## Fancy Stats and Silly Climate Contests

Climate skeptics seem to have a thing for contests and bets. For example, there’s Armstrong’s proposed bet, baiting Al Gore. Amusingly (for data nerds anyway), the bet, which pitted a null forecast against the taker’s chosen climate model, could have been beaten easily by either a low-order climate model or a less-naive null forecast. And, of course, it completely fails to understand that climate science is not about fitting a curve to the global temperature record.

Another instance of such foolishness recently came to my attention. It doesn’t have a name that I know of, but here’s the basic idea:

• The author generates 1000 time series:

Each series has length 135: the same length as that of the most commonly studied series of global temperatures (which span 1880–2014). The 1000 series were generated as follows. First, 1000 random series were obtained (for more details, see below). Then, some of those series were randomly selected and had a trend added to them. Each added trend was either 1°C/century or −1°C/century. For comparison, a trend of 1°C/century is greater than the trend that is claimed for global temperatures.

• The challenger pays \$10 for the privilege of attempting to detect which of the 1000 series are perturbed by a trend, winning \$100,000 for correctly identifying 90% or more.

The best challenger managed to identify 860 series, so the prize went unclaimed. But only two challenges are described, so I have to wonder how many serious attempts were made. Had I known about the contest in advance, I would not have tried it. I know plenty about fitting dynamic models to data, though abstract statistical methods aren’t really my thing. But I still have to ask myself some questions:

• Is there really money to be made, or will the author simply abscond to the pub with my \$10? For the sake of argument, let’s assume that the author really has \$100k at stake.
• Is it even possible to win? The author did not reveal the process used to generate the series in advance. That alone makes this potentially a sucker bet. If you’re in control of the noise and structure of the process, it’s easy to generate series that are impossible to reliably disentangle. (Tellingly, the author later revealed the code to generate the series, but it appears there’s no code to successfully identify 90%!)

For me, the statistical properties of the contest make it an obvious non-starter. But does it have any redeeming social value? For example, is it an interesting puzzle that has something to do with actual science? Sadly, no.

The hidden assumption of the contest is that climate science is about estimating the trend of the global temperature time series. Yes, people do that. But it’s a tiny fraction of climate science, and it’s a diagnostic of models and data, not a real model in itself. Science in general is not about such things. It’s about getting a good model, not a good fit. In some places the author talks about real physics, but ultimately seems clueless about this – he’s content with unphysical models:

Moreover, the Contest model was never asserted to be realistic.

Are ARIMA models truly appropriate for climatic time series? I do not have an opinion. There seem to be no persuasive arguments for or against using ARIMA models. Rather, studying such models for climatic series seems to be a worthy area of research.

Liljegren’s argument against ARIMA is that ARIMA models have a certain property that the climate system does not have. Specifically, for ARIMA time series, the variance becomes arbitrarily large, over long enough time, whereas for the climate system, the variance does not become arbitrarily large. It is easy to understand why Liljegren’s argument fails.

It is a common aphorism in statistics that “all models are wrong”. In other words, when we consider any statistical model, we will find something wrong with the model. Thus, when considering a model, the question is not whether the model is wrong—because the model is certain to be wrong. Rather, the question is whether the model is useful, for a particular application. This is a fundamental issue that is commonly taught to undergraduates in statistics. Yet Liljegren ignores it.

As an illustration, consider a straight line (with noise) as a model of global temperatures. Such a line will become arbitrarily high, over long enough time: e.g. higher than the temperature at the center of the sun. Global temperatures, however, will not become arbitrarily high. Hence, the model is wrong. And so—by an argument essentially the same as Liljegren’s—we should not use a straight line as a model of temperatures.

In fact, a straight line is commonly used for temperatures, because everyone understands that it is to be used only over a finite time (e.g. a few centuries). Over a finite time, the line cannot become arbitrarily high; so, the argument against using a straight line fails. Similarly, over a finite time, the variance of an ARIMA time series cannot become arbitrarily large; so, Liljegren’s argument fails.

Actually, no one in climate science uses straight lines to predict future temperatures, because forcing is rising, and therefore warming will accelerate. But that’s a minor quibble, compared to the real problem here. If your model is:

`global temperature = f( time )`

you’ve just thrown away 99.999% of the information available for studying the climate. (Ironically, the author’s entire point is that annual global temperatures don’t contain a lot of information.)

No matter how fancy your ARIMA model is, it knows nothing about conservation laws, robustness in extreme conditions, dimensional consistency, or real physical processes like heat transfer. In other words, it fails every reality check a dynamic modeler would normally apply, except the weakest – fit to data. Even its fit to data is near-meaningless, because it ignores all other series (forcings, ocean heat, precipitation, etc.) and has nothing to say about replication of spatial and seasonal patterns. That’s why this contest has almost nothing to do with actual climate science.

This is also why data-driven machine learning approaches have a long way to go before they can handle general problems. It’s comparatively easy to learn to recognize the cats in a database of photos, because the data spans everything there is to know about the problem. That’s not true for systemic problems, where you need a web of data and structural information at multiple scales in order to understand the situation.

## Summary for Suckers

The NIPCC critique is, ironically, a compelling argument in favor of the IPCC assessment. Why? Well, science is about evaluation of competing hypotheses. The NIPCC report collects a bunch of alternatives to mainstream climate science in one place, where it’s easy to see how pathetic they are. If this is the best climate skeptics can muster, their science must be exceedingly weak.

The NIPCC (Nongovernmental International Panel on Climate Change, a.k.a. Not IPCC) is the Heartland Institute’s rebuttal of the IPCC assessments. Apparently the latest NIPCC report has been mailed to zillions of teachers. As a homeschooling dad, I’m disappointed that I didn’t get mine. Well, not really.

It would probably take more pages to debunk the NIPCC report than it occupies, but others are chipping away at it. Some aspects, like temperature cherry-picking, are like shooting fish in a barrel.

The SPM, and presumably the entire report that it summarizes, seems to labor under the misapprehension that the IPCC is itself a body that conducts science. In fact, the IPCC assessments are basically a giant literature review. So, when the Heartland panel writes,

In contradiction of the scientific method, the IPCC assumes its implicit hypothesis is correct and that its only duty is to collect evidence and make plausible arguments in the hypothesis’s favor.

we must remember that “the IPCC” is shorthand for a vast conspiracy of scientists, coordinated by an invisible hand.

The report organizes the IPPC argument into 3 categories: “Global Climate Model (GCM) projections,” “postulates,” and “circumstantial evidence.” This is a fairly ridiculous caricature of the actual body of work. Most of what is dismissed as postulates could better be described as, “things we’re too lazy to explore properly,” for example. But my eye strays straight to the report’s misconceptions about modeling.

First, the NIPCC seems to have missed the fact that GCMs are not the only models in use. There are EMICS (models of intermediate complexity) and low-order energy balance models as well.

The NIPCC has taken George Box’s “all models are wrong, some are useful” and run with it:

… Global climate models produce meaningful results only if we assume we already know perfectly how the global climate works, and most climate scientists say we do not (Bray and von Storch, 2010).

How are we to read this … all models are useless, unless they’re perfect? Of course, no models are perfect, therefore all models are useless. Now that’s science!

NIPCC trots out a von Neumann quote that’s almost as tired as Box:

with four parameters I can fit an elephant, and with five I can make him wiggle his trunk

In models with lots of reality checks available (i.e. laws of physics), it just isn’t that easy. And the earth is a very big elephant, which means that there’s a rather vast array of data to be fit.

The NIPCC seems to be aware of only a few temperature series, but the AR5 report devotes 200 pages (Chapter 9) to model evaluation, with results against a wide variety of spatial and temporal distributions of physical quantities. Models are obviously far from perfect, but a lot of the results look good, in ways that exceed the wildest dreams of social system modelers.

NIPCC doesn’t seem to understand how this whole “fit” thing works.

Model calibration is faulty as it assumes all temperature rise since the start of the industrial revolution has resulted from human CO2 emissions.

This is blatantly false, not only because it contradicts the actual practice of attribution, but because there is no such parameter as “fraction of temp rise due to anthro CO2.” One can’t assume the answer to the attribution question without passing through a lot of intermediate checks, like conforming to physics and data other than global temperature. In complex models, where the contribution of any individual parameter to the outcome is likely to be unknown to the modeler, and the model is too big to calibrate by brute force, the vast majority of parameters must be established bottom up, from physics or submodels, which makes it extremely difficult for the modeler to impose preconceptions on the complete model.

Similarly,

IPCC models stress the importance of positive feedback from increasing water vapor and thereby project warming of ~3-6°C, whereas empirical data indicate an order of magnitude less warming of ~0.3-1.0°C.

Data by itself doesn’t “indicate” anything. Data only speaks insofar as it refutes (or fails to refute) a model. So where is the NIPCC model that fits available data and yields very low climate sensitivity?

The bottom line is that, if it were really true that models have little predictive power and admit many alternative calibrations (a la the elephant), it should be easy for skeptics to show model runs that fit the data as well as mainstream results, with assumptions that are consistent with low climate sensitivity. They wouldn’t necessarily need a GCM and a supercomputer; modest EBMs or EMICs should suffice. This they have utterly failed to demonstrate.

## Polar Bears & Principles

Amstrup et al. have just published a rebuttal of the Armstrong, Green & Soon critique of polar bear assessments. Polar bears aren’t my area, and I haven’t read the original, so I won’t comment on the ursine substance. However, Amstrup et al. reinforce many of my earlier objections to (mis)application of forecasting principles, so here are some excerpts:

The Principles of Forecasting and Their Use in Science

… AGS based their audit on the idea that comparison to their self-described principles of forecasting could produce a valid critique of scientific results. AGS (p. 383) claimed their principles ‘summarize all useful knowledge about forecasting.’ Anyone can claim to have a set of principles, and then criticize others for violating their principles. However, it takes more than a claim to create principles that are meaningful or useful. In concluding our rejoinder, we point out that the principles espoused by AGS are so deeply flawed that they provide no reliable basis for a rational critique or audit.

Failures of the Principles

Armstrong (2001) described 139 principles and the support for them. AGS (pp. 382’“383) claimed that these principles are evidence based and scientific. They fail, however, to be evidence based or scientific on three main grounds: They use relative terms as if they were absolute, they lack theoretical and empirical support, and they do not follow the logical structure that scientific criticisms require.

Using Relative Terms as Absolute

Many of the 139 principles describe properties that models, methods, and (or) data should include. For example, the principles state that data sources should be diverse, methods should be simple, approaches should be complex, representations should be realistic, data should be reliable, measurement error should be low, explanations should be clear, etc. … However, it is impossible to look at a model, a method, or a datum and decide whether its properties meet or violate the principles because the properties of these principles are inherently relative.

Consider diverse. AGS faulted H6 for allegedly failing to use diverse sources of data. However, H6 used at least six different sources of data (mark-recapture data, radio telemetry data, data from the United States and Canada, satellite data, and oceanographic data). Is this a diverse set of data? It is more diverse than it would have been if some of the data had not been used. It is less diverse than it would have been if some (hypothetical) additional source of data had been included. To criticize it as not being diverse, however, without providing some measure of comparison, is meaningless.

Consider simple. What is simple? Although it might be possible to decide which of two models is simpler (although even this might not be easy), it is impossible’”in principle’”to say whether any model considered in isolation is simple or not. For example, H6 included a deterministic time-invariant population model. Is this model simple? It is certainly simpler than the stationary, stochastic model, or the nonstationary stochastic model also included in H6. However, without a measure of comparison, it is impossible to say which, if any, are ‘simple.’ For AGS to criticize the report as failing to use simple models is meaningless.

A Lack of Theoretical and Empirical Support

If the principles of forecasting are to serve as a basis for auditing the conclusions of scientific studies, they must have strong theoretical and (or) empirical support. Otherwise, how do we know that these principles are necessary for successful forecasts? Closer examination shows that although Armstrong (2001, p. 680) refers to evidence and AGS (pp. 382’“383) call the principles evidence based, almost half (63 of 139) are supported only by received wisdom or common sense, with no additional empirical or theoretical support. …

Armstrong (2001, p. 680) defines received wisdom as when ‘the vast majority of experts agree,’ and common sense as when ‘it is difficult to imagine that things could be otherwise.’ In other words, nearly half of the principles are supported only by opinions, beliefs, and imagination about the way that forecasting should be done. This is not evidence based; therefore, it is inadequate as a basis for auditing scientificÂ studies. … Even Armstrong’s (2001) own list includes at least three cases of principles that are supported by what he calls strong empirical evidence that ‘refutes received wisdom’’”that is, at least three of the principles contradict received wisdom. …

Forecasting Audits Are Not Scientific Criticism

The AGS audit failed to distinguish between scientific forecasts and nonscientific forecasts. Scientific forecasts, because of their theoretical basis and logical structure based upon the concept of hypothesis testing, are almost always projections. That is, they have the logical form of ‘if X happens, then Y will follow.’ The analyses in AMD and H6 take exactly this form. A scientific criticism of such a forecast must show that even if X holds, Y does not, or need not, follow.

In contrast, the AGS audit simply scored violations of self-defined principles without showing how the identified violation might affect the projected result. For example, the accusation that H6 violated the commandment to use simple models is not a scientific criticism, because it says nothing about the relative simplicity of the model with respect to other possible choices. It also says nothing about whether the supposedly nonsimple model in question is in error. A scientific critique on the grounds of simplicity would have to identify a complexity in the model, and show that the complexity cannot be defended scientifically, that the complexity undermines the credibility of the model, and that a simpler model can resolve the issue. AGS did none of these.

There’s some irony to all this. Armstrong & Green criticize climate predictions as mere opinions cast in overly-complex mathematical terms, lacking predictive skill. The instrument of their critique is a complex set of principles, mostly derived from opinions, with undemonstrated ability to predict the skill of models and forecasts.

## Unprincipled Forecast Evaluation

I hadn’t noticed until I heard it here, but Armstrong & Green are back at it, with various claims that climate forecasts are worthless. In the Financial Post, they criticize the MIT Joint Program model,

… No more than 30% of forecasting principles were properly applied by the MIT modellers and 49 principles were violated. For an important problem such as this, we do not think it is defensible to violate a single principle.

As I wrote in some detail here, the Forecasting Principles are a useful seat-of-the-pants guide to good practices, but there’s no evidence that following them all is necessary or sufficient for a good outcome. Some are likely to be counterproductive in many situations, and key elements of good modeling practice are missing (for example, balancing units of measure).

It’s not clear to me that A&G really understand models and modeling. They seem to view everything through the lens of purely statistical methods like linear regression. Green recently wrote,

Another important principle is that the forecasting method should provide a realistic representation of the situation (Principle 7.2). An interesting statement in the MIT report that implies (as one would expect given the state of knowledge and omitted relationships) that the modelers have no idea to what extent their models provide a realistic representation of reality is as follows:

‘Changes in global surface average temperature result from a combination of emissions and climate parameters, and therefore two runs that look similar in terms of temperature may be very different in detail.’ (MIT Report p. 28)

While the modelers have sufficient latitude in their parameters to crudely reproduce a brief period of climate history, there is no reason to believe the models can provide useful forecasts.

What the MIT authors are saying, in essence, is that

T = f(E,P)

and that it is possible to achieve the same future temperature T with different combinations of emissions E and parameters P. Green seems to be taking a leap, to assume that historic T does not provide much constraint on P. First, that’s not necessarily true, given that historic E cannot be chosen freely. It could still be the case that the structure of f(E,P) means that historic T provides a weak constraint on P given E. But if that’s true (as it basically is), the problem is self-diagnosing: estimates of P will have broad confidence bounds, as will forecasts of T. Green completely ignores the MIT authors’ explicit characterization of this uncertainty. He also ignores the fact that the output of the model is not just T, and that we have priors for many elements of P (from more granular models or experiments, for example). Thus we have additional lines of evidence with which to constrain forecasts. Green also neglects to consider the implications of uncertainties in P that are jointly distributed in an offsetting manner (as is likely for climate sensitivity, ocean circulation, and aerosol forcing).

A&G provide no formal method to distinguish between situations in which models yield useful or spurious forecasts. In an earlier paper, they claimed rather broadly,

‘To our knowledge, there is no empirical evidence to suggest that presenting opinions in mathematical terms rather than in words will contribute to forecast accuracy.’ (page 1002)

This statement may be true in some settings, but obviously not in general. There are many situations in which mathematical models have good predictive power and outperform informal judgments by a wide margin.

A&G’s latest paper with Willie Soon, Validity of Climate Change Forecasting for Public Policy Decision Making, apparently forthcoming in IJF, is an attempt to make the distinction, i.e. to determine whether climate models have any utility as predictive tools. An excerpt from the abstract summarizes their argument:

Policymakers need to know whether prediction is possible and if so whether any proposed forecasting method will provide forecasts that are substantively more accurate than those from the relevant benchmark method. Inspection of global temperature data suggests that it is subject to irregular variations on all relevant time scales and that variations during the late 1900s were not unusual. In such a situation, a ‘no change’ extrapolation is an appropriate benchmark forecasting method. … The accuracy of forecasts from the benchmark is such that even perfect forecasts would be unlikely to help policymakers. … We nevertheless demonstrate the use of benchmarking with the example of the Intergovernmental Panel on Climate Change’s 1992 linear projection of long-term warming at a rate of 0.03Â°C-per-year. The small sample of errors from ex ante projections at 0.03Â°C-per-year for 1992 through 2008 was practically indistinguishable from the benchmark errors. … Again using the IPCC warming rate for our demonstration, we projected the rate successively over a period analogous to that envisaged in their scenario of exponential CO2 growth’”the years 1851 to 1975. The errors from the projections were more than seven times greater than the errors from the benchmark method. Relative errors were larger for longer forecast horizons. Our validation exercise illustrates the importance of determining whether it is possible to obtain forecasts that are more useful than those from a simple benchmark before making expensive policy decisions.

There are many things wrong here:

1. Demonstrating that unforced variability (history) can be adequately forecasted by a naive benchmark has no bearing on whether future forced variability will continue to be well-represented, or whether models can predict future emergence of a signal from noise. AG&S’ procedure is like watching an airplane taxi, concluding that aerodynamics knowledge is of no advantage, and predicting that the plane will remain on the ground forever.
2. Comparing a naive forecast for global mean temperature against models amounts to a rejection of a vast amount of information. What is the naive forecast for the joint behavior of temperature, preciptiation, lapse rates, sea level, and their spatial and seasonal patterns? These have been evaluated for models, but AG&S do not suggest benchmarks.
3. A no-change forecast is not necessarily the best naive forecast for a series with unknown variability, if that series has some momentum or structure which can be exploited to do better. The particular no change forecast selected byAG&S is suboptimal, because it uses a single year as a forecast, unneccesarily projecting annual variation into the future. In general, a stronger naive forecast (e.g., a smoothed value of a few recent years) would strengthen AG&S’ case, so it’s unclear why they’ve chosen an excessively naive benchmark. Fortunately, their base year, 1991, was rather “average”.
4. The first exhibit presented is the EPICA ice core temperature. Roughly 85% of the data shown has a time interval too long to show century-scale temperature variations, and none of it could be expected to fully reveal decadal-scale variations, so it’s mostly irrelevant with respect to the kind of forecasts they seek to evaluate.
5. The mere fact that a series has unknown historic variability does not mean that it cannot be forecast [corrected 8/18/09]. The EPICA and Vostok CO2 records look qualitatively much like the temperature record, yet CO2 accumulation in the atmosphere is quite predictable over decadal time scales, and models could handily beat a naive forecast.
6. AG&S’ method of forecast evaluation unduly weights the short term, like the A&G sucker bet does. This is not strictly a problem, but it does make interpretation of the bounds on AG&S’ alternate forecast (“The benchmark forecast is that the global mean temperature for each year for the rest of this century will be within 0.5Â°C of the 2008 figure.”) a little tricky.
7. The retrospective evaluation of the 1990/1992 IPCC projection of 0.3C/decade ignores many factors. First, 0.3C/decade over a century does not imply a smooth trend over short time scales; models and reality have substantial unforced variability which must be taken into account. The paragraph cited by AG&S includes the statement, “The rise will not be steady because of the influence of other factors.” Second, the 1992 report (in the very paragraph AG&S cite) notes that projections do not account for aerosols, so 0.3C/decade can’t be taken as a point prediction for the future, even if contingency on GHG emissions is resolved. Third, the IPCC projection stated approximate bounds – 0.2 to 0.5 C/decade – that should be accounted for in the evaluation, but are not. Still, the IPCC projection beats the naive benchmark.
8. AG&S’ evaluation of the 0.3C/decade future BAU projection as a backcast over 1851-1975 is absurd. They write, “It is not unreasonable, then, to suppose for the purposes of our validation illustration that scientists in 1850 had noticed that the increasing industrialization of the world was resulting in exponential growth in ‘greenhouse gases’ and to project that this would lead to global warming of 0.03Â°C per year.” Actually, it’s completely unreasonable. Many figures in the 1990 FAR clearly indicate that the 0.3C/decade projection was not valid on [-infinity,infinity]. For example, figures 6, 8, and 9 from the SPM – just a few pages from material cited by AG&S – clearly show a gentle trend <0.05C/decade through 1950. Furthermore, even the most rudimentary understanding of the dynamics of GHG and heat accumulation is sufficient to realize that one would not expect a linear historic temperature trend to emerge from the emissions signal.

How do AG&S arrive at this sorry state? Their article embodies a “sh!t happens” epistemology. They write, “The belief that ‘things have changed’ and the future cannot be judged by the past is common, but invalid.” The problem is, one can say with equal confidence that, “the belief that ‘things never change’ and the past reveals the future is common, but invalid.” In reality, there are predictable phenomena (the orbits of the planets) and unpredictable ones (the fall of the Berlin wall). AG&S have failed to establish that climate is unpredictable or to provide us with an appropriate method for deciding whether it is predictable or not. Nor have they given us any insight into how to know or what to do if we can’t decide. Doing nothing because we think we don’t know anything is probably better than sacrificing virgins to the gods, but it doesn’t strike me as a robust strategy.

## Take the bet, Al

I’ve asserted here that the Global Warming Challenge is a sucker bet. I still think that’s true, but I may be wrong about the identity of the sucker. Here are the terms of the bet as of this writing:

The general objective of the challenge is to promote the proper use of science in formulating public policy. This involves such things as full disclosure of forecasting methods and data, and the proper testing of alternative methods. A specific objective is to develop useful methods to forecast global temperatures. Hopefully other competitors would join to show the value of their forecasting methods. These are objectives that we share and they can be achieved no matter who wins the challenge.

Al Gore is invited to select any currently available fully disclosed climate model to produce the forecasts (without human adjustments to the model’s forecasts). Scott Armstrong’s forecasts will be based on the naive (no-change) model; that is, for each of the ten years of the challenge, he will use the most recent year’s average temperature at each station as the forecast for each of the years in the future. The naÃ¯ve model is a commonly used benchmark in assessing forecasting methods and it is a strong competitor when uncertainty is high or when improper forecasting methods have been used.

Specifically, the challenge will involve making forecasts for ten weather stations that are reliable and geographically dispersed. An independent panel composed of experts agreeable to both parties will designate the weather stations. Data from these sites will be listed on a public web site along with daily temperature readings and, when available, error scores for each contestant.

Starting at the beginning of 2008, one-year ahead forecasts then two-year ahead forecasts, and so on up to ten-year-ahead forecasts of annual ‘mean temperature’ will be made annually for each weather station for each of the next ten years. Forecasts must be submitted by the end of the first working day in January. Each calendar year would end on December 31.

The criteria for accuracy would be the average absolute forecast error at each weather station. Averages across stations would be made for each forecast horizon (e.g., for a six-year ahead forecast). Finally, simple unweighted averages will be made of the forecast errors across all forecast horizons. For example, the average across the two-year ahead forecast errors would receive the same weight as that across the nine-year-ahead forecast errors. This unweighted average would be used as the criterion for determining the winner.

I previously noted several problems with the bet:

The Global Warming Challenge is indeed a sucker bet, with terms slanted to favor the naive forecast. It focuses on temperature at just 10 specific stations over only 10 years, thus exploiting the facts that (a) GCMs do not have local resolution (their grids are typically several degrees) (b) GCMs, unlike weather models, do not have infrastructure for realtime updating of forcings and initial conditions (c) ten stations is a pathetically small sample, and thus a low signal-to-noise ratio is expected under any circumstances (d) the decadal trend in global temperature is small compared to natural variability.

It’s actually worse than I initially thought. I assumed that Armstrong would determine the absolute error of the average across the 10 stations, rather than the average of the individual absolute errors. By the triangle inequality, the latter is always greater than or equal to the former, so this approach further worsens the signal-to-noise ratio and enhances the advantage of the naive forecast. In effect, the bet is 10 replications of a single-station test. But wait, there’s still more: the procedure involves simple, unweighted averages of errors across all horizons. But there will be only one 10-year forecast, two 9-year forecasts … , and ten 1-year forecasts. If the temperature and forecast are stationary, the errors at various horizons have the same magnitude, and the weighted average horizon is only four years. Even with other plausible assumptions, the average horizon of the experiment is much less than 10 years, further reducing the value of an accurate long-term climate model.

However, there is a silver lining. I have determined, by playing with the GHCN data, that Armstrong’s procedure can be reliably beaten by a simple extension of a physical climate model published a number of years ago. I’m busy and I have a high discount rate, so I will happily sell this procedure to the best reasonable offer (remember, you stand to make \$10,000).

## More on Climate Predictions

No pun intended.

Scott Armstrong has again asserted on the JDM list that global warming forecasts are merely unscientific opinions (ignoring my prior objections to the claim). My response follows (a bit enhanced here, e.g., providing links).

Today would be an auspicious day to declare the death of climate science, but I’m afraid the announcement would be premature.

JDM researchers might be interested in the forecasts of global warming as they are based on unaided subjective forecasts (unaided by forecasting principles) entered into complex computer models.

This seems to say that climate scientists first form an opinion about the temperature in 2100, or perhaps about climate sensitivity to 2x CO2, then tweak their models to reproduce the desired result. This is a misperception about models and modeling. First, in a complex physical model, there is no direct way for opinions that represent outcomes (like climate sensitivity) to be “entered in.” Outcomes emerge from the specification and calibration process. In a complex, nonlinear, stochastic model it is rather difficult to get a desired behavior, particularly when the model must conform to data. Climate models are not just replicating the time series of global temperature; they first must replicate geographic and seasonal patterns of temperature and precipitation, vertical structure of the atmosphere, etc. With a model that takes hours or weeks to execute, it’s simply not practical to bend the results to reflect preconceived notions. Second, not all models are big and complex. Low order energy balance models can be fully estimated from data, and still yield nonzero climate sensitivity.

I presume that the backing for the statement above is to be found in Green and Armstrong (2007), on which I have already commented here and on the JDM list. Continue reading “More on Climate Predictions”

## On Limits to Growth

It’s a good idea to read things you criticize; checking your sources doesn’t hurt either. One of the most frequent targets of uninformed criticism, passed down from teacher to student with nary a reference to the actual text, must be The Limits to Growth. In writing my recent review of Green & Armstrong (2007), I ran across this tidbit:

Complex models (those involving nonlinearities and interactions) harm accuracy because their errors multiply. Ascher (1978), refers to the Club of Rome’s 1972 forecasts where, unaware of the research on forecasting, the developers proudly proclaimed, “in our model about 100,000 relationships are stored in the computer.” (page 999)

Setting aside the erroneous attributions about complexity, I found the statement that the MIT world models contained 100,000 relationships surprising, as both can be diagrammed on a single large page. I looked up electronic copies of World Dynamics and World3, which have 123 and 373 equations respectively. A third or more of those are inconsequential coefficients or switches for policy experiments. So how did Ascher, or Ascher’s source, get to 100,000? Perhaps by multiplying by the number of time steps over the 200 year simulation period – hardly a relevant measure of complexity.

Meadows et al. tried to steer the reader away from focusing on point forecasts. The introduction to the simulation results reads,

Each of these variables is plotted on a different vertical scale. We have deliberately omitted the vertical scales and we have made the horizontal time scale somewhat vague because we want to emphasize the general behavior modes of these computer outputs, not the numerical values, which are only approximately known. (page 123)

Many critics have blithely ignored such admonitions, and other comments to the effect of, “this is a choice, not a forecast” or “more study is needed.” Often, critics don’t even refer to the World3 runs, which are inconvenient in that none reaches overshoot in the 20th century, making it hard to establish that “LTG predicted the end of the world in year XXXX, and it didn’t happen.” Instead, critics choose the year XXXX from a table of resource lifetime indices in the chapter on nonrenewable resources (page 56), which were not forecasts at all. Continue reading “On Limits to Growth”

## Evidence on Climate Predictions

Last Year, Kesten Green and Scott Armstrong published a critique of climate science, arguing that there are no valid scientific forecasts of climate. RealClimate mocked the paper, but didn’t really refute it. The paper came to my attention recently when Green & Armstrong attacked John Sterman and Linda Booth Sweeney’s paper on mental models of climate change.

I reviewed Green & Armstrong’s paper and concluded that their claims were overstated. I responded as follows: Continue reading “Evidence on Climate Predictions”