiments for 25 years.

        As I said in a previous response, the problem of relating flux to temperature, the queation is whether one can deduce the presence of feedback from observing these variables. As I have stated one problem lies in the quality of the data , a problem as a professional in my field, I am only too familiar with.

        I we had good enough data, we test formally whether the system was linear or not. If this were possible, we could then test whether the the system was behaving in a manner that implied feedback or not.

        That would be a matter of experiment, not theoretical posturing.

        If it did, more deterministic studies could in principle determine if this was actually feedback.

        One thing I have noticed from this post, is that there are people, who do not use their real names, make lofty statements from an Olympean state of knowledge, and tell other people that they are naive. Not being a “climate” scientist, I probably am. But I am a scientist and when I see the extraordinarily low intellectual rigor shown in the analysis of SB2011 and D2011, (which assumes the things you are castigating me for, i.e.: linear systems, the presence of not of feedback), incorrect mathematics and a method of analysis that simply wrong, as a professional, I am underwhelmed. I have simply said in my post is that if you are going to take the standpoint of SB2011 and D2011, it might be better if you tried to use some proper maths and actually use data analytical concepts that are correct.

        I did take some time to read read Dr Curry’s chapter on thermodynamic feedback and then it took a whole 2 minutes to think of and analyse the “model” that I have used to illustrate a problem of data analysis that has been used, completely incorrectly in my view, to deduce the presence or not of feedback. I am not claiming that this is profound and it would be the sort of thing that one might teach to first year undergraduates in an exercise in critical thought on the dangers of modelling.

      • While the latent heat transfer from surface to atmosphere may be small relative to the oceans’ total heat content, experiments show that it outstrips all other transfer mechanisms (radiation, conduction) combined. Thus the load that it puts on surface temperature is large. That, however, is not central to my more fundamental objections to any presumption of any linear “temperature feedback system” in Earth’s climate. The lack of a direct response to those clearly stated objections leaves me perplexed. You speak instead entirely in hypothetical terms of “deducing feedback” from “better data,” ignoring the lack of coherence between surface temperature and cloudy sky radiative fluxes. Instead of instantly recognizing that no linear system, with or without feedback, would manifest such incoherence, you complain about anonymous comments from “Olympean heights.”

        We can agree, nevertheless, that neither S&B nor D have done any proper dynamicc aba analysis of the relationship between those variables. We should leave it at that.

      • Richard Saumarez,

        Nice to see a professional pointing out that sometimes one does not need to spend ten years learning “climate science” to point out basic deficiencies in peer reviewed papers on occasion.

        I am uneducated, so some years ago it took around two minutes to realise that the “radiative addition” beloved of “climate scientists” appears to break the principle that energy can neither be created nor destroyed.

        It is interesting to listen to all the deniers of science (who are unable to provide one reproducible experiment to back up their “theorising”) loudly declaiming from the Fortress of Arrogance, that we are all idiots.

        May you live well and prosper.

      • “A demo of that was recently seen on a Dessler-related post at CA, where Bart derived an “impulse response function” for the “cloud-temperature” system.”

        “Bart” is I. And, you clearly do not know what you are talking about.

    • John S.,
      You are bringing up an essential point discussed also by many others in this thread.

      Much of the discussion of feedbacks is on local and relatively fast phenomena. By local I mean a small fraction of the globe and relatively fast refers to time scales of less than a decade, thus much of ENSO falls in this category. Such phenomena involve responses that may be called feedbacks, but calling them feedbacks may also be crossly misleading. These phenomena cannot be mapped precisely on models of control theory, but have some similarities with them. Whether the similarities or differences dominate is decisive for the extent of applicability of the concept of feedback.

      Whatever is the answer to the above considerations, the issue is very different of the stationary feedback present in the hypothetical equilibrium climate response (or the near stationary one in the transient climate sensitivity). These feedbacks can be defined, but they cannot be related directly to totally different phenomena I discuss in the previous paragraph.

      Both above paragraphs discuss the same climate system, but the concept of feedback has very different meanings in them. One can learn about the latter from the former only through the use of a full climate model, because the direct connections between the feedbacks are so weak.

      • Before replying, I’m going to ruminate overnight on your philosophical remarks.

      • Having reread your comment several times, I remain unsure about its thrust regarding the issue taken up by S&B and B. When considered from the standpoint of a complex feed-through system with thermal capacitance elements, the distinction you make between “local, fast” phenomena and the “hypothetical equilibrium climate response” seems more a question of frequency range than a matter of different system configurations or nomenclature.

        No matter, how complex the system there is nothing essentially different about the rate at which capacitive components absorb and discharge thermal energy. The reason I call attention to the diurnal and seasonal cycles is because they represent strong, well-studied thermal forcings, the coherent response to which provides a far-better indication of the sensitivity of surface temperature than is provided by climatic anomalies.

  48. Current best estimates of cloud feedback suggest that the overall cloud feedback for perturbations relative to current climate, is small, and very likely, slightly positive.

    “Small” compared to what? Could be large compared to the CO2 effect, couldn’t it?

    Why “very” likely slightly positive? To what perturbation is the feedback positive (surface temperature?), and what is the evidence?

  49. One thing Dr. Saumarez may have covered, but if he did or another correspondent has, I’ve missed it.

    Feedback makes logical sense.

    It’s absolutely mathematically certain that there are feedbacks in the climate system.

    Analyses of feedback may make less sense, given the noise in the data, the complexity of the system, and the difficulty in selecting a model that validly captures exactly and only the information to be analysed.

    Discussion of analyses of feedback that does not narrowly and rigorously set out the parameters of signal:noise, error, confidence and other meaningful dataset properties as apply, of the dynamism and disorder in the system on the scope and scale under discussion, of difficulties with and constraints on the feedback model.. utterly useless and a waste of time. The province only of obfuscation and error.

    So, we ought move on until adequate foundation is established, which it appears we are not yet there.

    • Bart, without a doubt you are right. The variety of feedbacks possible and the different possible time frames of the feedbacks are amazingly complex.

      It would be easy to misinterpret the magnitude of a long term feedback and even its sign, like the situation with UV change that seems to be developing.

  50. Here are some additional papers that discuss sensitivity and feedback within the framework of simple models.

    J. R. Bates, Some considerations of the concept of climate feedback, Quarterly Journal of the Royal Meteorological Society, 133: 545–560 (2007)
    Published online in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/qj.62

    ABSTRACT: A conceptual study of climate feedbacks is carried out using two simple linear two-zone models and the commonly-used zero-dimensional model to which they reduce under simplifying assumptions. The term ‘feedback’ is used in many different senses in the climate literature. Two prototype usages, stability-altering feedback (defined in terms of a system’s asymptotic response to an impulsive forcing, negative when stability-enhancing) and sensitivity-altering feedback (defined in terms of a system’s steady-state response to a step-function forcing, negative when sensitivity-diminishing) have been isolated for study. These two climate feedback concepts are viewed against the background of control theory, which provides a generalized feedback perspective embracing all forms of forcing and which is often seen as providing the paradigm for the concept of feedback as used in climate studies.

    The relationship between the prototype climate feedbacks is simple in the context of the zero-dimensional model. Here, the stability-altering and sensitivity-altering feedbacks provided by a given interaction are of the same sign, and the sign of the stability-altering feedback as measured by initial tendencies always coincides with its sign as measured by the defining asymptotic tendencies. Even in this simple model, however, the sign of the prototype climate feedbacks can be opposite to the sign of the system’s feedback as defined in control theory.

    In the two-zone models, the relationship between the prototype climate feedbacks is not so simple. It is shown that, contrary to the common assumption, these feedbacks can be of opposite signs. Moreover, the sign of the stability-altering feedback as measured by initial tendencies can be opposite to its sign as measured by asymptotic tendencies. It is further shown that there is no simple relationship between the sign of either of the prototype climate feedbacks in the two-zone models and the sign of these models’ feedback as defined in control theory.

    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

    J. Ray Bates, Climate stability and sensitivity in some simple conceptual models, Climate Dynamics, 2010. Published Online December 2010. DOI 10.1007/s00382-010-0966-0

    Abstract
    A theoretical investigation of climate stability and sensitivity is carried out using three simple linearized models based on the top-of-the-atmosphere energy budget. The simplest is the zero-dimensional model (ZDM) commonly used as a conceptual basis for climate sensitivity and feedback studies. The others are two-zone models with tropics and extratropics of equal area; in the first of these (Model A), the dynamical heat transport (DHT) between the zones is implicit, in the second (Model B) it is explicitly parameterized. It is found that the stability and sensitivity properties of the ZDM and Model A are very similar, both depending only on the global-mean radiative response coefficient and the global-mean forcing. The corresponding properties of Model B are more complex, depending asymmetrically on the separate tropical and extratropical values of these quantities, as well as on the DHT coefficient. Adopting Model B as a benchmark, conditions are found under which the validity of the ZDM and Model A as climate sensitivity models holds. It is shown that parameter ranges of physical interest exist for which such validity may not hold. The 2 × CO2 sensitivities of the simple models are studied and compared. Possible implications of the results for sensitivities derived from GCMs and palaeoclimate data are suggested. Sensitivities for more general scenarios that include negative forcing in the tropics (due to aerosols, inadvertent or geoengineered) are also studied. Some unexpected outcomes are found in this case. These include the possibility of a negative global-mean temperature response to a positive global-mean forcing, and vice versa. [pay-walled]

    J. R. Bates, On climate stability, climate sensitivity and the
    dynamics of the enhanced greenhouse effect
    , Danish Center for Earth System Science, DCESS REPORT Number 3, 2003.

    Abstract
    The dynamics of the enhanced greenhouse effect resulting from a CO2 increase are studied using a simple two-zone hemispheric atmosphere-ocean model on an aquaplanet that is simple enough to allow analytical solution. The model’s sensitivity to forcing is viewed against the background of its stability to free perturbations. Free perturbations in SST, regarded as representative of temperature perturbations in the mixed layers beneath, are subject to a destabilizing influence from the effects of the water vapor infrared radiative (WVIR) feedback and are stabilized by evaporation, which results in moist convection and precipitation that deposit the latent heat removed from the surface above the level of the main water vapor absorbers, whence it is radiated to space. The rate of evaporation depends on the surface wind strength and the air-sea humidity deficit. In the model, the former is parameterized in terms of the atmospheric angular momentum (AM) transport, which depends on the SSTs in both zones, and the latter in terms of the local SST through the Clausius-Clapeyron relationship. Using estimates of the parameters derived from observation and detailed radiative model calculations, the model gives an equilibrium temperature increase for a CO2 doubling that lies within the range of that given by GCMs. As in the GCMs, it is found that the warming is greatest in the extratropics. Unlike the case of the GCMs, the mechanism of the warming in the simple model can be fully understood. The model’s equilibrium sensitivity is found to be inversely proportional to the value of the stability determinant (which measures the product of the decay rates of the fast and slow normal modes) and to be strongly influenced by the strength of a ventilation feedback. Both of these factors are sensitively dependent on the strength of the extratropical WVIR feedback, and the ventilation feedback in addition depends critically on the latitudinal distribution of the surface forcing

    J. R. BATES, A dynamical stabilizer in the climate system: a mechanism suggested by a simple model, Tellus (1999), 51A, 349–372.

    Abstract
    A simple zonally averaged hemispheric model of the climate system is constructed, based on energy equations for two ocean basins separated at 30° latitude with the surface fluxes calculated explicitly. A combination of empirical input and theoretical calculation is used to determine an annual mean equilibrium climate for the model and to study its stability with respect to small perturbations. The insolation, the mean albedos and the equilibrium temperatures for the two model zones are prescribed from observation. The principal agent of interaction between the zones is the vertically integrated poleward transport of atmospheric angular momentum across their common boundary. This is parameterized using an empirical formula derived from a multiyear atmospheric data set. The surface winds are derived from the angular momentum transport assuming the atmosphere to be in a state of dynamic balance on the climatic timescales of interest. A further assumption that the air–sea temperature difference and low level relative humidity remain fixed at their mean observed values then allows the surface fluxes of latent and sensible heat to be calculated. Results from a radiative model, which show a positive lower tropospheric water vapour/infrared radiative feedback on SST perturbations in both zones, are used to calculate the net upward infrared radiative fluxes at the surface. In the model’s equilibrium climate, the principal processes balancing the solar radiation absorbed at the surface are evaporation in the tropical zone and net infrared radiation in the extratropical zone. The stability of small perturbations about the equilibrium is studied using a linearized form of the ocean energy equations. Ice-albedo and cloud feedbacks are omitted and attention is focussed on the competing effects of the water vapour/infrared radiative feedback and the turbulent surface flux and oceanic heat transport feedbacks associated with the angular momentum cycle. The perturbation equations involve inter-zone coupling and have coefficients dependent on the values of the equilibrium fluxes and the sensitivity of the angular momentum transport. Analytical solutions for the perturbations are obtained. These provide criteria for the stability of the equilibrium climate. If the evaporative feedback on SST perturbations is omitted, the equilibrium climate is unstable due to the influence of the water vapour/infrared radiative feedback, which dominates over the effects of the sensible heat and ocean heat transport feedbacks. The inclusion of evaporation gives a negative feedback which is of sufficient strength to stabilize the system. The stabilizing mechanism involves wind and humidity factors in the evaporative fluxes that are of comparable magnitude. Both factors involve the angular momentum transport. In including angular momentum and calculating the surface fluxes explicitly, the model presented here differs from the many simple climate models based on the Budyko–Sellers formulation. In that formulation, an atmospheric energy balance equation is used to eliminate surface fluxes in favour of top-of-the-atmosphere radiative fluxes and meridional atmospheric energy transports. In the resulting models, infrared radiation appears as a stabilizing influence on SST perturbations and the dynamical stabilizing mechanism found here cannot be identified. [pay-walled]

  51. 1. “For some reason, filtering a signal with a rectangular impulse response and then decimating the signal is commonly used in climate “to reduce noise”. This is highly undesirable because it may force aliasing on previously correctly sampled signal.”

    See comment here.

    2. Cloud feedback is significant, and negative. Those who think otherwise, or disbelieve my analysis, simply do not understand it.

    • Bart – I explained in response to your same comment upthread why you are incorrect. However, it strikes me that you are exceedingly dogmatic. That’s unfortunate, because to understand climate system feedbacks, you have to understand climate behavior and the nature and source of climate data, and not merely the mathematical treatment of feedbacks.

      Cloud feedback remains a source of uncertainty, but we now have enough observational data to conclude that it is probably net positive long term, and almost certainly not strongly negative. Absolute certainty will have to await more data, but I don’t think it can be rushed by making pronouncements.

      • “I explained in response to your same comment upthread why you are incorrect.”

        No, you didn’t “explain” anything. You merely asserted, with a vague reference to some outside source.

        Show me some appropriately analyzed data which you think demonstrates I am wrong and we can talk. Not much longer tonight, but I will look back when able.

      • Well, that’s fair enough, and there are certainly data to demonstrate long term cloud changes of a net warming nature that have accompanied warming from anthropogenic emissions. In the meantime, though, let me leave you with a thought. In one of your comments, you stated:

        “Climate science is not my field:

        Well, I had already surmised as such from what I perceive to be your misconceptions about cloud feedback, but your additional statement seems to me to illustrate some of your misunderstanding:

        “The general layman can be taken in with facile arguments to the effect that, humankind is pushing on one end, so some payback has to be accumulating. But, this is not necessarily so in a feedback system. It is, in fact, the entire reason we create feedback systems, to reduce sensitivity to disturbances…The Earth and all of its climate systems and subsystems comprise a remarkably robust feedback system – they must, because otherwise, we would not be here. It would be an amazing happenstance if the fragile Earth proponents were right, and we just managed to stay balanced on the tip of a pin by luck.”

        I gather from the above that you think there is a belief within climate science that the climate is in some type of metastable situation that can easily be tipped to grow increasingly out of balance by some slight nudge due to greenhouse gases or other perturbations. I would therefore urge you to learn something about the concept of feedbacks as they apply to climate. One of the things you would discover is that the system responds in a way to stabilize it rather than to destabilize. The main stabilizing influence is the Planck Response, which ultimately overrides net positive feedbacks from clouds, water vapor, snow/ice albedo changes, etc., and returns the climate to a new radiative balance, albeit at a new temperature appropriate for the forcing. What is sometimes confusing about this is that the Planck Response is often not referred to as a feedback, although it plays a role equivalent to negative feedback in control system theory. This principle is universally understood within the science itself, but the terminology has understandably confused outsiders to the science, and so a belief in a metastable “tip of a pin” balance is something one can blame on climate science semantics. In any case, unless your reference to “fragile Earth proponents” signifies individuals who disbelieve the basic principles understood within climate science, it is inaccurate. Otherwise, it would seem simply to be a straw man. Feedbacks can be net “positive” in the sense that they amplify the temperature response to a forcing beyond what would occur with only the Planck Response operating, but overall, they are still ultimately stabilizingnet negative when the Planck Response, whatever one calls it, is included in the calculations.

      • I am quite aware of this. See my earlier response to another poster here.

      • “… is probably net positive long term, and almost certainly not strongly negative.”

        Based on what method of analysis? Linear trends on phase plane plots? These are absolutely worthless. No question about it. It isn’t being dogmatic. It is being knowledgeable.

        Have some other means been used? What, exactly?

        You are correct that I am not very knowledgeable about the “nature and source” of the climate data. But, nobody has ever attacked my analysis on that basis. I simply used the same data everyone else appeared to be using, saw it behaved the same way in the phase plane as they had observed, then used a more appropriate analysis tool to show what was really going on.

        So, yes, I am not standing on especially steady ground with the foot I have in the climate science realm. But, they are practically slamming their knees on their chins with the legs they have poked into mine.

  52. In general, Dr. Saumarez, you are on the right track. Climate science is not my field, but it is encroaching upon it, and blundering about flailing wildly. Hopefully, people in the field with eyes to see and minds to reason it out will, at least, start using proper analysis techniques for the problems at hand.

    The general layman can be taken in with facile arguments to the effect that, humankind is pushing on one end, so some payback has to be accumulating. But, this is not necessarily so in a feedback system. It is, in fact, the entire reason we create feedback systems, to reduce sensitivity to disturbances.

    The Earth and all of its climate systems and subsystems comprise a remarkably robust feedback system – they must, because otherwise, we would not be here. It would be an amazing happenstance if the fragile Earth proponents were right, and we just managed to stay balanced on the tip of a pin by luck. I do not believe in luck. If something bad can happen, it will happen, with regularity.

    Thank you for pushing these concepts further.

    • I salute you Bart….the climate folk do not want to understand what you are bringing to their party…