NOTE: Comments for this post have all been flagged as pending for some reason. I’m testing the spam blocker to see what the problem might be. Until it is fixed, I might have to manually approve comments as I have time during the day.

A recent paper by Jonathan Gregory and co-authors in Climate Dynamics entitled How accurately can the climate sensitivity to CO2 be estimated from historical climate change? addresses in considerable detail the issues which limit our ability to determine that global warming holy grail, “equilibrium climate sensitivity” (ECS, the eventual global average surface warming response to a doubling of atmospheric CO2). Despite decades of research, climate models still exhibit climate sensitivities that range over a factor of three (about 1.5 to 4.5 deg. C for 2XCO2), and a minority of us believe the true sensitivity could be less than 1.5 deg. C.

Obviously, if one could confidently determine the climate sensitivity from observations, then the climate modelers could focus their attention on adjusting their models to reproduce that known sensitivity. But so far, there is no accepted way to determine climate sensitivity from observations. So, instead the climate modeling groups around the world try different approaches to modeling the various physical processes affecting climate change and get a rather wide range of answers for how much warming occurs in response to increasing atmospheric CO2.

One of the problems is that increasing CO2 as a climate forcing is unique in the modern instrumental record. Even if we can measure radiative feedbacks in specific situations (e.g., month to month changes in tropical convection) there is no guarantee that these are the same feedbacks that determine long-term sensitivity to increasing CO2. [If you are one of those who believe the feedback paradigm should not be applied to climate change — you know who you are — you might want to stop reading now to avoid being triggered.]

The Lewis Criticism

The new paper uses climate models as a surrogate for the real climate system to demonstrate the difficulty in measuring the “net feedback parameter” which in turn determines climate sensitivity. While I believe this is a worthwhile exercise, Nic Lewis has objected (originally here, then reposted here and here) to one of the paper’s claims regarding errors in estimating feedbacks through statistical regression techniques. It is a rather obscure point buried in the very long and detailed Gregory et al. paper, but it is nonetheless important to the validity of Lewis and Curry (2018) published estimates of climate sensitivity based upon energy budget considerations. Theirs is not really a statistical technique (which the new paper criticizes), but a physically-based technique applied to the IPCC’s own estimates of the century time scale changes in global radiative forcing, ocean heat storage, and surface temperature change.

From what I can tell, Nic’s objection is valid. Even though it applies to only a tiny portion of the paper, it has significant consequences because the new paper appears to be an effort to de-legitimize any observational estimates of climate sensitivity. I am not questioning the difficulty and uncertainty in making such estimates with current techniques, and I agree with much of what the paper says on the issue (as far as it goes, see the Supplement section, below).

But the authors appear to have conflated those difficulties with the very specific and more physics-based (not statistics-based) climate sensitivity estimates of the Lewis and Curry (2018) paper. Based upon the history of the UN IPCC process of writing its reports, the Gregory et al. paper could now be invoked to claim that the Lewis & Curry estimates are untrustworthy. The fact is that L&C assumes the same radiative forcing as the IPCC does and basically says, the century time scale warming that has occurred (even if it is assumed to be 100% CO2-caused) does not support high climate sensitivity. Rather than getting climate sensitivity from a model that produces too much warming, L&C instead attempt to answer the question, “What is the climate sensitivity based upon our best estimates of global average temperature change, radiative forcing, and ocean heat storage over the last century?”

Vindication for the Spencer and Braswell Studies

I feel a certain amount of vindication upon reading the Gregory et al. paper. It’s been close to 10 years now since Danny Braswell and I published a series of papers pointing out that time-varying radiative forcing generated naturally in the climate system obscures the diagnosis of radiative feedback. Probably the best summary of our points was provided in our paper On the diagnosis of radiative feedback in the presence of unknown radiative forcing (2010). Choi and Lindzen later followed up with papers that further explored the problem.

The bottom line of our work is that standard ordinary least-squares (OLS) regression techniques applied to observed co-variations between top-of-atmosphere radiative flux (from ERBE or CERES satellites) and temperature will produce a low bias in the feedback parameter, and so a high bias in climate sensitivity. [I provide a simple demonstration at the end of this post]. The reason why is that time-varying internal radiative forcing (say, from changing cloud patterns reflecting more or less sunlight to outer space) de-correlates the data (example below). We were objecting to the use of such measurements to justify high climate sensitivity estimates from observations.

Our papers were, of course, widely criticized, with even the editor of Remote Sensing being forced to resign for allowing one of the papers to be published (even though the paper was never retracted). Andrew Dessler objected to our conclusions, claiming that all cloud variations must ultimately be due to feedback from some surface temperature change somewhere at some time (an odd assertion from someone who presumably knows some meteorology and cloud physics).

So, even though the new Gregory et al. paper does not explicitly list our papers as references, it does heavily reference Proistosescu et al. (2018) which directly addresses the issues we raised. These newer papers show that our points were valid, and they come to the same conclusions we did — that high climate sensitivity estimates from the observed co-variations in temperature and radiative flux were not trustworthy.

The Importance of the New Study

The new Gregory et al. paper is extensive and makes many good conceptual points which I agree with. Jonathan Gregory has a long history of pioneering work in feedback diagnosis, and his published research cannot be ignored. The paper will no doubt figure prominently in future IPCC report writing.

But I am still trying to understand the significance of CMIP5 model results to our efforts to measure climate sensitivity from observations, especially the model results in their Fig. 5. It turns out what they are doing with the model data differs substantially with what we try to do with radiative budget observations from our limited (~20 year) satellite record.

First of all, they don’t actually regress top of atmosphere total radiative fluxes from the models against temperature; they first subtract out their best estimate of the radiative forcing applied to those models. This helps isolate the radiative feedback signal responding to the radiative forcing imposed upon the models. Furthermore, they beat down the noise of natural internal radiative and non-radiative variability by using only annual averages. Even El Nino and La Nina events in the models will have trouble surviving annual averaging. Almost all that will remain after these manipulations is the radiative feedback to just the CO2 forcing-induced warming. This also explains why they do not de-trend the 30-year periods they analyze — that would remove most of the temperature change and thus radiative feedback response to temperature change. They also combine model runs together before feedback diagnosis in some of their calculations, further reducing “noise” from internal fluctuations in the climate system.

In other words, their methodology would seem to have little to do with determination of climate sensitivity from natural variations in the climate system, because they have largely removed the natural variations from the climate model runs. The question they seem to be addressing is a very special case: How well can the climate sensitivity in models be diagnosed from 30-year periods of model data when the radiative forcing causing the temperature change is already known and can be subtracted from the data? (Maybe this is why they term theirs a “perfect model” approach.) If I am correct, then they really haven’t fully addressed the more general question posed by their paper’s title: How accurately can the climate sensitivity to CO2 be estimated from historical climate change? The “historical climate change” in the title has nothing to do with natural climate variations.

Unfortunately — and this is me reading between the lines — these newer papers appear to be building a narrative that observations of the climate system cannot be used to determine the sensitivity of the climate system; instead, climate model experiments should be used. Of course, since climate models must ultimately agree with observations, any model estimate of climate sensitivity must still be observations-based. We at UAH continue to work on other observational techniques, not addressed in the new papers, to tease out the signature of feedback from the observations in a simpler and more straightforward manner, from natural year-to-year variations in the climate system. While there is no guarantee of success, the importance of the climate sensitivity issue requires this.

And, again, Nic Lewis is right to object to their implicit lumping the Lewis & Curry observational determination of climate sensitivity work from energy budget calculations in with statistical diagnoses of climate sensitivity, the latter which I agree cannot yet be reliably used to diagnose ECS.

Supplement: A Simple Demonstration of the Feedback Diagnosis Problem

Whether you like the term “feedback” or not (many engineering types object to the terminology), feedback in the climate sense quantifies the level to which the climate system adjusts radiatively to resist any imposed temperature change. This radiative resistance (dominated by the “Planck effect”, the T^4 dependence of outgoing IR radiation on temperature) is what stabilizes every planetary system against runaway temperature change (yes, even on Venus).

The strength of that resistance (e.g., in Watts per square meter of extra radiative loss per deg. C of surface warming) is the “net feedback parameter”, which I will call λ. If that number is large (high radiative resistance to an imposed temperature change), climate sensitivity (proportional to the reciprocal of the net feedback parameter) is low. If the number is small (weak radiative resistance to an imposed temperature change) then climate sensitivity is high.

[If you object to calling it a “feedback”, fine. Call it something else. The physics doesn’t care what you call it.]

I first saw the evidence of the the different signatures of radiative forcing and radiative feedback when looking at the global temperature response to the 1991 eruption of Mt. Pinatubo. When the monthly, globally averaged ERBE radiative flux data were plotted against temperature changes, and the data dots connected in chronological order, it traced out a spiral pattern. This is the expected result of a radiative forcing (in this case, reduced sunlight) causing a change in temperature (cooling) that lags the forcing due to the heat capacity of the oceans. Importantly, this involves a direction of causation opposite to that of feedback (a temperature change causing a radiative change).

The newer CERES instruments provide the longest and most accurate record of changes in top-of-atmosphere radiative balance. Here’s the latest plot for 19 years of monthly Net (reflected shortwave SW plus emitted longwave LW) radiative fluxes versus our UAH lower tropospheric temperatures.

Note I have connected the data dots in chronological order. We see than “on average” (from the regression line) there appears to be about 2 W/m2 of energy lost per degree of warming of the lower troposphere. I say “appears” because some of the radiative variability in that plot is not due to feedback, and it decorrelates the data leading to uncertainty in the slope of the regression line, which we would like to be an estimate of the net feedback parameter.

This contaminating effect of internal radiative forcing can be demonstrated with a simple zero-dimensional time-dependent forcing-feedback model of temperature change of a swamp ocean:

Cp[dT(t)/dt] = F(t) – λ [dT(t)]

where the left side is the change in heat content of the swamp ocean with time, and on the right side F is all of the radiative and non-radiative forcings of temperature change (in W/m2) and λ is the net feedback parameter, which multiplies the temperature change (dT) from an assumed energy equilibrium state.

While this is probably the simplest time-dependent model you can create of the climate system, it shows behavior that we see in the climate system. For example, if I make time series of low-pass filtered random numbers about zero to represent the known time scales of intraseasonal oscillations and El Nino/La Nina, and add in another time series of low-pass filtered “internal radiative forcing”, I can roughly mimic the behavior seen in Fig. 1.

Now, the key issue for feedback diagnosis is that even though the regression line in Fig. 2 has a slope of 1.8 W m-2 K-1, the feedback I specified in the model run was 4 W m-2 K-1. Thus, if I had interpreted that slope as indicating the sensitivity of the simple model climate system, I would have gotten 2. 1 deg. C, when in fact the true specified sensitivity was only 0.9 deg. C (assuming 2XCO2 causes 3.7 W m-2 of radiative forcing).

This is just meant to demonstrate how internal radiative variability in the climate system corrupts the diagnosis of feedback from observational data, which is also a conclusion of the newer published studies referenced above.

And, as I have mentioned above, even if we can diagnose feedbacks from such short term variations in the climate system, we have no guarantee that they also determine (or are even related to) the long-term sensitivity to increasing CO2.

So (with the exception of studies like L&C) be prepared for increased reliance on climate models to tell us how sensitive the climate system is.

While the vast majority of our monthly global temperature updates are pretty routine, September 2019 is proving to be a unique exception. The bottom line is that there is nothing wrong with the UAH temperatures we originally reported. But what I discovered about last month is pretty unusual.

It all started when our global lower tropospheric (LT) temperature came in at an unexpectedly high +0.61 deg. C above the 1981-2010 average. I say “unexpected” because, as WeatherBell’s Joe Bastardi has pointed out, the global average surface temperature from NOAA’s CFS model had been running about 0.3 C above normal, and our numbers are usually not that different from that model product.

[By way of review, the three basic layers we compute average temperatures from the satellites are, in increasing altitude, the mid-troposphere (MT), tropopause region (TP), and lower stratosphere (LS). From these three deep layer temperatures, we compute the lower tropospheric (LT) product using a linear combination of the three main channels, LT = 1.548MT – 0.538TP +0.01LS.]

Yesterday, John Christy noticed that the Southern Hemisphere was unusually warm in our lower stratosphere (LS) temperature product, while the Northern Hemisphere was unusually cool. This led me to look at the tropical results for our mid-troposphere (MT) and ‘tropopause’ (TP) products, which in the tropics usually track each other. A scatterplot of them revealed September 2019 to be a clear outlier, that is, the TP temperature anomaly was too cool for the MT temperature anomaly.

So, John put a notice on his monthly global temperature update report, and I added a notice to the top of my monthly blog post, that we suspected maybe one of the two satellites we are currently using (NOAA-19 and Metop-B) had problems.

As it turns out, there were no problems with the data. Just an unusual regional weather event that produced an unusual global response.

Blame it on Antarctica

Some of you might have seen news reports several weeks ago that a strong stratospheric warming (SSW) event was expected to form over Antarctica, potentially impacting weather in Australia. These SSW events are more frequent over the Arctic, and occur in winter when (put very simply) winds in the stratosphere flow inward and force air within the cold circumpolar vortex to sink (that’s called subsidence). Since the stratosphere is statically stable (its temperature lapse rate is nearly isothermal), any sinking leads to a strong temperature increase. CIRES in Colorado has provided a nice description of the current SSW event, from which I copied this graphic showing the vertical profile of temperature normally (black like) compared to that for September (red line).

By mass continuity, the air required for this large-scale subsidence must come from lower latitudes, and similarly, all sinking air over Antarctica must be matched by an equal mass of rising air, with temperatures falling. This is part of what is called the global Brewer-Dobson circulation in the stratosphere. (Note that because all of this occurs in a stable environment, it is not ‘convection’, but must be forced by dynamical processes).

As can be seen in this GFS model temperature field for today at the 30 mb level (about 22 km altitude) the SSW is still in play over Antarctica.

The following plot of both Arctic and Antarctic UAH LS temperature anomalies shows just how strong the September SSW event was, with a +13.7 deg. C anomaly averaged over the area poleward of 60 deg. S latitude. The LS product covers the layer from about 15 to 20 km altitude.

As mentioned above, when one of these warm events happens, there is cooling that occurs from the rising air at the same altitudes, even very far away. Because the Brewer-Dobson circulation connects the tropical stratosphere to the mid-latitudes and the poles, a change in one region is mirrored with opposite changes elsewhere.

As evidence of this, if I compute the month-to-month changes in lower stratospheric temperatures for a few different regions, I find the following correlations between regions (January 1979 through September 2019). These negative correlations are evidence of this see-saw effect in stratospheric temperature between different latitudes (and even hemispheres).

Tropics vs. Extratropics: -0.78

Arctic vs. S. Hemisphere: -0.70

Antarctic vs. N. Hemisphere: -0.50

N. Hemis. vs. S. Hemis.: -0.75

Because of the intense stratospheric warming over Antarctica, it caused an unusually large difference in the NH and SH anomalies, which raised a red flag for John Christy.

Next I can show that the SSW event extended to lower altitudes, influencing the TP channel which we use to compute the LT product. This is important because sinking and warming at the altitudes of the TP product (roughly 8-14 km altitude) can cause cooling at those same altitudes very far away. This appears to be why I noticed the tropics having the lowest-ever TP temperature anomaly for the MT anomaly in September, which raised a red flag for me.

In this plot of the difference between those two channels [TP-MT] over the Antarctic, we again see that September 2019 was a clear outlier.

Conceptually, that plot shows that the SSW subsidence warming extends down into altitudes normally considered to be the upper troposphere (consistent with the CIRES plot above). I am assuming that this led to unusual cooling in the tropical upper troposphere, leading to what I thought was anomalous data. It was indeed anomalous, but the reason wasn’t an instrument problem, it was from Mother Nature.

Finally, Danny Braswell ran our software, leaving out either NOAA-19 or Metop-B, to see if there was an unusual difference between the two satellites we combine together. The global LT anomaly using only NOAA-19 was +0.63 deg. C, while that using only Metop-B was +0.60 deg. C, which is pretty close. This essentially rules out an instrument problem for the unusually warm LT value in September, 2019.

UPDATE: (10/3/2019, 4:55 p.m. CDT): We have discovered that the last 1-2 months of LT data could be biased high. This is based upon a quick analysis of tropical temperatures where our mid-tropospheric (MT) and upper-tropospheric product (TP) anomalies are usually in good agreement. September 2019 is a clear outlier, with TP much too cold compared to MT. MT was cooler in the tropics in than in August, but because TP fell so much more, their weighted difference produced a spuriously warm result for LT. Furthermore, the tropical LS (lower stratospheric temperature) is at a record low in the tropics, a result which I do not believe. I will provide an update when we figure out the problem.

The Version 6.0 global average lower tropospheric temperature (LT) anomaly for September, 2019 was +0.61 deg. C, up considerably from the August value of +0.38 deg. C.

The linear warming trend since January, 1979 remains at +0.13 C/decade (+0.11 C/decade over the global-averaged oceans, and +0.18 C/decade over global-averaged land).

Various regional LT departures from the 30-year (1981-2010) average for the last 21 months are:

YEAR MO GLOBE NHEM. SHEM. TROPIC USA48 ARCTIC AUST
 2018 01 +0.29 +0.51 +0.06 -0.10 +0.70 +1.39 +0.52
 2018 02 +0.24 +0.28 +0.21 +0.05 +0.99 +1.22 +0.35
 2018 03 +0.28 +0.43 +0.12 +0.08 -0.19 -0.32 +0.76
 2018 04 +0.21 +0.32 +0.09 -0.14 +0.06 +1.02 +0.84
 2018 05 +0.16 +0.38 -0.05 +0.01 +1.90 +0.14 -0.24
 2018 06 +0.20 +0.33 +0.06 +0.11 +1.11 +0.76 -0.42
 2018 07 +0.30 +0.38 +0.22 +0.28 +0.41 +0.24 +1.48
 2018 08 +0.18 +0.21 +0.16 +0.11 +0.02 +0.11 +0.37
 2018 09 +0.13 +0.14 +0.13 +0.22 +0.89 +0.23 +0.27
 2018 10 +0.19 +0.27 +0.12 +0.30 +0.20 +1.08 +0.43
 2018 11 +0.26 +0.24 +0.27 +0.45 -1.16 +0.68 +0.55
 2018 12 +0.25 +0.35 +0.15 +0.30 +0.25 +0.69 +1.20
 2019 01 +0.38 +0.35 +0.41 +0.35 +0.53 -0.15 +1.15
 2019 02 +0.37 +0.47 +0.28 +0.43 -0.02 +1.04 +0.05
 2019 03 +0.34 +0.44 +0.25 +0.41 -0.55 +0.96 +0.58
 2019 04 +0.44 +0.38 +0.51 +0.53 +0.50 +0.92 +0.91
 2019 05 +0.32 +0.29 +0.35 +0.39 -0.61 +0.98 +0.38
 2019 06 +0.47 +0.42 +0.52 +0.64 -0.64 +0.90 +0.35
 2019 07 +0.38 +0.33 +0.44 +0.45 +0.11 +0.33 +0.87
 2019 08 +0.38 +0.38 +0.39 +0.42 +0.17 +0.44 +0.23
 2019 09 +0.61 +0.64 +0.58 +0.60 +1.21 +0.75 +0.57

This makes September, 2019 the warmest September in the 41 year satellite record.

The UAH LT global anomaly image for September, 2019 should be available in the next few days here.

The global and regional monthly anomalies for the various atmospheric layers we monitor should be available in the next few days at the following locations:

Lower Troposphere: http://vortex.nsstc.uah.edu/data/msu/v6.0/tlt/uahncdc_lt_6.0.txt
Mid-Troposphere: http://vortex.nsstc.uah.edu/data/msu/v6.0/tmt/uahncdc_mt_6.0.txt
Tropopause: http://vortex.nsstc.uah.edu/data/msu/v6.0/ttp/uahncdc_tp_6.0.txt
Lower Stratosphere: http://vortex.nsstc.uah.edu/data/msu/v6.0/tls/uahncdc_ls_6.0.txt

The radiative resistance to global temperature change is what limits the temperature change in response to radiative forcing from (say) increasing CO2, or the sun suddenly deciding to pump out a 1 percent more sunlight.

If the climate system sheds only a little extra energy with warming, it warms even more until radiative energy balance is restored. If it sheds a lot of energy, then very little warming is required to restore global energy balance. This is the climate sensitivity holy grail, and it will determine just how much warming results from increasing CO2 in the atmosphere.

John Christy and I are preparing a paper based upon Dept. of Energy-sponsored research explaining why the tropical troposphere hasn’t warmed as much in nature as in climate models. (The discrepancy exists for surface temperature trends; for both RSS and UAH tropical tropospheric trends; as well as for global reanalysis datasets). Danny Braswell and I did a lot of research on this subject about 5-10 years ago, and published several papers.

Without going into the gory details of why it is so difficult to measure “feedbacks” (how strong the climate system radiatively resists a temperature change in response to radiative forcing), I’m going to present one graph of new results from our work that suggests where the problem with the models might be.

The plot I will show is based upon month-to-month variations in area-averaged tropical (30N-30S) tropospheric temperatures. When those temperature changes are the largest, we expect to see the clearest signal of radiative resistance (negative “feedback”) which, by definition, is a response to that temperature change. In contrast, if the month-to-month temperature change was zero, any change in radiative flux would result in an infinite feedback parameter, which is clearly unphysical.

So, let’s focus on the biggest observed temperature changes. If we take the 10% of the 224 months of detrended CERES satellite radiative flux data (March 2000 through October 2018) which have the LARGEST month-to-month temperature changes (warming and cooling) in detrended UAH LT data, and compare them, we get the following plot of diagnosed feedback parameter (flux change divided by temperature change) versus average absolute temperature change. Also included in the plot are the results computed in the same manner from 19 different CMIP5 climate models, where I have used the model surface to 500 mb geopotential thickness converted to temperature to approximate the UAH LT product.

There is a clear discrepancy between the 19 different climate models and the observations. The observations suggest a much larger resistance to a temperature change (vertical axis) than the models do, by over a factor of 4, for the same temperature change. This large feedback parameter is probably why the observations also show the smallest month-to-month temperature changes (horizontal axis) compared to the models (about 50% weaker than the models): the radiative resistance to temperature change actually reduces the month-to-month temperature fluctuations.

What Does this Mean?

The results are qualitatively consistent with Lindzen’s “infrared iris” effect, as we find the discrepancy between models and observations is larger in the infrared (LW) component of radiative flux than in the reflected solar (SW) component (SW and LW plots not shown here).

Interestingly, I had to exclude the GISS model results because they show increasing temperatures lead to a feedback parameter with the wrong sign, which is not physically possible for a stable climate system. It could be the GISS model has issues with energy conservation.

Just how these results would impact global warming projections remains to be seen. First, improvements in how tropical convection and its associated clouds and vertical distributions of water vapor *change with temperature* would have to be put into the models. Then, the models would have to be run with increasing CO2 to see whether model projections of warming are reduced.

My prediction is that, if this was done, the models would produce considerably less tropical warming than they currently do. This might also extend to reduced warming rates outside of the tropics, since the tropics export excess heat energy to higher latitudes. If less heat builds up in the tropics, less will be exported out of the tropics.

We have many more results on this issue, including comparisons to a simple time-dependent forcing-feedback model that can replicate both the observations and the CMIP5 model behavior.

This has nothing to do with climate or climate change, but as a photographer it interests me.

Some version of the following image has been making the rounds on social media for many years. The accompanying claim goes something like this:

“These two blocks are exactly the same shade of grey. Hold your finger over the seam and check.”

I can demonstrate that this is not the case.

The two blocks actually are very different in their shades of gray, given the source of illumination as implied by (1) the area between them and (2) the shadow below them on the ground.

If you cover up that seam (and the shadow as well), they only appear to be the same shade of gray because your brain then assumes (without any other visual cues) that they are both illuminated equally. But given the knowledge of the direction of the illumination, your brain is telling you that they really are different shades of gray.

If you still don’t believe me, you could demonstrate this with two different pieces of paper having very different shades of gray and take them out in the sun, orienting them like the two objects above. You would need to find two shades of gray (say, two paint swatch cards) where their apparent brightness (as measured by, say, taking a photo and analyzing the digital counts in Photoshop) would be approximately the same. In that case, would you say, “These two cards have the same shade of gray because I measured them in Photoshop?”

Of course not.

Now, the question arises, why do the center of the surfaces still appear to be different brightness, even though they are the same? As a photographer, I’ve noticed that when you take a photo of a very contrasty scene, your eye can see details in the shadows that the recorded camera image cannot. Similarly, very bright areas might show details to the eye, but be totally washed out in the camera image.

I don’t believe this is just the differences in dynamic range of the eye versus a camera, because the iris opening of the eye is the same for the entire scene, and the inherent integration time of the eye-brain system is presumably the same across your rods and cones. I think it’s because our brain does a sort of localized contrast enhancement within our field of view, making shadowed things seem brighter and very bright things seem dimmer. (You can make similar adjustments using “curves” in Photoshop).

It’s sort of the visual equivalent of audio compression. The brain alters perceived brightness locally to enhance contrasts. I believe this is why we photographers often use adjustments in software to get the image to look more like what our eye and brain perceived.

I just discovered that my explanation involving localized contrast enhancement seems to be supported by a 1999 article in The Journal of Neuroscience entitled, An Empirical Explanation of the Cornsweet Effect.

Have you ever wondered, “How can we predict global average temperature change when we don’t even know what the global average temperature is?”

Or maybe, “How can climate models produce any meaningful forecasts when they have such large errors in their component energy fluxes?” (This is the issue I’ve been debating with Dr. Pat Frank after publication of his Propagation of Error and the Reliability of Global Air Temperature Projections. )

I like using simple analogies to demonstrate basic concepts

Pots of Water on the Stove

A pot of water warming on a gas stove is useful for demonstrating basic concepts of energy gain and energy loss, which together determine temperature of the water in the pot.

If we view the pot of water as a simple analogy to the climate system, with a stove flame (solar input) heating the pots, we can see that two identical pots can have the same temperature, but with different rate of energy gain and loss, if (for example) we place a lid on one of the pots.

A lid reduces the warming water’s ability to cool, so the water temperature goes up (for the same rate of energy input) compared to if no lid was present. As a result, a lower flame is necessary to maintain the same water temperature as the pot without a lid. The lid is analogous to Earth’s greenhouse effect, which reduces the ability of the Earth’s surface to cool to outer space.

The two pots in the above cartoon are analogous to two climate models having different energy fluxes with known (and unknown) errors in them. The models can be adjusted so the various energy fluxes balance in the long term (over centuries) but still maintain a constant global average surface air temperature somewhere close to that observed. (The model behavior is also compared to many observed ocean and atmospheric variables. Surface air temperature is only one.)

Next, imagine that we had twenty pots with various amounts of coverage of the pots by the lids: from no coverage to complete coverage. This would be analogous to 20 climate models having various amounts of greenhouse effect (which depends mostly on high clouds [Frank’s longwave cloud forcing in his paper] and water vapor distributions). We can adjust the flame intensity until all pots read 150 deg. F. This is analogous to adjusting (say) low cloud amounts in the climate models, since low clouds have a strong cooling effect on the climate system by limiting solar heating of the surface.

Numerically Modeling the Pot of Water on the Stove

Now, let’s say we we build a time-dependent computer model of the stove-pot-lid system. It has equations for the energy input from the flame, and loss of energy from conduction, convection, radiation, and evaporation.

Clearly, we cannot model each component of the energy fluxes exactly, because (1) we can’t even measure them exactly, and (2) even if we could measure them exactly, we cannot exactly model the relevant physical processes. Modeling of real-world systems always involves approximations. We don’t know exactly how much energy is being transferred from the flame to the pot. We don’t know exactly how fast the pot is losing energy to its surroundings from conduction, radiation, and evaporation of water.

But we do know that if we can get a constant water temperature, that those rates of energy gain and energy loss are equal, even though we don’t know their values.

Thus, we can either make ad-hoc bias adjustments to the various energy fluxes to get as close to the desired water temperature as we want (this is what climate models used to do many years ago); or, we can make more physically-based adjustments because every computation of physical processes that affect energy transfer has uncertainties, say, a coefficient of turbulent heat loss to the air from the pot. This is what model climate models do today for adjustments.

If we then take the resulting “pot model” (ha-ha) that produces a water temperature of 150 deg. F as it is integrated over time, with all of its uncertain physical approximations or ad-hoc energy flux corrections, and run it with a little more coverage of the pot by the lid, we know the modeled water temperature will increase. That part of the physics is still in the model.

This is why climate models can have uncertain energy fluxes, with substantial known (or even unknown) errors in their energy flux components, and still be run with increasing CO2 to produce warming, even though that CO2 effect might be small compared to the errors. The errors have been adjusted so they sum to zero in the long-term average.

This directly contradicts the succinctly-stated main conclusion of Frank’s paper:

“LWCF [longwave cloud forcing] calibration error is +/- 144 x larger than the annual average increase in GHG forcing. This fact alone makes any possible global effect of anthropogenic CO2 emissions invisible to present climate models.”

I’m not saying this is ideal, or even a defense of climate model projections. Climate models should ideally produce results entirely based upon physical first principles. For the same forcing scenario (e.g. a doubling of atmospheric CO2) twenty different models should all produce about the same amount of future surface warming. They don’t.

Instead, after 30 years and billions of dollars of research they still produce from 1.5 to 4.5 deg. C of warming in response to doubling of atmospheric CO2.

The Big Question

The big question is, “How much will the climate system warm in response to increasing CO2?” The answer depends not so much upon uncertainties in the component energy fluxes in the climate system, as Frank claims, but upon how those energy fluxes change as the temperature changes.

And that’s what determines “climate sensitivity”.

This is why people like myself and Lindzen emphasize so-called “feedbacks” (which determine climate sensitivity) as the main source of uncertainty in global warming projections.

NOTE: This post has undergone a few revisions as I try to be more precise in my wording. The latest revision was at 0900 CDT Sept. 12, 2019.

If this post is re-posted elsewhere, I ask that the above time stamp be included.

Yesterday I posted an extended and critical analysis of Dr. Pat Frank’s recent publication entitled Propagation of Error and the Reliability of Global Air Temperature Projections. Dr. Frank graciously provided rebuttals to my points, none of which have changed my mind on the matter. I have made it clear that I don’t trust climate models’ long-term forecasts, but that is for different reasons than Pat provides in his paper.

What follows is the crux of my main problem with the paper, which I have distilled to its essence, below. I have avoided my previous mistake of paraphrasing Pat, and instead I will quote his conclusions verbatim.

In his Conclusions section, Pat states “As noted above, a GCM simulation can be in perfect external energy balance at the TOA while still expressing an incorrect internal climate energy-state.”

This I agree with, and I believe climate modelers have admitted to this as well.

But, he then further states, “LWCF [longwave cloud forcing] calibration error is +/- 144 x larger than the annual average increase in GHG forcing. This fact alone makes any possible global effect of anthropogenic CO2 emissions invisible to present climate models.”

While I agree with the first sentence, I thoroughly disagree with the second. Together, they represent a non sequitur. All of the models show the effect of anthropogenic CO2 emissions, despite known errors in components of their energy fluxes (such as clouds)!

Why?

If a model has been forced to be in global energy balance, then energy flux component biases have been cancelled out, as evidenced by the control runs of the various climate models in their LW (longwave infrared) behavior:

Importantly, this forced-balancing of the global energy budget is not done at every model time step, or every year, or every 10 years. If that was the case, I would agree with Dr. Frank that the models are useless, and for the reason he gives. Instead, it is done once, for the average behavior of the model over multi-century pre-industrial control runs, like those in Fig. 1.

The ~20 different models from around the world cover a WIDE variety of errors in the component energy fluxes, as Dr. Frank shows in his paper, yet they all basically behave the same in their temperature projections for the same (1) climate sensitivity and (2) rate of ocean heat uptake in response to anthropogenic greenhouse gas emissions.

Thus, the models themselves demonstrate that their global warming forecasts do not depend upon those bias errors in the components of the energy fluxes (such as global cloud cover) as claimed by Dr. Frank (above).

That’s partly why different modeling groups around the world build their own climate models: so they can test the impact of different assumptions on the models’ temperature forecasts.

Statistical modelling assumptions and error analysis do not change this fact. A climate model (like a weather forecast model) has time-dependent differential equations covering dynamics, thermodynamics, radiation, and energy conversion processes. There are physical constraints in these models that lead to internally compensating behaviors. There is no way to represent this behavior with a simple statistical analysis.

Again, I am not defending current climate models’ projections of future temperatures. I’m saying that errors in those projections are not due to what Dr. Frank has presented. They are primarily due to the processes controlling climate sensitivity (and the rate of ocean heat uptake). And climate sensitivity, in turn, is a function of (for example) how clouds change with warming, and apparently not a function of errors in a particular model’s average cloud amount, as Dr. Frank claims.

The similar behavior of the wide variety of different models with differing errors is proof of that. They all respond to increasing greenhouse gases, contrary to the claims of the paper.

The above represents the crux of my main objection to Dr. Frank’s paper. I have quoted his conclusions, and explained why I disagree. If he wishes to dispute my reasoning, I would request that he, in turn, quote what I have said above and why he disagrees with me.

UPDATE: (1300CDT, Sept. 11, 2019). I’ve added a plot of ten CMIP5 models’ global top-of-atmosphere longwave IR variations in the first 100 years of their control runs.

UPDATE #2: 0800 CDT Sept. 12, 2019) After comments from Dr. Frank and a number of commenters here and at WUWT, I have posted Additional Comments on the Frank (2019) Propagation of Error Paper, where I have corrected my mistake of paraphrasing Dr. Frank’s conclusions, when I should have been quoting them verbatim.

I’ve been asked for my opinion by several people about this new published paper by Stanford researcher Dr. Patrick Frank.

I’ve spent a couple of days reading the paper, and programming his Eq. 1 (a simple “emulation model” of climate model output ), and included his error propagation term (Eq. 6) to make sure I understand his calculations.

Frank has provided the numerous peer reviewers’ comments online, which I have purposely not read in order to provide an independent review. But I mostly agree with his criticism of the peer review process in his recent WUWT post where he describes the paper in simple terms. In my experience, “climate consensus” reviewers sometimes give the most inane and irrelevant objections to a paper if they see that the paper’s conclusion in any way might diminish the Climate Crisis™.

Some reviewers don’t even read the paper, they just look at the conclusions, see who the authors are, and make a decision based upon their preconceptions.

Readers here know I am critical of climate models in the sense they are being used to produce biased results for energy policy and financial reasons, and their fundamental uncertainties have been swept under the rug. What follows is not meant to defend current climate model projections of future global warming; it is meant to show that — as far as I can tell — Dr. Frank’s methodology cannot be used to demonstrate what he thinks he has demonstrated about the errors inherent in climate model projection of future global temperatures.

A Very Brief Summary of What Causes a Global-Average Temperature Change

Before we go any further, you must understand one of the most basic concepts underpinning temperature calculations: With few exceptions, the temperature change in anything, including the climate system, is due to an imbalance between energy gain and energy loss by the system. This is basic 1st Law of Thermodynamics stuff.

So, if energy loss is less than energy gain, warming will occur. In the case of the climate system, the warming in turn results in an increase loss of infrared radiation to outer space. The warming stops once the temperature has risen to the point that the increased loss of infrared (IR) radiation to to outer space (quantified through the Stefan-Boltzmann [S-B] equation) once again achieves global energy balance with absorbed solar energy.

While the specific mechanisms might differ, these energy gain and loss concepts apply similarly to the temperature of a pot of water warming on a stove. Under a constant low flame, the water temperature stabilizes once the rate of energy loss from the water and pot equals the rate of energy gain from the stove.

The climate stabilizing effect from the S-B equation (the so-called “Planck effect”) applies to Earth’s climate system, Mars, Venus, and computerized climate models’ simulations. Just for reference, the average flows of energy into and out of the Earth’s climate system are estimated to be around 235-245 W/m2, but we don’t really know for sure.

What Frank’s Paper Claims

Frank’s paper takes an example known bias in a typical climate model’s longwave (infrared) cloud forcing (LWCF) and assumes that the typical model’s error (+/-4 W/m2) in LWCF can be applied in his emulation model equation, propagating the error forward in time during his emulation model’s integration. The result is a huge (as much as 20 deg. C or more) of resulting spurious model warming (or cooling) in future global average surface air temperature (GASAT).

He claims (I am paraphrasing) that this is evidence that the models are essentially worthless for projecting future temperatures, as long as such large model errors exist. This sounds reasonable to many people. But, as I will explain below, the methodology of using known climate model errors in this fashion is not valid.

First, though, a few comments. On the positive side, the paper is well-written, with extensive examples, and is well-referenced. I wish all “skeptics” papers submitted for publication were as professionally prepared.

He has provided more than enough evidence that the output of the average climate model for GASAT at any given time can be approximated as just an empirical constant times a measure of the accumulated radiative forcing at that time (his Eq. 1). He calls this his “emulation model”, and his result is unsurprising, and even expected. Since global warming in response to increasing CO2 is the result of an imposed energy imbalance (radiative forcing), it makes sense you could approximate the amount of warming a climate model produces as just being proportional to the total radiative forcing over time.

Frank then goes through many published examples of the known bias errors climate models have, particularly for clouds, when compared to satellite measurements. The modelers are well aware of these biases, which can be positive or negative depending upon the model. The errors show that (for example) we do not understand clouds and all of the processes controlling their formation and dissipation from basic first physical principles, otherwise all models would get very nearly the same cloud amounts.

But there are two fundamental problems with Dr. Frank’s methodology.

Climate Models Do NOT Have Substantial Errors in their TOA Net Energy Flux

If any climate model has as large as a 4 W/m2 bias in top-of-atmosphere (TOA) energy flux, it would cause substantial spurious warming or cooling. None of them do.

Why?

Because each of these models are already energy-balanced before they are run with increasing greenhouse gases (GHGs), so they have no inherent bias error to propogate.

For example, the following figure shows 100 year runs of 10 CMIP5 climate models in their pre-industrial control runs. These control runs are made by modelers to make sure that there are no long-term biases in the TOA energy balance that would cause spurious warming or cooling.

If what Dr. Frank is claiming was true, the 10 climate models runs in Fig. 1 would show large temperature departures as in the emulation model, with large spurious warming or cooling. But they don’t. You can barely see the yearly temperature deviations, which average about +/-0.11 deg. C across the ten models.

Why don’t the climate models show such behavior?

The reason is that the +/-4 W/m2 bias error in LWCF assumed by Dr. Frank is almost exactly cancelled by other biases in the climate models that make up the top-of-atmosphere global radiative balance. To demonstrate this, here are the corresponding TOA net longwave IR fluxes for the same 10 models shown in Fig. 1. Clearly, there is nothing like 4 W/m2 imbalances occurring.

The average yearly standard deviation of the LW flux variations is only 0.16 W/m2, and these vary randomly.

And it doesn’t matter how correlated or uncorrelated those various errors are with each other: they still sum to nearly zero in the long term, which is why the climate model trends in Fig 1 are only +/- 0.10 C/Century… not +/- 20 deg. C/Century. That’s a factor of 200 difference.

This (first) problem with the paper’s methodology is, by itself, enough to conclude the paper’s methodology and resulting conclusions are not valid.

The Error Propagation Model is Not Appropriate for Climate Models

The new (and generally unfamiliar) part of his emulation model is the inclusion of an “error propagation” term (his Eq. 6). After introducing Eq. 6 he states,

“Equation 6 shows that projection uncertainty must increase in every simulation (time) step, as is expected from the impact of a systematic error in the deployed theory“.

While this error propagation model might apply to some issues, there is no way that it applies to a climate model integration over time. If a model actually had a +4 W/m2 imbalance in the TOA energy fluxes, that bias would remain relatively constant over time. It doesn’t somehow accumulate (as the blue curves indicate in Fig. 1) as the square root of the summed squares of the error over time (his Eq. 6).

Another curious aspect of Eq. 6 is that it will produce wildly different results depending upon the length of the assumed time step. Dr. Frank has chosen 1 year as the time step (with a +/-4 W/m2 assumed energy flux error), which will cause a certain amount of error accumulation over 100 years. But if he had chosen a 1 month time step, there would be 12x as many error accumulations and a much larger deduced model error in projected temperature. This should not happen, as the final error should be largely independent of the model time step chosen. Furthermore, the assumed error with a 1 month time step would be even larger than +/-4 W/m2, which would have magnified the final error after a 100 year integrations even more. This makes no physical sense.

I’m sure Dr. Frank is much more expert in the error propagation model than I am. But I am quite sure that Eq. 6 does not represent how a specific bias in a climate model’s energy flux component would change over time. It is one thing to invoke an equation that might well be accurate and appropriate for certain purposes, but that equation is the result of a variety of assumptions, and I am quite sure one or more of those assumptions are not valid in the case of climate model integrations. I hope that a statistician such as Dr. Ross McKitrick will examine this paper, too.

Concluding Comments

There are other, minor, issues I have with the paper. Here I have outlined the two most glaring ones.

Again, I am not defending the current CMIP5 climate model projections of future global temperatures. I believe they produce about twice as much global warming of the atmosphere-ocean system as they should. Furthermore, I don’t believe that they can yet simulate known low-frequency oscillations in the climate system (natural climate change).

But in the context of global warming theory, I believe the largest model errors are the result of a lack of knowledge of the temperature dependent changes in clouds and precipitation efficiency (thus free-tropospheric vapor, thus water vapor “feedback”) that actually occur in response to a long-term forcing of the system from increasing carbon dioxide. I do not believe it is because the fundamental climate modeling framework is not applicable to the climate change issue. The existence of multiple modeling centers from around the world, and then performing multiple experiments with each climate model while making different assumptions, is still the best strategy to get a handle on how much future climate change there *could* be.

My main complaint is that modelers are either deceptive about, or unaware of, the uncertainties in the myriad assumptions — both explicit and implicit — that have gone into those models.

There are many ways that climate models can be faulted. I don’t believe that the current paper represents one of them.

I’d be glad to be proved wrong.

It’s been ten years since I addressed this issue in a specific blog post, so I thought it would be useful to revisit it. I mention it from time to time, but it is so important, it bears repeating and remembering.

Over and over again.

I continue to strive to simply these concepts, so here goes another try. What follows is as concise as I can make it.

1. The temperature change in anything, including the climate system, is the result of an imbalance between the rates of energy gain and energy loss. This comes from the First Law of Thermodynamics. Basic stuff.
2. Global warming is assumed to be due to the small (~1%) imbalance between absorbed sunlight and infrared energy lost to outer space averaged over the Earth caused by increasing atmospheric CO2 from fossil fuel burning.
3. But we don’t know whether the climate system, without human influence, is in a natural state of energy balance anyway. We do not know the quantitative average amounts of absorbed sunlight and emitted infrared energy across the Earth, either observationally or from first physical principles, to the accuracy necessary to blame most recent warming on humans rather than nature. Current best estimates, based upon a variety of datasets, is around 239-240 Watts per sq. meter for these energy flows. But we really don’t know.

When computer climate models are first constructed, these global-average energy flows in and out of the climate system do not balance. So, modelers adjust any number of uncertain processes in the models (for example, cloud parameterizations) until they do balance. They run the model for, say, 100 years and make sure there is little or no long-term temperature trend to verify balance exists.

Then, they add the infrared radiative effect of increasing CO2, which does cause an energy imbalance. Warming occurs. They then say something like, “See? The model proves that CO2 is responsible for warming we’ve seen since the 1950s.”

But they have only demonstrated what they assumed from the outset. It is circular reasoning. A tautology. Evidence that nature also causes global energy imbalances is abundant: e.g., the strong warming before the 1940s; the Little Ice Age; the Medieval Warm Period. This is why many climate scientists try to purge these events from the historical record, to make it look like only humans can cause climate change.

I’m not saying that increasing CO2 doesn’t cause warming. I’m saying we have no idea how much warming it causes because we have no idea what natural energy imbalances exist in the climate system over, say, the last 50 years. Those are simply assumed to not exist.

(And, no, there is no fingerprint of human-caused warming. All global warming, whether natural or human-caused, looks about the same. If a natural decrease in marine cloudiness was responsible, or a decrease in ocean overturning [either possible in a chaotic system], warming would still be larger over land than ocean, greater in the upper ocean than deep ocean, and greatest at high northern latitudes and least at high southern latitudes).

Thus, global warming projections have a large element of faith programmed into them.

Summary: Twenty-two major hurricanes have struck the east coast of Florida (including the Keys) since 1871. It is shown that the observed increase in intensity of these storms at landfall due to SST warming over the years has been a statistically insignificant 0.43 knots per decade (0.5 mph per decade). Thus, there has been no observed increase in landfalling east coast Florida major hurricane strength with warming.

In the news reporting of major Hurricane Dorian which devastated the NW Bahamas, it is commonly assumed that hurricanes in this region have become stronger due to warming sea surface temperatures (SSTs), which in turn are assumed to be caused by human-caused greenhouse gas emissions.

Here I will use observational data since the 1870s to address the question: Have landfalling major hurricanes on the east coast of Florida increased in intensity from warming sea surface temperatures?

The reason I am only addressing landfalling hurricanes on the east coast of Florida is three-fold: (1) this area is a hotbed of major hurricane activity; (2) the record is much longer for landfalling hurricanes, since before the early 1970s the intensity of major hurricanes well offshore was much more uncertain; and (3) the coastal population there is now several million people, the region south of West Palm Beach is historically prone to major hurricane strikes, and so the question of whether hurricane intensity there has increased due to ocean warming is of great practical significance to many people.

First let’s start with the record of major hurricane strikes on the east coast of Florida, including the keys. There have been 22 such storms since 1871, occurring quite irregularly over time.

While there has been a slight increase in the intensity of these storms over time, amounting to +0.8 knots per decade, the correlation is quite low (0.21) and the quantitative relationship is only barely significant at the 1-sigma level.

But this doesn’t tell us the role of sea surface temperatures (SSTs). So, next let’s examine how SSTs have changed over the same period of time. Since all of these major hurricanes made landfall in the southern half of Florida, I chose the following boxed region (22N-28N, 75W-82W) to compute area-averaged SST anomalies for all months from 1870 through 2018 (HadSST data available here).

Since 18 of the 22 major hurricane strikes occurred in either August (4) or September (14), (and 4 were in October), I focused on the average SST anomaly for the 2-month periods August-September. Here’s the 2-month average SST anomalies for 1870-2018.

Note that the years with major hurricane strikes are marked in red. What surprised me is that the SST warming in this region during peak hurricane season (August/September) has been very weak: +0.02 C/decade since 1871, and +0.03 C/decade since 1950.

If we then compare SST anomaly with storm intensity at landfall, we get the following plot. Here I took into account which month the hurricane occurred in for the purposes of computing a 2-month SST anomaly. For example, if the storm hit in October, I used the September/October average. If landfall was in August, I used the July/August average.

There is a weak relationship between SST and storm intensity (correlation = 0.19), but the regression coefficient (+13.5 kts/deg. C warming) is not statistically significant at the 1-sigma level.

Now, if we just ignore statistical lack of significance and assume these quantitative relationships are mostly signal rather than noise, we can multiply the 0.03 C/decade SST warming trend since 1950 by the 13.5 kts/deg C “warming sensitivity parameter”, and get +0.43 kts/decade of storm intensity increase per decade due to SST warming, which is almost exactly 0.5 mph per decade.

This is an exceedingly small number. That would be 5 mph per century.

So, based upon the observed SST data from the Hadley Centre, and hurricane data from the National Hurricane Center, we conclude that warming SSTs have caused a tiny increase in intensity of landfalling major hurricanes by 0.5 mph per decade.

I suspect a statistician (which I am not) would say that this is in the noise level.

In other words, there is no observational evidence that warming SSTs have made landfalling hurricanes on the east coast of Florida any stronger.