Hypothesis testing and long range memory

What is the actual hypothesis you are testing when you compare a model to an observation? It is not a simple as ‘is the model any good’ – though many casual readers might assume so. Instead, it is a test of a whole set of assumptions that went into building the model, the forces driving it, and the assumptions that went in to what is presented as the observations. A mismatch between them can arise from a mis-specification of any of these components and climate science is full of examples where reported mismatches ended up being due to problems in the observations or forcing functions rather than the models (ice age tropical ocean temperatures, the MSU records etc.). Conversely of course, there are clear cases where the models are wrong (the double ITCZ problem) and where the search for which assumptions in the model are responsible is ongoing.

As we have discussed, there is a skill required in comparing models to observations in ways that are most productive, and that requires a certain familiarity with the history of climate and weather models. For instance, it is well known that the individual trajectory of the weather is chaotic (in models this is provable; in the real world, just very likely) and unpredictable after a couple of weeks. So comparing the real weather at a point with a model simulation outside of a weather forecast context is not going to be useful. You can see this by specifying exactly what the hypothesis is you are testing in performing such a comparison in a climate model – i.e. “is a model’s individual weather correlated to the weather in the real world (given the assumptions of the model and no input of actual weather data)”. There will be a mismatch between model and observation, but nothing of interest will have been learnt because we already know that the weather in the model is chaotic.

Hypotheses are much more useful if you expect that there will be a match; a mismatch is then much more surprising. Your expectations are driven by past experience and are informed by a basic understanding of the physics. For instance, given the physics of sulphate aerosols in the stratosphere (short wave reflectors, long wave absorbers), it would be surprising if putting in the aerosols seen during the Pinatubo eruption did not reduce the planetary temperature while warming the stratosphere in the model. Which it does. Doing such an experiments is much more a test of the quantitative impacts then, rather than the qualitative response.

With that in mind, I now turn to the latest paper that is getting the inactivists excited by Demetris Koutsoyiannis and colleagues. There are very clearly two parts to this paper – the first is a poor summary of the practice of climate modelling – touching all the recent contrarian talking points (global cooling, Douglass et al, Karl Popper etc.) but is not worth dealing with in detail (the reviewers of the paper include Willie Soon, Pat Frank and Larry Gould (of Monckton/APS fame) – so no guessing needed for where they get their misconceptions). This is however just a distraction (though I’d recommend to the authors to leave out this kind of nonsense in future if they want to be taken seriously in the wider field). The second part is their actual analysis, the results of which lead them to conclude that “models perform poorly”, and is more interesting in conception, if not in execution.

Koutsoyiannis and his colleagues are hydrologists by background and have an interest in what is called long term persistence (LTP or long term memory) in time series (discussed previously here). This is often quantified by the Hurst parameter (nicely explained by tamino recently). A Hurst value of greater than 0.5 is indicative of ‘long range persistence’ and complicates issues of calculating trend uncertainties and the like. Many natural time series do show more persistent ‘memory’ than a simple auto-regression (AR) process – in particularly (and classically) river outflows. This makes physical sense because a watershed is much more complicated than just a damper of higher frequency inputs. Soil moisture can have an impact from year to year, as can various groundwater reservoirs and their interactions.

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