Liberals tell us that the science of global warming is settled, and that the truth of the alarmists’ theory can be demonstrated by a high school science project. Therefore, climate change “deniers” are “anti-science.” Of course, no science project, high school or otherwise, has attempted to replicate, let alone succeeded in replicating, the almost infinite complexity of the Earth’s climate. In truth, climate science is in its infancy, and fascinating scientific debates are raging across a broad range of issues relevant to the CAGW theory.

To take just one example, alarmists are desperately trying to rescue their theory from the fact that there hasn’t actually been any global warming for around 18 years, as shown by satellite measurements. One example of this effort is a paper by Jochem Marotzke and Piers Forster, published in *Nature*. The paper argues that climate models, viewed over time, are not as inconsistent with reality as they may seem. The paper’s conclusion states:

The differences between simulated and observed trends are dominated by random internal variability over the shorter timescale and by variations in the radiative forcings used to drive models over the longer timescale. For either trend length, spread in simulated climate feedback leaves no traceable imprint on GMST trends or, consequently, on the difference between simulations and observations. The claim that climate models systematically overestimate the response to radiative forcing from increasing greenhouse gas concentrations therefore seems to be unfounded.

Unfortunately, as Nicholas Lewis argues at Climate Audit, the statistical methods on which the Marotzke paper relies are inept. Before getting to the details, let’s note this comment by statistician Gordon Hughes:

The statistical methods used in the paper are so bad as to merit use in a class on how not to do applied statistics.

All this paper demonstrates is that climate scientists should take some basic courses in statistics and Nature should get some competent referees.

Now on to the fine points. You don’t have to fully grasp Lewis’s analysis to realize the absurdity of liberals’ claims that climate skeptics are “anti-science.”

To a physicist, the result that variations in model α and κ have almost no effect on 62-year trends is so surprising that the immediate response should be: ‘what has Marotzke done wrong?’

Some statistical flaws are self evident. Marotzke’s analysis treats the 75 model runs as being independent, but they are not. Only 18 models are analysed, and only one set of predictor variables is used per model. The difference between temperature simulations from each individual run by a model with multiple runs and the run-ensemble mean for that model is accordingly noise that one could not expect to be explained by the regression. The use of all the individual runs invalidates the simple statistical model used and the error estimates derived from it. Also, moving from equation (1) to (3) above will have made the errors correlated with the predictor variables, biasing the coefficient estimates. Uncertainty in the values of the parameters α and κ and in the forcing time series is also ignored. As I show later, uncertainty in κ, at least, is large. And in equation (1) α and κ appear only in terms of their sum. Allowing a separate predictor variable for each of them may result in part of the internal variability being misallocated.

However, there is an even more fundamental problem with Marotzke’s methodology: its logic is circular.

The ΔF values were taken from Forster et al (2013)[v]. For each model, historical/RCP scenario time series for ΔF were diagnosed by Forster et al using an equation of the form:

ΔF = α ΔT + ΔN

where ΔT and ΔN are the model-simulated GMST and TOA radiative imbalance respectively, and α is the model feedback parameter, diagnosed in the same paper.

Moreover, κ had been diagnosed from the model transient climate response[vi] (TCR) as Marotzke_F2x_TCR. Therefore, the denominator in equation (1) is simply Marotzke_F2xoverTCR, termed ρ (rho) in Forster et al (2013). Note that F2xCO2, the ERF from a doubling of CO2 concentration, does not take a standard value (3.71 Wm‑2 per IPCC AR5) but is a diagnosed value that differs significantly between models.

One can therefore restate the ‘physical foundation of energy balance’, with added random term representing internal variability, (equation (1)) as:

ΔT = (α ΔT+ ΔN ) / ρ + ε

As is now evident, Marotzke’s equation (3) involves regressing ΔT on a linear function of itself. This circularity fundamentally invalidates the regression model assumptions. Accordingly, reliance should not be placed on any of the results in the Nature paper. That is particularly the case for the 62-year trend results, where the offending, non-exogenous ΔF’ term dominates the ensemble spread of GMST trends for start years from the 1920s on.

Since the ΔF predictor variable is a linear function of the response variable ΔT, which becomes larger relative to noise as the start year progresses, it is hardly surprising that the across-ensemble variations of ΔF are the main contributor to the ensemble spread of GMST 62-year trends starting from the 1920s onwards. As the start date progresses the intermodel variation in 62-year trends in ΔF is increasingly determined by intermodel variation in trends in α ΔT: ΔN trends are noisy but intermodel variation in trends in ΔN is of lesser relative importance for later start years. However, since ΔT is not an exogenous variable, domination in turn of intermodel variation in trends in GMST by variation in trends in ΔF tells one nothing reliable about the relative contributions of forcing, feedback and ocean heat uptake efficiency to the intermodel spread in GMST trends.

There is much more, but you get the drift. Let’s close with this:

Another reason why Marotzke’s approach is doomedAnother major problem with this type of attribution approach, even if the circularity could be removed by somehow diagnosing ΔF differently and other statistical problems dealt with, is that the underlying assumption that the previously diagnosed α and κ values for individual models are realistic enough to use in equation (1), or in its circularity-free reduced κ-only version (6), appears to be false.

I have compared κ values based on the ratio of ΔN and ΔT trends over 1951–2012 from the model-simulations with the values used by Marotzke, which as explained were diagnosed in Forster et al 2013 by a quite different method. The ΔN / ΔT trend-based estimates vary from 0.54 times to 2.48 times those Marotzke uses; for only five models are the two estimates the same within 10%. Estimates of κ based on the 2005–2066 period under the RCP8.5 scenario, which provides a strong greenhouse gas forcing ramp with little influence from variations in aerosol forcing, range from 0.46 times to 1.09 times those Marotzke uses, and from 0.18 times to 1.75 times those estimated from changes over 1951–2012. And estimates of κ based on changes in the rate of simulated ocean heat uptake during 1961–2005,[viii] rather than simulated TOA radiative imbalance, are substantially different again. It seems doubtful that estimates of α values would be robust enough either.

With this degree of apparent variation in κ when estimated by different methods and over different periods, one would expect equation (6) to have very little explanatory power (regressing ΔT on ΔN / κ). And that is indeed the case. The intermodel spread in GMST trend is dominated by internal variability over both 15 and 62-year periods, whether towards the start or end of the analysis period. The more valid, circularity-free, version of the surface energy-balance equation is useless for investigating the intermodel spread in GMST trends. The same applies when using a regression equation based on (6) but separating the and κ terms, leading to this form:

Not a day goes by without scientific debate of this sort taking place, with the alarmists just about always, as best I can judge, getting the worst of it. This particular exchange would be a good one to bring up next time one of your liberal friends tells you that as a climate skeptic–I would say, climate realist–you must be “anti-science.”