Energy budgets, climate system domains and internal variability

by Dan Hughes

It is not a boundary value problem.

Abstract

The total energy equation is applied to Earth’s entire atmosphere and sub-systems to investigate requirements that the energy content of Earth’s climate system remains constant. The results are somewhat more complex than usually appears in the literature. The analysis method clearly illustrates the potential for physical phenomena and processes both within and between sub-systems to affect Earth’s energy balance.

Justification for the validity of very long-range climate change modeling and calculations is based solely on the notion that the problem is a Boundary Value Problem (BVP); and that solely radiative energy transport and trace gases in the atmosphere critically dominate and set the BVP. The results of this analysis show that modelling and calculation of Earth’s energy budget is not a Boundary Value Problem.

Due to coupling between sub-systems, the wide ranges of time scales involved, and the presence of non-linear physical phenomena and processes, the notion that Earth’s climate system represents a spatial-temporal chaotic system can be heuristically argued. This matter, however, is not directly addressed in these notes.

Introduction

The objectives of these notes include a look into how natural internal variations within Earth’s climate system affect the radiative energy budget at the Top of the Atmosphere (ToA). The initial focus is on energy exchanges between sub-systems that make up Earth’s climate system. To this end, the local-instantaneous energy conservations equations, and averages of these, are examined in a little detail.

Unfortunately, no quantitative results are obtained or presented. The analysis is basically a general over-view of the energy-budget of the climate system with a focus on the significant potential for variations on a wide range of time and spatial scales. Maybe notes will provide food for thought and discussions.

Background

Earth’s climate system is made up of several sub-systems, including:

  1. humans
  2. other inhabitants
  3. atmosphere, with condensing and non-condensing gases, liquid and solid particles,
  4. water vapor in the atmosphere
  5. non-condensing gases in the atmosphere
  6. solid particulate aerosols in the atmosphere
  7. oceans and other large bodies of liquid water,
  8. land,
  9. trees, plants, and other flora, on land and in water bodies,
  10. snow and ice solid phases of water, on both land and liquid water,
  11. organic materials that experience chemical interactions with adjacent materials,
  12. inorganic materials that experience chemical interactions with adjacent materials, and
  13. maybe a couple of others.

The solid, liquid, and vapor phases of water are present in the atmosphere, and are critically important relative to the radiative energy budget of Earth’s climate system. In this regard, clouds maybe should be a separate sub-system. Other, generally solid materials labeled aerosols, are also present in the atmosphere and also are critically important to the radiative energy budget. Non-condensing gases that interact with radiative energy transport, such as methane, are also relatively important. These are included as separate sub-systems in the above list.

The physical phenomena and processes occurring within the sub-systems can be significantly influenced by the activities of humans through the effects of these activities within and at the boundaries of the sub-systems. Darkening of the surface of snow and ice fields, for example, by solid aerosols produced by human activities and then precipitate out of the atmosphere.

We are interested in the biological, chemical, mass, momentum, and energy states of the entire climate system, the physical phenomena and processes occurring within each sub-system and at the interfaces between sub-systems. Many aspects of the phenomena and processes of an individual sub-system will be coupled to other sub-systems. The physical couplings involve a multitude of the biological, chemical, mass, momentum, and energy aspects that are of interest. Some of the phenomena and processes of interest will be affected by the interactions of humans with the systems.

In these initial notes we are primarily interested in the energy aspects of the physical phenomena and processes that occur both within the sub-systems and at the boundaries between sub-systems. Mass and energy aspects are coupled in the sense that mass exchanges occurring between sub-systems represent also exchanges of energy.

The atmosphere sub-system, for example, interfaces with just about all the other domains listed above. And the other sub-systems likewise interface with the atmosphere. The flora sub-system, for example, has interfaces with both the atmosphere and land; the canopy of forests and crops cultivated by humans, and the roots within the land sub-system.

The spatial variation and interactions of the sub-systems are the focus of these initial notes. Relative to Earth’s climate system, however, temporal variations both within and between sub-systems are also important. In this respect, the sub-systems identified above might be additionally divided relative to the Northern and Southern hemispheres of the planet, as well as by the local time-of-day and yearly seasonal variation. The Northern and Southern hemispheres experience the yearly seasonal variations at different times during the year. Additionally, the daily variations at a fixed location are among the largest temporal variations experienced by Earth’s climate system. The effects of the temporal variations will not be considered in detail in these notes. It is noted, however, that the significant temporal variations within Earth’s climate system, over a wide range of time scales, are potentially equally important as the spatial variations that are considered here.

Let’s consider that the total volume occupied by Earth’s climate system can be divided into the portions occupied by the sub-systems. The outer boundary of the total volume is at the Top of the Atmosphere (ToA). The inner, or lower, boundary can vary with the sub-system under consideration, and the physical phenomena and processes of interest. The deep oceans, for example, might be divided into: (1) the upper regions within which there are significant variations that interact with the mass and energy balances of the planet, and (2) the very deepest regions that might be taken to represent a more-or-less passive sink of energy. The portions of the total volume filled with the solid phases of water might consider that all the solid-water mass and some part of the material on which it rests should be included in the sub-system volume: the effects of the state of the water on which sea-ice floats, for example. Other examples are available for other sub-systems.

Generally, the deep details of all the sub-systems will not be necessary for these initial investigations.

The primary objective of this initial investigation is to attempt to get a handle on how variations within and between the sub-systems affect Earth’s overall energy budget. While we might eventually look into the thermal, kinetic, and potential energy budgets within a sub-system, the primary focus is on energy exchanges between the sub-systems and the effects of these exchanges on the ToA energy budget. The equations that govern fluid motions and thermodynamic processes are the primary tools of the work. Other aspects will be introduced as necessary.

[ The link below will load a pdf copy of the sections that have the development in them. The document is heavy of equations, and this is an easy way to get a usable copy of those sections. After you finish that document return to this blog post to leave/read comments.

If you arrange to have the pdf material open at the same time as the blog post is open, that will make for a good way to have the material at hand while you write your comments and read the comments of others. I think right/control/option/command-click will open the file in a new window. Whatever your case, carry it out for your fav browser. ]

this is the link below

Discussion and Conclusions

The concept that radiative energy transport at the Top of the Atmosphere will eventually obtain balance needs deeper study ( especially the part about carbon dioxide being the sole aspect of importance ). The results obtained herein clearly show that modeling and calculation of future states of Earth’s climate system is not a Boundary Value Problem. It is impossible for the problem to be set as a BVP because the physical domain does not allow that. The out-going radiative energy at the ToA is determined by the states of the sub-systems within Earth’s climate system.

Actually, the concept an equilibrium radiative-energy transport state for Earth’s climate systems is a little fuzzy, and is simply postulated to be attainable at some future time. The future time at which this state will be present is not well defined. Additionally, the time period over which the response metric should be measured in order to verify the postulate is also not well defined. It’s all kind of fuzzy.

A response function and its associated metric that averages out all the physical phenomena and processes occurring within the physical domain is not a valid measure of the state of Earth’s climate systems. It is also not useful for estimating the outcomes, both good and bad, at future time.

Instead the energy transport and exchanges within the climate system should also enter into considerations. The results show that in order for a purely radiative balance to obtain, energy and mass exchanges at the interfaces between sub-systems must also reach balance.

The developments discussed do not begin to address the nitty-gritty details of the multitude of physical phenomena and processes that enter into the interface exchanges. Unfortunately, the mathematical models and numerical solution methods for these details are potential sources for a lack of attaining balances.

Our day-to-day experiences indicate that variations in almost all aspects of the climate system change at a very wide range of time scales. Radiative balance between in-coming and out-going energy is said to be instantaneous. However, the states of the climate’s sub-system, all of which affect radiative energy transport do not change at that rate. The potential for temporal variations in mass and energy budgets both in and between sub-systems is such that it is very likely that temporal variations are the expected state. So far as I am aware, there are no damping mechanisms that act to ensure states of exact balance in the natural processes occurring in Earth’s climate system.

It has been known for a very long time that the over-simplified, purely radiative energy balance could not be the complete picture. Otherwise the expenditure of billions of funding on models, methods, and software developments, not to mention 100s of millions on dedicated super-computing hardware, would not be necessary. Maybe these notes have made that awareness more explicit and concrete.

Climate Science should re-consider using extremely over-simplified summaries such as Laws of Physics, Exact Equality of Radiative Energy Transport, and Boundary Value Problem. These proclamations are not only over-simplified, they border on being purposeful mischaracterizations.

437 responses to “Energy budgets, climate system domains and internal variability

  1. That’s a lot of words to say that the climate system is a complex nonlinear dynamical system, and so is capable of causing its own climate change. But how does this in any way argue against the notion that adding CO2 (say, 2XCO2) changes the radiative rules and so most likely affects global temperatures? That sure sounds like a boundary value problem to me, because the presence of CO2 changes the climate system compared to if CO2 was not there. More CO2, by itself, surely causes a warming “tendency”, but how all of the various subsystems respond (feedbacks) is so uncertain we can’t really say how much warming (if any) there will be. This is how the paradigm is commonly phrased, and I don’t see any good reason to abandon the paradigm. It’s just that the feedbacks (which are not only upon temperature, but upon the presence of more CO2 itself) are probably more numerous and complex than we can conceive of right now.

    • Don Monfort

      Thank you Dr. Spencer. We should now move on to the next post.

      • well, I’m open to new ways of looking at things… it’s just very rare that I ever see a new paradigm. We are usually just rephrasing old ones.

      • It does go to the questions of what exactly is predictable.

        To understand radiative forcing a little better, I ran a radiative model on analysis atmospheres ( GFS ). Increased CO2 modifies TOA radiance for nearly all atmospheric profiles. So even if dynamics modify some locations ( at perhaps a compensating change in other locations ), it would seem likely that that any RF increase would still tend toward warming.

        On the other hand, those studying meteorology rightly focus on the dynamics, which are unpredictable. And most of “Climate Change” is due to unpredictable motion. Storms, precipitation, drought, temperature extremes, etc. are due to unpredictable dynamics.

        So,
        increase in global mean temperature: more predictable
        climate change ( precipitation, drought, storms, extremes ): not predictable.

      • verytallguy

        Yes Don, it’s fascinating, in a train wreck kind of way, why Judith promotes such embarrassing nonsense, isn’t it?

        It’s must be obvious to her just how poor it is, yet she chooses to continue to trash any remaining reputation she may have to push it.

        Most bizarre.

      • Dr. Spencer,
        Speaking of paradigms, have you heard of a type of machine learning called Reservoir Computing?
        A recent paper published in APS’s Physical Review Letters titled “Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach” (https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.120.024102)
        claims that their application of machine learning can extend predictability beyond current weather models. The key observation seems to be the ability to analyze huge data sets and reverse engineer the underlying equations that describe the emergent physics.
        This appears to be a pretty new application of ML although the basic algorithms of reservoir computing have been around for several years.
        Search terms: “Machine Learning Ability to Predict Chaos”

      • Roy Spencer
        There is ice on land both hemispheres. The ice does considerable cooling by reflecting and thawing. The ice volume in each cache of ice determines the ice flow rate. When ice volume and weight is high, ice flow rate exceeds ice thaw rate and ice extent increases. When ice volume and weight is low, ice flow rate is less than ice thaw rate and ice extent decreases. When ice extent decreases, temperature increases. When ice extent increases, temperature decreases. When ice shelf extent and sea ice extent are less, cooling from reflecting and thawing is lower and temperature is higher, water exposure area to the atmosphere is more, evaporation rate is more and snowfall rate and land ice accumulation rate is more. When ice shelf extent and sea ice extent is more, cooling from reflecting and thawing is more and temperature is lower, water exposure area to the atmosphere is less, evaporation rate is less and snowfall rate and land ice accumulation rate is less.

        These simple facts, that it snows more on land in cold places where ice is sequestered when oceans are warm and thawed and that it snows less on land in cold places where ice is sequestered when oceans are cold and frozen, are ignored by all consensus and lukewarm and most skeptic climate scientists and other people.

        These ice cycles are a major factor in bounding of temperature in narrow bounds. We have ice core data that supports this in both hemispheres. The modern ten thousand years have new really narrow bounded cycles in both hemispheres, There is ice core data for one major Northern Hemisphere ice age cycle and for the four bigger major and multiple lesser major ice cycles in the Southern Hemisphere. There is temperature records and ice accumulation records for all of this. There is more than enough data to study and understand this. There are internal ice cycles and there is no outside forcing that could have caused everything. Internal ice cycles resonated with external forcing cycles but did not resonate in proper phase with any single or combined external forcing cycle. It was always coldest when ice extent was greatest. It was always warmest when ice extent was least. This is cause and not result. Examine data and history to verify this. A coldest time in an ice age was when ice extent was the most. A warmest time was when ice extent was the least.

        Climate change is natural, normal, necessary and unstoppable!

        CO2 is 400 parts per million, that is four in ten thousand. One molecule in ten thousand is man-made, that is a measure of its influence on temperature. Not much. I would like to hear a sensible theory about how one more hot molecule heats up ten thousand.

        Proper study and understanding of past and present natural climate forcing and internal response is the only thing that can ever defeat climate alarmism.

        This is not a new paradigm, it was published by EWING and DONN in the 1950’s.

        You wrote: “I’m open to new ways of looking at things” You have written that, try it. You have not been open to discussing this with me.

      • Don Monfort

        page 1, paragraph 2, Sky Dragon Handbook:

        “CO2 is 400 parts per million, that is four in ten thousand. One molecule in ten thousand is man-made, that is a measure of its influence on temperature. Not much. I would like to hear a sensible theory about how one more hot molecule heats up ten thousand.”

        The first paragraph is something about CO2 being plant food and people have been drinking a lot of it for more than a century in Coca Cola, with no discernible harmful effects. Radiative physics be damned. Go with your gut.

      • Climate changes in natural cycles and man has not and does not cause them.

      • Don Monfort

        So, you are going with radiative physics be damned. Molecules be tiny little things. Plant food. Coca Cola. Ice is cold. Snow is white. blah blah blah

    • Roy W. Spencer | May 22, 2018 at 10:03 am

      That’s a lot of words to say that the climate system is a complex nonlinear dynamical system, and so is capable of causing its own climate change. But how does this in any way argue against the notion that adding CO2 (say, 2XCO2) changes the radiative rules and so most likely affects global temperatures?

      It argues against that notion by pointing out that there is no reason to assume that everything but “forcings” average out. This idea of “ceteris paribus” is the bane of modern climatology. The climate is a dynamic system which responds to changes in variables, often in unexpected ways.

      As one example among many, because of the existence of emergent climate phenomena such as clouds, a change in say CO2 may well be offset by a change in the timing of cloud emergence, and so most likely does NOT affect global temperatures in any meaningful manner.

      Best regards,

      w.

      • Willis, I don’t know what you mean by, “It argues against that notion by pointing out that there is no reason to assume that everything but “forcings” average out.” “Feedbacks” are how we describe other changes in the climate system which could, conceiveably, mean that the climate system doesn’t really care how much CO2 we put in the atmosphere. Your example of a change in clouds is just one of many examples of “feedback”, so again I see no reason to abandon the current forcing-feedback paradigm. Cloud feedback might entail changes in the timing of formation or dissipation, structure, drop size distribution, precipitation efficiency, areal cloverage, cloud water content, and who knows what else. It is ALL wrapped up into “cloud feedback”.

      • The higher one goes in the atmosphere, the more significant radiative terms become and the less significant dynamic transfers become.

        To accept this, consider that at the “top of the atmosphere”, the only significant energy exchange is radiation to and from space.

      • Roy W. Spencer | May 22, 2018 at 1:09 pm |

        Willis, I don’t know what you mean by, “It argues against that notion by pointing out that there is no reason to assume that everything but “forcings” average out.” “Feedbacks” are how we describe other changes in the climate system which could, conceivably, mean that the climate system doesn’t really care how much CO2 we put in the atmosphere.

        Thanks, Dr. Roy. I understand that “feedbacks” are as you say. However, I’m not talking about the simple climate feedbacks of the type you describe. I’m talking about a governor.

        The “cruise control” in your car is an example of a governor. It is not simple feedback such as you are talking about. Instead, the cruise control governor actively uses both positive and negative feedbacks to maintain the speed of the car at a fixed rate, regardless of varying loads on the vehicle. Describing automotive cruise control as a “feedback” is a totally incorrect paradigm. It is a governor, which is a very different beast.

        Similarly, thinking that the change in temperature comes down to a constant “lambda” time the change in forcing is a totally incorrect paradigm, one that leads to the also incorrect idea that this is a “boundary problem”. Climate is no more a “boundary problem” than would be the analysis of an automobile’s cruise control …

        Best regards,

        w.

      • Roy W. Spencer | May 22, 2018 at 1:09 pm |

        Willis, I don’t know what you mean by, “It argues against that notion by pointing out that there is no reason to assume that everything but “forcings” average out.”

        Sorry for my lack of clarity. By “everything but the forcings average out”, I mean the oft-repeated incorrect claim that

        ∆T = λ ∆F

        where ∆T is change in temperature, ∆F is change in forcing, and λ is a constant called “climate sensitivity”.

        For this to be true, everything but forcings must average out.

        w.

      • The climate is a dynamic system which responds to changes in variables, often in unexpected ways.

        The climate is a dynamic system which responds to changes the same way it changed in past climate cycles, in expected ways. It gets colder after it has been warmer. It gets warmer after it has been cooler. This is expected, based on past data, and it keeps happening, time and time again.

        Expectations based on flawed theory and models does happen in unexpected ways. Expecting history to repeat causes things to unfold in expected ways. This warm period will stay warm like the Roman and Medieval warm periods stayed warm, a few hundred years. Then it will get colder just like the Roman and Medieval warm periods ended with a colder period.

      • Describing automotive cruise control as a “feedback” is a totally incorrect paradigm. It is a governor, which is a very different beast.

        Automotive cruise control controls to a value. A governor increases efforts to catch up or reduces efforts when it is ahead, it does not control to a value. A good governor stays close.

        A climate cycle does not act like either. Climate cools past the set point and then warms past the set point. This is different. This cycle does not care if forcing changes, it is a thermostat, The AC is turned on when needed and turned off when not needed and temperature cycles up and down past the thermostat set point, which is the temperature that salt water freezes and thaws. More warming, the AC comes on sooner and runs longer. Less warming, the AC comes on later and runs shorter.

    • David Wojick

      Roy, to avoid confusion (which we already have) you need to be a lot clearer about just what you are calling the paradigm. If it is this — “adding CO2 (say, 2XCO2) changes the radiative rules and so most likely affects global temperatures” — then if the system is properly chaotic, that paradigm is clearly false, because no outcome is most likely.

      This is especially true if by most likely you mean most likely to increase, as doubling CO2 can just as well make the temperature go down. It is a normal feature of intrinsic unpredictability due to chaos that no probabilities can be assigned to different outcomes.

    • Mike Jonas

      Dr Roy Spencer – by my reading, the article (paper?) does not in any way argue against the notion that adding CO2 can affect global temperature. Your wording here is to my mind a bit strange, because you talk of the addition of CO2 changing the radiative rules, whereas I would have thought that the rules would remain unchanged: the addition of CO2 just changes the situation upon which the rules operate. But there are uses of the word “rules” which can allow a different interpretation, so I’ll let it pass.
      One of the major ideas in the article begins with the sentence “The concept that radiative energy transport at the Top of the Atmosphere will eventually obtain balance needs deeper study (especially the part about carbon dioxide being the sole aspect of importance)” and goes for two paragraphs.

      This is one of the places where – to my mind – the climate modellers go off the rails. How long is “eventually”? The shorter that “eventually” is, the greater the effect of CO2 upon the climate (as calculated by the models). The IPCC, very conveniently for themselves, do not stick their neck out and do not quantify “eventually”. It was conceivably possible from the early IPCC reports to deduce that they were operating on the basis that “eventually” was less than a century. The continual erosion of ECS (Equilibrium Climate Sensitivity) in the IPCC reports and in other sources since then suggests that “eventually” has been getting longer.

      The longer “eventually” is, the less is the effect of CO2 on the climate. At some point, it becomes almost entirely irrelevant, because its timescale enters the timescales of some of the natural factors that clearly have major long-term impacts on Earth’s climate (causing glacial periods, inter-glacials, etc), and CO2’s effect on climate is clearly dwarfed by them.

      But looking at Earth’s past history, and the fact that climate has never remained stable over any discernible period, indicates pretty clearly that “eventually” is not far from “never”. And as soon as you take note of the thermal mass of the oceans, it becomes obvious that “eventually” must indeed be a very long time. The model-based researchers themselves indicated that they realise this, because they referred to the “missing” heat hiding in the deep ocean. If the missing heat does indeed hide in the deep ocean, then it will be a very very long time indeed before their claimed CO2 effect can have any disernible impact on climate.

      For this and many other reasons, I endorse the idea put forward in the last sentence of the article that the proclamations by the climate science community are not only over-simplified, they border on being purposeful mischaracterizations.

      • Mike Jonas:

        You bring up a good point. Push the ECS out further and further in time. It become pointless for policy. We can’t do policy for the next 10 years. Push it out 200 years. In 200 years, we’ll get 3 C. Push it out to 300 years. The more you push it out, the more people say, who cares? The further you push it out, and assuming it means something, the less it means. I’d rather push a problem out 400 years than 50.

        So the ECS battle is fought an won and we narrow the range to 0.5 C. If the time frame is 150 years, who cares?

        You are right. Nobody knows how many years to ECS. It’s a floating anchor.

    • Tim Palmer has a mechanical analogue at about … – an anthropogenic wedge ’tilting the odds’ in a dynamic and complex system. Cloud, ice, dust, vegetation, biology – and the effects on the Earth’s energy budget – clustered in Hurst effects over ages. Quasi turbulent engines of the planet shift heat north and south to merge with planetary waves of a spinning planet in quasi standing waves in the spatio-temporal chaos of Earth’s flow field. Perturb the flow and the pattern of quasi standing waves shifts. To what is unknowable.

      • Robert I Ellison

        Thank you for the Tim Ball YouTube. It seems to me that his lecture is highly informative yet goes off the rails around minute 40 when he diverges from analysis of equations into what I call: the confusion of clouds. Clouds are described as a 100 meter problem and computer models are at the 100 kilometer scale. Further on, Dr. Ball describes clouds as potentially creating clear sky adjacent to accumulated stratus/thunderstorm clouds whereby heat energy will escape to space. Later on in the talk, when Dr. Ball describes the inexact computation idea to represent aspects of parameterization involved in computer climate models, it appears to me this methodology introduces yet more process errors. Not only initial conditions variations are at issue, but systemically adding less information by adding less precise information, all for the sake of saving computer energy costs.

        I like the idea of the human brain at exaflop computing with 20 watts of energy. I am awaiting patiently for my “Eureka” moment.

      • “Finally, Lorenz’s theory of the atmosphere (and ocean) as a chaotic system raises fundamental, but unanswered questions about how much the uncertainties in climate-change projections can be reduced. In 1969, Lorenz [30] wrote: ‘Perhaps we can visualize the day when all of the relevant physical principles will be perfectly known. It may then still not be possible to express these principles as mathematical equations which can be solved by digital computers. We may believe, for example, that the motion of the unsaturated portion of the atmosphere is governed by the Navier–Stokes equations, but to use these equations properly we should have to describe each turbulent eddy—a task far beyond the capacity of the largest computer. We must therefore express the pertinent statistical properties of turbulent eddies as functions of the larger-scale motions. We do not yet know how to do this, nor have we proven that the desired functions exist’. Thirty years later, this problem remains unsolved, and may possibly be unsolvable.” http://rsta.royalsocietypublishing.org/content/369/1956/4751 – I’m in moderation again but here’s the quote.

      • Tim Ball?

        It’s Tim Palmer.

      • The scale problem is why such powerful computing is needed. Julia Slingo and Tim Palmer – the guy in the video – have a wonderful Edward Lorenz quote on this.

        “Finally, Lorenz’s theory of the atmosphere (and ocean) as a chaotic system raises fundamental, but unanswered questions about how much the uncertainties in climate-change projections can be reduced. In 1969, Lorenz [30] wrote: ‘Perhaps we can visualize the day when all of the relevant physical principles will be perfectly known. It may then still not be possible to express these principles as mathematical equations which can be solved by digital computers. We may believe, for example, that the motion of the unsaturated portion of the atmosphere is governed by the Navier–Stokes equations, but to use these equations properly we should have to describe each turbulent eddy—a task far beyond the capacity of the largest computer. We must therefore express the pertinent statistical properties of turbulent eddies as functions of the larger-scale motions. We do not yet know how to do this, nor have we proven that the desired functions exist’. Thirty years later, this problem remains unsolved, and may possibly be unsolvable.”

        The physical properties are still more or less known. The planetary response – including cloud, ice, vegetation, biology… – less. But climate evolves out these Hurst effect, dynamical complexity data patterns. Regimes and shifts adding up to variability at very long time scales.

    • Steven Mosher

      Thanks Roy.

    • Well, I think people are a little confused on the the technical mathematical terminology here. Initial value problem is a time dependent PDE with the initial unknown functions specified. Boundary value problem refers to the boundary of the domain and having specified values there even though it can refer to specified values in the interior of the domain too. So, for the atmosphere, the velocity being zero at the surface (as is true for any viscous fluid) is a boundary value.

      When you change the properties of the fluid, that is technically neither of the above, its rather like changing the coefficients of the PDE.

      In any case, the “boundary value” problem statement is usually used by those who wish to draw an analogy to well posed problems like linear structural analysis where the boundary values (and forcings by the way) uniquely determine the solution and the solution is a stable function of these boundary values and forcings. This analogy is completely wrong. Nonlinear dynamical systems do not behave this way.

      Those who emphasize the initial value problem idea are usually suggesting that climate is unpredictable because of the ill-posedness of the initial value problem for any chaotic system. This is also wrong. However, climate may indeed be unpredictable as most mathematically sophisticated scientist will admit.

      There is one consequence of the ill posedness of the initial value problem however that is profound and that is that classical methods of numerical error control are impossible because the adjoint operator diverges. This means that in fact, we have little idea really what role numerical errors play in simulations of chaotic systems. That’s a serious problem for those who peddle these simulations as “accurate.”

      The truth is that for any nonlinear dynamical system there is an attractor and in the long term the solution will be found on this attractor. The problem is that we know nothing really about the attractor, its shape, its dimension, or how attractive it is. We do know through counterexamples, that the “climate of the attractor” can be totally wrong in any give numerical calculation because it can be a strong function of time step, gridding, numerical truncation errors, sub grid model choices, and indeed initial conditions. In short, there is no fundamental understanding of the “accuracy” of any given simulation, or indeed of any “ensemble” of simulations.

      The problem here is that its a huge (and long term) project to try to quantify things like sensitivities of the simulation to all the things I listed above. Especially the subgrid model parts are highly nonlinear and can have a huge effect on the outcome. This type of work is happening a little for example with regard to turbulence models and cloud and convection models, but its just a baby step.

      In short, these pseudo-mathematical sounding explanations (boundary value problem vs. initial value problem) are all misleading. This area of simulations of chaotic systems is an area of deep ignorance and even in vastly simpler engineering calculations, we really have a poor handle of the “accuracy” of our simulations.

      The other thing to bear in mind is that modeling papers generally suffer from a strong positive bias. It’s common to “select” the best simulations from a large set of “learning” runs that are less convincing. That’s classical selection bias of course. People should show all their runs so as to give an idea of the sensitivity of the result to parameter choices.

      • dpy6629, thank you for one of the clearest expositions of the lunacy of the current mainstream climate paradigm. The climate is orders of magnitude more complex than any system we have tried to model, yet many people, even folks like Dr. Roy who should know better, keep claiming that it is just “simple physics” or it’s an “initial value problem” or a “boundary value problem”. As you point out, it is none of the above.

        Also, thanks for highlighting the “pick the best of a hundred runs” method for climate model results. As you say, ALL of the runs should be shown to at least give us an idea of the uncertainty in the chosen run …

        Very well done,

        w.

      • dpy6629: Well, I think people are a little confused on the the technical mathematical terminology here.

        That was short and sweet. Well done.

      • dpy6629
        It’s common to “select” the best simulations from a large set of “learning” runs that are less convincing. That’s classical selection bias of course.
        You’ve nailed the reproducibility crisis in science!
        This happens in biology too (c.f. Amgen study).

      • David L. Hagen

        Climate hubris founded on profound ignorance
        “Climate science” tackles modeling weakly coupled non-linear chaotic systems with vastly different time constants and with poorly known initial conditions.

        DPY6629 eloquently summarizes our profound ignorance of climate:
        “classical methods of numerical error control are impossible because the adjoint operator diverges”
        “we have little idea really what role numerical errors play in simulations of chaotic systems”
        “we know nothing really about the attractor, its shape, its dimension, or how attractive it is“
        “simulations of chaotic systems is an area of deep ignorance and even in vastly simpler engineering calculations, we really have a poor handle of the “accuracy” of our simulations.”

        Dan Hughes notes:
        “Due to coupling between sub-systems, the wide ranges of time scales involved, and the presence of non-linear physical phenomena and processes” . . .12 sub-systems and “maybe a couple of others”
        That includes at least 12 further coupled nonlinear chaotic systems of:
        Sun’s Corona, chromosphere, Photosphere, Chromosphere, convection zone, radiative zone, Core, magnetosphere, solar wind, galactic cosmic rays, earth’s magnetosphere, and geosphere,

        rpielke dDetails the challenges of initial value conditions.

        Nigel Fox of NPL details how poor our satellite data needing at least 30 years to statistically distinguish anthropogenic climate trends. He proposes to improve uncertainty at least ten fold to give a 3 fold reduction in time to distinguish trends to about 10 years. https://bit.ly/2s51ttC

        Current “97% climate science consensus” on majority anthropogenic global warming is pure lysenkoism founded on hubris and compounded by ignorance.

      • Thanks everyone. This is an issue that took me a while to understand but it still surprises me that there is no clear correct explanation anywhere on the web or at RealClimate for example.

      • So, for the atmosphere, the velocity being zero at the surface (as is true for any viscous fluid) is a boundary value.

        Since the surface of the earth includes water that is in motion, the velocity of the atmosphere at much of the surface is not zero because the velocity of much of the surface is not zero.

    • The article was actually a very decent characterization of how intensely non-linear effects enter into the radiative balance and diminish the concept that the system can be reduced to grade-schoolish notions of ‘radiative balance’.
      But, considering the rampant prevalence of mathematical infantilism and false-mathematical-snobbery that rages within the community of climate sciences, it is no wonder the point was not understood.

    • the climate system is a complex nonlinear dynamical system

      More CO2, by itself, surely causes a warming “tendency”

      We call this cognitive dissonance in the mathematical community.

    • Essentially, my objection to Dr. Spencer’s snipe at the author is that he:
      1) agrees with the basic premise of the author.
      2) Agrees with the common mind numbing paradigm of climate being a linear radiative transfer problem.
      3) proceeds to affirm that #2 is wrong, and that the system is actually as in #1, hopelessly complicated.
      4) Concludes that the old paradigm, and the old jilted language, which gives the whole game away to the climate millenialists (a linear system can only either a-blow up or b-drive to zero) must stand.

    • Roy
      WADR, I think you missed the point – the article is saying something subtly different.
      Energy movement between subsystems (we’re mainly talking about the ocean) is not meant as an argument that CO2 doesn’t cause an atmosphere based warming. That’s another argument.
      No – it’s about attribution. What it is saying is – look at that recent warming so often automatically attributed to CO2. For many the very existence of this recent warming is enough to prove CO2 AGW. What if that warming were caused by this subsystem energy transfer over various time scales? Then recent warming per se ceases to be proof of CO2 warming. It becomes logically possible for CO2 to be having zero effect.

      Please note that in this logical question the whole issue of radiative backradiation, IR etc. is irrelevant. It is a different question, and to conflate them is to sow confusion and cloud the debate.

      The climate can warm and cool by itself. So warming per se is not sufficient proof that its CO2 wot dunnit.

  2. The climate system is an initial-boundary value problem. We discuss this is

    Pielke, R.A., 1998: Climate prediction as an initial value problem. Bull. Amer. Meteor. Soc., 79, 2743-2746. http://pielkeclimatesci.wordpress.com/files/2009/10/r-210.pdf

    Rial, J., R.A. Pielke Sr., M. Beniston, M. Claussen, J. Canadell, P. Cox, H. Held, N. de Noblet-Ducoudre, R. Prinn, J. Reynolds, and J.D. Salas, 2004: Nonlinearities, feedbacks and critical thresholds within the Earth’s climate system. Climatic Change, 65, 11-38. http://pielkeclimatesci.wordpress.com/files/2009/10/r-260.pdf

    Sveinsson, O.G.B., J.D. Salas, D.C. Boes, and R.A. Pielke Sr., 2003: Modeling of long-term variability of hydroclimatic processes. J. Hydrometeor., 4, 489-505. http://pielkeclimatesci.wordpress.com/files/2009/10/r-255.pdf

    See also

    Climate Science Myths And Misconceptions – Post #4 On Climate Prediction As An Boundary Value Problem. https://pielkeclimatesci.wordpress.com/2011/04/29/climate-science-myths-and-misconceptions-post-4-on-climate-prediction-as-an-boundary-value-problem/

    Further Comments Demonstrating that Climate Prediction Is An Initial Value Problem. https://pielkeclimatesci.wordpress.com/2006/12/22/further-comments-demonstrating-that-climate-prediction-is-an-initial-value-problem/

    The bottom line. IPCC and others mischaracterize the climate system when they claim it is a boundary value problem.

    As we wrote in

    Pielke Sr., R.A., R. Mahmood, and C. McAlpine, 2016: Land’s complex role in climate change. Physics Today, 69(11), 40.https://pielkeclimatesci.files.wordpress.com/2016/11/r-384.pdf

    “…. are CO2 levels and global averaged surface temperature sufficient to generate accurate and meaningful forecasts? Two leading hypotheses
    have emerged.

    The first argues that the accuracy of climate forecasts emerges only at
    time periods beyond a decade, when greenhouse gas emissions dominate
    over other human forcings, natural variability, and influences of initial
    value conditions. The hypothesis assumes that changes in climate are
    dominated by atmospheric emissions of greenhouse gases, of which CO2 is
    the most important. It represents the current stance of the Intergovernmental Panel on Climate Change and was adopted as the basis of the Paris agreement.

    A second hypothesis is that multidecadal forecasts incorporating detailed
    initial value conditions and regional variation set an upper bound on the accuracy of climate projections based primarily on greenhouse gas emissions. According to that view, successful models must account for all important human forcings—including land surface change and management—and accurately treat natural climate variations on multidecadal time scales. Those requirements significantly complicate the task of prediction.

    Testing the hypotheses must be accomplished by using “hindcast” simulations that attempt to reproduce past climate behavior over multidecadal time scales. The simulations should be assessed by their ability to predict not just globally averaged metrics but changes in atmospheric and ocean circulation patterns and other regional phenomena”

    I am pleased to see this subject being discussed on Climate Etc.

    Roger A. Pielke Sr..

    • yes, of course climate is also an initial value problem, which is a necessary inference from my comments about chaotic changes, which by definition are a sensitive dependence on initial conditions. I was merely objecting to saying climate change is NOT a boundary value problem, too.

      • maksimovich1

        IVP implies any initial condition eg De Cruz 2018.
        The dynamics of the atmosphere and the climate system is characterised by the property of sensitivity to initial states (Kalnay,2003). This feature implies that any small errors in the initial conditions will progressively amplify until the forecast becomes useless, or in other words cannot be distinguished from any random state taken from the climatology of the system. This property was already recognised in the early developments of weather forecasts (Thompson, 1957) and was associated with the nonlinear nature of deterministic dynamical systems by Lorenz (1963). These pioneering works sowed the seeds for the development of predictability theories for the atmosphere and climate, and for important progress in the context of dynamical systems, in particular the development of chaos theory (Eckmann and Ruelle, 1985). This sensitivity property affects not only the dynamics of errors in the initial conditions but also the errors that are present either in the model parametrizations, known as model errors, or in the boundary conditions (Nicolis, 2007; Nicolis et al., 2009).

        https://www.nonlin-processes-geophys-discuss.net/npg-2017-76/

        Chaos in often invoked on the grounds of temporal constraint (often correctly) and the role of chance is often overlooked and from time to time needs a more significant statement eg Guckenheimer on the role of large el nino events..

        We have demonstrated here that interactions of only a few degrees of freedom in the highly reduced JT model can produce unpredictability of strong El Niño events and a new type of ENSO complexity on a decadal timescale. This is a stronger statement than saying that that ENSO is chaotic. It places a timescale on the sensitive dependence on initial conditions. More specifically, our results show that epochs of relatively regular cycles of strong El Niño events like those observed during the past century might not continue. If they do cease, they may resume at any time.

        https://academic.oup.com/climatesystem/article/2/1/dzx004/4675218

      • The Lorenz attractor. Beauty in chaos. Each point in those lines is one state. The states are constrained by the strange attractor of a chaotic system. Still we cannot determine the sequence of states over time, which is the prediction of future states. Each state is a number in a lottery. We can know all the possible numbers but we can only win the lottery by chance.

    • The climate system is an initial-boundary value problem

      Not really. There is no boundary.
      Actually, it is a coupled radiative transfer/fluid transport problem.

      The author’s language gets a little awkward, but, I think, what he is arguing, is that this is not simply a radiative transfer problem.

  3. johninboston

    This is a blog re-post from the Alumni of Energy Incorporated (Intergalactic Energy Consultants) that Climate Etc. should make clear is a cross-post, not an original post.

    https://eialumni.blog/2018/05/13/a-test/

    You can also read Dan’s other piece entitled ‘Drag Queens amongst EI Management’ at https://eialumni.blog/2017/12/11/drag-queens-amongst-ei-management/ which, ironically, is actually more interesting.

    Either way, I would think a member of the Intergalactic Energy Consultants would understand the necessity of not wasting energy and get to the point.

  4. Yes, posted there as A Test to check that it works as a blog post. I’ll take it down.

  5. Curious George

    I don’t see a day and night, a summer or winter. These are huge variations of temperature, and to account for them we need thermal capacities of atmosphere and surface.

    • The Background section has this paragraph:

      The spatial variation and interactions of the sub-systems are the focus of these initial notes. Relative to Earth’s climate system, however, temporal variations both within and between sub-systems are also important. In this respect, the sub-systems identified above might be additionally divided relative to the Northern and Southern hemispheres of the planet, as well as by the local time-of-day and yearly seasonal variation. The Northern and Southern hemispheres experience the yearly seasonal variations at different times during the year. Additionally, the daily variations at a fixed location are among the largest temporal variations experienced by Earth’s climate system. The effects of the temporal variations will not be considered in detail in these notes. It is noted, however, that the significant temporal variations within Earth’s climate system, over a wide range of time scales, are potentially equally important as the spatial variations that are considered here.

  6. I see no allowance for exchanges between surface water and groundwater. The mass transport is likely significant. Groundwater mining is a widespread human activity. My thinking about the energy transport is as follows; Normal heat gradient from surface to groundwater is positive. This is due to the core of the earth being hot. Therefore, water entering the groundwater system would on average be heated. Water leaving the groundwater and mixing with surface water would on average heat the surface water. This is likely only a few degrees of temperature, however when we are talking about warming from CO2 we are only talking about a couple of degrees (if that much). Therefore, on average the fact that humans are and have been pumping water would lead to a heating of water in large bodies such as lakes and oceans.

  7. “It’s all kind of fuzzy”

    Well, sure it is, unless we get some basics right. Most notoriously our climate models, or should I say the GHE-theory itself, are completely wrong on cloud forcing. In its AR5 the IPCC claims (positive) cf was a mere 30W/m2. Of course the IPCC, as any apologist, will argue very low cf as it directly competes with GHGs in providing a “GHE” of around 150W/m2 (sic!). Actually it is considerably less than this, as surface emissivity is about 0.92 and thus surface emissions just 360W/m2 instead of 390W/m2 (or even 398!?).
    In reality cf is massive, well in the two digit region. The video below (taken at surface temperatures <10°C) demonstrates this pretty well. Opaque clouds do emit (or rather reflect) massive amounts of LWIR, which are obviously very close to what the surface itself emits. Now you only need to assume a realistic percentage for average cloud coverage, and you can estimate cf. For instance 30% * 360W/m2 = 108W/m2. That is largely enough to satisfy the "GHE" of 120W/m2.
    So the GHE is nothing else but the obtrusive denial of cf.

  8. I’ve never found the concept of cloud forcing to be particularly useful, because when comparing the radiative fluxes between cloudy and clear areas, the assumption is made that clouds did not affect the radiative fluxes in the clear areas, which is not true. Clear areas (subsidence) would not exist without the latent heat release in cloud systems causing ascent. Nevertheless, I suppose CF can be used as a metric to compare models to observations.

    • Roy, what do you make of the recent decrease in CERES albedo?

    • Sorry, but the question is not if there is some transcendent connection of radiative fluxes between cloudy and clear skies. The problem I am talking about has the sublety of a sledgehammer.
      I will not point to my own complex research, it should be enough to outline to contradiction within the GHE theory itself. While the IPCC states in its AR5 that clouds had 50W/m2 in negative forcing (albedo effect), 30W/m2 in positive forcing, and a net negative effect of 20W/m2, essentially the same “consensus” people draw this chart:

      There you have a negative forcing of 110W/m2 (23% + 9% of 342), which may be accurate. The question is just how to get from 110 to 30 for the opposite side of the coin, without breaking the rules of mathematics, or claiming an absurdly strong net cooling effect by clouds.
      The IPCC is quite creative in this. They cut the albedo effect by roughly 30W/m2, next they “forget” that clouds will emit into space (brings another 30W/m2), and finally they claim a net cooling effect of 20W/m2, which I am afraid does not exist either.

      This is so stupid, it would be fun, if was not that serious. This utter nonsense is what the whole GHE-theory and thus global warming is based on.

      • That diagram is propaganda, masquerading as science. Just one more example why I trust nothing the climate faithful say. They condemn themselves with their own words.

  9. Professor Lindzen:

    …climate is a remarkably complex system that cannot be reduced to a CO2 knob, something you turn up or down like your house thermostat, to control global temperature.

    • This raises the distinction between global mean temperature and climate.

      Could be that changes in RF change global mean temperature.

      But global mean temperature is not a term in the equations of motion.

      So CO2 is a knob, just not a significant one for the scare stories.

      • Unfortunately, the reason that the Left changed ‘Global Warming’ to ‘Climate Change’ was to continue taking advantage of public ignorance (for propaganda purposes) and not the result of a refinement of the science to emphasize the finding that, while CO2 may be a factor, it is not a significant enough factor to justify the catastrophist hyperbole of global warming alarmists.

  10. Bruce Moran

    Basically, the Heuristical model is based on uncertainty = possibilities = computing the values, are intrinsically limited by the scope of input data [error = bias + variance]

    I find it fascinating that the Volcano calculation for atmospheric impact (sulphur – hydrochloric acid), in and of itself, has a significant value whose determinants play a role in the overall climate variance – which I was eluding to in the book — but not in this manner

    ________________________________

  11. “Unfortunately, no quantitative results are obtained or presented.”

    We got some quantitative results – from the models:
    The energy balance over land and oceans: an assessment based on direct observations and CMIP5 climate models – Wild et al 2014

    The range of energy fluxes between models is 10-fold the estimated global energy accumulation (0.6 W/m2).

    Here are some examples of the range of energy fluxes that is spanned out by the models:
    (See Table 2: Simulated energy balance components averaged over land, oceans and the entire globe from 43 CMIP5/IPCC AR5 models at the TOA, atmosphere, and surface)

    Surface (All units: W/m2):

    Solar down: 18.6
    Solar up: 10.5
    Solar net: 17.2
    Thermal down: 18.5
    Thermal up: 11.8
    Thermal net: 15.7
    Net radiation: 17.2
    Latent heat: 13.9
    Sensible heat: 13.1
    (Averages are taken over the period 2000–2004)”
    —————-
    a) Taking into account that the current energy accumulation on earth is estimated from observation of ocean warming to be around 0.6 W/m2 (ref.: IPCC;AR5;WGI;page 181; 2.3.1 Global Mean Radiation Budget: Ref.: “considering a global heat storage of 0.6 W m–2»),

    b) Also taking into account that the models arrive at similar results for global energy imbalance despite a variation in energy fluxes (both up and down) between the models that seem to be 10 fold the observed global energy accumulation.

    I think it is fair to assume that the models would have been all over the place if not constrained by parametrization and heavy tuning to various observations.

    I also think it is pretty clear that a model result cannot be regarded as a valid argument for anything before the predictive capabilities of the model have been demonstrated for the relevant context.

  12. The essay inserts a lot of unknown functions in place of the natural language descriptors of a bunch of poorly known spatially and temporally averaged processes. It then shows that the assumption of strict equilibrium imposes constraints on the derivatives of the unknown functions. I don’t see how that gets us anywhere.

    Consider what happens if the spatially and temporally averaged Earth surface temperature increases 1C. Then the spatially and temporally averaged transfers of heat from surface to atmosphere by radiation, evapotranspiration, and advection/convection increase — but by how much? Those equations are not even one step forward.

  13. Even complex systems have a linear response to small perturbations with the possibility of tipping points thrown in, as seen with the Ice Ages. And these perturbations are small in the big picture. The forcing from doubling CO2 is about a 1% change in the total. While the Lewis assumption of a constant λ is too simple, a time-varying (increasing) one would capture the linear behavior along with its transient response.
    What we have had so far is a forcing change of about 2.5 W/m2, most of which has been responded to with surface warming through the λ term, and the rest going into a remaining imbalance of about 0.7 W/m2. This imbalance tells us that all the warming so far has not kept up with the rapidly changing forcing that has accelerated from 0.1 W/m2/decade 60 years ago to 0.3 W/m2/decade now. The decadal warming rate has matched this acceleration demonstrating a linear response and predicting a future trend as long as the forcing continues to grow with GHG levels. Tipping points would occur with ice sheet collapses that drive a much more nonuniform response as was seen several times after the last glacial maximum.

    • Don Monfort

      Not too bad, yimmy. Almost seems plausible. Is that really you? Anyway: “…the rest going into a remaining imbalance of about 0.7 W/m2.” Where is it?

      • Most of it is measured as the rate of change of ocean heat content. It can be viewed as the inertia of the system. The surface doesn’t respond immediately to forcing because of this inertia.

      • Imbalance is a made up thing. It is used to cover for anything that is happening that you don’t understand or any happening that you made up that does not exist. To make up an imbalance of about 0.7 W/m2 you would only need 0.7 error in a climate model that has never been right for anything else.

        Climate models have never forecast skillfully and this is where that number came from.

      • Don Monfort

        You just got scorched by a Sky Dragon, yimmy.

    • stevefitzpatrick

      JimD,
      Much better than your usual “OMG, CO2 is rising!!!” analysis. Progress.

    • There are no tipping points. There are larger and smaller cycles, but there are always cycles that reverse. The warm times promote more snowfall and it snows until it gets colder. The cold times promote less snowfall and it don’t snow more until it gets warmer. This is what ice core data clearly shows.

      • You get more rain when it is warmer, not snow.

      • Don Monfort

        I don’t think he is talking about at the equator, yimmy. You should ask him.

      • I’m talking about at 600-700 ppm. The earth becomes an iceless hothouse. CO2 does that and it can’t be ignored.

      • Don Monfort

        Can you give us a woodfortrees chart that shows the earth as an iceless hot house at whatever ppm, yimmy? We miss your woodfortrees stuff. Or, have they banned you?

      • afonzarelli

        You mean there will be no more winter? As in, our children won’t know what snow is? (ya don’t wanna let down fitz here, jim, i think yer backslidin’… ☺)

      • Peter Lang

        Jim D

        “I’m talking about at 600-700 ppm. The earth becomes an iceless hothouse. ”

        That’s rubbish. Earth cannot get anywhere near to a hothouse condition. That would require more than 10 C of warming from here. Average temperature for the past 540 Ma has been about 7C warmer than now [1]. And that is arguably the optimum temperature for life on Earth.

        Earth is currently experiencing about the severest coldhouse since complex life began [1]. Any warming to get us out of this is beneficial.

        I’d suggest you really do need to challenge your beliefs read something other than the left wing ideological clap rap you keep regurgitating.

        [1] Scotese 2016. Some Thoughts on Global Climate Change: The Transition for Icehouse to Hothouse Conditions. https://www.researchgate.net/publication/275277369_Some_Thoughts_on_Global_Climate_Change_The_Transition_for_Icehouse_to_Hothouse_Conditions

      • verytallguy

        So, whilst environmentalists are criticised for wanting to return us to the Stone Age, Peter Lang insouciantly demands a return to the Silurian!

        To put this in context, at the start of the Silurian, vascular plants were yet to appear and invertebrate animals were only just emerging on land. 

        There were multiple mass extinction events even during this relatively stable period, all characterised by sea level change.   These were however minor compared to some in the period Lang lionises for its “optimum temperature”.  For instance the Permian – Triassic event 250 million years ago, aka the “great dying”, wiped out 90%+ of all species and took tens of millions of years to recover from. 

        A near – instant in geological terms change in temperatures back to these “optimum” conditions may now be in progress.   

        Even if the “optimum for life” were true of a climate radically different to present, “optimum for current life” is self – evidently not true. 

        Examining the current rate of change of climate compared to timescales for ecosystem development and then evolution of complex organisms, shows just how misplaced this notion is. 

      • Peter Lang

        VTG,

        You have totally misrepresented what I said, as usual. Do try to understand. In simple language, what I am saying, is that 3C of warming is less that half way to optimum temperature for life on Earth, and indicative that such a temperature rise is no threat at all, – in fact beneficial.

        I made no mention of Silurian. Your strawman is a clear sign of intellectual dishonesty https://judithcurry.com/2013/04/20/10-signs-of-intellectual-honesty/ . It also is a clear indication you didn’t read or didn’t understand the reference I cited.

      • verytallguy

        what I am saying, is that 3C of warming is less that half way to optimum temperature for life on Earth, and indicative that such a temperature rise is no threat at all, – in fact beneficial.

        And what I am saying, Peter, is that is palpable nonsense, as exemplified by the most cursory examination of actual conditions during the period you reference, which does include the Silurian.

        intellectual dishonesty, indeed.

      • verytallguy

        It also is a clear indication you didn’t read or didn’t understand the reference I cited.

        That would be the reference to the unfinished paper that doesn’t discuss the optimum conditions for life you claim?

        Or did I miss something?

      • You get more rain when it is warmer, not snow.

        Rain AND SNOW!
        Ice Core Data clearly shows more snow in cold places where ice was sequestered. We know this is true because the ice is still there and is growing faster now than it was 200 years ago.

        As long a you ignore the best proxy data, ice core data, you will never understand natural climate cycles and the causes.

        Earth temperature behaves like the inside of an air conditioned house. When it gets warm, above the thermostat set point, the cooling is turned on and it stays on until the temperature goes below the thermostat set point. The thermostat set point is the freezing and thawing of ocean water in the Polar and near polar regions. In cold times, more ocean is frozen and it provides too little moisture for snowfall. In warm times, more ocean is thawed and it provides too much moisture for more snowfall than there is ice thawing. This causes cycles. e

        The ice cycles are natural, normal, necessary and unstoppable. It cannot get too hot or too cold because the snowfall is adjusted to keep temperature in bounds. The bounds have changed over the past fifty million years because the continents drifted, changing how much warm tropical water circulated in Polar Regions. The bounds have changed because the balance of water in the oceans vs ice sequestered on land has changed.

      • Jim D: I’m talking about at 600-700 ppm. The earth becomes an iceless hothouse.

        There is no reason to think that, based on scientific research results. That’s less than a doubling from now, and even with one of the relatively high estimates of sensitivity lots of ice will remain on mountain tops and in the arctic and antarctic regions.

      • You only have to look back 40-50 million years for those CO2 levels and the iceless hothouse conditions. Note also that 2/3 of the peak glacier ice was removed by a fairly modest forcing change from the Milankovitch effect. The other 1/3, that we still have now, is not that hard to remove too.

      • Don, you can Google alligators in Greenland to see what I mean. There seems to be much science that has just passed you by.

      • David L. Hagen

        Verytallguy Peter gave a quantitative argument that 3C warming is a benefit. Are your arguments so weak that you resort to the logical fallacy of ad hominem attacks?

      • verytallguy

        Peter gave a quantitative argument that 3C warming is a benefit.

        Really?

        What I read was

        (1) evidence that the earth used to be hotter
        (2) an assertion without evidence that hotter temperatures are “optimum”
        (3) an assertion without evidence that a rapid step change in temperature towards former, hotter climate would be beneficial.

        If you think that’s a quantitative argument, your definition is different to mine.

        I’d call it plucking figures out of the air.

      • verytallguy

        ad hominem attacks

        You’re going to have to provide a link to those David. Or was it just a gratuitous insult without evidence?

      • Peter Lang, if there is one lesson about life in paleoclimate, it is that rapid extinctions occur with fast climate changes and life does best in a stable climate. Ecosystems get disrupted when the climate changes, and little survives intact. What we have now is a fast climate change, almost a step change by historical standards, but the good news is that how much it changes is under our control.

      • Peter Lang

        Jim D says:

        Peter Lang, if there is one lesson about life in paleoclimate, it is that rapid extinctions occur with fast climate changes and life does best in a stable climate.

        These are unsupported assertions. The evidence is that:

        1. Life thrived in warmer climates than now and struggled in colder
        2. Warming during the past century has been beneficial
        3. Life thrived during rapid warmings in the past, that were much faster than the present rate of change.
        4. Climate is always changing, often rapidly
        5. The disruption causes competition: some species die out, new ones start up, and others thrive.
        6. Most of the period since complex life began was much warmer than now, and life thrived for most of that, and thrived best around the average – which was about 7C warmer than now.

        Ecosystems get disrupted when the climate changes, and little survives intact.

        What do you meant by disrupted? Agree if you mean large meteorite impact? Disagree if you mean rapid warming from severe glacial periods as Earth is currently experiencing and will continue to experience for tens of millions of years.

        What we have now is a fast climate change, almost a step change by historical standards,

        Not correct! Comparing apples and oranges.

      • verytallguy

        Peter,

        Pretty much that whole list is unsupported assertions.

        Several are demonstrably false, as we discovered earlier when considering the Silurian.

        Come back if you can cite any evidence to support them.

    • Tipping points would occur with ice sheet collapses that drive a much more nonuniform response as was seen several times after the last glacial maximum.

      Energy in is close to constant. Thawing rate of ice is determined by energy in and exposed ice extent and is close to constant for a given exposed extent. The nonuniform response was due the the releasing of trapped melted water in irregular surges as ice dams and other obstructions to releasing the trapped water gave way. It takes energy to thaw water, there is no nonuniform solar in to cause nonuniform responses.

  14. Is the assumption that knowing small features and short-time period processes are not important not an equivalent assumption to the “wisdom of the crowd”, the operation of the “unseen hand” and the “efficiency of scale”? That the small cancel each other and let the large show through?

    In my examples, we know that is false. Crowds give us moral crises, unseen hands give us market crashes and large businesses like GM give us the Saturn moneyhole. (Government is also an example of efficiency and scale being inappropriate in the same sentence.)

    Assumptions like these are common and commonly cause us grief.

    All of these assumptions, including those about the climate, depend on the existence of a stable, normal distribution of causes and interconnections that are expressed within a short time period. Otherwise we routinely get end-member expressions. An “average” is simply a mathematical construct of a variable system. It tells you nothing that’s “real”.

    Consider: A rollercoaster, on average, is a still car 20 feet above the platform. Back and forth, up and down, side to side all cancel out during the ride. That does not reflect a life lived on a rollercoaster.

    We exist within a non-linear, non-normally distributed world of forces and energies that operate over a wide range of time scales. It is shocking how predictable this world is – which isn’t much and only appears to us predictable because each generation believes the world began the day it came to think by itself. History, the past, are irrelevant when the “now” and those “in the now” are considered special.

    Fluctuation is the “norm”, not stability.

    • Fluctuation is the “norm”, not stability.

      Climate cycles that alternate cooler and warmer is the “norm” and a hockey stick average temperature is not the “norm”!

    • douglasproctor: An “average” is simply a mathematical construct of a variable system. It tells you nothing that’s “real”.

      What is your view of the center of mass of an aircraft and the center of lift of its wings? If not “real”, are they nevertheless “useful”? How about the atomic masses of the isotopes of carbon? Are they real? Even if an atom is real, there is no way of measuring the mass of just one of them, is there?

  15. Geoff Sherrington

    Two comments.
    1. Given the importance of the value of the TOA radiative imbalance, how certain are we that the present measurement system provides adequate accuracy?
    2. Closing the loops with energy balance requires that all forms of energy are included and that they are known with adequate accuracy. It is not hard to dream up examples of global energy that are not included in the models at all. For example, shock as from an earthquake can liquify parts of sediment piles like those in deltas of large rivers, releasing potential energy as mudslides happen. Does this potential energy enter into the model balance equations? Can the release of this energy, with seemingly random timing, trigger abrupt climate shifts? Then there are other effects like the seemingly unknown effects of synthetic chemical surfactants afloat on seas, lakes and oceans. What do they do for evaporation? For formation of wind driven droplet size? The point is that one should not be confident of a motley set of mass/energy terms summing to 100% when you do not include all possible effects, quantify them and include their inaccuracies in your estimates.
    (Analogy: In analytical chemistry, it is very hard to perform whole rock analysis to a final sum of 100.0% because of the occasional presence of unsuspected elements and because of the accumulation of errors as more and more elements are analysed and put into the sum, each with its own inaccuracies. To do this type of scheme on mass or energy balances for the globe must be rather much more difficult, yet to be useful, one has to shoot for accuracies similar to those in the lab example, where variables are ever so much better constrained. My personal view is that imagined prowess of climate modelling researchers likely exceeds their capability, as will be shown if or when proper error estimation is presented.)
    Geoff

    • My personal view is that imagined prowess of climate modelling researchers likely exceeds their capability, as will be shown if or when proper error estimation is presented.

      Their failed forecasts for decades is proper estimation of their error!

  16. Time Dependency

    In Eq. (1.21) I noted that the local-instantaneous radiative energy exchange was a function of the state of the climate and depends on the location of the interface, x, and time, t. In general, that dependency carries through to all the terms on the right-hand side of all the equations, especially for the terms in square brackets [ ], including the sensible and latent energy. The numerical values of these terms then vary throughout the day, and have variations during the yearly seasonal changes at different times in the Northern and Southern hemispheres. And of course vary considerably at different interface locations.

    I did not make the time dependency sufficiently explicit. The nomenclature, however, is already somewhat complex ( a belated rationalization ).

    I’ll not be around for almost all day and will get back to questions and comments tomorrow.

  17. Some of the language in the article seems to be a bit imprecise, and the concepts slightly jumbled, but, overall, I like the exercise of laying out the entire problem in a more descriptive, and, essentially, mathematical manner.

    The mathematical amateurism that dominates in climate science has led to the rampant use of language that is massively inaccurate, and leading-things like ECS, Climate Sensitivity, feedback, etc, etc… This language creates the paradigms that then become the accepted locus of discussion and research, and anything more realistic or mathematical is cordoned off and given over to dynamic science, not unlike how political correctness works in the political and cultural domains. And the artificiality of the language in these paradigms shape the outcome of the analysis.

    Considering the abject failure of modelling to date, the time for a new language is past due. And that language should be absolutely mathematical.

    I consider this study a step in that direction.

  18. The potential for temporal variations in mass and energy budgets both in and between sub-systems is such that it is very likely that temporal variations are the expected state.
    Yes.
    Climate change is the null hypothesis.
    As JC keeps on saying, its all about attribution.
    This insight makes attribution much more difficult, more interesting and less predictable.

  19. Earth climate is a massively complex, spatio/temporal chaotic, dynamical fluid and energy flow problem. The system boundary is the planet – where all energy in and out is electromagnetic. The planet equilibriates with incoming – or retained – energy at T^4 – at equilibrium entropy is maximized . But equilibrium is fleeting – even in incoming solar energy.

    Climate data is dynamical – it shows equivalently persistence, regimes, bifurcations, slowing down, shifts… Earth’s spatio/temporal quasi turbulent flow field has quasi standing waves on a spinning planet and energy budgets shift as massive energy cascades through powerful sub-systems and the earth responds with dynamic patterns in time and space of cloud, ice, dust, vegetation and biology.

    Models are temporal chaotic systems.


    “Generic behaviors for chaotic dynamical systems with dependent variables ξ(t) and η(t). (Left) Sensitive dependence. Small changes in initial or boundary conditions imply limited predictability with (Lyapunov) exponential growth in phase differences. (Right) Structural instability. Small changes in model formulation alter the long-time probability distribution function (PDF) (i.e., the attractor).”

    Trajectory divergence stems from initial differences.

    “Nevertheless, I advocate the hypothesis that plausible, chaotic AOS models have important levels of irreducible imprecision due to structural instability resulting from choices among a set of modeling options that cannot be clearly excluded. The level of irreducible imprecision will depend on the context, and this level is likely to be greater the more chaotic and multiply coupled the targeted flow regime is.” http://www.pnas.org/content/104/21/8709

  20. thomaskennedy2

    This is probably the best discussion on climate change that I have ever seen. Scientists and experts from a myriad of backgrounds arguing from different posts of view. My background is systems engineering so I see the climate as a system of systems. Others have different views – Boundary Value Problem etc. We all have “confirmation bias”!

  21. I think I have identified one problem relative to the Boundary Initial Value Problem issue.

    The sub-title of the post says: It is not a boundary value problem

    Just before Eq. (1.3) I state:

    The overall general problem is set as an Initial Value Boundary Value Problem (IVBVP). Sometimes Initial-Boundary Value Problem (IBVP)

    Following Eq. (1.16) where I am characterizing the Climate Science approach I write:

    Additionally, relative to mathematical modeling and calculation of Earth’s response function, Eq. (1.13), the problem is characterized as a Boundary Value Problem (BVP). However, the outgoing radiative energy transport at ToA, the left-hand side of Eq. (1.16), cannot be specified as a part of a BVP. That energy is a function of the state of all the sub-systems that make up Earth’s climate system, Eq. (1.7), and the interactions between the sub-systems. Not to mention that the concentration of carbon dioxide in the atmosphere is only a single one of the many entries represented (*) in Eq. (1.7) and that all of those entries affect radiative energy transport to lesser and greater degrees.

    Here I assumed that the fact that some Scientists in Climate Science characterize the problem as a Boundary Value Problem was well known. My interpretation of this characterization is as follows. Climate Science accepts the critically important problems associated with numerically calculated chaotic responses: Especially relative to long range “projections” of the response of climate to increasing quantities of CO2 in the atmosphere. In attempts to nullify arguments that such calculated responses are of very little value, the concept that Climate is a Boundary Value Problem has been put forward.

    Here is what Professor Steve Easterbrook has to say about the situation:

    “For understanding climate, we no longer need to worry about the initial values, we have to worry about the boundary values. These are the conditions that constraint the climate over the long term: the amount of energy received from the sun, the amount of energy radiated back into space from the earth, the amount of energy absorbed or emitted from oceans and land surfaces, and so on. If we get these boundary conditions right, we can simulate the earth’s climate for centuries, no matter what the initial conditions are. The weather itself is a chaotic system, but it operates within boundaries that keep the long term averages stable. Of course, a particularly weird choice of initial conditions will make the model behave strangely for a while, at the start of a simulation. But if the boundary conditions are right, eventually the simulation will settle down into a stable climate. (This effect is well known in chaos theory: the butterfly effect expresses the idea that the system is very sensitive to initial conditions, and attractors are what cause a chaotic system to exhibit a stable pattern over the long term)”

    Professor Easterbrook has also a TEDxUofT presentation on youtube
    TEDxUofT 2014: Computing the Climate
    . The audio is not so good. Maybe there’s a transcript somewhere.

    Note Professor Easterbrook’s characterization of the Climate Science Boundary Value Problem:

    These are the conditions that constraint the climate over the long term: (1) the amount of energy received from the sun, (2) the amount of energy radiated back into space from the earth, (3) the amount of energy absorbed or emitted from oceans and land surfaces, and (4) so on. [I have added numerical labels (n).]

    The first of these is indeed a boundary value. The second is not. The amount of energy radiated back into space can not ever be specified. That energy is determined by the state of the climate system, including all the sub-systems. In general, you can never specify the energy, and some other dependent variables, leaving a physical domain. They are called boundary values because they are constraints applied at the boundary. The solutions to the equations interior to the physical domain must satisfy the boundary conditions applied at the boundary. Applied boundary conditions are not determined by the state of the material interior to the physical domain. The third, like the second, can not be specified and is a result of the solutions of the model equations. Number 4, I don’t know about.

    The matter has been the subject of a post at Climate Etc. The heart of the climate dynamics debate. That post cites other related posts at Climate Etc.

    Additional to my assumption mentioned above, I also assumed that the words “Boundary Value Problem” are always used in the manner that they are used in formulation of mathematical problems. As noted by David Young,

    In any case, the “boundary value” problem statement is usually used by those who wish to draw an analogy to well posed problems like linear structural analysis where the boundary values (and forcings by the way) uniquely determine the solution and the solution is a stable function of these boundary values and forcings.

    I think David’s characterization is completely validated by Easterbrook’s mis-representations summarized above.

    In the sense of the concise meaning, and universal acceptance, of the phrase ‘Boundary Value Problem’ Climate is not.

    • Also a good summary Dan.

    • David Wojick

      Yes, it is clear from the present discussion that the concept of climate as a boundary value problem is confused, to say the least. It may be hopelessly confused.

      So is Easterbrook’s analysis. This in particular is very wrong: “But if the boundary conditions are right, eventually the simulation will settle down into a stable climate. (This effect is well known in chaos theory: the butterfly effect expresses the idea that the system is very sensitive to initial conditions, and attractors are what cause a chaotic system to exhibit a stable pattern over the long term).”

      Chaos is indeed a form of stability in that the system state will stay within the attractor. But the price of that stability is constant unpredictable irregular oscillation within the full range of states allowed by the attractor. So there is no stable pattern (hence no stable climate).

      Note that the long term statistics will also vary endlessly at all scales, so these endless oscillations never “average out” as they say. Plus attractors need not be stationary.

      We should stop studying the carbon cycle (a major USGCRP program) and start studying climate chaos.

    • Dan, following your lead I’ve numbered the “boundary conditions”:

      For understanding climate, we no longer need to worry about the initial values, we have to worry about the boundary values. These are the conditions that constraint the climate over the long term:

      1) the amount of energy received from the sun,

      2) the amount of energy radiated back into space from the earth,

      3) the amount of energy absorbed or emitted from oceans and land surfaces,

      4) and so on.

      If we get these boundary conditions right, we can simulate the earth’s climate for centuries, no matter what the initial conditions are.

      Let’s start with number 1, and we’ll need to go no further to see the foolishness of this approach.

      The amount of energy that the climate system receives from the sun is inter alia a function of the amount of clouds, the timing of clouds, the kind of clouds, the color of clouds, the location of clouds, the amount of ice, the timing of ice, the color of ice, the location of ice, the amount of vegetation, the timing of vegetation, the location of vegetation, the amount of wind over the ocean, the timing of wind over the ocean, the location of wind over the ocean, the amount of aerosols, the timing of aerosols, the color of aerosols, the location of aerosols, the type of aerosols … and this is a “boundary condition”???

      Anyone who thinks that they can get that so-called ‘boundary condition’ right for some unknown period into the future needs to go to the back of the class … we can’t predict all of those for next year, much less for the next century.

      w.

    • The way to check if it is a boundary value problem (namely forcing driven) is to plot the temperature response against the dominant forcing, as Lovejoy has done for the period since 1750.

      If these relate linearly to each other that means that the dominant temperature signal is due to the boundary change, or the CO2 forcing change in this case, and it is a boundary value problem. The “skeptical” view is that the fact that this looks so much like a boundary problem is just coincidence, and that there is no possibility that it is truly a boundary value problem for some reason.

      • Don Monfort

        I think there is a possibility that it is a boundary value problem, yimmy. I would even say it’s plausible. But you don’t jump from there to earth is going to be a iceless hothouse, yimmy. Use your head.

      • That has been the equilibrium climate at 600-700 ppm. Do we want that? That is the question you should be asking, because it is within our reach by burning enough fossil fuels. Anyway, you are a bit more advanced than the people who deny the possibility of the CO2 level pretty much determining the temperature, despite the paleo evidence, so good job on that part. There’s hope for you yet.

      • JimD, There are also previous periods in the Holocene where CO2 was increasing but the climate was cooling. So much for the “control knob” theory. We know that even when the total forcing is constant, changes in the distribution of that forcing can in fact lead to large changes, for example the ice ages. Bottom line, “boundary value problem” has a specific meaning and abusing that definition is a trick to get you to believe the “control knob” theory.

      • In the climate context, the boundary is the forcing. This applies whether it is orbital or solar or volcanic variations doing the forcing, or changing GHGs. These forcing effects are all measurable and seen in the record. CO2 happens to be quantifiably the largest of all these in recent centuries with a commensurate temperature change.

      • stevefitzpatrick

        Lovejoy is not someone you should quote if you want to avoid snickers from people who are not climate alarmed. Total net forcing, not CO2 forcing, is what matters.

      • CO2 is about 80-100% of the total net, and Lewis has told you that the other anthropogenic factors are proportional to it, much as Lovejoy has said too. Lovejoy’s graph tells you that even as the forcing rate of change accelerated, even tripled, in recent decades, the temperature kept up. Note how nonlinear the time is on that graph. It’s a very interesting graph to ponder.

      • stevefitzpatrick | May 24, 2018 at 9:10 pm |

        Total net forcing, not CO2 forcing, is what matters.

        Jim D | May 24, 2018 at 9:25 pm |

        CO2 is about 80-100% of the total net, and Lewis has told you that the other anthropogenic factors are proportional to it, much as Lovejoy has said too.

        Huh? Water vapor absorbs about 60% of the upwelling longwave radiation, leaving only 40% to be split up among all the rest …

        w.

      • Obviously water vapor is not part of the external forcing as it does not change except in response to the temperature. Check what Lewis lists as forcings and you won’t see H2O there.

      • The graph shows it determines a lot of it as also shown by paleoclimate. I just point to the evidence which may seem like haranguing because it is difficult to face the facts.

      • Don Monfort

        I’d get right on it, but that link won’t work for me. I have a brain.

      • It’s not something you would get from your regular media sources. Consider it for your edification.

      • Jim D | May 24, 2018 at 10:16 pm |

        Obviously water vapor is not part of the external forcing as it does not change except in response to the temperature.

        Obviously CO2 is not part of the external forcing as it does not change except in response to the biosphere … and the biosphere is definitely part of and affected by the climate system.

        In addition, your claim is simply not true. Evaporation varies linearly with wind speed, so water vapor is NOT a function of temperature alone.

        w.

      • Do you consider volcanoes as forcing? How about when they spew CO2? How about when we emit age-old fossil CO2 which wasn’t in the active biosphere?
        As for H2O, the global amount is not controlled by wind changes, only by temperature changes. Don’t confuse fluxes with amount. Different things.

      • Jim D | May 25, 2018 at 12:09 am |

        As for H2O, the global amount is not controlled by wind changes, only by temperature changes. Don’t confuse fluxes with amount. Different things.

        Thanks, Jim. I don’t confuse fluxes with amounts. Global wind speed changes total water vapor. You seem to believe that the atmosphere is totally saturated and can’t hold either more or less water vapor than it does today. See e.g. Global Variations in Oceanic Evaporation (1958–2005): The Role of the Changing Wind Speed.
        And while you’re at it, you might consider this as well: A cubic relationship between air‐sea CO2 exchange and wind speed.

        Best regards,

        w.

      • Evaporation is a flux not an amount. You said you understood the difference, but there is scant evidence. When you look at global water vapor which is about 4000 ppm, it is rising slowly with temperature and wind has nothing to do with it. Warmer air holds more water, and that’s all you need to explain it. This is why the tropics has more H2O than colder areas.

      • Don Monfort

        Willis must have missed this:”Do you consider volcanoes as forcing? How about when they spew CO2? How about when we emit age-old fossil CO2 which wasn’t in the active biosphere?”

        We are sure he knows the answers.

      • Maybe he’s a closet Salbyite.

      • Jim D | May 25, 2018 at 1:11 am |

        Evaporation is a flux not an amount. You said you understood the difference, but there is scant evidence. When you look at global water vapor which is about 4000 ppm, it is rising slowly with temperature and wind has nothing to do with it. Warmer air holds more water, and that’s all you need to explain it. This is why the tropics has more H2O than colder areas.

        Jim, you mistake me for a theoretician. I just looked at the RSS total precipitable water data, which covers 60°N/S over the ocean.

        Now, IF total water in the atmosphere were a function of temperature alone as you foolishly claim, the graph of average gridcell temperature versus total precipitable water would be a thin line. Wherever the ocean was that temperature, it would have the same amount of precipitable water above it. But that’s not the case at all. Here’s the graph:

        At an ocean temperature of 26°C, for example, precipitable water varies from 33 to 52 kg per square metre … so your claim about total water in the atmosphere being a function of temperature alone doesn’t even pass the laugh test.

        You don’t seem to understand. I’m not a theoretician, I’m a student of the real world who has spent most of my life outside, much of it on the ocean. I’m a man who believes in, analyzes, and discusses OBSERVATIONS. You seem to think you can blow your theories past me, but they go hard aground on a reef of solid facts …

        w.

      • At least now you are talking about precipitable water, not the evaporation red herring. Is it a fixed function of temperature? Not any more than RH is. What is fixed by temperature is the upper limit, and warming temperatures raise that lid, which raises the mean. Your plot demonstrates that the tropics can hold more water simply because it is warmer.

      • Don Monfort

        Yimmy always exaggerates, but your chart seems to indicate that temperature has got a lot to do with precipitable water. Do you have a chart that shows precipitable water and average global temperature over a 1000 year period? 100 years, or ten? We expect experienced sailors to have that kind of info at their fingertips. If you got it, we will pretend to not have noticed your failure to address:

        1. Do you consider volcanoes as forcing?
        2. How about when they spew CO2?
        3. How about when we emit age-old fossil CO2 which wasn’t in the active biosphere?

      • In short, if it was a thin line as Willis thinks it should be, we wouldn’t have weather. RH does vary. Warming raises the upper limit of PW which raises the mean. If RH is fixed, it is about 7% more PW per degree. This is well known physics already.

      • Don Monfort

        Or, just give us the numbers for the parts of the globe not included in your chart. Stop the cherry picking.

      • Don Monfort | May 25, 2018 at 2:48 am |

        Yimmy always exaggerates, but your chart seems to indicate that temperature has got a lot to do with precipitable water.

        I’m sorry, but you appear to have misunderstood what was claimed. Jim said that precipitable water was a function of temperature alone. The graph clearly demonstrates that it is not. Q. E. D.

        Do you have a chart that shows precipitable water and average global temperature over a 1000 year period? 100 years, or ten?

        That graph shows average precipitable water and global temperature over a 16 year period. Thanks for not asking.

        We expect experienced sailors to have that kind of info at their fingertips.

        Piss off with your insinuations. I already gave it to you.

        If you got it, we will pretend to not have noticed your failure to address:

        1. Do you consider volcanoes as forcing?
        2. How about when they spew CO2?
        3. How about when we emit age-old fossil CO2 which wasn’t in the active biosphere?

        I did not “fail” to address those, and I don’t care for your tone. I chose not to address them because I truly don’t care what gets called a “forcing” or not. This is because I don’t believe the central climate paradigm that change in temperature is a constant (“climate sensitivity”) times change in “forcing”, whatever you might call a forcing.

        Instead, I hold that emergent climate phenomena act as a thermostat to keep the temperature of the planet within a narrow range (e.g. ± 0.3°C over the entire 20th century), pretty much regardless of what the various “forcings” do or don’t do.

        Best regards,

        w.

      • PW is a function of temperature in a climate average. What you need to do is average out the weather and compare the mean PW over a cold region with that over a warm region, and you will see that relationship quite clearly if you haven’t already inferred it from your plot. It stands to reason that if the global temperature changes by a degree PW increases in response. It is a part of the feedback which is why you never see H2O listed as a forcing (see Spencer or Lindzen or Lewis or even Monckton(!), and argue with them about this).

      • WillisEschenbach: See e.g. Global Variations in Oceanic Evaporation (1958–2005): The Role of the Changing Wind Speed.
        And while you’re at it, you might consider this as well: A cubic relationship between air‐sea CO2 exchange and wind speed.

        Thank you for the links.

      • verytallguy

        Instead, I hold that emergent climate phenomena act as a thermostat to keep the temperature of the planet within a narrow range (e.g. ± 0.3°C over the entire 20th century), pretty much regardless of what the various “forcings” do or don’t do.

        Under this interesting paradigm, we can note that ice ages are impossible and turning off the sun doesn’t affect the earth’s temperature. Fascinating stuff.

      • Yes, if you plot CO2 forcing against temperature, it is fairly linear with no sign of tailing off. Melting ice only amplifies this sensitivity.

      • verytallguy | May 25, 2018 at 4:05 am |

        Instead, I hold that emergent climate phenomena act as a thermostat to keep the temperature of the planet within a narrow range (e.g. ± 0.3°C over the entire 20th century), pretty much regardless of what the various “forcings” do or don’t do.

        Under this interesting paradigm, we can note that ice ages are impossible and turning off the sun doesn’t affect the earth’s temperature. Fascinating stuff.

        I’m sorry, but that’s simply not true. For example, your thermometer-controlled furnace keeps your house temperature within a narrow range. So according to you, following your logic above, turning off the gas won’t affect the house’s temperature?? … that’s just dumb. The thermostat doesn’t PROVIDE the heat, it REGULATES the heat …

        Next, any thermostat can only handle a certain range of conditions. Even your body’s thermostat can be overwhelmed by immersion in cold water. But that doesn’t mean your body doesn’t have a thermostat …

        Similarly, the earth’s thermostat can be overwhelmed by a change in the orbital parameters that ends up covering the northern regions with ice and totally changes the albedo of the planet … but that doesn’t mean the earth doesn’t currently have a thermostat.

        Best regards,

        w.

      • Adding insulation to your house for a fixed heating rate by a furnace increases its temperature. There is no thermostat. It’s adding blankets.

      • verytallguy

        So according to you, following your logic above, turning off the gas won’t affect the house’s temperature?? … that’s just dumb.

        It sure is dumb, but it’s your logic, not mine. Your claimed thermostat is independent of the heat source, and you claim that changes in forcing (heat source) do not change the temperature. Your claim. Not mine.

        the earth’s thermostat can be overwhelmed by a change in the orbital parameters that ends up covering the northern regions with ice and totally changes the albedo of the planet … but that doesn’t mean the earth doesn’t currently have a thermostat.

        Curiouser and curiouser. The “thermostat” *does* work for CO2 forcing, but *not* for orbital forcing.

        Even though the former forcing is larger. Remarkable.

      • verytallguy:

        At some point a thermostat will lose. If it gets too cold. If the Earth is hit by a 250 meter asteroid. With orbital forcing and a GMST drop, we may see what can be called a stepped thermostat. Say during a glacial phase. Colder but holding. This is at a global scale. They may be also regional and more local scale thermostats. The fact the world exists as it does with all its life in various regions argues that such thermostats exist in nature.

        The control knob theory says we found the control knob. Another theory is that we found that nature has its own control knob that reacts to CO2 and other forcings or whatever is the acceptable word.

      • There is no thermostat. We are adding insulation. It gets warmer. We see it getting warmer at a transient rate of over 2 C per doubling, much as expected.

      • In addition, your claim is simply not true. Evaporation varies linearly with wind speed, so water vapor is NOT a function of temperature alone.

        Not true, water becomes disturbed and exposes more water to the air and the evaporation rate increases much more than linearly.

      • verytallguy

        Another theory is that we found that nature has its own control knob that reacts to CO2 and other forcings or whatever is the acceptable word.

        A theory falsified by observing the temperature change induced by the change in forcing due to volcanic eruptions.

      • verytallguy:

        Theory supported by return to pre-volcano conditions given time. There are fast and slow, large and small thermostats in nature.

        The fact that we have a lot of liquid water still after billions of years means that our water doesn’t beeline to a lifeless extreme.

      • verytallguy

        So…

        There is a “thermostat” that regulates the earth’s temperature.

        Except for volcanic forcing because that’s too short a timescale.

        Except for orbital cycles because something or other.

        Except for any forcing that exceeds a certain mysterious threshold.

        Is that right?

      • …and we even see the weak 11-year solar cycle in the temperature, so it isn’t doing much with that either. This thermostat does look very selective and also doesn’t fit the warming data.

      • Do you have a chart that shows precipitable water and average global temperature over a 1000 year period?

        Ice core data shows the ice accumulation results of precipitable water and temperature for 800 thousand years in Antarctic and 140 thousand years in Greenland.

      • Except for volcanic forcing because that’s too short a timescale.

        volcanic heat is prevented from doing much warming really quick when the hot stuff hits water.

      • It’s the cooling from volcanic aerosols that is seen, of course.

      • verytallguy

        volcanic heat is prevented from doing much warming really quick when the hot stuff hits water.</

      • verytallguy

        and again…

        volcanic heat is prevented from doing much warming really quick when the hot stuff hits water.

        Poe makes it difficult on t’internet but let’s give you the benefit of the doubt and assume this was humour.

      • Not funny, hot water vapor and steam convect up and radiates to space from up high, removing much of the heat released from the molten core quickly and effectively.

      • mysterious thresholds are mysterious because they only exist in models, not in real data.

      • verytallguy

        Not funny, hot water vapor and steam convect up and radiates to space from up high, removing much of the heat released from the molten core quickly and effectively.

        Oh my. I never realised. I’m so sorry. Here you go.

        http://bfy.tw/IJKF

      • Under this interesting paradigm, we can note that ice ages are impossible and turning off the sun doesn’t affect the earth’s temperature.

        The sun did not get turned off while taking data that relates to this. Ice ages are possible, we are still in an ice age, The thermostat turned snowfall on when there was much more warmer ocean available to provide moisture for snowfall. It was the same thermostat working with deeper warmer ocean, so it snowed more. Facts that matter include the balance between ice volume and extent and ocean volume and extent.

  22. Don Monfort

    We don’t precisely know the facts, yimmy. Stop pretending. However, it would be silly to argue that adding ACO2 forcing doesn’t matter. You got a house with a lot of energy going in and out various surfaces. We don’t need to know all the details. What would you expect adding more insulation in the attic and walls to do to the temperature inside the house?

    • Exactly. We’re adding insulation. What do you expect to happen? Some are not making that connection even as we see the temperature changing very linearly with the insulation increase.

      • Maybe on the Lewis threads they would agree with you because there the forcing was everything, but on this thread it is nothing. Depends what thread you ask it on.

      • Maybe they need to be debating each other, but neither thread has much of a debate on the denialist side. They just accept stuff.

      • Don Monfort

        Denialists have their own dogma, yimmy. They are chiral images of the left loon dogmatic alarmists.

        What percentage of denizens would you classify as denialists, yimmy?

        Anyway, you should appreciate the deniers. The rest of us regularly tar your little hide.

      • A denialist is a person that doesn’t agree with the IPCC consensus statement that extremely likely most and most likely all of the warming has been anthropogenic. I suspect over 90% of the denizens here are denialists by that definition. They would say unlikely most and definitely not all.

      • Does that make you a denialist against your wishes? A person denies or accepts the consensus which is sufficiently vague.

      • Don Monfort

        I don’t feel any obligation to fully agree with the IPCC, yimmy. Calling me a denialist is just stupid. It does not help your cause. You are just making a fool of yourself here. But it is amusing.

      • There is also a skeptic category that says they could believe it but there is not enough evidence yet, but that doesn’t describe many of the denizens who are more likely to agree with unlikely most and definitely not all.

      • Geoff Sherrington

        Jim D says “A denialist is a person that doesn’t agree with the IPCC consensus statement that extremely likely most and most likely all of the warming has been anthropogenic”

        Jim D, In order to make that statement, you have to be able to identify what man is doing to create alleged warming and then to quantify the effect with equations, physics, chemistry, etc.

        As a first simplification some say that the dominant effect of mankind is the creation of more atmospheric CO2. Unless you wish to reject that simplification, you then have to show the mathematical/physical relation between CO2 and warming. Some name this ‘sensitivity’. So, where is the equation that links CO2 to measured temperature?

        I have been waiting for it since about 1995. Despite its importance to you, nobody has produced the critical equation. There was a plausible Nobel Prize in science for the first author to provide the seminal paper. No, we still await the paper.

        How do you explain that er.. ‘difficulty’, Jim D? Can you not grasp that some whom you would label ‘denialists’ have justification for their stance? How do you explain this away, Jim D, and please do not insult me by suggesting that you must be right because the IPCC position is similar to yours. Geoff.

      • The sensitivity is known as an emergent property of the system. It is not an input like a single equation, but an output effect of a lot of physics. Arrhenius derived the sensitivity for a global atmosphere. To do that you just need to know the global atmospheric state and what CO2 does to it radiatively. All that is known.

      • We expect the thermostat set point to be exceeded and we expect that the AC will come on and provide as much cooling as necessary until the temperature drops below the set point. The added insulation may change the time but it will not change the set point or the upper or lower bounds of temperature.

      • Geoff Sherrington

        Jim D, | May 25, 2018 at 7:44 pm | “Arrhenius derived the sensitivity for a global atmosphere. To do that you just need to know the global atmospheric state and what CO2 does to it radiatively. All that is known.”

        Jim D,
        What, then, is the basic impediment to writing a climate sensitivity as a single figure (with uncertainty expressed), rather than a large range of figures per IPCC.
        Since ‘all that is known’.
        Are you saying that we do not know the global atmospheric state? Geoff.

      • Emergent properties of complex systems aren’t as simple as you seem to think they are. We know the current atmospheric and ocean state and the forcing produced by doubling CO2. You can only combine this information with a model of a complex system, or even by some hand calculations with simplifying assumptions about feedbacks as done by Arrhenius. We can also measure what we have seen so far, because that experiment is being done with half a doubling already, and that points to ~2 C per doubling as a transient rate, which implies a higher value for equilibrium.

      • David L. Hagen

        Jim D by his own definition is a science “denialist”, rejecting the foundational principles of science, by appealing to the authority of the IPCC. As a foundational principle of science, the Royal Society took the motto: “Nullius in verba” (“take no one’s word for it.”) https://royalsociety.org/about-us/history/

      • Their statement is suitably uncertain to be acceptable. Extremely likely most and most likely all. This a probability distribution based on the remaining levels of uncertainty within measurement. Science has many examples of probability distributions based on experiments. Rejection of those is a rejection of science.

      • The assessment reports are grey literature. Unreliable – go to the sources and you will find a diversity of opinion.

        Anastasios Tsonis, of the Atmospheric Sciences Group at University of Wisconsin, Milwaukee, and colleagues used a mathematical network approach to analyse abrupt climate change on decadal timescales. Ocean and atmospheric indices – in this case the El Niño Southern Oscillation, the Pacific Decadal Oscillation, the North Atlantic Oscillation and the North Pacific Oscillation – can be thought of as chaotic oscillators that capture the major modes of climate variability. Tsonis and colleagues calculated the ‘distance’ between the indices. It was found that they would synchronise at certain times and then shift into a new state.

        It is no coincidence that shifts in ocean and atmospheric indices occur at the same time as changes in the trajectory of global surface temperature. Our ‘interest is to understand – first the natural variability of climate – and then take it from there. So we were very excited when we realized a lot of changes in the past century from warmer to cooler and then back to warmer were all natural,’ Tsonis said.

        it makes for a more interesting, chaotic dynamic system in which the determination of of intrinsic and forced variability is correspondingly much more difficult.

        “Since “panta rhei” was pronounced by Heraclitus, hydrology and the objects it studies, such as rivers and lakes, have offered grounds to observe and understand change and flux. Change occurs on all time scales, from minute to geological, but our limited senses and life span, as well as the short time window of instrumental observations, restrict our perception to the most apparent daily to yearly variations. As a result, our typical modelling practices assume that natural changes are just a short-term “noise” superimposed on the daily and annual cycles in a scene that is static and invariant in the long run. According to this perception, only an exceptional and extraordinary forcing can produce a long-term change. The hydrologist H.E. Hurst, studying the long flow records of the Nile and other geophysical time series, was the first to observe a natural behaviour, named after him, related to multi-scale change, as well as its implications in engineering designs. Essentially, this behaviour manifests that long-term changes are much more frequent and intense than commonly perceived and, simultaneously, that the future states are much more uncertain and unpredictable on long time horizons than implied by standard approaches. Surprisingly, however, the implications of multi-scale change have not been assimilated in geophysical sciences. A change of perspective is thus needed, in which change and uncertainty are essential parts.”
        https://www.tandfonline.com/doi/pdf/10.1080/02626667.2013.804626

        The science denier is Jimmy – and that seems abundantly clear.

      • Their studies first detrend and then look at what’s left. Swanson writes “Removal of that hidden variability from the actual observed global mean surface temperature record delineates the externally forced climate signal, which is monotonic, accelerating warming during the 20th century.”
        What say you to that?

      • The dynamical studies do not detrend. Nor does the one Jimmy is quoting. And it is one that I have discussed a few times – even with Jimmy.

        http://www.pnas.org/content/106/38/16120

        What they do is remove intrinsic variability from the 22 year running mean surface temperature record using models.

        “Climate models provide a means to derive such a link, under the assumption that the current generation of climate models captures the essence of the signature of oceanic variability on the global mean temperature. To see that this is the case, we consider annual mean surface temperature fields extracted from 10 multicentury preindustrial control climate simulations, each derived from independently constructed models containing coupled ocean-atmosphere dynamics and advanced physical parameterizations.”

        It is btw an heroic assumption.

        e.g. https://www.nature.com/articles/srep09068

        The bottom line is rate of increase of some 0.1K/decade. Something that is clear in the surface record except to the most motivated of reasoning.


        Observed GISS 21-year running mean global mean surface temperature (heavy solid), along with that temperature cleaned of the internal signal, which is the mean over the eight active models of Fig. 1A (dashed). The cleaned global mean temperature warms monotonically, and closely resembles a quadratic fit to the observed 20th century global mean temperature (thin solid). The standard deviation of the cleaned temperature from the quadratic fit is 0.03 °C compared with 0.06 °C for the observed.”

        Nor do I expect natural 20th century warming to continue much into the 21st.

      • You skate on thin ice when you quote mainstream papers superficially and it is easy to find the mainstream views just beyond what you quote. I gave you a sentence that Swanson put into his abstract, for example. Tsonis and Swanson do not deny the dominant anthropogenic effect nor significant sensitivity and are also studying small wrinkles to that quantified by swings around a tenth of a degree in amplitude.

      • What is the rate of increase little Jimmy? How much is this ‘vigorous spectrum of interdecadal internal variability’?

        It is intellectually dishonest to rely on an unquantified statement without putting it into the context of the entire paper – or as illuminated in the wider literature.

      • That “vigorous” spectrum, as you can see, has an amplitude of a tenth of a degree for decadal averages, and it can be two tenths when you add in solar and volcanic perturbations. Vigorous enough for you perhaps, but not enough to count for much in multi-degree potential warming. Perspective is needed.

      • from the study you quoted.

        “This result is another link in a growing chain of evidence that internal climate variability played leading order role in the trajectory of 20th century global mean surface temperature.”

        Quite obviously this is another study you haven’t bothered reading and are incapable of putting in a rational context. Satellite data shows that recent warming was predominantly the result of cloud feedback from Pacific SST variability.

        It is only one study – science finds it impossible to distinguish quantitatively between intrinsic and forced variability. But Jimmy can. There is no intrinsic that matters – a very strange idea. You might think that something might give him pause – but no.

      • It is a clue when the energy provided by the anthropogenic forcing accounts for both the energy gain in the heat content and leaves some over for the surface warming response to offset part. The numbers leave no room for fanciful additions.

      • But the ‘wiggles’ in TOA power flux are so much fun and so meaningful. Denying data for narrative is the tell.

      • It’s like trying to get climate temperature trends over insufficient periods to filter ENSO variability and volcanoes. A hopeless endeavor and no one does that except you.

      • I don’t know what you are talking about Jimmy but that’s not uncommon.

        But the key to intrinsic climate variability is the tropical and subtropical Pacific – and people use monthly data to highlight those.

        No one Jimmy has read does it nothing but jimmy has read nothing but echo chamber blogs – so the survey is hardly convincing.

      • Lots of wiggles there. You must be in dreamland.

      • I should say a key. There are other modes of climate variability operating on different scales.

      • Take the average of all that and you don’t end up with much compared to typical values of sustained forcing.

      • The white noise conjecture again. It is wrong.

        “As a result, our typical modelling
        practices assume that natural changes are just a short-term “noise” superimposed on the daily and annual cycles in a scene that is static and invariant in the long run. According to this perception, only an exceptional and extraordinary forcing can produce a long-term change.”
        https://www.tandfonline.com/doi/pdf/10.1080/02626667.2013.804626

        The white noise conjecture is a climate meme – another one that is completely bonkers.
        For God’s sake read something that I link to.

      • Is this supposed to explain why all the energy for warming comes from GHGs, or does it imply a new source of energy that no one has heard of before that cancels the GHG energy exactly and acts instead? What are you saying here in the context of the energy budget?

      • Groan. What it says is that there are dynamic modes of variability that modulate TOA power flux over all time scales. Intrinsic climate variability is not random – not white noise. It doesn’t sum to zero. For God’s sake read something.

      • So why don’t we see them if they explain so much? Your measurements disprove them because there are no large missing terms. He is referring to a system that doesn’t have additional measurements for a budget, a level of ignorance that does not pertain here with OHC and forcing terms being well known.

  23. I’ve deleted a number of comments that are either off topic or personally insulting to other commenters. Once person has landed in moderation.

    Please keep your comments substantive, this is a very interesting and important topic. Keep any bickering or broader comments on “week in review’. Thank you for you cooperation.

  24. A denialist is someone who climate activists want to deligitimize. People with beliefs that Jim D has characterized as skeptics and lukewarmers are routinely called deniers.

    Barack Obama has been called a denier. James Hansen has been called a denier.

    The term obviously has nothing to do with what a person believes about climate science. It equally obviously has everything to do with what a person believes about climate policy.

    Jim D, you have to have really selective vision to tell us otherwise.

    xx

    • stevefitzpatrick

      tedpress,
      “It equally obviously has everything to do with what a person believes about climate policy.”

      Hear hear! James Hansen commits two unpardonable sins: supporting widespread nuclear power in place of fossil fuels, and describing the Paris accord as useless if the goal is significant reduction in CO2 emissions.

      It is not and has never been fundamentally a disagreement about “the science”. It is and has always been fundamentally a disagreement about suitable public policy, and the means the green/left has chosen to advance their desired public policies: never compromise, and shout “selfish”, “dishonest”, “science den!er”, “denier”, etc. The Paris accords are vigorously supported by the green/left not because they are going to lead to reduced fossil fuel use (they clearly won’t) but because they represent a step in the “right direction”, toward international control of national policies, which really could lead to their desired global restrictions on fossil fuels.

      So ultimately, the disagreement is mostly about personal values, priorities, goals, morals, perceived costs, and perceived benefits. If all technical questions and uncertainty were eliminated, there would still remain disagreement about suitable policy. There is little evidence of a willingness to compromise, and gridlock will continue for the foreseeable future.

  25. Ulric Lyons

    “So far as I am aware, there are no damping mechanisms that act to ensure states of exact balance in the natural processes occurring in Earth’s climate system.”

    I contend that multidecadal oceanic modes act as negative feedbacks to indirect solar forcing variability, and with considerable overshoot.

    https://www.linkedin.com/pulse/association-between-sunspot-cycles-amo-ulric-lyons

    • The essential – and by far largest negative – feedback is the Planck response. If there were no change in external or intrinsic conditions the Earth would be in energy equilibrium.

  26. I agree with the points that Dan Hauge is making that the Earth is either cooling or warming constantly and it does that locally, the equator does not how cold the Poles are and the poles do not know how warm the equator is. If the earth was a non rotating sphere without a moon and with no inclination to the Sun then there would be no flow of heat from the equator to the poles. I would put the analogy of heating something in a microwave where you have to keep stirring what you are heating to even out the temperature otherwise what you are heating will be very hot in places and very cold in other places. I do not see that saying the flow from the equator to the poles takes place over a longer time works if there is no flow to start with.

    • Ulric Lyons

      What about teleconnections? There is a linkage between El Nino events and warm pulses to the AMO with around an 8 month lag. E.g. August 1998, 2010, 2016:
      https://www.esrl.noaa.gov/psd/data/correlation/amon.us.data
      One solar day on Venus is nearly 117 Earth days long, but the atmosphere is stirred enough to keep the night side nearly as warm. Except that poleward heat transport is reduced with such high levels of climate forcing producing powerful polar vortexes, giving curiously colder polar regions. Saturn on the other hand has only a 10°C temperature difference between the mid latitudes and polar regions, due to powerful poleward heat transport mechanisms and weaker polar vortexes.
      https://phys.org/news/2012-10-curious-cold-layer-atmosphere-venus.html

      • Venus receives very little sunlight at the surface so it is not surprising that its night time temperature is the same as the daytime temperature and the lower density at the poles of Venus may explain the lower temperature there. Saturn spins on its axis fast and the polar diameter is 90 per cent of the equatorial diameter which might explain why the temperatures for these regions on Saturn are similar.

      • Ulric Lyons

        “Venus receives very little sunlight at the surface so it is not surprising that its night time temperature is the same as the daytime temperature..”

        The logic of that statement suggests that the daytime is as cold as the nighttime, rather than the nighttime being nearly as warm as the daytime.

    • If the earth was a non rotating sphere without a moon and with no inclination to the Sun then there would be no flow of heat from the equator to the poles.

      There would still be circulation of air and water. Cold polar air and water are heavy and sink. The air and water flows toward the warmer equator where the warmer air and water rise and flow toward the poles. This would be different without a rotating sphere but air and water would still flow. Warm water and air rises and cold water and air sinks. You can’t stop that.

  27. See the TWITTER in the right-hand corner under the Climate Etc. banner.

    Progress is finally underway . . . on identifying the real problem areas.

    Numerical solution methods matter . . . who would have thought?

    • Not surprising given how complex the system is. The problem here is that if you want to have a deterministic process you need to solve all the models simultaneously, but that’s vastly harder and more costly.

      • Looks to me like a pretty strong negative result. And it raises a troubling question about model tuning. How do you separate numerical errors (shown here to be large) from the errors in the sub grid models which other recent papers show are also large?

    • That Twitt/Tweet has gone away now. It referred to this Abstract and paper.

      Donahue, A. S., & Caldwell, P. M. (2018). Impact of physics parameterization ordering in a global atmosphere model. Journal of Advances in Modeling Earth Systems, 10, 481–499. https://doi.org/10.1002/2017MS001067

      Abstract
      Because weather and climate models must capture a wide variety of spatial and temporal scales, they rely heavily on parameterizations of subgrid-scale processes. The goal of this study is to demonstrate that the assumptions used to couple these parameterizations have an important effect on the climate of version 0 of the Energy Exascale Earth System Model (E3SM) General Circulation Model (GCM), a close relative of version 1 of the Community Earth System Model (CESM1). Like most GCMs, parameterizations in E3SM are sequentially split in the sense that parameterizations are called one after another with each subsequent process feeling the effect of the preceding processes. This coupling strategy is noncommutative in the sense that the order in which processes are called impacts the solution. By examining a suite of 24 simulations with deep convection, shallow convection, macrophysics/microphysics, and radiation parameterizations reordered, process order is shown to have a big impact on predicted climate. In particular, reordering of processes induces differences in net climate feedback that are as big as the intermodel spread in phase 5 of the Coupled Model Intercomparison Project. One reason why process ordering has such a large impact is that the effect of each process is influenced by the processes preceding it. Where output is written is therefore an important control on apparent model behavior. Application of k-means clustering demonstrates that the positioning of macro/microphysics and shallow convection plays a critical role on the model solution.

      The paper touches on several important aspects of numerical solution methods used in GCMs.

      • David Wojick

        Absolutely fabulous: “…reordering of processes induces differences in net climate feedback that are as big as the intermodel spread in phase 5 of the Coupled Model Intercomparison Project.”

        The intermodel spread in CMIP 5 is quite large, I think.

      • Dan Hughes: https://doi.org/10.1002/2017MS001067

        Thank you for the link.

        A very informative paper. It nourishes the suspicions some of us have about those global models.

      • Geoff Sherrington

        Dan Hughes,
        This quote is from your provided abstract “Like most GCMs, parameterizations in E3SM are sequentially split in the sense that parameterizations are called one after another with each subsequent process feeling the effect of the preceding processes”.

        Can we confirm from this that the Pat Frank analysis of compounding errors was valid; with the outcome that much of the large variety of GCM results is within huge error bounds, so correctly ignored? Geoff.

        https://wattsupwiththat.com/2016/11/22/the-needle-in-the-haystack-pat-franks-devastating-expose-of-climate-model-error/

      • Peter Lang

        I’d add my thanks for posting this abstract (I haven’t read the paper).

        My interest is in the information that is relevant for justifying policy. Global temperature change is irrelevant. What is relevant is the impacts of projected temperature change. Therefore, it is the impact of projected global warming, rather than in the science and the GCM projections of temperature change, that is relevant.

        The uncertainties in the impact functions used in the integrated assessment models are huge. Multiply the uncertainties in the GCM projections by the uncertainties in the impact functions, increases the uncertainties in the estimate of the impacts by perhaps an order of magnitude. So, the assumption that 2C of global warming is dangerous or net harmful is near baseless.

        Furthermore, it seems the impact function – for the one impact sector that is responsible for the projected impact of global warming being negative – may be grossly wrong. Instead of negative impact it may be positive or negligible. In which case global warming would be beneficial.

        It’s a pity few of the CE denizens seem to want to seriously consider this.

      • Geoff (above at May 27, 2018 at 7:23 am), As I understand the issues, they are not related. I’ll need to study the paper in more detail, but I think unbounded growth in the differences between the calculations is not mentioned. Nor is unbounded growth in any individual arrangement mentioned. The paper addresses a well-known problem area when numerical solution of a system of PDEs-plus-algebraic equations is the subject. Where in the time-stepping cycle and how the algebraic equations are evaluated can introduce numerical instability, in addition to the difference in solutions demonstrated in the paper. Results that are completely inconsistent with physical reality are also possible; energy flow against a driving potential, for example.

        Generally, the best arrangement is for all pieces-parts of the discrete approximations to be evaluated at the new-time level. This will be an extremely difficult goal for GCMs to attain. In the case of iterative numerical solutions of the non-linear equations, in contrast to a one-shot-through evaluation of the linear approximations, numerical stability of the iterative procedure is also required.

      • Steven Mosher

        “Can we confirm from this that the Pat Frank analysis of compounding errors was valid; with the outcome that much of the large variety of GCM results is within huge error bounds, so correctly ignored? Geoff.”

        err no because Pat is wrong. Always has been always will be.

      • Peter Lang, above at May 27, 2018 at 7:46 am:

        “Therefore, it is the impact of projected global warming, rather than in the science and the GCM projections of temperature change, that is relevant.”

        I agree. Probably every engineer who has been involved with public-policy decisions that are based in significant part on models, methods, and software, are appalled at the present state of the climate-change matter. Requirements that are codified in law for all other matters are simply ignored in Climate Science. It appears that public policy is attempting to be set based on un-proven technology. Not to mention the unprecedented global scale of the changes in public policy that are being suggested.

        Given this state of affairs in Climate Science, getting the very best understanding of the impacts before setting public policy should be the very first step. I think impacts will be local and thus all this focus on Global-Average Climate is mis-guided.

      • As a practical matter, its impossible to assess the numerical error in any GCM or for that matter much simpler time accurate chaotic simulations. The error can indeed grow but is counterbalanced by the fact that there is an attractor that tends to pull the solution back to the attractor.

        But exact quantification of numerical error is not needed. Recent papers such as the one Dan cited above on ordering the sub grid models show that its large, larger than the very small signal of perturbation to large energy flows modelers want to find. This means that GCM’s simply can’t reliably predict these small perturbations.

  28. Sensitivity to initial conditions emerges from the nonlinear math of climate models. Small differences diverge exponentially over the simulation time. Plausible differences occur because of the imprecision with which the system and it’s components are known. This includes ‘forcings’ with error bars and potentially a larger global uncertainty in estimates. Some are understood better than others.

    The result is multiple feasible solutions for any model. The outcome is uncertainty rather than certainly.

    http://rsta.royalsocietypublishing.org/content/369/1956/4751

    The difference between initial and boundary conditions is purely ideological. It is an immensely silly post hoc narrative denial of the significance of chaos in models.

    In the meantime climate evolves as a distinct system with abrupt shifts and regimes in space and time as a resonant response in the global flow field. Unpredictable, uncertain, unknown.

    As for little Jimmy’s new definition of denier as someone who doesn’t consider the throwaway statement from the IPCC that most warming was anthropogenic as definitive.

    Unlike El Niño and La Niña, which may occur every 3 to 7 years and last from 6 to 18 months, the PDO can remain in the same phase for 20 to 30 years. The shift in the PDO can have significant implications for global climate, affecting Pacific and Atlantic hurricane activity, droughts and flooding around the Pacific basin, the productivity of marine ecosystems, and global land temperature patterns. This multi-year Pacific Decadal Oscillation ‘cool’ trend can intensify La Niña or diminish El Niño impacts around the Pacific basin,” said Bill Patzert, an oceanographer and climatologist at NASA’s Jet Propulsion Laboratory, Pasadena, Calif. “The persistence of this large-scale pattern [in 2008] tells us there is much more than an isolated La Niña occurring in the Pacific Ocean.”

    Natural, large-scale climate patterns like the PDO and El Niño-La Niña are superimposed on global warming caused by increasing concentrations of greenhouse gases and landscape changes like deforestation. According to Josh Willis, JPL oceanographer and climate scientist, “These natural climate phenomena can sometimes hide global warming caused by human activities. Or they can have the opposite effect of accentuating it.” https://earthobservatory.nasa.gov/IOTD/view.php?id=8703

    Jimmy’s indubitable faith in his climate narratives – to the complete exclusion of intrinsic variability – are the real science denial.

      • Just the observations.
        http://woodfortrees.org/plot/gistemp/from:1950/mean:12/plot/esrl-co2/scale:0.01/offset:-3.2
        This is a transient rate of 2.3 C per doubling and fairly precisely. Let’s just go with what the observational record tells us because that is neutral ground. Models happen to support it, but that’s just a bonus point.

      • Just some hopelessly narrow memes with a great deal of intrinsic variability conveniently neglected due to agnotology. Relieve us of the memes repeated endlessly Jimmy. They are the essence of science denial in some sort tribal ideology.

        Here are 1000’s of solutions of a single model – that I have shown you before. Models do not agree internally – irreducible imprecision. Nor do they reproduce climate complexity at all well. The thick black line is mine.

        So why don’t you come back – again – with the claim that a model with initial differences of 10^-15 degrees K is representative of the range of plausible initial differences found with climate data?

      • You always want to divert from what the observations are telling you. Why not go with that instead if you don’t like the models?

      • I quite like models – I am a hydrodynamic modeler with decades of experience. Jimmy on the other hand is resolutely clueless. Models cannot realistically produce anything but pdf’s of a range of plausible outcomes. Most modelers have chosen to not go down that path and to gloss over irreducible imprecision in long term projections.

      • I like models too, but I see that the “skeptics” are having none of it, so let’s go with observations then, because they tell you all you need to know.

      • You have never run a model Jimmy – and your ‘observations’ are muddled interpretations of CO2 and temp that cannot possibly be definitive in the midst of multiple other mechanisms of energy budget variability. You are the science denier Jimmy.

      • You make it about people, not facts. I could show you the ocean heat content and you won’t trust what that tells you about a net gain for the last few decades either. And that net gain is easily accounted for with the net anthropogenic forcing change, being about half of its magnitude. The rest is balanced by the warming response, but you don’t go for budgets that include changing GHGs, so this is wasted on you. Again, just the observations, no models needed.

      • No Jimmy – you make it all about deniers who deny your silly little stories, inflexible agenda and scientifically naive, motivated reasoning. You are the science denier.

        This was unexpected because I expected ocean heat to look more like CERES energy imbalance. But it is blindingly obvious that there are other things happening than CO2.

        The large annual variability – 10’s of Watts/m2 – seems relatively important and neglected. Large and rapid ocean heat changes that must be accounted for in ideas of thermal inertia.

      • That’s the elliptical orbit effect. The earth is closer to the sun in January. Next question.

      • You might notice the orbital sketch if you actually read anything other than what confirms your biases. Next inanity.

      • OK, which part do you not understand then?

      • The part where you unthinkingly dismiss the implications.

      • The implication of a steady rise in OHC is that there is a positive imbalance and the warming is lagging the forcing. Circles.

      • Ocean heat and toa power flux monitoring came of age in this century. Argo does not show a steady rise – nor does CERES. Nor unless there is reference to toa power flux and its components can the source of ocean heat be determined. That there are always changes in energy dynamics is not something Jimmy can fit in his little gold fish bowl.

      • You dismiss this of course. You have to in order to make your ideas fit.

      • The early data relies on 10% coverage at most. I graphed Argo and it doesn’t look anything like the Levitus plots.

        And where there is more data – it suggests an alternative source of heat than CO2. 2.1 W/m2 SW change over this short timeframe is not AGW feedback.

      • You’re graphing the gradient and yes that is positive. I graphed the integrated energy change. Understand the difference?

      • You graphed nothing at all Jimmy.

        I graphed the gradient? Complete, irredeemable nonsense from Jimmy. I graphed temperature downloaded from the Argo Global Marine Atlas. The arbitrarily zeroed plot graphs changes in ocean heat V. cumulative energy imbalances at toa.

      • I showed the Levitus plot that you even referred to (maybe you forgot you did) which is the integrated energy that you tried to compare with your gradient of it. Not sure you understand the difference between W/m2 and J. It’s on the axes.

      • Loose lips again Jimmy? You copied the Levititus graph. You plotted nothing. My comment on this Levititus plot stands.

        I plotted the change in heat content – as temperature – and this claim that it is something other than what it is is a deluge of cr@p.

        The cumulative energy imbalance is Joules – a power flux maintained over a period. It is a totally different parameter. And I was interested in seeing if they co-varied.

        Perhaps he is confusing this with the Wong et al plot – that shows power flux into oceans and at TOA.

      • I’m sorry that you misunderstood. You also said your plot looked nothing like Levitus. No surprise, since one is the gradient of the other. The difference in units was the clue. Maybe you were referring to a plot other than the one you posted with that comment. Who knows?

      • You are clearly unable to distinguish TOA power flux from ocean heat. Sorry to confuse you by plotting both on the same graph.

      • Especially the part where you tried to compare it with Levitus. I should have looked at the graph and just ignored your words. My mistake.

      • Ler’sa just look at ocean temp if it makes it easier for you Jimmy.

        Argo data plotted from the Scipps Institute Argo global marine atlas.

      • Calculate how many Joules it gained and how much the CO2 forcing provided in the same timeframe. Spoiler alert. The latter exceeds the former.

      • Joules is just heat capacity times temperature. The rest is just impossible nonsense.

      • This inability to calculate that seems to be at the root of your problems. You can also do it in W/m2 if that is easier for you.

      • Heat capacity? Temperature?

      • The heat capacity of water is 4200 J/kg/K.

      • I am an engineer and environmental scientist. I have done the calculation in a number of contexts. I could convert it to Joules in a very simple calculation. It makes no difference to heat content and what is the point? Jimmy weirdness.

      • Enough is enough it seems – and as Jimmy is incapable of not getting the last word in an increasingly silly thread – it will have to be me giving up on a lost and addled cause again.

      • I thought you posted that graph because you wanted to look at all the warming it implies relative to CO2 forcing. Maybe not. Just another pretty picture to look at as long as we don’t mention budgets. OK, then. What next?

      • I wanted to see whether measured cumulative radiative imbalances co-varied with ocean heat. As I have said more than once. Unsurprisingly it does with CERES data allowing such detailed comparisons. One needs then to understand how and why the system has such large changes. For that a lot more data is required. As I have said.

        Your memes work only if you assume no intrinsic variability. That is quite obviously not the case.

      • CERES is noisy at the annual scale but it includes the CO2 forcing in the longwave part. In this period the anomaly is 1.5-2 W/m2 relative to pre-industrial and some of that is offset by the extra warming from the surface so you end up only looking at a net effect of the extra CO2 and the warming that has already taken place and noise from interannual variability.

      • The implications of 20W/m2 annual ‘noise’ is with rapid ocean warming and cooling not quite gelling with ideas of lags due to thermal inertia. But the budget is noisy – due to changes in ocean and atmospheric circulation – all the way down to millennial Hurst effects.

      • The net positive imbalance over that period is half the forcing due to CO2 alone. You want to discount the largest forcing contributor to the warming for some reason that you have not explained yet. The CO2 contribution is 2 W/m2 now and has been increasing at 0.3 W/m2 per decade. This is not a negligible contribution to the OHC change. It easily exceeds it, and you still search for another source.

      • There are other sources of large climate variability but until he can see past the tribal blinkers and not everything is reduced to his rabid reiteration of climate memes – there is not a lot that can be done for Jimmy.

      • It’s just the numbers. CO2 has provided more than enough forcing for all the increased ocean heat content that has been seen so far, just like emissions have provided more than enough CO2 for the observed increase in atmospheric concentration.

      • afonzarelli

        Too bad jimmy wasn’t there to rebut dr. curry on tucker. (tis a pity)…

      • Observation of surface temp is – btw – essential to this modeling methodology. But observation of CO2 and surface temperature is hopelessly inadequate for analyzing intrinsic variability. Why not go with the hopelessly inadequate like Jimmy? Why would I is the real question.

    • Robert I Ellison

      I have re-read the Slingo/Palmer article you referenced and wonder whose voice am I hearing and when. Not that I am all that picky, yet, when I read:

      “…physical parametrizations. These were based on a range of observational estimates and expert judgement,”

      Are experts better at guessing what sub-grid behavior is than some layman? As I suspect the answer is: no, and the experts seem to agree they then delve into stochastic approaches with relish.

      I agree that Edward Lorenz is giant having challenged Newton’s Force=Mass times Acceleration being applied to climate change outcomes.

      Where climatology seems stuck right now: “the major source of uncertainty then comes from the formulation of the models ([21]; figure 9), related particularly to the sensitivity of the climate system to greenhouse gas forcing.” is, trying to keep CO2 front and center; ie, the control knob when the likely scenario is; not much.

  29. David Wojick

    Energy balance not:

    Regarding this first and central sentence: “The total energy equation is applied to Earth’s entire atmosphere and sub-systems to investigate requirements that the energy content of Earth’s climate system remains constant.”

    It is virtually impossible that the energy content of the Earth’s climate system remain constant. Nothing in nature is constant and many of the components of the climate system are far from constant when it comes to energy. Variation is everywhere we look. It is virtually impossible that the energy combination of all these varying components is constant.

    If the models or other science are trying to impose the requirement of constant energy content on the climate system, then it is no wonder they getting it wrong. False assumptions typically lead to false conclusions.

    • Yes, that is poorly phrased. There are disturbances in the forcing, and those have consequences. The largest of these is the influx of GHGs to the atmosphere with equally large consequences. Nothing is constant at this time. Maybe it used to be, but not now for sure.

      • Disturbances in the force aye?

        Unless change in toa power flux and it’s source is understood – it is all bottom up fabrication of parameters and an assumption that this is all that matters. That there is no intrinsic variability. It is all so very obviously a wrong climate meme that derives from the very early characterization of climate as as a static system that only responds to forcing. It is a meme they have been trying to reanimate ever since.

      • It does respond to forcing. You see it with volcanoes and the 11-year solar cycle, and those are relatively small ones in the long term, and you always act as though this is all new to you when I tell you.

      • I’m certain that I have correctly summarized the Climate Science view of a steady-state climate system at some, undefined, future time. MY summary starts right after Equation (1.9), extends through Equation (1.16) and a couple of paragraphs following the latter equation. Let me know if you find fault with my interpretation of the concept. Explicit citation to equations and associated discussion will be appreciated.

        The Google will lead you to a very large number of places in which the concept is stated and discussed.

        Actually, let me know if you find fault with any of the concepts and equations in the post.

      • It is not true that the energy content of the earth system remains constant or is required to do so. The energy content is rising, mostly as OHC, in response to a rising forcing. This is the essence of climate change. The energy content is a major parameter in defining the state of the climate.

      • How and why the global energy budget changes is a matter of data and theory. We need hundreds of years of data that simply isn’t there. Needless to say – Jimmy doesn’t get it.

        https://www.facebook.com/Australian.Iriai

        The reality is far more interesting than Jimmy’s stories.

      • The CO2 forcing since pre-industrial times integrates to 3 GJ/m2. That measurably changes the energy content and the surface temperature reacts via the Planck response, but still lags, which is why there is an imbalance.

      • CO2 forcing causes temperature increases that result in emission increases in IR proportional to T^4. Your 3GJ has no physical meaning – it is not additional energy in the system. And unless you understand the dynamic large scale changes in ocean heat on an annual basis – your lag is meaningless as well. I have seen the math on heat diffusion – believing it is another story.

      • I don’t think it is worth trying to explain further what 3 GJ/m2 of integrated forcing means. It is self-explanatory.

      • It’s a number that discounts the planetary response – as the IPCC said. Means even less than your usual but unrelenting intellectual foibles.

      • Yes, forcing doesn’t include the response, by definition. It exceeds the response and the remainder is the imbalance. Not sure you understood that part.

      • The Planck response btw is the T^4 response. The evidence is for large changes in toa power flux caused by changes in ocean and atmospheric circulation. Wiggles that sum to zero according to Jimmy. Very likely untrue.

        e.g. http://climatescience.oxfordre.com/view/10.1093/acrefore/9780190228620.001.0001/acrefore-9780190228620-e-85

      • The Planck response has only opposed part of the forcing which is why the imbalance is still positive. All the warming so far is lagging the forcing change that is dominated by GHG changes. This is going in circles now.

      • The Planck response is negative and proportional to T^4. By far the largest ‘feedback’. And the so-called lag is said to be due to ocean thermal inertia. A dubious proposition sans any observable justification. Do try to get the basic concepts correct.

      • Planck Response aka Global Warming, and yes it is a large response. You got that right. It’s what this is about.

      • Planck response? AKA large negative feedback to AGW and intrinsic variability alike. There are precise descriptions and Jimmy’s rather flexible usages that seem more snide commentary.

      • You don’t get a Planck Response without surface warming. They are one and the same. I would distinguish a response from a feedback, because the response gets amplified by the feedback. The response is the output after the feedback loop has acted on the input forcing change. Separate things.

      • The large negative Planck response feedback is to warming or cooling. The response is via feedbacks – and the total is less than the original forcing. Hence climate stability in principle. Does Jimmy’s comment mean anything? Something more than imprecise trivia? I often think it is just verbiage designed to obfuscate rather than illuminate.

      • That was gibberish and I won’t even try to correct it.

      • The Planck response to date is -3.2W/m2. Offsetting water vapour and lapse rate feedbacks, all possible cloud feedbacks and much of the CO2 forcing.

        It is a simple enough idea.

      • It is also simple that it is due to warming (T^4 and all that), and is essentially the warming response itself. This is the part you somehow refuse to connect despite saying T*4 several times in describing it. Anyway.

      • Jimmy has no useful response to anything significant. The Planck response is in a nonlinear relation between temperature and atmospheric IR emissions. Higher temperature gives proportionately greater (T^4) emissions. It is the largest feedback – part of the response of the planet to changes in energy content. The response is what determines sensitivity.

        It is such a minor part of the whole – but arguing imprecise trivialities with Jimmy seems to be the game. Precise – and broad – science seems to matter less than debating points.

      • You wouldn’t have global warming without a Planck response, right? I equate them. One and the same process.

      • It is just one of the feedbacks. I can’t discern your purpose or intent in any of this – more erroneous and imprecise quibbling about very minor points

      • It’s all of the warming response amplified by the feedbacks. Input is forcing, output is response, between are the feedbacks that do the amplification.
        When you apply heat to a pot of water, the warming of the water is a response, not a feedback.

      • Trivial misdirection – it is a warming feedback. The planet warms or cools a little with incremental additions of greenhouse gases and the planet responds with various feedbacks. Forcing is a parameter defined as changes in radiative properties without feedbacks. It is a theoretical construct with little practical use other than giving an order of magnitude estimate of climate change potential. And there is no ‘amplification’ – net feedbacks are negative.

      • There is a no-feedback response, so you can have a response without feedbacks. This is what happens if earth’s surface just warms like a black body. The temperature changes in direct response to the forcing change via the Planck function.

      • Do you think he believes this?

      • Have you not heard of a no-feedback response?

      • I doubt that anyone has in any serioua context

      • It is a response with no positive or negative feedback, like when you heat water in a pot.

      • It is all circles with Jimmy. Denigration, a smug assumption that disagreement is ignorance and resolute imperviousness to science and data not in accordance with the with the same simple memes repeated endlessly and with overweening confidence.

        Where there should be an exploration of immense complexity and uncertainty in the climate system – we have Jimmy.

      • You don’t do budgets. Since 1980 the OHC has risen 25*10^22 J during which time CO2 forcing alone has provided about 40*10^22 J, and yet you look for other sources. Remarkable. This is like those people who don’t believe emissions account for the CO2 increase when the actual emissions are double the increase. It is both very clear where the CO2 is coming from and where the heat is coming from.

      • I’d have to reject the data – and I was on the fence for a long time. CERES is confirming mechanisms acting within the system.

        “In summary, although there is independent evidence for decadal changes in TOA radiative fluxes over the last two decades, the evidence is equivocal. Changes in the planetary and tropical TOA radiative fluxes are consistent with independent global ocean heat-storage data, and are expected to be dominated by changes in cloud radiative forcing. To the extent that they are real, they may simply reflect natural low-frequency variability of the climate system.” IPCC

        It is time to accept that this is real – but I am not holding my breath waiting for Jimmy to come on board. He is quite content throwing around big numbers that are devoid of any context. How long do you think that they can maintain the rage?

      • TOA includes a rather large added CO2 effect, currently up to 2 W/m2. The balance is tipped by that, and that is why there is so much surface warming already which offsets the net LW, and you only see the net of the forcing and response there which is the imbalance.

      • It’s like insulators Jimmy – so much that is imprecise and incomplete. GG forcing increases at 1^-15 W/m2/s. Very small increase – and it causes relatively rapid atmospheric warming which acts to increase IR emissions. The system tends to equilibrium and thus maximum entropy. It is assumed that there is a lag to equilibrium caused by ocean thermal inertia.
        The maths for this are gross simplifications involving derivation of a diffusion constant for which there is no data and which substitutes for the actual fast physical processes of turbulent heat transport and convection.

        Solar inputs to the ocean are variable by +/- 20W/m2 on an annual basis and the oceans heat and cool accordingly. The changes are many orders of magnitude greater than caused by the very small incremental increase in greenhouse gas forcing. In this formulation thermal inertia is far less significant than large changes in ocean heat caused by a strongly varying input signal. Radiant imbalances from greenhouse gases are accordingly less significant. Greenhouse gases leave a warmer planet and an exponentially decreasing effect on TOA power flux.

        On the other side of the ledger is the changes in cloud, dust, ice and vegetation that modulate the global energy budget in shortwave. Both IR and SW show vary large variability over the entire satellite record that are mostly intrinsic.

        Cumulative imbalances in the CERES record – a running sum of monthly incoming and outgoing energy – has trended up this century. One needs to determine then just how and why the global energy budget changes.

      • You are plotting graphs with a scale where you can see that a sustained 2 W/m2 CO2 forcing extended over decades would be a significant ongoing factor in the net radiation balance. That 2 W/m2 is the difference between 400 ppm and 280 ppm and getting to that level both drove up the surface temperature and led to an imbalance. It is a term large enough to dominate decadally averaged radiation balances.

      • If Jimmy stopped repeating himself there would be an awkward silence.

      • afonzarelli

        This is a good analogy by jim and where i think his argument jumps track. ACO2 only accounts for 5% of total emissions. If it merely sinks at a rate similar to natural emissions, then the rise is caused by a natural imbalance, not human emissions. (granted the imbalance may be caused by and for anthropogenic reasons) Now, this is not necessarily true, but it could be true. Assuming otherwise is what gets jimmy into trouble…

      • There is a net gain in both the atmosphere and ocean. It comes from emissions.

      • We are probably changing the composition of the atmosphere with unknown potential. But there is a biokinetic aspect to CO2 fluxes that make it an order of magnitude more complex than Jimmy allows with his simplistic straw numbers. Now if one assumes all warming is anthropogenic – then that implies that the biokenetic large CO2 feedbacks are anthropogenic. So Jimmy has no problem.

        But it is not clear either the limits of CO2 variability – or why stomata records universally show more variability than ice core records.

        I follow data where it leads and can quite comfortably accommodate uncertainty.

      • You can certainly mislead yourself looking at individual CO2 sites with no corroborating sites across the world, which is what you are doing here. Local CO2 levels can vary a lot as their surroundings change.

      • Jimmy’s ad hoc and superficial denial of science leads nowhere interesting.

        https://www.sciencedirect.com/science/article/pii/S0277379113000553

      • You want to lead it into rabbit holes like this. There is no support for that being global and they admit it doesn’t fit with other studies.

      • Be honest Jimmy – you have read yet another bit of real science.

      • You have a low bar if you believe those values are global without any other papers on it. Let’s just say I have a higher bar for evidence when it comes to paleo CO2 levels. A single paper just doesn’t cut it.

      • An open mind is its own reward Jimmy. Follow the clues and admit uncertainty.

        https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2562417/

      • Their estimated effect of CO2 fluctuations appears to be a tenth of a degree. This is not world-changing.

      • I am glad you have finally come to your senses Jimmy.

      • That would also be the consensus where the uncertainty in pre-industrial CO2 in the last millennium is about 10 ppm and it is not rock steady within 1 ppm, so if you are trying to be a skeptic on that, you failed. Welcome to the mainstream.

      • Jimmy’s mainstream is a muddy little pond – a wading pool of awkward little tribal climate memes. But he is king of this pond. To be otherwise is to embrace complexity and uncertainty – along with a certain curiosity for how the world really works. Not happening. The clue to why is the smug disdain of skeptics that is his entire cause. There are tribal memes to be defended – in ways that can only be described as post hoc rationalization of discordant facts. In the way of cognitive dissonance – everything is forced through the same narrow view of things. A sociological phenomenon – and one in which an open exploration of the natural philosophy of climate takes a back seat. The hard and fast rule is that ideas beyond the narrow focus of tribal memes must be defeated to forestall uncomfortable feelings of cognitive dissonance. The problem for Jimmy is that science evolves and continues to surprise.

      • Even you agree with the mainstream papers most of the time, right? What fraction of the published work do you think is out and out wrong? Probably small, and you would have trouble naming one too when you think about it.

      • Science is not a monolith. And as much as 90% of it is just wrong – based on research in the medical field. In the mud are transcendent gems that make up for it. You just have to recognize them find them Jimmy.

      • So far you haven’t identified any wrong ones in climate science. You more often quote papers to say they are right than. if ever, to say they are wrong. Have you examined your level of belief in publications?

      • I have recently said that I have scant regard for sensitivity papers – models or EBM. Rest assured I didn’t read them. Apart from that I have little to no patience with the legion of poor science and nearly always stop reading very quickly. I stopped reading the IPCC reports in 2007.

        Here’s a gem – although I surmise that the subtleties of an ‘abductive mode of inference’ is not high on your agenda.

        https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1002/2016WR020078

        It is a different approach. I don’t waste my time finding a quibbllng – and usually superficial – little criticism one paper at a time. That is very easy and seems the principle activity of the climate blogosphere. Not that I spend any time on blogs other than here. Instead the objective is a rich synthesis of the best science you can find. That’s where the magic happens. It is the joys of natural philosophy – of understanding the world in a fragmentary and uncertain way from a standpoint of the satisfaction of pure curiosity that is my goal.

        Emissions are being addressed pragmatically across a plurality of gases and sectors with a plethora of technologies and systems – underpinned by economic growth and development. Uncertainty creates the impetus to focus on pragmatic emission reductions regardless of short term climate variability. The bottom line is that the right questions to ask about climate change are not scientific but about appropriate responses to diverse human and environmental challenges.

        And this is where I differ essentially from pissant progressives like Jimmy. Of course another difference is that Jimmy has only a passing acquaintance with natural science, math, computing and policy. But he does have an inflexible and dogmatic set of memes that he repeats endlessly.

      • Based on what I have seen from you it is very believable that you have not read the physical basis part of IPCC AR5, because you display a complete unfamiliarity with all its concepts especially those pertaining to energy budgets and dominant forcings and the whole idea of feedbacks.

      • Oh for God’s sake – I read the first report back in 1990. I spend my time on the primary literature. It’s like the reformation – I don’t need the priesly caste to intercede in The Science for me. And I am afraid I know a hell of a lot more than Jimmy about global energy budgets, data on TOA flux, computer modeling and climate dynamics. It is just not the UNscience nonsense narratives of pissant progressives. I refrain from tales of imminent catastrophe – except in the broadest sense of the potential for extreme change regardless. And the resultant need to build prosperous and resilient communities. It goes well beyond simple radiative physics. These guys are most typically uneducated and uninterested in more interesting areas of natural science. Hydrology was my first love. Jimmy is hopelessly uneducated – just a climate alarmist echo chamber pack rat dedicated to repeating a simple set of climate memes.

        Frankly their entire rationale is the transformation of economies and societies. Unless they have catastrophic tales to tell – they have nada. I can get rude about it – but it is just a delusional fringe with nil hope of being taken seriously by anyone that matters.

      • Your last paragraph is the giveaway. You come at it from a political angle which is always a bad starting point, but fairly typical here. Your refusal to see the amount of GHG warming for what it is at 2 W/m2 in comparison to the wiggles you constantly present, is remarkable. Points for stubbornness there. No rational discussion to be had on the energy budget unless you can credit rising GHGs for their part in it. Diversion instead.

      • You consider that an adequate and informative response? With certainty I object to the policies of the loony left fringe – and the use of climate calamity narratives as a stalking horse for insane economic and political fantasies. The acid test seems to be narratives of catastrophe coupled with a refusal to consider practical and pragmatic options.

        “This pragmatic strategy centers on efforts to accelerate energy innovation, build resilience to extreme weather, and pursue no regrets pollution reduction measures — three efforts that each have their own diverse justifications independent of their benefits for climate mitigation and adaptation.” https://thebreakthrough.org/archive/climate_pragmatism_innovation

        Many people add land use changes to the list of pragmatic climate policy. Jimmy argued that this publication had been superceded by the Paris accord. It is however a very different, high energy strategy. Vastly removed from the 5 hours a day of a fan, an LED light and a transistor radio that the UN considers is adequate for peoples needs and dignity. Jimmy is a defender and I am profoundly contemptuous of the neo-Marxist agenda. Poor wee willies earnest belief in the power of an AI overlord to plan the global economy seems typically delusional inanity – and Jimmy is not far behind.

        Here’s some more wiggles. I have actually calculated the cumulative energy imbalance from CERES data. It turns out to be simple using raw data rather than anomalies. Multiplying by the number of seconds in a month would give the Joules accumulating in the system – a next step but I was originally just interested in how it co-varied with ocean heat. Cumulative radiant imbalances increased steadily over the CERES record. Looking in more detail shows net outgoing radiation in decline over the period. SW warming and IR cooling of a couple of W/m2 in just a couple of decades. A problem for Jimmy and Co. is that the pattern is similar in the earlier satellite data. 2.1W/m2 SW warming and 0.7W/m2 IR cooling. By the nature of things – this is predominantly cloud change.

        https://watertechbyrie.com/2018/05/05/a-maximum-entropy-climate-an-idea-under-construction/

        But data is not good enough for Jimmy if it is not in accord with the narrative.

      • Imbalance is the net shortwave and longwave. It turns out a lot of the response is in the shortwave as a positive albedo feedback which is why the imbalance is as large as 0.7 W/m2 as seen with the rate of OHC increase over the past few decades. Given any positive imbalance, this means that the forcing still exceeds the warming response which points to >100% attribution when you realize that the forcing is dominated by GHGs. This is an important point about the positive imbalance.

      • You have to hand it to Jimmy – he is totally outclassed by many here but keeps coming out swinging with wildly improbable and technically incompetent narratives.

        Radiative imbalance is the difference between incoming energy and outgoing energy – the latter both as IR and SW. That would seem to be a fundamental concept that Jimmy has fundamentally wrong. An embarrassing failure for an ordinary person not of Jimmy’s blog climate crusader stature – especially compared to the great unwashed of Climate etc. I’m sure he has another story to tell about this.

        Jimmy seems to have 2 numbers – 2W/m2 and 0.7 W/m2 – and this allows him to gloss over what would otherwise be cognitively dissonant facts about the workings of a chaotic dynamic system.

        Estimated AGW cloud feedback is 0.18 to 1.18 W/m2/K. Atmospheric – as opposed to surface – temps show no obvious rise. Thus no feedbacks. ENSO spikes do show up and this – along with the north eastern Pacific – is the dominant source of global cloud change (Clements et al 2009).

      • I don’t think you have accepted my two numbers yet, or the consequences of just that information to your worldview if you do. When you say atmospheric data shows no rise, you are selecting and misrepresenting older satellite data and ignoring the newer RSS that does agree with the surface rise rate.

      • The CO2 forcing is defined as the line by line calculation of specific changes in concentration without any planetary response. The planet does respond and thus the number has no direct bearing on current processes. Your ocean heat number assumes any change is anthropogenic. Utter nonsense little Jimmy.

        The frustration is that I keep going into greater detail with numbers – and Jimmy comes back with his two numbers that don’t explain much at all. A technically trivial exercise.

        As for RSS?

      • The primary forcing is anthropogenic CO2. That’s where the 2 W/m2 comes in, and it is 3 GJ/m2 integrated. Nothing else comes even close to providing that much energy to the system in the last century, except for the other GHGs.
        Not sure if you agree with RSS or not. Here it is with the surface temperature. You can decide for yourself whether what you said is true about lack of warming.
        http://woodfortrees.org/plot/rss/mean:12/offset:0.2/plot/best/from:1970/mean:12

      • We have talked about your silly numbers quite enough.

        Trends are unreliable over very short periods. I like Roy Spencer’s 13 month running mean as it shows maximums and minimums that reveal no statistically significant increase in peak temperatures this century in the atmosphere. RSS is pretty much the same.

        I expect that there has been warming this century – from net TOA radiant flux and increases in cumulative energy imbalances from CERES data on incoming and outgoing energy. I expect that some of the imbalance is contained in melted ice and water vapor. Argo data shows warming over the past few years. But the sources of power flux changes at TOA go well beyond greenhouse gases and involve ocean and atmospheric circulation – including most obviously ENSO.

      • Since 1980 the GHG-added energy has been 40-50 units and the OHC energy change has been 25 units. The difference is offset by surface warming. GHGs are enough to account for it all.

      • But then it isn’t all of it by a long shot.

      • More than all the OHC change.

      • This is demonstrably not true – although perhaps not to Jimmy’s motivated satisfaction.

      • The numbers show it is true.

      • your number? howls of derision.

      • I have sources for mine. You can provide your own estimate of the OHC rise since 1980 and energy provided by GHGs since 1980. I’ll wait.

      • I only have patience for Argo data.

        http://sio-argo.ucsd.edu/RG_Climatology.html

        There seems (visually) an inconsistency with climatologies based on Levitius – but that’s climate science for you.

      • You don’t even want to make a guess at the OHC change since 1980. Anyway just using the period since 2004, you get 12 units of OHC and 18 provided by CO2 alone.

      • As I said only Argo meets my criteria for reliable data – and even then climatologies appear to be radically different. I use the Argo Global Marine Mapper from the Scripps Institute. It is a fun little tool.

        But temperature is a measure of heat content – and the change over the past few years – the period of Argo warming – is 0.04 degrees C.

      • I gave you the energy numbers for the Argo era. Same conclusion. Using 0.04 C for 1900 m it is also close to 12 units.

      • A unit is 1^22 Joules. Let’s define it.

        I get 6.07905E+16 Joules – a lot less. You would have to show your working to get any credit at all.

        But the warming was both small and confined to the latter part of the record when El Nino was changing clouds.

      • You seem to be off by the number of kg of water in the 1900 m column.

      • Workings Jim or I can’t really be bothered.

      • Multiply your number by 1.9e6 which is the number of kg/m2 of water in the column.

      • Well that’s a fail.

      • warming * kg of water in column * heat capacity = J/m2
        * area of earth * 0.7 for water area
        = J
        Result 12 *10^22 J (also seen on Levitus plot by reading off the difference since 2004)
        Where did you go wrong?

      • 5.89E+20 (kg) * 0.04 (k) + 3895 (J. K^-1.kg^-1)
        = 2.356E+19 (Joules)

        All this warming happened since 2008 – quite different to the Levitus climatology it seems. Again.

        But this is all still trivial nonsense – the warming is 0.04K. And most of it is not CO2.

      • Even if you replace your + with a *, your own numbers don’t give your answer. Again, where did you go wrong?
        The point for the nth time is that the CO2 forcing provides more than enough energy for the warming.

      • why would i replace my multiplies convention for addition? Bizarre. But yes both the number and the dimensions add up.

        And the point for the nth time is that carbon dioxide quite evidently is not all there is to warming. El Nino is the pertinent example. And no ENSO does not sum to zero over millennia at least.

      • well yes the + was a typo that does appear in the spreadsheet. Mea culpa. The ocean warming is 0.04K since 2008.

      • afonzarelli

        Jim, even if the entire rise was natural, there would be a net gain in the atmosphere and in the oceans. (the mass of aco2 sinking at a rate similar to natural emissions would give a net gain to the oceans)…

      • Where does it come from if both the atmosphere and oceans are gaining at a rate consistent with added emissions?

      • Soils and vegetation due to increased respiration in warmer conditions and land use changes. Biokinetics. Much of the historic loss of carbon from these stores – some 180GtC – can be reversed.

        We ask them to contemplate complexity and uncertainty but there is little evidence that they can.

      • You wouldn’t have global warming without a Planck response

        Nope, there was warm and cold cycles that alternated when CO2 was not alternating. Something else is more important to the cycles and that is still dominate.

      • There are other forcing mechanisms. See Milankovitch.

      • Robert I Ellison: Thank you for the link to the essay about “uberty”. It isn’t the first essay on abduction, but hopefully it will be the last about “uberty”.

        Here is a quote:
        This commentary suggests that a world-directed, investigative approach to hydrology may serve as a productive complement to the prevailing hypothesis- (theory-) directed, approaches (Table 1). The emphasis of
        the former on discovery has the potential to be transformative for investigative hydrology.

        How you “take” the world as it is (cf table 1), instead designing research based on your understanding of it so far, is a problem. But since they propose their ideas as complementary to the prevailing approaches, that may not matter. The essay is fun enough, and will do no harm.

        Anyone writing of “abduction” ought to cite C. S. Peirce. Anyone who reads Thomas Kuhn ought to read Michael Polanyi and Abraham Pais as well. imho.

      • The essay is about synthesis as opposed to hypothesis testing. Two very different things. The lay understanding of science involves hypothesis and experiment – but the real work of science is to coral the disparate hypotheses into a coherent picture. This latter process is less certain but has more uberty.

  30. oops, My . . . not MY

  31. David Wojick

    To the list of climate subsystems I would add the 8000 mile diameter complex magnetic molten ball that the atmosphere, oceans and land are a thin film on. Lots of energy there, in many forms that affect climate.

  32. As others have pointed out there seems to be some confusion here. Let’s consider the boundary value issue. There’s not really an assumption that climate change is a boundary value problem; this is a conclusion from studying the system. For example, if you want to predict the weather in a few days time, then it’s important to get the initial values as close as you can to the actual conditions. Of course, it’s only really possible to make weather predictions a few days in advance because of the non-linear nature of the system.

    For climate, however, we more interested in typical weather conditions (averages), not the exact state. For this, it seems that it’s more important to get the boundary values correct, because these largely determine how the climate will change. This doesn’t mean that the initial conditions play no role (they do) but that the boundary conditions are important.

    • Except ATTP that you are spreading confusion yourself. Changes in composition of the atmosphere are NOT boundary values. The “boundary value” of solar flux is claimed by climate scientists to be constant.

      It’s a little like changing altitude in a CFD simulation. The air properties change but the boundary values don’t change. There is some truth in saying that the altitude “determines” the system “properties, except that there is a lot of falsehood in it too. It’s much more complicated because the atmosphere is very complicated and turbulent.

      The truth is much more complex as I discussed above. So why then do climate scientists keep repeating the “boundary value problem” meme? It is clearly to try to convince outsiders that GCM’s produce meaningful output. That meme is collapsing as a few younger scientists are showing it to be quite wrong.

      • Except ATTP that you are spreading confusion yourself. Changes in composition of the atmosphere are NOT boundary values.

        I don’t recall that I said this. However, changes in the composition of the atmosphere are often associated with boundary values because they influence the radiative flux at the boundary. See, this post, which says

        For understanding climate, we no longer need to worry about the initial values, we have to worry about the boundary values. These are the conditions that constraint the climate over the long term: the amount of energy received from the sun, the amount of energy radiated back into space from the earth, the amount of energy absorbed or emitted from oceans and land surfaces, and so on.

        My point, however, was actually that the suggestion that climate change is a boundary value, rather than an initial value, problem is not really an assumption, but a result of studying the system and seeing how it responds. Initial values are important if you want to predict the weather a few days in advance, boundary values are important if you want to see how the system responds – on average – to radiative perturbations.

      • Easterbrook also is contributing to the confusion in my opinion. A good starting point for any such discussion is the recent papers showing high sensitivity of GCM results to sub grid models and numerical details.

        I would suggest we simply abandon the initial value vs. boundary value problem language. We could call it a “dynamical system attractor problem.”

        This language conveys a technically correct description and highlights the fact that not a lot is known about the computability of “correct” solutions for these systems. It largely depends on the dimension of the attractor and how attractive it is, subjects about which we know virtually nothing.

        Climate scientists run the models and having nothing else (besides energy balance models) to predict the future then try to defend them with misleading analogies. That’s the dynamic we need to correct.

      • In mathematics boundary values are also labelled constraints. So when the word ‘constraint’ is read, the word is taken to mean ‘boundary value’; especially when the phrase ‘boundary value’ is used in the same context as ‘constraint’.

        I think there is one unique way to identify if a quantity is a boundary value/constraint as follows. Boundary value constraints are applied from the exterior of the modeled physical domain and are not calculated by the model equations interior to the domain. Boundary condition constraints are imposed at the boundary. The compatibility-condition vectors point from the exterior toward the interior. The solution of the model equations interior to the domain is required to satisfy the imposed boundary condition constrains as well as satisfy the model equations interior to the domain.

        So, if a quantity is calculated by the model equations interior to the domain that quantity is not a boundary condition constraint. As a practical matter, we can say that if we look into the coding we will see that boundary condition constraints do not change over the complete course of the calculation.

        Note Professor Easterbrook’s characterization of the Climate Science Boundary Value Problem:

        “For understanding climate, we no longer need to worry about the initial values, we have to worry about the boundary values. These are the conditions that constraint the climate over the long term: the amount of energy received from the sun, the amount of energy radiated back into space from the earth, the amount of energy absorbed or emitted from oceans and land surfaces, and so on. If we get these boundary conditions right, we can simulate the earth’s climate for centuries, no matter what the initial conditions are.”

        Above we have broken down Professor Easterbrook’s statement as follows:

        “These are the conditions that constraint the climate over the long term: (1) the amount of energy received from the sun, (2) the amount of energy radiated back into space from the earth, (3) the amount of energy absorbed or emitted from oceans and land surfaces, and (4) so on.” [I have added numerical labels (n).]

        Here’s a simple, direct, multiple-choice question. Which of the items labeled (1) through (4) are not calculated by the model equations interior to the domain? Those are the boundary condition constraints. The others are not boundary condition constraints.

        Note also the last sentence included in the above quote: “If we get these boundary conditions right, we can simulate the earth’s climate for centuries, no matter what the initial conditions are.”

        He explicitly labels all of items (1) through (4) ‘boundary conditions’. The first sentence also uses ‘boundary values’.

        The confusion does not exist in those who are objecting to Easterbrook’s characterization.

        The confusion exists in those who are attempting to (1) redefine mathematic fundamentals, and/or (2) minimize the known severely adverse properties of chaotic responses.

        The concept that the properties and associated boundary condition requirements of PDEs can be determined by observation is rather unique to my experiences. Using this method, how was it determined that the transient heat conduction equation is parabolic, and the steady-state form elliptic? Plus, by observation alone, how was it determined exactly what combinations of dependent variables and derivatives of these can be imposed in order to ensure the existence and uniqueness of solutions?

      • Yes Dan, This from Easterbrook lays bare why climate scientists are misrepresenting the issue.

        “If we get these boundary conditions right, we can simulate the earth’s climate for centuries, no matter what the initial conditions are.”

        It really is about our ability or lack thereof to predict the far future.

    • It’s worth a little more analysis of the “boundary value problem” word salad because its pretty clear why climate scientists adhere to it in my opinion. In some sense it goes to the scientists internal rational justification (and justification for getting money) of the entire field. To work on predicting the climate is a very hard problem requiring a big investment of money and time. This motivation is easier to generate if you believe that just around the corner is a breakthrough that will solve the prediction problem. A bare minimum would be that progress is possible. This explains also why the scientific literature is littered with positive bias in my view.

      There are actually 2 questions:
      1. Is the climate predictable and what are the uncertainty bounds?
      2. Is the climate computable?

      I don’t profess to know the answer to either question definitively. There is a lot of evidence that has crept through the bias of the literature that the answers are very complex. Certainly a confident yes to either one is a sign of either strong bias or self-motivational wishful thinking.

      • “In sum, a strategy must recognise what is possible. In climate research and modelling, we should recognise that we are dealing with a coupled non-linear chaotic system, and therefore that the long-term prediction of future climate states is not possible.” TAR 14.2.2.2

      • Yes, Robert, that’s what they say. I think the weight of evidence support that conclusion too.

  33. I’m going to say it again since I like the idea so much.

    To avoid confusion for climate scientists who are often not mathematical experts, lets just drop the initial value vs. boundary value problem language. Both of these are misleading in their own way. I think Easterbrook, ATTP, and even Roy are not very clear on it. Initial value problem proponents are also confused.

    Lets use the term

    Dynamical System Attractor Problem

    which has the virtue of being technically correct and highlighting how little we know about solving these problems.

    • I think that your suggestion highlights how little you know, rather than highlighting how little *we* know.

      • and Then There’s Physics: I think that your suggestion highlights how little you know, rather than highlighting how little *we* know.

        No, dpy6629 is right about this. There is no “equilibrium” and there is no “steady state”, so the closest mathematical approximations that might hope for some verisimilitude are nonstationary vector autoregressive models whose values stay in a range (which range may change with CO2) or dynamical systems and their attractors (which attractors may also change with CO2). Without the dynamic system being in an attractor, there is little hope for either short-term or medium-term approximate predictions.

        Note: (strictly speaking, the “attractor”, like the “dynamical system” and its differential equations, is a mathematical construct. as are “bifurcations”, singularities, and such. When we say that the physical dynamic system is “in an attractor” we mean that a closely fitting mathematical dynamic system is in an attractor.)

        Or, instead of saying “initial value problem” vs “boundary value problem”, we could say it is a problem for which we do not have even 1 accurate mathematical approximate solution.

    • It’s not useful because it does not separate externally imposed changes from internally emergent ones. I could say a boundary value problem is one where the attractor is changed by an externally imposed property like solar input or CO2 level. The key is the boundary value problems are constrained by certain specified external forcings, and those are what define the attractor.

    • The models are bedeviled by uncertainties in inputs
      including forcing – that result in exponentially divergent solutions. And by structural instability. In models the problem for prediction is purely one of nonlinear math. The idea that forcing causes solutions to converge from small initial differences is pure magical thinking.

      “Lorenz was able to show that even for a simple set of nonlinear equations (1.1), the evolution of the solution could be changed by minute perturbations to the initial conditions, in other words, beyond a certain forecast lead time, there is no longer a single, deterministic solution and hence all forecasts must be treated as probabilistic. The fractionally dimensioned space occupied by the trajectories of the solutions of these nonlinear equations became known as the Lorenz attractor (figure 1), which suggests that nonlinear systems, such as the atmosphere, may exhibit regime-like structures that are, although fully deterministic, subject to abrupt and seemingly random change.”
      http://rsta.royalsocietypublishing.org/content/369/1956/4751


      “Schematic of a probabilistic weather forecast using initial condition uncertainties. The blue lines show the trajectories of the individual forecasts that diverge from each other owing to uncertainties in the initial conditions and in the representation of sub-gridscale processes in the model. The dashed, lighter blue envelope represents the range of possible states that the real atmosphere could encompass and the solid, dark blue envelope represents the range of states sampled by the model predictions.”

    • ATTP, I though you were going to keep this technical and then you inserted your ad hominem.

      The boundary value problem description is simply wrong on all technical bases. Your word salad attempt here to justify it is all the proof most people would need. The initial problem description is also simply wrong in the long term. Mathematics can take a lot of work, you would be rewarded however by looking into Lyanopov constants a little.

    • All GCMs set the problem as an Initial-Boundary Value Problem (IBVP).

      Why not label them what they are?

      Why go against 100s of years of standard well-accepted mathematics in an attempt to make them into something that they clearly are not? Concise mathematical nomenclature gets destroyed in that process. The mathematical meanings of words are ignored. People reading/hearing the standard words think one thing and the users of the words mean something else.

      If a more nearly consistent description is desired, I suggest Ill-Posed Initial-Boundary Value Problem.

    • On third thought, David Young has a good idea. I suggest we label them an Ill-Posed Dynamical System Attractor Problem.

      • Dan Hughes:

        Thank you for another stimulating discussion.

        Looking at Dr. Roy W. Spencer’s comments, it occurred to me that because a problem has boundaries does not mean it is a “boundary value problem”. Before jumping into the ring, I thought I should review some text books.

        From Bender and Orszag “Advanced Mathematical Methods for Scientists and Engineers” (1978): There is a distinction between initial value and boundary value problems. Initial value problems are simpler. In many cases it is possible to show that a solution to an initial value problem exists and is complete in a particular region. Boundary value problems are inherently global. Existence and uniqueness theorems must be proved for all points; local analysis is not sufficient. Boundary value problems may have no solution, or infinitely many.

        From Wylie “Advanced Engineering Mathematics” (1960): The features of a simple boundary value problem are as follows. Assuming that solutions for the dependent variable exist in the form of products of functions of the respective independent variables, the original differential equation is broken down into several ordinary differential equations, each of which involves a parameter lambda which ranges over a continuous infinity of values. When boundary conditions are imposed, the lamdas must satisfy a characteristic equation of the problem. The roots of the characteristic equation are known as characteristic values and are the only solutions which satisfy both the partial differential equation and the given boundary conditions.

        It would seem that the existence of water phase changes, which produce sources and sinks of material and energy and which in turn can create or destroy boundaries, deny the continued existence of the characteristic solutions for either matter or energy flow.

        So I agree completely that “In the sense of the concise meaning, and universal acceptance, of the phrase ‘Boundary Value Problem’ Climate is not.”

        And for Dr. Roy, who said “yes, of course climate is also an initial value problem”, by this definition the climate system is not even a boundary value system, much less a simpler initial value problem. Having an initial value does not make a problem an initial value problem any more than having a boundary makes a problem a boundary value problem

        While the various toy radiation and fluid systems which do not involve evaporation and condensation may well be “boundary value problems”, the real world certainly is not.

        If we were arguing that the climate system is two coupled subsystems – one for radiation the other for fluids, the argument would be much more difficult to resolve and worth pursuing.

    • As I mentioned above. This is not useful because it hides the distinction between initial-value and boundary-value problems. How do you distinguish with one term for them all? This is step backwards unless you can come up with separate terms conveying the former meanings.

      • All climate models are initial value problems. The planet is a spatio-temporal chaotic flow field filled with regimes and abrupt shifts. It sure ain’t a boundary problem – except in the minds of those who believe climate to be static unless pushed by a large forcing. The latter is a dinosaur idea.

      • There is hysteresis and there are tipping points, but we also know that the earth can’t form the Greenland glacier at 500 ppm, and didn’t until the CO2 levels dropped below 400 ppm. When the boundary value is 500 ppm you don’t have a stable Greenland glacier whether you started with it or not. There is some determinism here. Forcing matters whether from CO2 or the sun.

      • Models are initial value problems – all of them all the time. Tipping points imply that climate is as well. Although Jimmy doesn’t seem to be able to distinguish between model space and the global climate system. And when Greenland was last free of ice it was far to the south and not nearly as elevated. I don’t make guesses like Jimmy’s that are based on simplistic analogies. Nor am I convinced that ice cores capture the true variability of carbon dioxide. I don’t think we need Jimmy’s impossible certainty in very unsophisticated concepts.

      • We went through that and concluded Greenland was much less than its length to the south, so your explanation failed. That’s typical of your arguments that amount to bad guesses that don’t stand up to actual numbers.

      • No Jimmy – from memory Greenland was some 2000km to the south and at sea level. As I remember you neglected north pole drift. Just one of the many things you neglect. As I said – I am reluctant to make a guess about something 1000’s of years in the future based on poor analogies and imprecise data. When I give numbers it is always data – usually the most up to date – and I consider the intrinsic veracity. You do nothing of the sort. You are no scientist of any sort, have never had any technical training, your reading in natural sciences is woefully inadequate and your numbers are hopelessly misguided. Then there is your habitual denigration, slights and smug but entirely misplaced – because of the depth and breadth of my training, experience and decades of study of hydrology, climate and environments – condescension. As Yoda said – bored I am. F@&k yourself you can.

      • Your numbers are faulty. We are talking about 10 million years ago.

      • You are full of it Jimmy.

        http://www.science20.com/news_articles/true_polar_wander_why_greenland_ice_took_so_long_to_develop-151977

        Over the past 5 million years mantle-plume pulses lifted eastern Greenland from sea level to some 3000 meters.

        As they say little Jimmy – you are entitled to your opinions – as silly as they are – but not to your own facts.

      • They say it was too warm for any ice prior to that, and remember Greenland wasn’t the only NH ice that formed in the last few million years. You can’t attribute the Ice Ages to continental drift and Greenland’s ice was a precursor that I view as rather related. I have some reservations about that study, which I suspect is not accepted as consensus because it is largely speculative. If the pole moved 12 degrees in 60 million years, it didn’t move much in the few million years that Greenland’s ice formed. The timing doesn’t work well and the significant reduction in CO2 was what enabled this to happen in the first place.

      • Of course it was too warm – Greenland was 3000 meters lower and 2000km to the south. Is what they actually say. Speculative doesn’t begin to describe Jimmy’s wild narratives. It is especially funny when he relies on his own authority.

      • They express this as a delay. So they expected global cooling from dropping CO2 levels to produce Greenland glaciers earlier. The paper is about an idea to explain why the glaciers did not occur earlier given Greenland’s location. If you agree with the authors you also would expect Greenland in its current location to have formed glaciers earlier in response to global cooling. Given your vigorous denials about connecting CO2 and glaciers, I suspect you don’t. The paper doesn’t discount this fundamental fact, but adds a wrinkle to it on timing.

      • “The big question geologically is why the glaciation of Greenland only developed so recently.

        It’s because of the interaction of three tectonic processes. Greenland literally had to be lifted up, so that the mountain peaks reached into sufficiently cold altitudes of the atmosphere. Greenland also needed to move sufficiently far northward, which led to reduced solar irradiation in winter. Then a shift of the Earth axis caused Greenland to move even further northward.”

        In the context of a cooling planet, reduction in albedo and natural declines in CO2? why did Greenland take so long to freeze?

        Greenland is still where and how high it is – and the change does no support any simple lessons about CO2 concentrations and Greenland ice shelves. This is a simple idea – physical states have changed and they bear little resemblance to conditions 10 million years ago. Despite Jimmy’s tortured reasoning there is no simple rule to predict Greenland ice loss.

      • They are explaining the delay. If Greenland was in its current position and with its current elevation it would have occurred earlier. Do you agree? Why would it have occurred at all in your view if it wasn’t for declining global temperatures? Why is it only a few million years ago we started to get Ice Ages? Is this a mystery to you or did global cooling have something to do with it?

      • A trivial hypothetical? If Greenland was just a little faster it would have frozen earlier? This is typical of the nonsense Jimmy comes out with.

        The complex of factors that initiated Quaternary glacials/interglacials is something you may read about elsewhere. It is not a simple story – interesting for that reason.

        http://www.pnas.org/content/early/2018/02/06/1708174115

        https://www.sciencedirect.com/science/article/pii/S1674987116300305

        There are a number of theories about why glacials/interglacials occur – including the shoaling of the Isthmus of Panama. Or the reason for the mid-Pleistocene transition.

        http://www.ajsonline.org/content/312/4/417.abstract

        It is of course a complex and dynamic system and CO2 in the paleo-atmosphere is a biokinetic feedback and not a cause. The minor source of change – although this doesn’t fit into Jimmy’s narratives.

      • OK, so are you dismissing that global cooling had something to do with it? Because, if so, that is where you depart into your own inventions. If not, I agree.

      • The planet was cooling due to ice, cloud, vegetation and respiration feedbacks. I wouldn’t agree with Jimmy – it is all so hopelessly biased – if he had a gun to my head. Well – perhaps I might.

      • That’s your invention. The authors of the paper you quote would have little patience with that. People studying paleoclimate attribute cooling to reducing CO2 levels and attribute reducing CO2 levels to geological processes. It’s a solid causal chain.

      • I didn’t actually quote – but I will.

        “We present here a simple and novel proposal for the modulation and rhythm of ice-ages and interglacials during the late Pleistocene. While the standard Milankovitch-precession theory fails to explain the long intervals between interglacials, these can be accounted for by a novel forcing and feedback system involving CO2, dust and albedo. During the glacial period, the high albedo of the northern ice sheets drives down global temperatures and CO2 concentrations, despite subsequent precessional forcing maxima. Over the following millennia more CO2 is sequestered in the oceans and atmospheric concentrations eventually reach a critical minima of about 200 ppm, which combined with arid conditions, causes a die-back of temperate and boreal forests and grasslands, especially at high altitude. The ensuing soil erosion generates dust storms, resulting in increased dust deposition and lower albedo on the northern ice sheets. As northern hemisphere insolation increases during the next Milankovitch cycle, the dust-laden ice-sheets absorb considerably more insolation and undergo rapid melting, which forces the climate into an interglacial period. The proposed mechanism is simple, robust, and comprehensive in its scope, and its key elements are well supported by empirical evidence.”

      • The question was why did the Ice Ages start only a few million years ago. Global cooling? Low enough CO2 levels?

      • There is a Quaternary ice age that includes glacials and integlacials – and Jimy’s inane question has been answered in terms of a complex of interacting process starting with ice sheet response to NH summer insolation.

        Do you not get this Jimmy? Read some papers on it.

      • My question is about what changed in going from the Tertiary (Neogene) to the Quaternary. A drop in CO2 levels and a lot of cooling.

      • Do you not get that CO2 is a temperature feedback? Albedo in response to changing NH insolation is the original proximate cause of temperature change – both going into and out of glacials. Albedo change is the dominant factor by far.

        The CO2 stomatal study Jimmy rejected yesterday suggests a bigger role for a more variable (than ice cores) CO2 concentration in the last glacial transition. Is there any uncertainty here? not according to Jimmy. It is all the CO2 control knob according to something he read on a blog somewhere. You are a waste of our time little Jimmy and you really should go away to another blog where they are more like you. A lovely little echo chamber perhaps.

      • You have decided that a drop of several hundred ppm CO2 prior to the Quaternary is in no way a major factor in the cooling. It figures. Sorry that mainstream science is so bothersome to hear about.

      • Precision Jimmy. I said that it was a secondary factor – both in size and timing.

      • Secondary to what, and what makes you sure?

      • afonzarelli

        Jim, your logic fail here knows no bounds (☺). 500 ppm is an indicator that it was a warmer world. Not necessarily that it was a warmer world because of higher levels of CO2. So, if CO2 doesn’t do all the warming that we’ve assigned to it, our artificially high co2 levels won’t erradicate the greenland glacier. This goes back to the problem that i (inadvertently) distracted you all from last night. Just because the forcing is there, it doesn’t necessarily mean that the accompanying warming is there. (similar to the fact that just because there is double the amount of emissions needed for our co2 rise, that doesn’t necessarily mean the rise is caused by those emissions) i’ll leave you now with an abrreviated quote from Dr. Spencer’s comment which opened this thread atop the page:

        More CO2, by itself, surely causes a warming “tendency”, but how all of the various subsystems respond (feedbacks) is so uncertain we can’t really say how much warming (if any) there will be.

        and

        It’s just that the feedbacks… …are probably more numerous and complex than we can conceive of right now.

      • Clearly at 500 ppm it was warmer enough not to have a Greenland glacier. That by itself should be significant information to you as we approach those levels again.

      • we also know that the earth can’t form the Greenland glacier at 500 ppm, and didn’t until the CO2 levels dropped below 400 ppm. When the boundary value is 500 ppm you don’t have a stable Greenland glacier whether you started with it or not

        The northern hemisphere was covered with massive ice in the cold part of the major ice ages. Earth has no trouble producing ice. There is no data to support the flawed idea that CO2 has anything to do with the production of ice. When you say, we know, you do not speak for me or for many others. To produce ice, warm thawed water is needed, any warming provides more energy to power the forming of ice. Ice ages occur after warm periods provide energy and moisture for forming ice. ice advances after it piles up enough and gets heavy enough to flow faster than thaw rates. A big ice machine requires energy to power it and energy removal. that only happens when oceans are warmer and more thawed.

        Cold times with less energy in the ocean water and less IR out don’t meet basic requirements for forming ice.

      • You probably know that the Ice Ages and those NH glaciers did not become possible until CO2 levels dropped below 400 ppm prior to the Pleistocene. They did not exist for hundreds of millions of years while CO2 levels were higher than that. This is a determining factor.

      • afonzarelli

        If a cooling world produces lower CO2 levels, then you may have correlation backwards. (how can you determine if lowering co2 was causing cooler temperatures or if it was only going along for the ride?)…

      • There is an impact of temperature on CO2. It is about 10-20 ppm per degree. The CO2 level went up by 100 ppm for about a 5-8 C rise coming out of the depth of the last Ice Age. That wasn’t emissions. It is due to an equilibrium between the air and surface carbon levels which is temperature dependent. Warming causes outgassing. It can be seen with warmer years still generally having higher CO2 levels than cooler ones once you subtract the larger emissions effect. We have had a degree of warming in the last century or so, so 10-20 ppm has come from outgassing, about 10%, a positive feedback. The rest is us.

      • afonzarelli

        Jim, that’s irrelevant to my point. You’re claiming lower co2 levels caused the advent of glaciers and the ice ages. Cooler temps caused the ice and caused the lower co2 levels. (correlation goes from cooler temps causing lower co2 and, thus, not necessarily lower co2 causing the cooler temps)…

      • Scaling from what happened since the Ice Ages, 100 ppm for 6 C, you need 18 C for a 300 ppm drop. The temperature dropped maybe 4 C. That ratio goes with how CO2 drives temperature, not vice versa.

      • afonzarelli

        Jim, then whatever factors caused co2 levels to exist at 500 ppm does not mean that if we were to artificially return co2 levels back to 500 ppm then we would get a similar temperature result…
        Let’s say, for example, we are stuck at the bottom of a glacial and co2 levels are at 190 ppm. And let’s say we add 90 ppm to that anthropogenically. Even at an ECS of 3°C, the resultant rise in temperarure would only be a third of what we normally would see during the glacial to interglacial transition. In the same way, a return to levels of 500 ppm artificially will not produce temperatures near enough to eradicate the greenland glacier. This is one of the oldest sceptic arguments that i know of. (and you most certainly should know of it by now yourself)…

      • The albedo feedback adds a lot to the sensitivity in these longer-term changes. At 400 ppm Greenland is already net losing ice at a rate that first appeared slowly around 2000 and has accelerated since. At 500 ppm, it will be even more so. It is already unstable and will be contributing the majority to sea level rise rates along with parts of Antarctica.

    • It’s worth examining in detail ATTP’s and Easterbrook’s word salad since its the verbal formulation lots of climate scientists use and claim its “physical understanding.” That’s usually means “pseudo-physics”, i.e, unquantifiable formations similar to what in an earlier age would be called theological explanations. I’ve seen this hundreds of times in my career. These “explanations” are inherently vague making it nontrivial to “disprove” them. Of course the right question is why give them any credence.

      There’s not really an assumption that climate change is a boundary value problem; this is a conclusion from studying the system.

      And what do we mean by “studying the system?” Well in this case, we must mean running climate models and there are lots of recent negative results ATTP avoids mentioning that call into strong question such a strategy. It is key of course to avoid mentioning negative results because they call into question the “pseudo-physics.”

      Lets take a vastly simpler system, i.e., an aircraft flying in the atmosphere. ATTP’s “forcings” would be the thrust, angle of attack, speed, altitude, etc. So the translation of the “boundary value problem” doctrine would be that these forcings determine the final state of the system while the initial conditions are irrelevant. And that is patently untrue as a lot of new research is showing.

      In fact, its very old research, and was known 60 years ago. Initial conditions do matter quite a lot in these matters as non-unique and multiple solutions are quite common. In particular initial conditions make a far bigger difference in CFD simulations than in reality. There is also lots of “noise.” We get around this by doing steady state RANS calculations that seem to work reasonably well, but that model unsteady fluctuations. In climate as Matt pointed out above that’s not possible. It’s an very unfortunate circumstance that makes climate science quite uncertain.

      One could argue that in the “linear range” multiple solutions aren’t that important. Once again proven wrong by recent research.

      • dpy6692

        Sorry for this intrusion into this enlightening discussion.

        “And what do we mean by “studying the system?” Well in this case, we must mean running climate models and there are lots of recent negative results ATTP avoids mentioning that call into strong question such a strategy.”

        I am interested in the source for this statement: “there are lots of recent negative results ATTP avoids”, I am assuming climate model runs with negative outcomes, possibly demonstrating cooling by adding CO2 to the atmosphere, right?

        My ignorance knows no boundaries.

      • One pal ce to start is Zhoa et al 2016. Nic Lewis’ summary is that the ECS of one GCM is a strong function of cloud microphysics parameters that cannot be convincingly constrained with data.

        Another one was caught by Dan earlier in this thread. Basically, the order of applying the sub grid models on any time step has a strong impact on the ultimate “climate” in a GCM.

        These are in my view quite disturbing results and show that modelers when they submit runs to the IPCC chose their “best” model run and omit the less convincing ones. That’s unfortunately a standard practice in the modeling of chaotic flows.

      • It is known that there is a variety of models with different skill levels even compared to all the current data. Emergent constraints are a way to weed out the weaker models. In this method they are compared to observations of various kinds and if they fail those tests, their sensitivity is weighted less than those that do better.

      • Steven Mosher

        “Another one was caught by Dan earlier in this thread. Basically, the order of applying the sub grid models on any time step has a strong impact on the ultimate “climate” in a GCM.”

        this is not exactly correct. If you tune a model using one process order and then change the process order you get different answers. not surprising and not relevant.

      • “AOS models are therefore to be judged by their degree of plausibility, not whether they are correct or best. This perspective extends to the component discrete algorithms, parameterizations, and coupling breadth: There are better or worse choices (some seemingly satisfactory for their purpose or others needing repair) but not correct or best ones. The bases for judging are a priori formulation, representing the relevant natural processes and choosing the discrete algorithms, and a posteriori solution behavior.” http://www.pnas.org/content/104/21/8709

        Until they can model tipping points – a priori formulation may leave a lot to be desired. A posteriori solution behavior? There are of course many divergent solutions possible from small initial differences. It is funny that they pull the correct solution out of their arses. Now you know where Jimmy gets it from.

      • dpy6692

        Thank you for the clue re: Zhao et al 2016. It seems that Zhao is a common Chinese name. I did find M. Zhao re: exploring climate sensitivity through cloud precipitation modeling or something close to that:

        https://doi.org/10.1175/JCLI-D-15-0191.1

        What I noticed in reading several references, like Dan Hughes statements regarding the order of time step additions of sub-grid systems; the first 40 minutes of the UTube of Tim Palmer; and this Zhao article on GCM modeling of internal microphysics: sub-grid systems matter, they are not well represented in GCMs; and for me, the money statement: clouds are a 100 meter problem and the GCMs resolution are at 100 Kilometer problem. And like you say, efforts to model/parameterize these internal variables are underway, yet the resolved microphysics outcomes do not appear to repeat. Hence, there is no apparent similarities of these internal sub-grid system outcomes of the past nor likelihood of a future equilibrium state.

        Pursuing ECS, as in current climate modeling just seems like “churning”, as in doing the same thing over and over again, expecting a different outcome. (of course paraphrasing Mr. Einstein)

      • RiH008, Well stated. You are much more knowledgable than you gave yourself credit for earlier.

      • We know from Milankovitch cycles that small forcing changes can have large climate impacts, and it is not always just linear. There are tipping points that can be triggered by forcing changes. So, no, boundary changes are not always deterministic in a linear ECS sense. There are some large amplifiers, especially related to global ice cover, that may not show up immediately, but can show up in response to forcing changes.

  34. Pingback: Weekly Climate and Energy News Roundup #317 | Watts Up With That?

  35. Pingback: Weekly Climate and Energy News Roundup #317 |

  36. Berényi Péter

    If the climate system were a reproducible thermodynamic system, that is microstates belonging to the same macrostate would always evolve into the same macrostate, then it would imply it is subject to the Maximum Entropy Production Principle.

    In the climate system the vast majority of entropy is produced when incoming short wave radiation gets thermalized. Which means the less short wave radiation is reflected back to space, the higher the rate of entropy production. Therefore a reproducible system is pitch black as seen from space.

    On the other hand, Earth is not black, but white-blue (its albedo is ~30%). Therefore it is not a reproducible system, that is, microstates belonging to the same macrostate can evolve into different macrostates in a short time.

    It may be because it is a chaotic system. But in that case this fact does not only imply its future state can’t be calculated exactly, but it also determines its albedo, which is a very visible feature.

    • On the other hand, Earth is not black, but white-blue (its albedo is ~30%). Therefore it is not a reproducible system,

      When albedo gets below 30%, warm thawed ocean will provide more moisture for snowfall and it will snow more until albedo gets above 30%. When albedo gets above 30% a more frozen ocean will provide less moisture for snowfall and it will snow less until albedo gets below 30%.

      That number, 30%, has been a higher number in much colder times and has been a lower number in much warmer times, but now, it is around 30%.

      • Berényi Péter

        I know that, but Dewar says the Maximum Entropy Production Principle applies for all stationary, open, non-equilibrium thermodynamic systems, provided their Jaynes entropy can be defined, that is, they are reproducible.

        https://arxiv.org/ftp/cond-mat/papers/0005/0005382.pdf

        Now, the MEPP obviously does not apply to the terrestrial climate system, because Earth is not black. Therefore this system is not reproducible, possibly due to its chaotic dynamics.

        That means microstates belonging to the same macrostate can evolve into different macrostates in a short time.

        So. The ~30% albedo observed is not caused by a simple feedback, as you suggest, but chaos plays an essential role in it.

        Moreover, terrestrial albedo is highly regulated, as shown by Voigt at al.

        https://journals.ametsoc.org/doi/full/10.1175/JCLI-D-12-00132.1

        We just do not fully understand it, for theory of chaotic regulation is underdeveloped.

      • We just do not fully understand it, for theory of chaotic regulation is underdeveloped.

        Earth climate is chaotic only because what is a most important factor is not understood and not included. The 30% is made up of many parts. The part that earth adjusts to do the regulation inside the bounds of the other factors is the ice. Ice Extent is adjusted to regulate cooling by thawing and reflection (albedo). Ice volume is adjusted to regulate ice flow rate. Snowfall rate is adjusted to regulate ice volume. Sea ice extent is adjusted to regulate snowfall. The temperature that sea ice freezes and thaws is the set point for the thermostat. It always snows more when the oceans are more thawed. It always snows less when the oceans are more frozen. This causes cold times to always follow warm times and it causes warm times to always follow cold times. These cycles are in sometimes in phase and sometimes out of phase with other forcing factor, but ice extent is always in phase with temperature. Ice core data shows this to be true.

      • When you treat ice as a result of external forcing, the data is chaotic.
        When you treat ice as a major internal factor the chaos is gone.

        Try it, you will like it!

      • Forget the complicated stuff, when temperature is bounded as well as earth, in both very different hemispheres with alternating external forcing from the sun, something simple and powerful is causing the bounding. Water in all of its wonderful states, with different phases that can take in or release energy with freezing and thawing and evaporating and condensing, is responsible for our wonderful climate. The balance between ice on land and water in the oceans does explain the climate change for the past fifty million years. Each hemisphere produces enough thawed ocean and resulting snowfall to keep sending temperatures below the set point where oceans freeze and turn off the snowfall until it warms again.

      • Cooling from thawing ice is as important as the cooling from more albedo due to increased ice extent. The cooling from thawing is ignored by climate scientists.

        In warm times, much of the IR out comes from producing ice. That much cooling is done later when the ice thaws. A large ice machine requires much energy to power it and it requires much energy to be removed. This only happens when the oceans have been warmed and thawed. When earth is cold, there is not enough energy in or energy removed to produce ice. Think about these simple principles.

  37. Internal variability

    I noted this recent paper in a comment above:

    Donahue, A. S., & Caldwell, P. M. (2018). Impact of physics parameterization ordering in a global atmosphere model. Journal of Advances in Modeling Earth Systems, 10, 481–499. https://doi.org/10.1002/2017MS001067

    Abstract

    Because weather and climate models must capture a wide variety of spatial and temporal scales, they rely heavily on parameterizations of subgrid-scale processes. The goal of this study is to demonstrate that the assumptions used to couple these parameterizations have an important effect on the climate of version 0 of the Energy Exascale Earth System Model (E3SM) General Circulation Model (GCM), a close relative of version 1 of the Community Earth System Model (CESM1). Like most GCMs, parameterizations in E3SM are sequentially split in the sense that parameterizations are called one after another with each subsequent process feeling the effect of the preceding processes. This coupling strategy is noncommutative in the sense that the order in which processes are called impacts the solution. By examining a suite of 24 simulations with deep convection, shallow convection, macrophysics/microphysics, and radiation parameterizations reordered, process order is shown to have a big impact on predicted climate. In particular, reordering of processes induces differences in net climate feedback that are as big as the intermodel spread in phase 5 of the Coupled Model Intercomparison Project. One reason why process ordering has such a large impact is that the effect of each process is influenced by the processes preceding it. Where output is written is therefore an important control on apparent model behavior. Application of k-means clustering demonstrates that the positioning of macro/microphysics and shallow convection plays a critical role on the model solution.

    [ Figure 1 provides an illustration of some of the sub-systems and physical phenomena and processes used in my post.]

    The results of the analyses show directly that by simply making changes in the order in which sub-grid parameterizations are evaluated, significant changes in response functions of interest are produced. This is a well-known problem area when numerical methods are developed for equation systems composed of PDEs plus algebraic equations. The time level at which the latter are evaluated requires close investigations.

    It is an excellent assumption that the boundary condition constraints remained un-altered during the series of executions of the model.

    Changing the order of parameterization evaluation, with boundary condition constraints fixed, changes the internal variability of the simulated climate.

    It is not a boundary value problem. It is an Ill-Posed Initial-Boundary Value Problem.

    The results also illustrate other aspects of real-world climate modeling, including: parameterizations, tuning, Verification, and Validation.

    Parameterization:
    The paper focus is on a few parameterizations, not the numerical solution methods for the basic continuous equations. In many real-world, messy and complex problems, parameterization is very important in order to set a tractable computational problem. Hopefully the parameterizations are not critically important relative to achieving high fidelity to the physical domain. That is, something is needed to close the problem, but does not significantly and directly impact the responses of interest. However that is not always the case and the parameterizations are critically important to the extent that more nearly correct representation of the phenomena or process is required. The parameterizations that are important in Climate Science can be identified due to the use of certain of them in tuning the model to meet historical data records. You don’t use unimportant parameters for tuning exercises.

    Tuning:
    One target for tuning, I think, might be to get the radiative energy transport at the ToA such that incoming and outgoing radiative energy are equal for pre-industrial conditions.

    For a variety of reasons, the model continuous equations, numerical solution methods, and grid resolution cannot represent the actual state of Earth’s climate system. Given the model equations, solution method, grid resolution, and parameter values, among other aspects, the model determines the modelled physical phenomena and processes in the sub-systems that comprise the model. These include the hydrodynamic, thermodynamic, chemical, and biological state of the materials in the system.

    When a parameter associated with one sub-system or the interface between sub-systems is changed, that causes changes in the calculated states: the changes in the parameter cause the previous states and distributions to be altered. The new states also do not correspond to the actual state of the climate system. Given the immense complexity of the problem, there is no way to know that, while the tuning objective might be more nearly on target, the states of some sub-systems might be farther from the actual states. The re-distributions of the energy content, for example, might be altered in a non-physical manner. The focus on a given response function and metric can be such that other aspects are ignored.

    Verification:
    The exercises investigated in the paper also address Verification ( solving the equations right ) of (1) numerical methods, (2) coding, and (3) calculations. These are critically important aspects of real-world scientific and engineering software development.

    Validation:
    The exercises address also Validation ( solving the right equations ) in that the calculated results are compared with measured data.

    I think the paper is a very important addition to the scientific computation literature in Climate Science. It points to the direction of much future work.

    The paper represents a sharp contrast to the imaginary world of Laws of Physics, Boundary Value Problem, Exact Equality of Radiative Energy Transport, Global Functional Response Functions and Associated Metrics, and dismissal of the need for Independent Verification and Validation.

  38. “AOS models are members of the broader class of deterministic chaotic dynamical systems, which provides several expectations about their properties (Fig. 1). In the context of weather prediction, the generic property of sensitive dependence is well understood (4, 5). For a particular model, small differences in initial state (indistinguishable within the sampling uncertainty for atmospheric measurements) amplify with time at an exponential rate until saturating at a magnitude comparable to the range of intrinsic variability. Model differences are another source of sensitive dependence. Thus, a deterministic weather forecast cannot be accurate after a period of a few weeks, and the time interval for skillful modern forecasts is only somewhat shorter than the estimate for this theoretical limit. In the context of equilibrium climate dynamics, there is another generic property that is also relevant for AOS, namely structural instability (6). Small changes in model formulation, either its equation set or parameter values, induce significant differences in the long-time distribution functions for the dependent variables (i.e., the phase-space attractor). The character of the changes can be either metrical (e.g., different means or variances) or topological (different attractor shapes). Structural instability is the norm for broad classes of chaotic dynamical systems that can be so assessed (e.g., see ref. 7). Obviously, among the options for discrete algorithms and parameterization schemes, and perhaps especially for coupling to nonfluid processes, there are many ways that AOS model equation sets can and will change and hence will be vulnerable to structurally unstable behavior…


    Fig. 1. Generic behaviors for chaotic dynamical systems with dependent variables ξ(t) and η(t). (Left) Sensitive dependence. Small changes in initial or boundary conditions imply limited predictability with (Lyapunov) exponential growth in phase differences. (Right) Structural instability. Small changes in model formulation alter the long-time probability distribution function (PDF) (i.e., the attractor)…

    Sensitive dependence and structural instability are humbling twin properties for chaotic dynamical systems, indicating limits about which kinds of questions are theoretically answerable. They echo other famous limitations on scientist’s expectations, namely the undecidability of some propositions within axiomatic mathematical systems (Gödel’s theorem) and the uncomputability of some algorithms due to excessive size of the calculation (see ref. 26).” http://www.pnas.org/content/104/21/8709#F2

    The mechanics of the evolution of trajectories of solutions of a nonlinear set of equations for a single model is difficult to visualize. It involves the interactions of process equations for many factors at many scales. But the experiment has been done. Even with trajectories arbitrarily confined to the vicinity of surface temps – the range is broader than IPCC opportunistic ensembles.


    https://www.nature.com/articles/ngeo1430

    The thick black line is mine. The thing to note about IPCC ensemble members is that they pull the ‘correct solution’ out of their a posteriori.

  39. Of all the comments and points, it seems this quote is the most significant.

    “Perhaps we can visualize the day when all of the relevant physical principles will be perfectly known.”

    Until that day it’s best for everyone to maintain a little humility.

    • The rest of that quote – Julia Slingo and Tim Palmer quoting Edward Lorenz- is quite good too.

      “Thirty years later, this problem remains unsolved, and may possibly be unsolvable.”

    • afonzarelli

      One thing we can know is by looking at the 100k year ice ages. If we’re generous, we can assign one third of the warming from glacial to interglacial as due to GHGs. And if we’re even more charitable, we could assign one third of the GHG warming to changes in CO2. Given all that gift, we would then come to the conclusion that ECS is no more than 1°C. (and if we’re not quite so kind, it’s more than likely even less) The only question after that is whether or not the one time dumping of ACO2 somehow differs from the experiment concluded by the ice ages…

      • if we look at the ice age cycles. one thing is very clear, cold times had more ice extent and warm times had less ice extent. This is cause and not result. warm times have more snowfall and it gets cold after that. cold times have less snowfall and it gets warm after that. The natural cycles are normal, natural, necessary, and unstoppable.

        We can assign nothing to GHG’s.

      • afonzarelli

        Pope, i hear you. It’s beyond belief that GHGs could have had much of anything to do with warming coming out of glacials. (let alone co2 by itself) The massive changes in ice albedo alone should dwarf any contribution from GHGs. Somethin’ jus’ don’t add up here…

  40. Meanwhile back in the Pacific – it looks like we’ll all be waiting for el Ninot for a while yet…

    http://www.bom.gov.au/climate/enso/#tabs=Outlooks

    • That’s the problem with models – but something is more likely than not to happen in the Austral spring.

      The fundamental ENSO mode is the La Nina normal. That is modulated by the strength of the South Pacific gyre. While the AAO remains negative – La Nina is more likely.

  41. Pingback: Initial value problem vs boundary value problem | …and Then There's Physics

  42. I commented on this blog several years ago that climate modellers don’t know what the term “boundary value problem” means. This is part of basic terminology of differential equations that I remember from undergraduate lectures, and is confirmed here: https://en.wikipedia.org/wiki/Boundary_value_problem

    I strongly recommend reading that.

    A BVP is one is which the independent variable is *given* on some *boundary*. A common example is a drum head in which the displacement is zero at the edge of the drum. Solving the PDE gives you the possible modes of oscillation of a drum with the given shape.

    What is the boundary in the climate system, what value is given (i.e. known at the outset, not having to be calculated) at the boundary?

    As used in climate science BVP seems to mean some generalized constraint on the system, such as energy, or even just that we are interested in the extreme values between which the system might oscillate.

    Neither of these meanings has anything to to with the actual meaning of a BVP.

    Take for example a chaotic pendulum. https://en.wikipedia.org/wiki/Double_pendulum

    The system conserves energy. The energy is a constraint on the motion of the system. It is not a boundary value, and this is not a BVP. It is an initial value problem. (A conserved quantity is an integral of the motion, not a BV)

    Incidentally, when I realized that many prominent “climate scientists” don’t even understand the basic terminology of differential equations is when I stopped being surprised that their climate models spew out rubbish and have zero predictive value.

  43. Request for information.

    After citing mathematical literature from the last quarter of the 20th century, I was recently admonished to focus on the 21st century properties of GCMs. I’m trying to find out how many of the mainline GCMs used for the IPCC Assessment Report are still based on the hydrostatic equilibrium assumption.

    In December 2013, early in the 21st century, Professor Dargan M. W. Frierson, University of Washington, Department of Atmospheric Sciences, in this presentation summarized the the status of the GCMs that supplied results for CMIP3:

    Of 24 models in the CMIP3 archive (models used for IPCC AR4): 1 was non-hydrostatic (Had-GEM)

    So, early in the 21st century, 23 of the 24 GCMs are all Ill-Posed Initial-Boundary Value Problem models.

    I seem to have lost my Google mojo and have not been successful in finding the same information for CMIP5, or CMIP6. Chapter 9 of the IPCC AR5 report lists the models used for that report, but does not mention numerical solution methods: At all, which I find interesting in itself. There’s a lot of stuff in that chapter, maybe I’ve missed it. Several Googles have not resulted in any useful hits.

    Does anyone have this information handily summarized? Tracking down the status GCM-by-GCM is a procedure of last resort.

    On a related matter, Professor Frierson also said this:

    This (and other accompanying small aspect ratio approximations) are the only approximations made in dynamical cores

    Where ‘this’ refers to ‘hydrostatic assumption’ and the bold is in the original. As we all are well aware, it’s a very long, challenging, iterative, and mathematically hazardous, path from the continuous equations to the printed output numbers.

    Thanks for any information.

    • Dan, I don’t know the answer to your question about current GCM’s. I do know that they have a stability problem in all GCM’s and they cure it with “hyper viscosity.” This is purely a numerical thing and might dissipate waves too quickly. Browning had some references on that that he gave at Climate audit a while ago.

  44. Pingback: Of boundary and initial conditions | Climate Etc.

  45. What if Earth obeys electric field equations like this:
    http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elesph.html

    Gravitational charge:
    TSI/8g²=(4/3)/(4/3)
    and
    4g²=384N/m²=384W/m²=287K
    and
    ∆U(TSI)=4Q(4σ256⁴)+4W(4g²)

    I think there is a lot to learn about our orbiting planet/electron.