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Absence and Evidence

Guest commentary by Michael Tobis, a retired climate scientist. He is a software developer and science writer living in Ottawa, Ontario.

A recent opinion piece by economist Ross McKitrick in the Financial Post, which attracted considerable attention in Canada, carried the provocative headline “This scientist proved climate change isn’t causing extreme weather – so politicians attacked”.

In fact, the scientist referenced in the headline, Roger Pielke Jr., proved no such thing. He examined some data, but he did not find compelling evidence regarding whether or not human influence is causing or influencing extreme events.

Should such a commonplace failure be broadly promoted as a decisive result that merits public interest?

ABSENCE OF EVIDENCE VERSUS EVIDENCE OF ABSENCE

Statistics is a vital tool of science, but it is not the only one. It is most effective when dealing with large quantities of data. Using statistical methods to detect the effect of one factor among several amounts to proving that the other factors did not align as a matter of happenstance. The more abundant the data, the less likely such a coincidence.

In the case of extreme weather, the number of sample points is small because extreme events by definition are rare. Up until the beginning of the satellite era, records of past events are often incomplete. There is little we can do to improve the amount of such data at hand. Because the data are irredeemably scarce, and time series short, using purely “frequentist” statistical methods to decide whether or not climate change makes a certain type of severe event more likely will tend to be inconclusive.

Limiting attention only to the most severe storms of a particular type, and then further limiting it to those causing the most extreme financial damage, drastically reduces the number of samples considered, and so further reduces the likelihood that a real trend will be detected.

It’s a well-known motto in research that “absence of evidence” is not “evidence of absence”. It’s well known because it is a common beginners’ error to conflate these. Scientists in training quickly learn that “we find no evidence of phenomenon P” is not the same as “we found evidence that phenomenon P is false”. The proposition in question could well be true but the analysis may lack enough data to show it. (The test is said to be underpowered). Yet a systematic neglect of this simple point is pervasive among those skeptical of the risks of climate change.

Those who wish to avoid vigorous climate policy have gotten a lot of mileage out of inconclusive results.

HOW TO GET INCONCLUSIVE RESULTS

There is, along the periphery of climate science, an enthusiastic audience for null results: people who don’t want to accept the seriousness of climate risk will celebrate any absence of a demonstrated trend or inconclusive attribution. But it’s always possible to obtain a null result, i.e., a lack of statistical significance, if one seeks it, by reducing the amount of data under consideration.

Most science works the other way around, looking for relationships and trends that actually do seem to be happening! There is, under ordinary circumstances an audience for significant results. Were we not operating in a politicized context, detection would be considered more important than lack thereof.

To increase the likelihood of detection, we can look at larger categories of event. For example, in a 2013 report, the European Academies’ Science Advisory Council, examined trends in the specific extremes of heat and cold, precipitation, storms, winds and surges, and drought. The agency found evidence for “overall increases in the frequency and economic costs of extreme events”.

Much of Pielke’s work focuses largely on insurance costs of landfalling hurricanes in the USA, an especially rare phenomenon influenced by numerous factors and one with especially peculiar statistics. It’s an ideal field in which to get a null result, if that’s what the investigator is seeking.

An important point in looking at actuarial damages is that building standards and warning systems have systematically improved. In the absence of a climate-driven trend, we’d expect damages to decline. This counter-argument is made in many places, for example Dr. Kevin Trenberth in a book review:

[Pielke] ignores the benefits from improvements in hurricane warning times, changes in building codes, and other factors that have been important in reducing losses.”

Another approach to hide climate-driven damage is to blur trends. We expect (from physical arguments and models) and find (from observations) increasing precipitation at higher latitudes and decreasing precipitation in dry subtropical latitudes. Aggregating them, the net result is no global trend in drought, and true to form McKitrick celebrates this result as well.

Source: A dryer southwest and wetter northeast, so no overall trend. An example of how averaging can obscure significant results.

Aggregating such non-results and obscured results brings us to McKitrick’s sweeping conclusion.

“There’s no trend in hurricane-related flooding in the U.S. Nor is there evidence of an increase in floods globally. Since 1965, more parts of the U.S. have seen a decrease in flooding than have seen an increase. And from 1940 to today, flood damage as a percentage of GDP has fallen to less than 0.05 per cent per year from about 0.2 per cent. And on it goes. There’s no trend in U.S. tornado damage (in fact, 2012 to 2017 was below average). There’s no trend in global droughts. Cold snaps in the U.S. are down but, unexpectedly, so are heatwaves.”

McKitrick leaves the impression that all these conclusions are unequivocal, and that none of them have been hamstrung by approaches that are unlikely to yield significant trends.

Even at face value these specific claims, combined with a world-weary “and on it goes” isn’t enough to logically support his broad conclusion that “The bottom line is there’s no solid connection between climate change and the major indicators of extreme weather.”

Jumping from specific observations to a broad conclusion, as McKitrick does, is rhetorical, not scientific. In addition to being a logical fallacy, it ignores a great deal of evidence to the contrary. 

“This cow is black, and that one, and that one, and on it goes,” is not enough to prove that all cows are black when there are spotted cows aplenty in the field.

TIME AND TIDE

The evidence to the effect that there is a connection between anthropogenic climate change and increasing severe events, far from being absent, is in fact rapidly accumulating.

McKitrick makes much of Pielke’s role in a 2006 conference on severe weather which released a consensus document, the Hohenkammer Consensus, that was a fair assessment of knowledge at the time. That report asserts that “In the near future the quantitative link (attribution) of trends in storm and flood losses to climate changes related to GHG emissions is unlikely to be answered unequivocally.”

It is in exactly this pool of equivocality that Pielke has been content to operate. But is that pool shrinking?

Both science and climate change itself are advancing at a rapid pace. What was true in the “near future” of 2006 is not necessarily true today! So in using more advanced methods to study a more advanced disruption, has the situation changed?

In fact it has. Methods for attributing individual severe events partially to climate change have emerged. In 2016, the National Academy of Science of the USA issued a report entitled Attribution of Extreme Weather Events In the Context of Climate Change, which enumerates the ongoing efforts. Among its key conclusions:

“The ability to understand and explain extreme events in the context of climate change has developed very rapidly over the past decade. In the past, a typical climate scientist’s response to questions about climate change’s role in any given extreme weather event was, ‘We cannot attribute any single event to climate change.’ The science has advanced to the point that this is no longer true.”

While not without complexity or controversy, attribution studies are complex and subject to the usual debates and disagreements that evolving fields of science undergo. Such work is extensive and carried out by multiple research groups in multiple countries (see also Going To Extremes from this site).

The Bulletin of the American Meteorological Society has, since 2011, been releasing special issues on the subject of extreme event attribution. In recent issues, cases of severe events have been identified that would have been essentially impossible in the undisturbed climate. New examples have been published recently, indicating that heat waves in Europe and North America and in Japan couldn’t have occurred in the absence of human-caused climate change.

So McKitrick’s claim that “the bottom line is there’s no solid connection between climate change and the major indicators of extreme weather, despite Trudeau’s claims to the contrary” is at best out-of-date and ill-informed. Some might call it deceptive.

One can always dismiss evidence one doesn’t like as not “solid”, of course. But by now, there’s quite a lot of evidence to dismiss and McKitrick, rather than addressing it avoids any mention of any of it whatsoever. One expects better from an academic.

SO WHAT IS REALLY GOING ON?

While determining exactly which severe events are more likely already under climate change, and which will become so, we should begin by focusing on what is known currently.

Quoting from the aforementioned 2006 consensus document that McKitrick celebrates, it was already known that:

  • Climate change is real, and has a significant human component related to greenhouse gases
  • For future decades the IPCC (2001) expects increases in the occurrence and/or intensity of some extreme events as a result of anthropogenic climate change
  • Direct economic losses of global disasters have increased in recent decades with particularly large increases since the 1980s
  • There is evidence that changing patterns of extreme events are drivers for recent increases in global losses.

McKitrick leaves the reader with the impression that the report had other conclusions. The 2006 report only said that the reasonably inferred causality between human-caused climate change and increasing severe events wasn’t as yet proven.

Since the time of that conference, not only climate change but increases in the frequency of disruptive events have become rather obvious in many regions of the world, including Canada. The evidence has shifted remarkably. 

These are the troublesome events we expect, and many of these troubles appear to be happening with increased frequency and severity.

If someone argues, as they may, that the connection is not yet proven to their satisfaction, they may or may not have a case. Indeed, I (the author of this article) have expressed some concerns about the validity of the single-event attribution approach. But questioning an approach is one thing. To claim or imply that something is disproved by systematically ignoring evidence to the contrary is another thing entirely. To do so is to undermine discourse. It’s simply misleading and irresponsible.

WHAT ABOUT CANADA?

Environment and Climate Change Canada recently released “Canada’s Changing Climate Report”. As with most scientific consensus documents, it is careful to emphasize scientific uncertainty. Its opening sentence is nevertheless unequivocal: “There is overwhelming evidence that the Earth has warmed during the Industrial Era and that the main cause of this warming is human influence. “

Regarding the specific issues raised by McKitrick, the report’s conclusion is

“In the future, a warmer climate will intensify some weather extremes. Extreme hot temperatures will become more frequent and more intense. This will increase the severity of heatwaves, and contribute to increased drought and wildfire risks. While inland flooding results from multiple factors, more intense rainfalls will increase urban flood risks. It is uncertain how warmer temperatures and smaller snowpacks will combine to affect the frequency and magnitude of snowmelt-related flooding.”

Katherine Hayhoe, in an article in Chatelaine, a popular magazine published in Canada, points out that

The Insurance Bureau of Canada estimates “catastrophic losses due to natural disasters have increased dramatically” over the last 10 years, with $1.9 billion of insured loss in 2018 alone. Extreme weather-related losses reported during the ’90s and 2000s averaged around half a billion dollars per year. Even leaving out damages from the record-breaking Fort McMurray wildfires, losses in the 2010s are still three times higher, averaging almost $1.5 billion per year through 2018.”

insured losses from environmental disasters in Canada, in constant dollars via Insurance Bureau of Canada.

This is what climate science expects, and this is what we see. There are conflating influences  – more property value exists, and conceivably it is, for some extraneous reason, more at risk. Still the trend in Canada is particularly striking.

One can argue whether the connection is as yet “proven” in the sense of statistical hypothesis testing, but it’s far from being disproven. To the contrary, it is reasonable to expect the proof to continue to emerge.

SCIENCE, POLITICS AND REASON

Scientists, being humans living on the Earth, are not immune from political and policy preferences. While as scientists they are trained to resist such biases, no one denies that such influences exist and need to be considered. But this cuts both ways.

Of course, taking climate change seriously will require substantial shifts in public policy, and many are threatened by these, whether by direct financial motivation or a strong philosophical preference for laissez-faire organization of society. Those scientists who are most popular among those so threatened are ones who seem to actively look for inconclusive results. In doing so they may advance their own careers, but they hardly advance either science or public discourse.

When one-sided articles like McKitrick’s come out that are rife with logical fallacies, it’s more than a little bit ironic to see them accusing their opposition of bias.

Democracies, including Canada. historically have been especially capable of arguing about contentious issues from common values and shared understanding of facts. Recent adverse trends in political discourse have been very disturbing.

McKitrick’s article is a part of this disturbing trend – it amounts to a personal attack on Prime Minister Trudeau, selecting and bending facts to create a misleading conclusion. The attacks imply that the Prime Minister and his government are casually misinformed, and concede nothing to those with whom the author disagrees.

This is not the way to solve problems or maintain a civil society. Let’s do better.

139 Responses to “Absence and Evidence”

  1. 101
    David Young says:

    Paul Pukite, Your long list of irrelevancies is silly and beside the point.

    Gravity forces are essentially constant and can have little effect on weather which is what this post is about. The main point is that temperature enters the equation only as a gradient. Likewise for pressure. Thus, the main driver of changes in weather is changes in temperature gradients and possibly pressure gradients. You might read #73 in which Adam Lea explains my point in thermodynamic terms.

    Dan Hughes does a good deconstructing your misrepresentations in detail.

  2. 102
    nigelj says:

    David Young @93

    “The IPCC says that there is only weak evidence of increases in severe weather. ”

    The summary for policy makers says “A.1.3 Trends in intensity and frequency of some climate and weather extremes have been detected over time spans during which about 0.5°C of global warming occurred (medium confidence). This assessment is based on several lines of evidence, including attribution studies for changes in extremes since 1950. {3.3.1, 3.3.2, 3.3.3} .” This is clearly something more than weak evidence.

  3. 103
    David Young says:

    Nigel, Your proof text quote is very vague and largely meaningless. Which events? Have others like tornados been decreasing? How much have they increased? This is so typical of these conversations. Usually more cautious scientists don’t say much on these subjects because the trends are small (with the exception of tornado decreases) and the fundamental physics not very conclusive. BTW, the data that are most reliable such as tornadoes and US land falling hurricanes show a decrease or little trend.

  4. 104

    David Young said:

    ” There are external “forces” in the Navier-Stokes such as gravity forces. These generally are close to constant just like solar insolation and so have only a minor effect on weather or indeed climate. This is particularly true for severe storms which are almost totally a function of gradients in temperature and pressure.”

    Keep digging that hole, DY. How can gravity forces have only a minor effect when the dynamic gravitational cycles associated with lunisolar forcing is responsible for ocean tides? In 1776, Pierre-Simon Laplace formulated his namesake Laplace’s Tidal Equations which can be used to model fluid displacements across the rotating earth. These equations, also known as the shallow-water equations and a subset of the primitive equations used in GCMs, are actually a linearization of the complete set of Navier-Stokes equations.

    What bothers me so much about DY’s debating approach is that he tries so hard to be an impediment to any geophysical fluid dynamics research — always claiming that some aspect of Navier-Stokes makes it impossible to produce valid results.

    Yet, what we find with a practical application of the tidal equations is that the complexity completely drops out and we are left with a solution that is a simple forced response directly from the known tidal factor periods … Oops … not so difficult after all!

    I tend to give the benefit of the doubt that breakthroughs are still possible and would hate to see scientists give up on working on GFD problems because some wind-tunnel engineer thinks it’s all pointless.

  5. 105
    Killian says:

    Re# 66 Michael Tobis said Too much of a doomer bent has among its more severe consequences the weakening of the credibility of the actual evidence of the actual very serious situation. (Another is that it supports Macpherson-ite doomer fatalism and withdrawal from the battle to save what can still be saved.)

    This is over-simplified, revealing your own “bent” against straight talk. That you use “doomerism” pejoratively says much, also. In fact, the climate agenda was essentially stalled until ExtinctionRebellion and SchoolStrike stated the obvious: Doom, doom and more doom, unless we act.

    To call the truth doomerism does far more damage than fools like McPherson because, for chrissake, man, you’re (scientists, high profile activists, knowledgeable politicians, et al) seen as an authority. When you speak of extinction as doomerism, *you* are slowing action on climate.

    The fact is, extinction is underway and all the news is bad. The last couple of weeks of newly published science has been astoundingly bad news. We ARE headed for extinction or something very close to it. The kids, I guess because they’re kids, have it right and have finally gotten mass movement action started. This is *not* because they accepted the admonitions to speak softly and carry no goddamned stick at all, but because they stomped and picked up a big damned stick and swung hard.

    Now, I have been doing the same for a decade to pretty much zero effect, have been called a doomer, and alarmist, catastrophist, etc., so I am very sensitive to people saying obviously ridiculous things like you do in the quote above. I was right. Time was short. The message that would galavanize people was the long-tail threat coupled with viable solutions, not soft paeans to scientific semi-certitude and averages and the constant underestimates seemingly inherent to climate science.

    You are, Michael, conflating what should be said scientifically with what should be said policy-wise and public discussion-wise. The science is always behind reality, so policy must necessarily be forward-looking and taking the risk if overreacting. So be it. Better safe than sorry.

    So, let me fix your statement: There is no such thing as too much of a “doomer” bent as the threat is, in fact, scientifically measured and codified, extinction. However, such talk has among its more severe consequences the weakening of the credibility of the actual evidence of the very serious situation if not coupled with a coherent approach to mitigation (and adaptation to changes already in the pipeline that no amount of mitigation can change, such as some minimum level of SLR – likely several meters.) Shouting, gnashing teeth and rending garments about the existential threat without fully engaging solutions supports Macpherson-ite doomer fatalism (which is logically useless and scientifically unsupported.)

  6. 106
    David B. Benson says:

    David Young — You may care to read the Wikipedia page on Katabatic Winds.

    “… down a slope under the force of gravity.”

  7. 107
    Ray Ladbury says:

    David Young: “Gravity forces are essentially constant and can have little effect on weather which is what this post is about.”

    Cough, cough, katabatic (e.g. Chinook) winds, cough, cough.

  8. 108
    Dan Hughes says:

    At #92 Paul Pukite said:
    Dan Hughes gyrations reminds me of his contorted reasoning in defending Judith Curry when she tried to apply Bose-Einstein statistics to droplet and ice nucleation. (Look it up)

    I’ll save interested readers the trouble of searching. The text in question is given in this book.

    My comments on the book include the review at the Amazon store, and 2 comments in a post at Climate etc. in which the material is first discussed: Thermodynamics, Kinetics and Microphysics of Clouds.

    You can search in the post for my comments; I’ll not repeat them here. None of my 3 brief comments address the focus of Paul’s comment above.

    Importantly, again in stark contrast to Paul’s characterization; … defending Judith Curry when she tried to apply Bose-Einstein statistics to droplet and ice nucleation., my comments do not in any way address Curry’s application of B-E statistics to droplet and ice nucleation. That’s because Curry has never made any such applications. Yet another SOP blatant mis-characterization by Paul.

    There was a follow-up post at Climate etc. by Vitaly Khvorostyanov the first author of the book:
    Vitaly Khvorostyanov responds.

    The response was considered necessary because Paul’s comments consisted only of completely false claims and mis-characterizations. In that post you’ll find this statement:

    “no rebuttal from WHUT, instead WHUT has gone over to ATTP to continue sniping” (WHUT is an ID used by Paul Pukite)

    Paul’s hi-jacking of technical threads in Blog World goes back to at least 2012. By now, the threads that he has destroyed must be almost uncountable.

    Finally, note that in his comment above ( and all of his comments, generally ), Paul does not cite any specific parts of any of my comments. Instead he again mis-characterizes and falsely and blatantly denigrates my comments as gyrations and contorted reasoning. How are the firmly-established, universally accepted, and validated physical phenomena of conservative forces, and associated mathematics of vector gradients and scalar potentials “gyrations”?

  9. 109
    David Young says:

    Benson and Ladbury, The point is that gravity forces are constant in time and thus can not cause changes in weather. Of course this post is about changes in weather events.

    Pukite, Your latest comment has not technical content. Gravity is constant over time and thus has no net effect on changes in weather. Your “point” is a total red herring. You have a history of attacking people for supposed “errors” that are not errors at all. What I said is correct in that its temperature gradients that cause weather.

  10. 110
    David Young says:

    #104. You just can’t help yourself Paul P. You keep misrepresenting what Ive said over and over again. Research is good and progress is possible. You perhaps should read up on settled science however. Your grey literature “publications” don’t measure up.

    https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3270390/

    Dan Hughes is right, you seem to be able to say nothing that is actually true and you seem to always misrepresent the comments of everyone else.

  11. 111

    In addition to katabatic winds mentioned by David Benson and Ray Ladbury, one would think that any reference to gravity wind or gravity wave would give it away from the name alone.

    As for the protestation of Dan Hughes, many climate scientists have backgrounds in condensed matter physics (such as Prof. Mann and others) and likely find it just as odd that a scientist would randomly apply statistics intended for near-absolute-zero behaviors to something that is clearly a higher temperature phenomena.

    Curry with her Bose-Einstein statistics is the physics version of Dan Quayle’s “potatoe” for grammar nerds. So I encourage Hughes to keep on defending Curry, as it’s not my credibility that’s at steak ;)

    “(WHUT is an ID used by Paul Pukite)”

    Like no kidding, it’s right in my Twitter ID

  12. 112

    DY said:

    “Benson and Ladbury, The point is that gravity forces are constant in time and thus can not cause changes in weather. Of course this post is about changes in weather events.

    Pukite, Your latest comment has not technical content. Gravity is constant over time and thus has no net effect on changes in weather. Your “point” is a total red herring. You have a history of attacking people for supposed “errors” that are not errors at all. “

    Hint: What is the effective gravity along the thermocline?

  13. 113
    Matthew R Marler says:

    111, Paul Pukite: scientist would randomly apply statistics intended for near-absolute-zero behaviors to something that is clearly a higher temperature phenomena.

    Who said “randomly”? Since the other models do not model the phenomena (note, that’s plural) closely, why not try an model? Who exactly has ever proved or tested the range of temperatures over which the Bose-Einstein probability distribution might be a good approximation?

    Curry with her Bose-Einstein statistics is the physics version of Dan Quayle’s “potatoe” for grammar nerds

    That is absurd. It was a modest conjecture in a substantial work far exceeding anything Dan Quayle ever accomplished.

  14. 114
    David B. Benson says:

    Ray Ladbury @107 — Chinook winds are not katabatic. Santa Ana are and most importantly the typical Antarctic wind.

    David Young — The Antarctic katabatic wind begins in the stratosphere and proceeds to sea level: gravity is not constant. And for those over wintering in Antarctica, this wind is the weather.

  15. 115
    Dan Hughes says:

    At #111 Paul Pukite says; …and likely find it just as odd that a scientist would randomly apply statistics intended for near-absolute-zero behaviors to something that is clearly a higher temperature phenomena. [bold by edh]

    Paul continues to endlessly insist that an action that has never occurred has in fact occurred. The onus is on him to now, finally, explicitly identify where and when the action occurred.

    His failure to validate his assertions will be the final proof that his statements have all been without factual foundation. By the same token, his success in explicitly identifying where and when such an application did in fact occur will invalidate my comments.

    Paul’s success or failure to validate his comments should end this matter, once and for all after 5 years.

    As of now, I continue to stand by my comment made on September 8, 2014:

    A search of the Kindle edition shows that the Bose-Einstein concept is discussed in the text in Sections 3.2.4, 4.5, 8.2.3 and 8.3.2. The hit in Section 8.3.2 is the last hit in the text of the book. Equations 8.3.13 and 8.3.14 for the nucleation rate, which seem to be the results of interest, are not ever cited. This indicates to me that the Bose-Einstein results are not used whenever validation and applications of the models and methods is the focus.

    These findings were validated by the authors of the book.

    When Paul provides his evidence that Curry has applied B-E statistics to nucleation in ordinary water, the above will be invalidated.

    Paul also says; So I encourage Hughes to keep on defending Curry, as it’s not my credibility that’s at steak ;)

    No, Paul, your creditability is not at stake. You have failed to validate your claims, after having about 5 years to carry out a validation. You have self-established your complete lack of creditability.

    This comment by Paul contains (1) appeal to authority: authorties that so far as I am aware have never expressed any interest whatsoever in Paul’s false representations on the subject, and (2) a pure ad hominem. A two-fer in comment failure.

  16. 116

    Dan Hughes said

    “My comments on the book include the review at the Amazon store, …

    A search of the Kindle edition shows that the Bose-Einstein concept is discussed in the text in Sections 3.2.4, 4.5, 8.2.3 and 8.3.2. “

    It looks like thou doth protest too much. The fact remains, Curry’s book applied Bose-Einstein statistics to a material well above absolute zero, which is a howler to anyone that has studied condensed-matter physics or statistical mechanics. Was she really expecting to find the fifth-state of matter in the clouds?

  17. 117
    David Young says:

    Benson, The gravity field is nearly constant in time (with small perturbations due to the moon). The solar radiation field is nearly constant in time (with small perturbations due to the solar cycle). Both fields vary in space of course and both cause weather events. Neither has a significant effect on climate or can cause CHANGES in weather patterns or events over time. What you point out does not contradict what I said. It’s a red herring.

  18. 118
    Dan Hughes says:

    A long ways upthread, MT said: If you want to engage people, explain what you mean by a gradient and why that calls into question the simple “more energy – more bad weather” claim.

    This comment is long. The issue cannot be summarized in a few short blurb-type sentences. Due to the extreme off-topic nature of the thread so far, catching up with the technical issues is somewhat compressed.

    Specific, on-topic, corrections to incorrectos will be appreciated. It will help maintain focus if (1) the specific statement that contains the incorrecto is quoted, (2) identification of the specific aspect of the statement that is incorrect is explicit, and (3) the correcto is equally focused and explicit. Comments that do not meet these requirements will be ignored.

    Gradient, as a mathematical/technical concept, is in general not a word in most people’s day-to-day lives. I’ll take a cut at an zeroth-order summary. I did not ever bother to learn MML, and I don’t want to construct a detailed mathematical comment (tons of these are available by way of The Google), so this will be greatly distilled.

    As introductions, check out Differential Calculus of Vector Fields and Vector Integral Calculus by Freynman, and The Wiki divergence theorem. An accessible detailed exposition of the divergence theorem is available in Who Gave you the Epsilon?: And Other Tales of Mathematical History.

    The Feynman material is detailed mathematics and contains very much more than is necessary to address just the gradient matter. The Wiki material also is mathematical, as it must be. There might be a more nearly accessible discussion within the framework of the heat conduction equation; especially the one-dimensional case, see below.

    All flows, including hydrodynamic, thermodynamic, chemical, among others, require driving potentials. Such flows are generally described mathematically with the gradient of the driving potential; generally a spatial derivative of the driving potential. Heat, the flow of energy, requires a temperature gradient, electric current flow requires a voltage potential, are a couple examples.

    One important application of the concept lies in the Gauss/Stokes/Ostrogradsky divergence theorem discussed in The Wiki article mentioned above. When fundamental equations are applied on an averaged basis, as in discrete approximations to the continuous equations, they are generally averaged over a Representative Control Element (RCE) of the material. Finite-volume methods make application of the divergence theorem explicit: Finite Volume Methods for Hyperbolic Problems.

    A brief, big-picture, top-down application of the divergence theorem to the total energy equation, which can be written in terms of gradients, to Earth’s climate systems.

    The first equation in the Wiki article (doesn’t have a number) can be used to illustrate this application. In that equation, suppose the vector field, F, is the Fourier heat flux vector. For a one-dimensional case, the heat flux vector reduces to a single component F = -k (dT/dx), where k is the thermal conductivity and (dT/dx) is the temperature gradient. Then volume-averaging the continuous form of the fundamental heat conduction equation over a representative control volume, and using the divergence theorem to convert, as appropriate, volume integrals to surface integrals, the right-hand side of the Wiki equation says that F, the gradient of the temperature, is evaluated over the surface bounding the representative element.

    Frequently, in many practical applications, the spatial resolution used in numerical solution methods is not sufficient to accurately estimate the spatial derivatives and its variation along the bounding surface. In some cases, the critical, controlling physical mechanisms occur on such spatial scales that resolution would result in intractable problem formulation; turbulent flows, for example. The geometry of the bounding surface might be such that the details of the interface cannot be resolved and/or the variation of conditions along the interface are also complex.

    This is also especially the case whenever an interface between two different materials is present such as that between the atmosphere and the oceans. The divergence theorem then requires that the spatial gradient in each be resolved at the interface. Not to mention that numerically locating the interface is an exceedingly complex problem in and of itself. Almost universally in practical applications the gradient of the driving potential is estimated by an algebraic expression that includes the value of the driving potential on each side of the interface. For example, transport of sensible energy between the atmosphere and oceans will be estimated by an equation that is a heat transfer coefficient times the temperature difference between the atmosphere and ocean; h_c ( T_a – T_o ). It is the potential difference, and not the level of the potential, that drives the flow of sensible energy.

    Generally, for a given amount of energy addition into Earth’s climate systems, everything else remaining fixed at the initial values, the gases in the atmosphere will increase in temperature more rapidly than the liquid water in the oceans. That being the case, those regions of the oceans that are at temperature less than the atmosphere temperature will experience increased sensible energy exchange into the water. The ocean regions that are at temperature greater than the atmosphere temperature will experience a decrease in sensible energy exchange into the atmosphere. The changes in the temperature difference, and the change in the temperature level of the atmosphere also will affect changes in gravity-driven-dominated natural-convection fluid flows near the interfaces. Weather-scale atmospheric flows in nature are generally not simple, local gravity-driven-dominated natural-convection. They are instead large scale flows driven by the pressure distribution in the atmosphere and significantly influenced by Earth’s rotation, and the large scale topology of Earth’s surface.

    This example illustrates that it is not changes in energy content in and of itself that drives physical phenomena. Instead, it is the distribution, driven by potential gradients, of the energy among the systems, and the nature of the response of the individual systems to changes in energy content. As indicated above, if each of the interacting systems respond in the same manner, the driving potentail, while at an increased level, does not change.

    The complete energy exchange at the atmosphere-ocean interface, comprised of both sensible and latent energy, and the energy exchange mechanisms including both convective and radiative aspects, is more complex than this simple sensible-energy case. For example:

    Nicholas Siler, Gerard H. Roe, Kyle C. Armour, and Nicole Feldl (2018), Revisiting the surface-energy-flux perspective on the sensitivity of global precipitation to climate change, Climate Dynamics, Published online: 25 July 2018. https://doi.org/10.1007/s00382-018-4359-0

    Abstract
    Climate models simulate an increase in global precipitation at a rate of approximately 1-3% per Kelvin of global surface warming. This change is often interpreted through the lens of the atmospheric energy budget, in which the increase in global precipitation is mostly offset by an increase in net radiative cooling. Other studies have provided different interpretations from the perspective of the surface, where evaporation represents the turbulent transfer of latent heat to the atmosphere. Expanding on this surface perspective, here we derive a version of the Penman–Monteith equation that allows the change in ocean evaporation to be partitioned into a thermodynamic response to surface warming, and additional diagnostic contributions from changes in surface radiation, ocean heat uptake, and boundary-layer dynamics/relative humidity. In this framework,temperature is found to be the primary control on the rate of increase in global precipitation within model simulations of greenhouse gas warming, while the contributions from changes in surface radiation and ocean heat uptake are found to be secondary. The temperature contribution also dominates the spatial pattern of global evaporation change, leading to the largest fractional increases at high latitudes. In the surface energy budget, the thermodynamic increase in evaporation comes at the expense of the sensible heat flux, while radiative changes cause the sensible heat flux to increase. These tendencies on the sensible heat flux partly offset each other, resulting in a relatively small change in the global mean, and contributing to an impression that global precipitation is radiatively constrained.

    As this paper shows, while the potentail gradient is replaced by algebraic representations of the potential across the interface, the physical phenomena and processes that drive the flows occur at the interface.

  19. 119
    nigelj says:

    David Young @103

    “Your proof text quote is very vague and largely meaningless. Which events? Have others like tornados been decreasing? How much have they increased? ”

    Thank’s for the responses, however I don’t have time for an extensive copy and paste exercise! The following is from the IPCC Report 2013 Summary for Policy makers. It expands slightly on what I posted, and answers some of your questions to some extent, and fuller details and applicable research is in the body of the report if you are interested. Again this appears to contradict your claims that evidence of changes in the weather in recent decades is weak, although I’m certainly not suggesting the evidence is as strong as we would like.

    https://www.ipcc.ch/site/assets/uploads/2018/02/WG1AR5_SPM_FINAL.pdf

    “Changes in many extreme weather and climate events have been observed since about 1950 (see Table SPM.1 for details). It is very likely that the number of cold days and nights has decreased and the number of warm days and nights has increased on the global scale6. It is likely that the frequency of heat waves has increased in large parts of Europe, Asia and Australia. There are likely more land regions where the number of heavy precipitation events has increased than where it has decreased. The frequency or intensity of heavy precipitation events has likely increased in North America and Europe. In other continents, confidence in changes in heavy precipitation events is at most medium. {2.6}.”

    I was reading the following article this morning:

    https://www.nytimes.com/2019/07/11/climate/hurricane-tropical-storms.html

    “And Tropical Storm Barry, which may become a Category 1 hurricane before making landfall, will drop rain on already saturated land. On Wednesday, the region was hit by severe thunderstorms, which dropped as much as seven inches of rain according to preliminary National Weather Service data.”

    “Climate change is in general increasing the frequency and intensity of heavy rainfall storms,” said Andreas Prein, a project scientist with the National Center for Atmospheric Research….”

    You say “This is so typical of these conversations. Usually more cautious scientists don’t say much on these subjects because the trends are small (with the exception of tornado decreases) and the fundamental physics not very conclusive. BTW, the data that are most reliable such as tornadoes and US land falling hurricanes show a decrease or little trend.”

    I’m sure there are cautious scientists, and very opinionated scientists and scientists in the middle. I’m a layperson with just some basic university background in the issues. I pay attention to what scientists in the middle are saying, because I think history tends to show its these people who are the most reliable, and the IPCC reports, which are known to be if anything a bit conservative. I certainly don’t think it would be wise to put all our faith in the most cautious of scientists, just as I don’t assume the most alarmist are going to always be correct.

    As pointed out above The IPCC are finding changes in some aspects of the weather with 1) at least medium confidence and 2) based on several lines of evidence which is quite compelling.

    You say “the fundamental physics is not very conclusive” however you dont explain why you think that, and one doesn’t need to have a physics degree to work out more evaporation leads to changes in rainfall patterns at the very least, and this is fairly basic physics. It is also not the impression given by the IPCC so its a case of who do I believe as a non expert, you or the IPCC? Given you are getting some heat from various people, I defer to the IPCC. Although I think you are right about the gravity issue fwiw.

    Numbers of land falling Atlantic hurricanes do show a decreasing trend, but this is one event, its not a long term trend, and it doesn’t say much about total numbers of hurricanes, and hurricane intensity and rainfall content. My understanding is there is some evidence atlantic hurricane intensity is increasing and that there is better evidence pacific hurricanes are increasing in both frequency and intensity. The numbers of large tornados are decreasing but smaller ones are increasing.

    Perhaps the real issue that comes out of this is to try to work out all the changes in weather events (and climate events) and categorise which ones have postives for humanity and which ones have negatives. I don’t know of a study trying to evaluate this, and would be interested, but when I look at the data in the IPCC summary for policy makers on both climate and weather event trends, and they have looked at a wide range of issues, it leaves a very distinct impression that problematic changes in weather events from humanities perspective outweigh any positive changes. In fact the main obvious positive is warmer winters in countries that are currently in the colder end of the temperate zone, but almost all other weather and climate changes look negative for humanity. This is at global scale on average, obviously it varies from region to region.

    I’m not one to catastrophise, or be captured by my own biases, in fact I get heat for allegedly being a bit over cautious at times, and heat for being an alarmist at other times. I’m in the middle. In contrast you appear very determined to minimise the problem as much as possible for whatever reason.

  20. 120
    zebra says:

    #118 Dan Hughes,

    “more energy, more bad weather”

    I think most of us would agree that “bad weather” refers to various well-characterized phenomena, like intense rainfall that increases the likelihood of flooding.

    The paper you cite talks about global precipitation, which has no bearing on that question. In fact, there is very little relevance in the rest of your comment as well; we can understand the mechanism involved with simple quantitative reasoning.

    In the near term, meaning with the current and near-future increases in system energy, increased energy results in increased water vapor, so that when it does rain, the probability of increased intensity is higher. This is an effect local in space and time.

    I really am puzzled how people who appear to have some science background consistently make this mistake in reasoning about complex non-linear systems.

  21. 121
    David B. Benson says:

    David Young @ 117 — I’m not sure just what you stated, but it appeared that you were leaving out gravity and electrostatic forces.

    Thank you for the reminder about the moon. A recent paper from the University of Washington, across the state from me, points out that the moon affects precipitation by about 1%.

    The tidal effects in the oceans, not just at the beaches, appear to have some import in understanding the earth system, possibly through interactions with organisms.

    One cannot hope to understand thunder storms without taking electrostatic effects into account.

    I always encourage those with sufficient background to study “Principles of Planetary Climate” by Ray Pierrehumbert.

  22. 122
    Dan Hughes says:

    #114 David Benson.

    David Young said gravity is constant in time.

    Your comment is unrelated to David’s.

    #116

    Quoting Hughes selectively Paul Pukite said:

    A search of the Kindle edition shows that the Bose-Einstein concept is discussed in the text in Sections 3.2.4, 4.5, 8.2.3 and 8.3.2.”

    Paul, you left off this path:

    Equations 8.3.13 and 8.3.14 for the nucleation rate, which seem to be the results of interest, are not ever cited. This indicates to me that the Bose-Einstein results are not used whenever validation and applications of the models and methods is the focus. [bold by edh]

    Note that I said ‘indicates to me’, because a negative can’t be proven. The authors of the book agree with my assessment.

    And then you say:

    The fact remains, Curry’s book applied Bose-Einstein statistics to a material well above absolute zero, … [bold by edh]

    You on the other hand assert a positive, which can be proven. You have yet to explicitly identify, even after 5 years of your claims, when and where your claim occurred.

    By your own lack of validation, it is not a fact.

    Given that for 5 years you have insisted that an event occurred, and given your inability to offer evidence that in fact the event did actually occur, it must instead be a delusional fantasy on your part. Not to mention your obsession with your delusion for over 5 years. Your self-defined lack of creditably and failure continues.

    Benson and Pukite apparently think, “If I can’t find anything to comment on, I’ll just make stuff up”.

    That this thread is appearing at Real Climate is almost beyond comprehension.

  23. 123

    David Young said:

    “Benson, The gravity field is nearly constant in time (with small perturbations due to the moon).”

    The sun has almost as significant a gravitational effect as the moon.

    Munk & Wunsch have noted the impact of tidal forces on ocean mixing.

    “A few decades ago the suggestion that the Moon played a role in determining global ocean properties was considered lunatic; now it is considered obvious (Wunsch and Munk were more comfortable working in the earlier times).” — Munk (2007)

    There has been fascinating research carried out by NASA JPL on this topic. I was working with JPL on a DARPA project a few years ago and knew about their research on tidal links to climate. One such proposal called “Importance of the Earth-Moon system for reducing uncertainties in climate modelling and monitoring” (2009) submitted by Perigaud apparently never got funded, even though it’s full of examples showing strong correlations.

    It’s too tempting to ignore all this research, so I’ve continued to work it on my own and the correlations I have independently found are just as striking, synchronizing several geophysical and climate behaviors to tidal forcing. BTW, that’s mostly peer-reviewed and published.

    I have no idea why there is so little interest on this topic, and that’s why I have a hard time with someone like Young — who obviously hasn’t put any real effort into climate science — constantly creating canards.

    The main takeaway to all this is that natural variations in climate need to be better understood before we completely understand what contributes to extremes.

  24. 124
    David Young says:

    Nigel, Thanks for your long response. I think though it kind of illustrates my point.

    Barry has been typically overhyped by the American yellow journalists. There was not even an evacuation and rainfall was not nearly as high as predicted. There was a cloudburst that dumped 7 inches in an hour but New Orlean’s pump system quickly pumped it out of the city. I wouldn’t trust any “mainstream” media source on any of this. They are totally biased and merely trying to generate clicks.

    You acknowledge that strong tornadoes are decreasing but assert that “small” ones are increasing. I would argue that this may be an artifact of undercounting in the early 20th century. You are aware that now we an count every one of these using radar even if they don’t even touch down.

    Perhaps the most reliable data I think is for land falling US hurricanes and it shows no strong trend.

    As I said may times above, the fundamental physics here is that storm intensity might be argued to be decreasing.

    Heavy rainfall is one thing where the physics may indicate an expected increase. However precipitation is a function of temperature gradients and not the absolute amount of water vapor in the air. It’s just not that easy to calculate the small offsetting effects. One might also expect a decrease in drought if precipitation increases.

    So bad weather is just a very weak talking point for activists even though the level of dishonesty is generally very high in the media about it.

  25. 125

    Dan Hughes said:

    “That this thread is appearing at Real Climate is almost beyond comprehension.”

    Half of the time, threads here discuss some bizarre aspect of AGW denialism. Nucleation in clouds is off the bat a difficult topic because there is little real experimental control involved, or even possible. Nucleation from the vapor phase was actually my thesis topic (for semiconductor applications) and so I realize BS when I see it. I’m not going to be recommending a book by someone shooting from the hip suggesting Bose-Einstein stats when I know what’s actually involved. And this couldn’t have been some slip-up, as Bose-Einstein was considered by Curry for both liquid droplet formation AND ice crystal formation. Almost as if they are trying to make stuff up!

    “Given that for 5 years you have insisted that an event occurred”

    It even has section headers, which is how I found it by scanning the TOC!

    https://imagizer.imageshack.com/img922/4959/1dyIPy.png

    ‘Benson and Pukite apparently think, “If I can’t find anything to comment on, I’ll just make stuff up.’

    As long as you keep trying to psychologically project Curry’s or David Young’s failings on to me, I will continue to point out how it is just you people making stuff up.

  26. 126
    Dan Hughes says:

    The paper you cite talks about global precipitation, which has no bearing on that question. …

    The complete paper is available at this URL.

    None of the equations in the paper contain a characterization of spatial scale. The equations describe the local physical phenomena and processes occurring at the interface between the atmosphere and liquid water. The locally-focused approach is almost universally the case for phenomenological/mechanistic models of general applicability. Mathematical descriptions that do contain a macroscopic spatial scale are limited in terms of general applicability.

    In fact, the Abstract says: The temperature contribution also dominates the spatial pattern of global evaporation change, leading to the largest fractional increases at high latitudes. Indicating that the model equations are applied at spatial scales that are less than global.

    Scale-free models can then be integrated over regions that include such an interface to obtain estimates of the response at any scale. The model described in the paper can be implemented into GCMs or ESMs, for example, to obtain local, regional, and global responses. The algebraic model equations can also be directly evaluated at any scale for which the independent variables in the model are known.

    And that’s exactly what was carried out for the paper: See Figure 1 and Tables 1 and 2. Figure 1 shows a representation of resolved spatial scales mapped to representations of Earth. An interesting aspect of Tables 1 and 2 is that it is shown, to no surprise, that the SST specified, slab-ocean results and the coupled atmosphere-ocean results are different for the GCMs/ESMs applications of the model. The slow temporal response of the oceans, and other massive bodies, allows quasi-static approximations such as specified SST, the so-called BVP approach, to be somewhat useful. The different responses are also shown in Figure 2.

  27. 127
    Dan Hughes says:

    #68 Said by Paul Pukite, not said by David Young. Failure by Paul Pukite.

    #85 Correct statement by David Young. Failure by Paul Pukite

    #92 Claimed by Paul Pukite. But, applications of B-E to water by Curry, or anyone else, has never happened. Failure by Paul Pukite.

    #94 False claim by Paul Pukite, based on made-up statement by Paul Pukite in #68. Failure by Paul Pukite.

    #111 False claim by Paul Pukite. Curry has never applied B-S statistics to water. Failure by Paul Pukite.

    #116 False claim by Paul Pukite. Curry has never applied B-S statistics to water. Pukite fails to validate his assertions. Failure by Paul Pukite.

    #125 Paul Pukite continues to fail to validate his assertions. Failure by Paul Pukite.

    Now we see that Paul has somewhat backed off his assertions that Curry applies B-E to water. However, now Paul Pukite claims to have the unique ability to completely and accurately obtain and ascertain the detailed contents of highly technical mathematical materials by simply scanning the ToC.

    For 5 years, Paul has made numerous declarative statements about application of B-E statistics to water. For 5 years Paul Pukite has failed to validate his statements. Failure by Paul Pukite.

    Footnote:

    Apparently, some participating in this thread mistakingly think they can attain and summarize the contents of peer-reviewed papers by simply repeating a single word from the title of the paper.

    ps:
    Comment policy. Please note that if your comment repeats a point you have already made, or is abusive, or is the nth comment you have posted in a very short amount of time, please reflect on the whether you are using your time online to maximum efficiency. Thanks.

  28. 128
    Matthew R Marler says:

    125 Paul Pukite: It even has section headers, which is how I found it by scanning the TOC!

    Indeed, section 8.2.3, with the word “application” even in the title, is a little less than 1 page long. It says that the Boltzman distribution (whose application Paul Pukite does not object to) is a special case of the Bose-Einstein distribution; the section outlines how previous derivations “should be” repeated for the Bose-Einstein distribution.

    If your examination of the 725 pp of text and 40 pp of references is to “scan the TOC!”, you might falsely conclude that Khvorostyanov and Curry assign great weight to the Bose-Einstein distribution. In fact, it is clear from actually reading their slightly less than 1 p presentation (), that K and C merely suggest that the B-E distribution might fit better than the Boltzman distribution because it is more general (as explained in sections 3.2.4, 3.2.5, 3.2.6). And they present the mathematical expression of the condition in which B-E might fit better: deltaF(cr) > > kT.

    Anybody who cares about Paul Pukite’s opinion on this matter ought to read the text.

  29. 129

    Dan Hughes, You’re just making it worse. Dan Quayle never got past the “potato” vs “potatoe” incident either. And Judith Curry is no Jack Kennedy ;)

  30. 130
    Matthew R Marler says:

    92, Paul Pukite: Judith Curry when she tried to apply Bose-Einstein statistics to droplet and ice nucleation. (Look it up)

    Don’t just look it up, read it.

    Section 3.2 (pp 49 – 56) presents 5 distributions, the Gibbs distribution, the Maxwell distribution, the Boltzmann distribution, the Bose-Einstein distribution, and the Fermi-Dirac distribution. Figure 3.1, p 56, presents a quantitative comparison of the Boltzmann, Bose-Einstein, and Fermi-Dirac distributions as functions of “Relative Energy” (defined in the text.) About the Bose-Einstein distribution Khvorostyanov and Curry write: “Bose-Einstein statistics apply when quantum effects are important, the particles are indistinguishable, and they have integer spin (internal momentum of rotation); that is counted in integer numbers of Planck constant h .Bose-Einstein statistics was introduced for photons and then later generalized to atoms. Important applications of Bose-Einstein statistics include: blackbody radiation (which can be considered as an ideal gas of photons); evaluation of heat capacities of solids; ice nucleation at low temperatures.” The section has 5 equations in about 1.25 pp. The sequel of the text does not depend on any of the applications of the Bose-Einstein distribution.

    If all you read is Paul Pukite’s commentary on the book, you might come away with the mistaken idea that it was necessary for him to school K & C about the origin and limits of the B-E distribution.

    Sorry for the repetition, but read K & C, not what PK has written about their text.

  31. 131

    PP 123: The sun has almost as significant a gravitational effect as the moon.

    BPL: Same order of magnitude, yes. But measured by the height of mid-ocean tides as a result of tidal stresses, solar tides are about 46% of lunar.

  32. 132
    Ray Ladbury says:

    Matthew Marler,
    Dude, you’re not really helping Aunt Judy’s case. That sounds like a Freshman physics student regurgitating everything they can remember about an irrelevant subject when they don’t understand the question on the exam.

  33. 133

    Marler said:

    “Sorry for the repetition, but read K & C, not what PK has written about their text”

    It says right there, in a section titled 8.3.2 Application of Bose-Einstein Statistics for Freezing: “If dF_act < kT, then the more general Bose-Einstein distribution should be used to describe the effect of activation energy on the crystal nucleation in super-cooled water”

    Probably agree with whatever PK said since any scientist schooled in condensed matter physics or statistical mechanics should find that passage to be a howler. First of all, it takes carefully controlled laboratory conditions (which definitely precludes the atmosphere) to get anywhere close to the absolute zero temperature needed for B-E statistics to kick in. And elsewhere they say “the Boltzmann distribution can become inapplicable, and the Bose-Einstein should be used” and some BS about “or in the presence of strong surfactants”, LOL cringe-worthy! In fact B-E statistics need never considered anywhere in understanding earth sciences.

    So the options are that the authors are (1) ignorant of 1st-order physics, or (2) adding all sorts of unnecessary junk filler to meet some sort of page count requirement. You just don’t do that kind of thing if you want to demonstrate your bonafides as a condensed matter physicist.

    The reason I brought the Curry fiasco up in the first place is that there are ways to detect the D-K effect from what they write. I simply mentioned that Dan Hughes was going through all sorts of rationalizations to defend David Young’s assertion that gravity has no effect on fluid dynamics, and that those contorted rationalizations were similar to what he has done in the past to defend Curry.

  34. 134
    Matthew R Marler says:

    133, Paul Pukite: (1) ignorant of 1st-order physics, or (2) adding all sorts of unnecessary junk filler to meet some sort of page count requirement.

    Right. “Junk filler”.

    You can not support either (1) or (2).

    The reason I brought the Curry fiasco up in the first place is that there are ways to detect the D-K effect from what they write.

    That is absurd. But “junk filler” is worthy of being framed, displayed, and remembered.

  35. 135
    David Young says:

    Just to put Pukite’s credibility in context, this comment from Carrick on the post where P. Pukite originally made his point. Other comments there point out Pukite’s typically juvenile behavior.

    https://judithcurry.com/2014/09/04/thermodynamics-kinetics-and-microphysics-of-clouds/#comment-625676

    Carrick | September 7, 2014 at 4:15 pm |
    WHUT, the jury is out on you (some might say it’s come in and rendered a verdict).

    You said in comments on this very thread:

    . But not for physical matter such as water molecules, which obey the Pauli Exclusion principle and thus every molecule must exist in a different state.

    So where is the citation in the textbook for the claim that homogeneous nucleation can be modeled with Bose-Einstein statistics? Or was that just made up? No need to torture equations to get what you want to see

    and this:

    So right there in Section 8.2.3 is a bad description of statistical mechanics. Yes, Bose-Einstein stats are more general than Maxwell-Boltzmann stats, but it doesn’t apply to the kinds of particles you are talking about. Instead, in the case of Boltzmann should be if anything a simplification of Fermi-Dirac statistics which forbids two particles from occupying the same state.

    You tried to wave this off as “joking”. But this is not joking: You are substantively wrong on the very issue that you are ankle-biting Judith’s book over. You got one part of an argument partly right and flubbed the rest.

    Why should people take you seriously? You aren’t able to converse as an adult, and what you do write is riddled with mistakes.

  36. 136
    Matthew R Marler says:

    132, Ray Ladbury: That sounds like a Freshman physics student regurgitating everything they can remember about an irrelevant subject when they don’t understand the question on the exam.

    That is because you are not reading along with me, even though I gave the section numbers. PK depends upon no one reading it. Perhaps you don’t have the book? In about 3 pp K&C describe the B-E distribution, including the mathematical formula, and describe the conditions for which it was derived. They compare it with the Boltzmann distribution and Fermi-Dirac distribution. They do not “apply” it or depend upon it in any of the rest of the book.

    Actually, I did quite well on my freshman physics exams, but that was decades ago. Do you agree with PK that the text is unnecessary junk filler?

  37. 137
    Dan Hughes says:

    #129
    WTF Now we have Dan Quayle, potatoe, and JFK all wrapped into yet another off-topic and fact free comment.

    #133
    Well I’ll be ding-dong double WTF. Paul Pukite yet again makes up a bald faced lie about what someone has said;

    I simply mentioned that Dan Hughes was going through all sorts of rationalizations to defend David Young’s assertion that gravity has no effect on fluid dynamics, and that those contorted rationalizations were similar to what he has done in the past to defend Curry. [bold by edh]

    As in the case of all other false, made-up claims of statements made by others, it is impossible for Pukite to validate this one. Another case of self-invalidation by Pukite. The latest in the endless list of failures by Paul ‘Not Even Wrong’ Pukite. It’s plainly obvious that because David has never made such a statement, I could not have have been going through all sorts of rationalizations to defend … . Such comments do not exist, another case of self-invalidation by Pukite.

    Equation 2 in this peer-reviewed publication contains the body force as the first term on the right-hand side:
    Gustafson K.E., Young D.P. (1982) Computation of solenoidal (divergence-free) vector fields. In: Hinze J. (eds) Numerical Integration of Differential Equations and Large Linear Systems. Lecture Notes in Mathematics, vol 968. Springer, Berlin, Heidelberg.

    Apparently, Paul ‘Not Even Wrong’ Pukite would have us believe that someone who thinks the gravitational force has no effect on fluid dynamics would nevertheless include that term in the momentum equations.

    So, here we have a case of evidence that Paul ‘Not Even Wrong’ Pukite makes stuff up; especially made-up stuff that he permits himself to knowingly falsely denigrate [ disparage, belittle, deprecate, decry, cast aspersions on, criticize, attack; speak ill of, give someone a bad name, defame, slander, libel; run down, abuse, insult, revile, malign, vilify, slur ] people while at the same time completely avoiding technical issues.

    We can hope that Paul Pukite has finally hit the nadir of his ad hominem, false, made-up, and fact-free comment repertoire. However, I have strong reasons to think, based on his self-validated lack of creditability in past performances, he can go even lower. We’ll be lucky if this is even the pre-penultimate member of his fact-free comment repertoire.

    I wonder if potatoe is kind of like Paul’s #111; … as it’s not my credibility that’s at steak …

    Why have the principals of RealClimate:

    The current permanent contributors to content on this site are:
    Gavin Schmidt, Michael Mann, Rasmus Benestad, Ray Bradley, Stefan Rahmstorf, Eric Steig, David Archer, and Ray Pierrehumbert

    allowed what are clearly off-topic comments to hijack this thread. The comments also are not consistent with the Comment policy of RealCimate. RealClimate has allowed Paul Pukite to introduce into discussions about a guest post, the subjects Dan Quayle, Potatoe, and JFK.

    Almost all the comments by Paul Pukite, in addition to being off-topic, not to mention being in plain violation of RealClimate Comment policy, additionally not to mention their obsessive and personal nature, are based on false statements made up by Paul. Paul set the trend of his sub-thread with #68 in which he made up words that clearly were not the words of persons to which he claimed.

    The current permanent contributors at RealClimate have enabled Paul’s subsequent false, off-topic comments to head downhill at a rapid rate.

  38. 138
    Ray Ladbury says:

    Matthew, Since the subject the authors are discussing is clearly in the classical, not the quantum realm, the text is worst than junk filler. It’s a pathetic attempt to seem smarter than they are. It’s like bringing up time dilation while driving in a Buick from Topeka to Wichita or the red shift to explain why the light on a caboose is red.

  39. 139

    Keep slamming away Dan Hughes. I have written quite a bit on topics relating to evidence-based attribution, so you can take it over to PubPeer.com. I don’t get disturbed by comments on my research.

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