Consensus Climatology in a Nutshell: Betrayal of Integrity

Steve Mosher brought up Dr. Patrick Brown’s critique in several posts, starting here.

Rud Istvan has also weighed in positively on Dr. Brown’s critique, especially here and here.

Dr. Brown mistakes the rmse ±4 W/m^2/year calibration uncertainty statistic as a positive sign 4 W/m^2 forcing error. This misconstrues a statistic as an energy. This mistake alone is fatal to pretty much his entire argument.

Steve Mosher knows nothing of science. His attacks on me always display that ignorance. He regularly and uncritically quotes disproven criticisms. So, it’s no surprise that he should post excited declamations about Dr. Brown’s video.

However Rud is pretty well trained, and I’m surprised he didn’t catch Dr. Brown’s obvious misconstrual of a statistic for an energy, and uncertainty for physical error.

As these two have brought Dr. Brown’s video to the fore, I’ve decided to post my opening critique of it here as a reference for those interested in the debate here.

I’ll link this post upthread at Mosher’s and Rud’s comments.

The conversation at Dr. Brown’s site continued after the post below. Dr. Brown’s argument did not prevail. It got pretty desperate with his claim that in a division, the numerator includes the dimension of the denominator. But in any case Dr. Brown never accepted that a rmse statistic is not a forcing.
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Before proceeding, I’d like to thank Dr. Brown for kindly notifying me of his critique after posting it. His email was very polite and temperate; qualities that were very much appreciated. His video critique is thoughtful, very reasoned, and very clear and calm in presentation. Dr. Brown gave an accurate summary of my method. I also gratefully acknowledge Dr. Brown’s scientific integrity, very apparent in his presentation and especially in his deportment.

I also acknowledge that, in the first several minutes of his presentation, Dr. Brown correctly described the error propagation method I used.

I’ll begin by noting that my presentation shows beyond doubt that GCM global air temperature projections are no more than linear extrapolations of green house gas forcing. Linear propagation of error is therefore directly warranted.

GCMs make large thermal errors. Propagation of these errors through a global air temperature projection will inevitably produce large uncertainty bars.

Even a uncertainty of ±1 W/m² in tropospheric thermal energy flux will propagate out to an uncertainty of ±4.3 C after 100 years, which is about the same size as the ~4 C mean 2000-2100 anomaly from RCP 8.5, and about 4 times the projection uncertainty admitted by the IPCC.

Before proceeding to specific points, I’ll mention that in minute 12:35, Dr. Brown observed that the ±17 C uncertainty envelope in RCP 8.5, derived from long wave cloud forcing (LCF) error is, “a completely unphysical range of uncertainty, so it’s totally not plausible that temperature could decrease by 15 degrees as we’re increasing CO₂. And it’s implausible as well that temperature could increase by 17 decrees as we’re increasing CO₂ under the RCP 8.5 scenario. But as I understand it, this is the point Dr. Frank is trying to make.”

A temperature uncertainty statistic is not a physical temperature. Statistical uncertainties cannot be “unphysical” in the sense Dr. Brown implies. The large uncertainty bars do not indicate possible increases or decreases in air temperature. They indicate a state of knowledge. The uncertainty bars are an ignorance width. I made this very point in my DDP presentation, when the propagated uncertainty envelopes were first introduced.

It is true that the very large uncertainty bars subsume any possible future air temperature excursion. This condition indicates that no future air temperature can falsify a climate model air temperature projection. No knowledge of future air temperature is contained in, or transmitted by, a climate model temperature expectation value.

Dr. Brown continued, “So he’s essentially saying that when you properly account for the uncertainty in the climate model projections, the uncertainty becomes so large so quickly that you can’t actually draw any meaning from the projections that the climate models are making.” On this, we are agreed.

The assessment below of Dr. Brown’s presentation is long. To accommodate readers who do not wish to read through it, here’s a summary. Dr. Brown has:

• throughout mistaken the time-average statistic of a dynamical response error for a time-invariant error;
• throughout mistaken theory-bias error for base-state error;
• repeatedly and wrongly appended a plus/minus to a single-sign offset error, in effect creating a fictitious root-mean-square (rms) error;
• repeatedly and improperly propagated the fictitious rms error to produce uncertainty envelopes with one fictitious wing;
• apparently does not recognize that only a unique model expectation value qualifies as prediction in science.

This list is not exhaustive, but in-and-of itself is sufficient to vitiate the analytical merit of Dr. Brown’s analysis, in its entirety.

Now to specifics:

Dr. Brown’s critique was presented under five headings:
1. Arbitrary use of 1 year as the compounding time scale.
2. Use of spatial root-mean-square instead of global mean net error.
3. Use of error in one component of the energy budget rather than error in net imbalance.
4. Use of a base state error rather than a response error.
5. Reality check: Hansen (1988) projection.

These are taken in turn. I assume the readers are familiar with the contents of Dr. Brown’s video.

Minute 15:07, 1. Arbitrary use of 1 year as the compounding time scale.

From Lauer and Hamilton, page 3831: “A measure of the performance of the CMIP model ensemble in reproducing observed mean cloud properties is obtained by calculating the differences in modeled (x_mod) and observed (x_obs) 20-yr means. These differences are then averaged over all N models in the CMIP3 or CMIP5 ensemble to calculate the multimodel ensemble mean bias delta_mm which is defined at each grid point as delta_mm = (1/N){sum_over[(x_mod)_i] – x_obs}, for all i= 1 to N.”

Page 3831 “The CF [cloud forcing] is defined as the difference between ToA [top of the atmosphere] all-sky and clear-sky outgoing radiation in the solar spectral range (SCF [short-wave cloud forcing]) and in the thermal spectral range (LCF [long-wave cloud forcing]).”

That is, the ±4 W/m² LCF root-mean-square-error (rmse) is the annual average CMIP5 thermal flux error. The choice of annual error compounding was therefore analytically based, not arbitrary.

Further, the ±4 W/m² is not a time-invariant error, as Dr. Brown suggested, but rather a time-average error of climate model cloud dynamics. It says that CMIP5 models will average ±4 W/m² error in long-wave cloud forcing each year, every year, while simulating the evolution of the climate.

Although Dr. Brown did not discuss it, part of my presentation showed that CMIP5 LCF error arises from a theory-bias error common to all tested models. A theory-bias error is an error in the physical theory deployed within the model. Theory-bias errors introduce systematic errors into individual model outputs, and continuing sequential errors into step-wise calculations.

CMIP5 models introduce an annual average ±4 W/m² LCF error into the thermal flux within the simulated troposphere, continuously and progressively each year and every year in a climate projection.

Next, Dr. Brown suggested that the annual average could be arbitrarily used for 20 years or for one second. It should now be obvious that he is mistaken. An annual average error can be applied only to a calculation of annual span.

Dr. Brown’s alternative propagation in 20-year steps used the ±4 W/m² one-year rmse LCF error. A 20-year time step requires a 20-year uncertainty statistic.

The CMIP5 ±4 W/m² annual average can be scaled back up to a 20-year average LCF rms uncertainty, “±u_20,” calculated as ±u_20 (W/m²) = sqrt[42*20] W/m² = ±17.9 W/m².

Using Dr. Brown’s RCP 8.5 scenario as the example, the 2000-2019 change in GHG forcing is 0.89 W/m². The year 2000 base greenhouse gas (GHG) forcing is taken as the sum of the contributions from CO₂+N2O+CH4, and is 32.321 W/m², calculated from the equations in G. Myhre, et al., (1998) GRL 25(14), 2715-2718. GHG forcing have recently been updated, but the difference doesn’t impact the force of this demonstration.

Starting from year 2000, and using the linear model, the uncertainty across a projection consisting of a single 20-year time-step is [(0.42*33.833*±17.9)/32.321] = ±7.9 C, where 33.833 C is the year 2000 net greenhouse temperature.

In comparison, at year 2019, i.e., after 20 years, the annual-step RCP 8.5 ±4 W/m² annual average uncertainty compounds to ±7.6 C.

Likewise, after a series of five 20-year time-steps, the propagated uncertainty at year 2100 is ±17.3 C.

In comparison, the RCP 8.5 centennial uncertainty obtained propagating the annual ±4 W/m² over 100 yearly time steps from 2000 to 2099 is ±17.1 C.

So, in both cases, the annually propagated uncertainties are effectively the same values as the propagated 20-year time-steps.

This comparison shows that, correctly calculated, the final propagated uncertainty is negligibly dependent on time-step size.

All of this demonstrates that Dr. Brown’s conclusion at the end of section 1 (minute 16:50), though true, is misguided and irrelevant to the propagated error analysis.

Minute 17:10, 2. Use of spatial root-mean-square instead of global mean net error.

In his analysis, Dr. Brown immediately and incorrectly characterized the CMIP5 ±4 W/m² annual average LCF rms error as a “base-state error.”

However, the LCF rms error was derived from 20 years of simulated climate — the 1986-2005 global climate states. These model years were extracted from historical model runs starting from an 1850 base state.

The actual “base-state” error would be the difference between the simulated and observed 1850 climate. However, the 1850 climate is nearly unknown. Therefore the true base-state error is unknowable.

In contrast, the model ±4 W/m² LCF error represents the annual average dynamical misallocation of simulated tropospheric thermal energy flux, during the 20 years of simulation. It is not a base-state error.

As a relevant aside, looking carefully at the scale-bar to the left of Dr. Brown’s graphic of LCF model error (minute 17:57), the errors vary in general between +10 W/m² and –10 W/m² across the entire globe, with a scatter of deeper excursions.

With these ±10 W/m² errors in simulated tropospheric thermal flux, we are expected to credit that the models can resolve the effect of an annual GHG forcing perturbation of about 0.035 W/m²; a perturbation ±286 times smaller than the general levels of error in Dr. Brown’s graphic.

Next, Dr. Brown says that by squaring the LCF error, one makes the error positive. This, he says, doesn’t make sense. However, that representation is incorrect. Squaring the error provides a positive variance. The uncertainty used is the square root of the error variance, which makes it “±,” i.e., plus/minus, not positive. This is not an “absolute value error,” as Dr. Brown represents.

In minute 18:30, Dr. Brown compares the mean LCF of 28 models with observed cloud LCF, showing that they are similar. By inference, this model mean error is what Dr. Brown means by “net error.”

However, taking a mean allows positive and negative errors to cancel. Considering only the mean hides the fact that models do in fact make both positive and negative errors in cloud forcing across the globe, as Dr. Brown’s prior graphic showed. These plus/minus errors indicate that the simulated climate state does not correspond to the physically correct climate state.

In turn, this climate state error puts uncertainty into the simulated air temperature because the climate simulation that produced the temperature is physically incorrect. Therefore, focusing on the mean model LCF hides the physical error in the simulated climate state, and confers a false certainty on the simulated air temperature.

The point is clearer when considering Dr. Brown’s minute 18:30 graphic. The 28 climate models shown there have differing LCF errors. Their simulated climate states not only do not represent the physically correct climate state, but their simulated states also are all differently incorrect.

That is, these models not only simulate the climate state incorrectly, but they produce simulation errors that vary across the model set. Nevertheless, the models all adequately reproduce the 1850-to-present global air temperature trend.

Temperature correspondence among the models means that the same air temperature can be produced by a wide variety of alternative and incorrectly simulated climate states. The question becomes, what certainty can reside in a simulated air temperature that is consistently produced by multiple climate states, all of which are not only physically incorrect, but also incorrect in different ways? Further, when it is known that climate states are simulated incorrectly, what certainty resides in the climate-state evolution in time?

Taking the mean error hides the plus/minus errors that indicate the simulated climate states are physically incorrect. The approach Dr. Brown prefers confers an invalid certainty on model results.

In minute 19:37, Dr. Brown then compared the FGOALS and GFDL climate models with widely differing mean LCF offset errors, of -9 W/m² or +0.1 W/m², respectively, and showed they produced hugely different uncertainty envelopes when propagated.

Propagating these errors is a mistake, however, because they are single-sign single-model mean offsets. They are not the root-mean-square error of each single-model global LCF simulation (see below).

Neither offset error is a plus/minus value. However, the right side of Dr. Brown’s graphic incorrectly represents them as “±.” Dr. Brown has incorrectly appended a “±” to these single-sign errors. The strictly positive GFDL error can produce only a small positive wing, while the FGOALS calculation is restricted to a large negative wing. That is, Dr. Brown’s double-winged uncertainty envelopes resulted from improperly appending a “±” to mean errors that are strictly positive or negative values.

Thus, both uncertainty calculations are wrong because a single-model single-sign mean offset was wrongly entered into a propagation scheme requiring a plus/minus rms error.

The global LCF error for a single model simulation is the rmse calculated from simulated minus observed LCF in the requisite unit-areas across the globe. Taking the root-mean-square of the individual errors produces the global mean single-model plus/minus LCF uncertainty. Propagation of the LCF “±” rmse then produces both positive and negative wings of the uncertainty envelope.

In minute 20:06, Dr. Brown asked, “Does it make sense that two models that predict similar amounts of warming by 2100 would have uncertainty ranges that differ by orders of magnitude?”

We’ve seen that Dr. Brown’s error ranges are wrongly calculated and pretty much meaningless.

Further, the fact that two models deploying the same physics make such different mean LCF errors shows that large parameter disparities are hidden in the models. In order to produce the same air temperature even though the respective mean LCF errors are widely different, the two models must have different suites of offsetting internal errors. That is, Dr. Brown’s objection here actually confirms my analysis. A large uncertainty must attach to a consistent air temperature emergent from disparately incorrect models.

Minute 20:30, 3. Use of error in one component of the energy budget rather than error in net imbalance.

Dr. Brown’s argument here does not take cognizance of the difference between the so-called instantaneous response to a forcing change and the equilibrium response. My analysis concerns the instantaneous response to GHG forcing. The equilibrium response includes the oceans, which respond on a much longer time scale. So, inclusion of the ocean heat capacity in Dr. Brown’s argument is a non-sequitur with respect to my error analysis.

Next, the choice of LCF rms error confines the uncertainty analysis to the tropospheric thermal energy flux, where GHG forcing makes its immediate impact on global air temperature. GHG forcing enters directly into the tropospheric thermal energy flux and becomes part of it. An uncertainty in tropospheric thermal energy flux imposes an uncertainty in the thermal impact of GHG forcing.

The CMIP5 ±4 W/m² annual average LCF error is ±114 times larger than the annual average ca. 0.035 W/m² forcing increase CO₂ emissions introduce into the troposphere.

Dr. Brown proposed that a model with perfect global net energy balance would produce no uncertainty envelope in an error-propagation. However, restricting the question to global net flux in a perfectly balanced model neglects the problem of correctly partitioning the available energy flux among and within the climate sub-states.

A model with offsetting errors among short-wave cloud forcing, long-wave cloud forcing, albedo, aerosol forcing, etc., etc., can have perfect net energy balance all the while producing physically incorrect simulated climate states, because the available energy flux is misallocated among all the climate sub-states.

The necessary consequence is very large uncertainty envelopes associated with the time-wise projection of any simulated observable, no matter that the total energy flux is in balance.

Cognizance of these uncertainties requires a detailed accounting of the energy flux distribution within the climate. As noted above, the LCF error directly impacts the ability of models to resolve the very small additional forcing associated with GHG emissions.

This remains true in any model with an overall zero error in net global energy balance, but with significant errors in partitioned energy-flux among climate sub-states. Presently, this caveat to Dr. Brown’s argument includes all climate models.

Minute 23:50, 4. Use of a base state error rather than a response error.

Dr. Brown’s opening statement suggests I used a base-state error rather than a response error. This claim was discussed under item 1, where it was noted that the LCF rms error is not a time-invariant error, as Dr. Brown suggested, but a time-average error.

At the risk of being pedantic, but just to be absolutely clear, a time-invariant error is constant across all time. A time-average error is calculated from individual errors that may, and in this case do, vary across time. The time-average error derived from many models allows one to calculate a time-wise uncertainty that is representative of those models.

This point was more extensively discussed under item 2 where it was noted that the model LCF error represents the model average of the dynamically misallocated simulated tropospheric thermal energy flux, not a base-state error.

In pursuing this line, Dr. Brown introduced a simple physical model of the climate, and investigated what would happen with a 5% positive offset (base-state) error in terrestrial emissivity in a temperature projection across 100 years, using that model.

However, a model positive offset error is not a correct analogy to global LCF rmse error. Correctly analogized to LCF rmse, Dr. Brown’s simple climate model should suffer from a rmse uncertainty of ±5% in terrestrial emissivity. Clearly a rmse uncertainty is not a constant offset error.

The positive offset error Dr. Brown invoked here represents the same mistaken notion as was noted under item 2, where Dr. Brown incorrectly used a strictly single-sign single-model mean LCF offset error rather than, properly, the single-model global LCF rms error.

In minute 26:55, Dr. Brown again improperly attached a “±” onto his strictly positive +5% emission offset error. This mistake allowed him to introduce the plus/minus uncertainty envelope said to represent the uncertainty calculated using the linear error model.

However, the negative wing of Dr. Brown’s uncertainty envelope is entirely fictitious. Likewise, as noted previously, a single-sign offset error cannot be validly propagated.

Next, when Dr. Brown’s model is correctly analogized, the ±5% emissivity error builds an uncertainty into the structure of the model. The emissivity of the base state has a ±5% uncertainty and so does the emissivity of the succeeding simulated climate states, because the ±5% uncertainty in emissivity is part of the model itself. The model propagates this error into everything it is used to calculate.

Correctly calculated, the base-state temperature suffers from an uncertainty imposed by the ±5% uncertainty in emissivity. The correct representation of base-state temperature is 288(+3.7/-3.5) C.

The model itself then imposes this uncertainty on the temperature of every subsequent simulated climate state in a step-wise projection.

The temperature of every simulation step “n-1” used to calculate the temperature of step “n” carries its “n-1” plus/minus temperature uncertainty with it. The temperature of simulated state “n” then suffers its own uncertainty because it was calculated with the model having the structural ±5% uncertainty in emissivity built into it. The total uncertainty of temperature “n” combines with the ±T uncertainty of step “n-1.”

These successive uncertainties combine as the root-sum-square (rss) in a temperature projection.

To show the effect of a ±5% uncertainty in emissivity, I duplicated Dr. Brown’s initial 100-year temperature calculation and achieved the same result, 288.04 C → 291.93 C after 100 years. I then calculated the temperature uncertainties resulting from a ±5% uncertainty in the value of the changing emissivity, as it step-wise reduced by 5% across 100 years. The rss error was then calculated for each step.

The result is that the initial 288(+3.7/-3.5) C became 289.95(+26.6/-25.0) C in the 50th simulation year, and 291.93(+37.6/-35.3) C in the 100th.

So, properly analogized and properly assessed, Dr. Brown’s model verifies the method and results of my original climate model error propagation.

Next, at minute 28:00, Dr. Brown showed that there is no relationship between model base-state error in global average air temperature and model equilibrium climate sensitivity (ECS). However, the Figure 9.42(a) he displayed merely shows the behavior of climate model simulations with respect to themselves. This is a measure of model precision. Figure 9.42(a) does not show the physical accuracy of the models, i.e., how well they represent the physically true climate.

The fact that Figure 9.42(a) says nothing about physical accuracy, means it also can say nothing about whether any actual systematic physical error leaks from a base-state simulation into projected states. There is no measure of physical error in Figure 9.42(a).

Figure 9.42(a) has another message, however. It shows that climate models deploying the same physical theory produce highly variable base-state temperatures and highly variable ECS values. This variability in model behavior demonstrates that the models are parameterized differently.

Climate modelers choose each parameter to be somewhere within its known uncertainty range. The high variability evident in Figure 9.42(a) shows that these uncertainty ranges are very significant. These parameter uncertainties must impose an uncertainty on any calculated air temperature. Indeed, there must be a large uncertainty in the air temperatures displayed in Figure 9.42(a). However, none of the points sport any uncertainty bars. For the same reason of hidden parameter uncertainties, the ECS values must be similarly uncertain, but there are no ECS uncertainty bars, either.

In standard physical science, parameter uncertainties are propagated through a calculation to indicate the reliability of a result. In consensus climate modeling, this is never done.

The parameter sets within climate models are typically tuned using known observables, such as the ToA flux, so as to generate parameter values that provide a reasonable base-state climate simulation and to project a reasonable facsimile of known climate observables over a validation time-range. However, tuned models are not known to accurately reproduce the physics of the true climate. Tuning a model parameter set to get a reasonable correspondence merely hides the uncertainty intrinsic to a simulation; an uncertainty that is obviously present when regarding Figure 9.42(a).

Next, Dr. Brown’s height-weight example is again an incorrect analogy because it is an empirical correlation within a non-causal epidemiological model, whereas a climate model is causal and deploys a physical theory. Dr. Brown’s comparison is categorically invalid.

A proper comparison would involve using some causal physical model of the human body complete with genetic inputs and resource availability to predict a future height vs. weight curve of a population given certain sets of conditions. Elements of this model would have plus/minus uncertainties associated with them that introduce uncertainties into the output.

Then, starting from year 2000, the calculation is made to predict the height vs. weight profile through to year 2100. The step-wise calculational uncertainties are propagated forward through the projection. The resulting uncertainty bars condition the prediction, and indicate its reliability.

The height-weight example marks the third time in his analysis that Dr. Brown improperly misrepresented a constant offset error as a plus/minus uncertainty. He has again incorrectly appended a “±” to a positive-sign offset error. The negative wing of his calculated uncertainty envelope (minute 29:48) is again entirely fictitious.

This example also again shows that Dr. Brown continued to mistake a theory-bias error, i.e., a plus/minus rmse uncertainty within the structure of a physical theory, for a single-value offset error as might be present in a single calculation. This mistaken notion ramifies through Dr. Brown’s entire analysis.

Finally, this same mistake does similar violence to Dr. Brown’s step-size example in minute 30:30, where he, once again, mis-analogized theory-error as a base-state error.

In his example, the correct analogy with rmse LCF error is a rmse plus/minus uncertainty in the size of each step.

Dr. Brown correctly propagated the 2-feet uncertainty in step-size as the rss, the distance traveled after three steps, with its correct uncertainty of 15±3.46 feet.

Dr. Brown’s 5-feet offset error only affects the uncertainty in the final distance from an initial reference point. It has nothing to do with an uncertainty in the distance traveled. It is not a correct analogy for the plus/minus LCF error statistic of climate models.

So, Dr. Brown’s final statement in this section (minute 31:53), that, “[A] bias or error in the base state should not be treated as the same thing as an error in the response (or change),” is correct, but completely irrelevant to propagation of the plus/minus LCF error statistic. The statement only illustrates Dr. Brown’s invariably mistaken notion of the sort of error under examination.

Again, the CMIP5 ±4 W/m² LCF error is not a constant, single-event base-state error, nor an offset error, nor a time-invariant error. The CMIP5 ±4 W/m² LCF error is a time-average error that arises from, and is representative of, the dynamical errors produced by climate models deploying an incorrect physical theory. It appears in every single step of a climate simulation and propagates forward through a time-wise projection.

Minute 32:14, 5. Reality check: Hansen (1988) projection.

Dr. Brown proposed a reality check, which was to plot the observed temperature trend over the Hansen, 1988 Model II scenario projections, shown in minute 34:02.

Dr. Brown’s mistake here is subtle but critically central. He is treating Hansen scenario B as a unique result; as though there were no other temperature projection possible, under the scenario GHG forcings.

Before getting to that, however, look carefully at Dr. Brown’s red overlay of observed temperatures. The ascent from scenario C to scenario B is due to the recent El Niño, which is presently in decline. Prior to 2015 – before this El Niño — the observed temperature trend matches scenario C quite well, but does not match scenario B.

According to NASA, air temperatures are now “returning to normal” after el Nino 2016. The current air temperature trend shown at Carbon Brief illustrates this decline back to the pre-existing, non-scenario B, state.

So, it appears that Dr. Brown’s model-observation correspondence claim rests upon a convenient transient.

Now back to the point concerning the absolutely critical need for unique results in the physical sciences. Unique results from theory are central to empirical test by falsification. Only unique results are testable against experiment or observation. If a physical model has so many internal uncertainties so as to produce a wide spray of outputs (expectation values) for the same set of inputs, that model cannot be falsified by any accurate single-valued observation. Such a model does not produce predictions in a scientific sense because even if one of its outputs corresponds to observations, a correspondence between the state of the model and physical reality cannot be inferred.

The discussion around Figure 9.42(a) above shows that the physics within climate models includes significantly large uncertainties. The models do not, and can not, produce unique results. Their projections are not predictions, and the internal state of the model does not imply the state of the physically real climate.

I discussed this point in detail in terms of “perturbed physics” tests of climate model projections, in a post at Anthony Watts’ Watts Up With That (WUWT) blog, here. Interested readers should refer to Figures 1 and 2, and the associated text, in that post.

The WUWT discussion featured the HADCM3L climate model. When model parameters are varied, the HADCM3L produces a large range of air temperature projections for the identical set of forcings. This result demonstrates the HADCM3L cannot produce a unique solution to the climate energy state. Nor can any other advanced climate model.

From the post, “No set of model parameters is known to be any more valid than any other set of model parameters. No projection is known to be any more physically correct (or incorrect) than any other projection.

“This means, for any given projection, the internal state of the model is not known to reveal anything about the underlying physical state of the true terrestrial climate.”

The same is true of Dr. Hansen’s 1988 projection. Variation of its parameters within their known range of uncertainties would have produced a large number of alternative air temperature trends. The displayed scenario B is just one of them, and is not unique to its set of forcings. Scenario B is not a prediction, and it is not validated as physically correct, merely because it happens to approximate the observed air temperature trend.

In his 2005 essay, “Michael Chrichton’s “Scientific Method,”” Dr. Hansen himself wrote that the agreement between his scenario B and observed air temperature is fortuitous, in part because the Model II ECS was too large and also because of “other uncertain factors.” Dr. Hansen’s modestly described, “other uncertain factors,” are likely to be the large parameter uncertainties and the errors in the physical theory, as discussed above. Dr. Hansen’s 2005 article is available here: http://www.columbia.edu/~jeh1/2005/Crichton_20050927.pdf.

Fortuitousness of agreement does not lend itself to Dr. Brown’s claim of predictive validity.

Dr. Hansen went on to say about his 1988 scenario B that, “it is becoming clear that our prediction was in the right ballpark”, showing that he, too, apparently does not understand the critical requirement – indeed the sine qua non — of a unique result to qualify a calculation from theory as a scientific prediction.

Similar criticism applies to Dr. Brown’s Figure at minute 34:52, “Modeled and Observed Global Mean Surface Temperature.” The air temperature uncertainty envelope is merely the standard deviation of the CMIP5 model projections around the ensemble model mean. This is a measure of model precision, and indicates nothing about the physical accuracy of the mean projection.

The models have all been tuned to produce alternative suites of parameters that permit a reasonable-seeming projection. The HADCM3L example illustrates that under conditions of perturbed physics, each of those models would produce a range of projections with a spread much larger than Dr. Brown’s Figure admits, all with the identical set of forcings.

Neither the mean projection, nor any of the individual model projections represent a unique result. Tuning the parameter sets and reporting just the one projection has merely hidden the large uncertainty inherent in each projection.

The correct plus/minus uncertainty in the mean projection is the [rms/(n-1)] uncertainty calculated from the uncertainties in the individual projections, meaning that the occult uncertainty in the ensemble mean is larger than the occult uncertainty in each individual projection.

Dr. Brown’s question at the end, “How long would observed temperature need to stay close to the climate model projections before we can say that climate models are giving us useful information about how temperature responds to greenhouse gas forcing?” is unfortunate.

Models have been constructed to require the addition of greenhouse gas forcing in order to reproduce global air temperature. Then turning around and saying that models with greenhouse gas forcings produce temperature projections close to observed air temperatures, is to invoke a circular argument.

Given the IPCC forcings, the linear model of my analysis reproduces the recent air temperature trend just as well as do the CMIP5 climate models. In the spirit of Dr. Brown’s question, we can just as legitimately ask, ‘How long would observed temperature need to stay close to the linear model projections before we can say that the linear model gives us useful information about how temperature responds to greenhouse gas forcing?’ The obvious answer is ‘forever,’ because the linear model will never ever give us such useful information.

And now that we know about the uncertainties hidden within the CMIP5, and prior, climate models, we also know the same, ‘forever, never, ever,’ answer applies to them as well.

We know the terrestrial climate has emerged from the Little Ice Age, and has been warming steadily since about 1850. Following Dr. Brown’s final question, even if the warming continues into the 21st century, and the projections of tuned, adjusted and tendentious (constructed to need the forcing from GHG emissions) climate models stay near that warming air temperature trend, the model projection uncertainties are so large and so and the expectation values are so non-unique, that any future correspondence cannot escape Dr. Hansen’s diagnosis of “fortuitous.”

Summary conclusion: Not one of Dr. Brown’s objections survives critical examination.