Thinking, small and big

The point that climate downscaling must pay attention to the law of small numbers is no joke.

The World Climate Research Programme (WCRP) will become a ‘new’ WCRP with a “soft launch” in 2021. This is quite a big story since it coordinates much of the research and the substance on which the Intergovernmental Panel on Climate Change (IPCC) builds.  


Until now, the COordinated Regional Downscaling EXperiment (CORDEX) has been a major project sponsored by the WRCP. CORDEX has involved regional modelling and downscaling with a focus on the models and methods rather than providing climate services. In its new form, the activities that used to be carried out within CORDEX will belong to the WCRP community called ‘Regional information for society’ (RifS). This implies a slight shift in emphasis.


With this change, the WCRP signals a desire for the regional modelling results to become more useful and relevant for decision-makers. The change will also introduce a set of new requirements, and hence the law of small numbers.


The law of small numbers is described in Daniel Kahneman’s book ‘Thinking, fast and slow‘ and is a condition that can be explained by statistical theory. It says that you are likely to draw a misleading conclusion if your sample is small.  


I’m no statistician, but a physicist who experienced a “statistical revelation” about a decade ago. Physics-based disciplines, such as meteorology, often approach a problem from a different angle to the statisticians, and there are often some gaps in the understanding and appreciation between the two communities.


A physicist would say that if we know one side of an equation, then we also know the other side. The statistician, on the other hand, would use data to prove there is an equation in the first place.


One of the key pillars of statistics is that we have a random sample that represents what we want to study. We have no such statistical samples for future climate outlooks, but we do have ensembles of simulations representing future projections.


We also have to keep in mind that regional climate behaves differently to global climate. There are pronounced stochastic variations on regional and decadal scales that may swamp the long-term trends due to greenhouse gases (Deser et al., 2012). These variations are subdued on a global scale since opposite variations over different regions tend to cancel each other.


CORDEX has in the past produced ensembles that can be considered as small, and Mezghani et al., (2019) demonstrated that the Euro-CORDEX ensemble is affected by the law of small numbers.

Even if you have a perfect global climate model and perfect downscaling, you risk getting misleading results with a small ensemble, thanks to the law of small numbers. The regional variations are non-deterministic due to the chaotic nature of the atmospheric circulation.


My take-home-message is that there is a need for sufficiently large ensembles of downscaled results. Furthermore, it is the number of different simulations with global climate models that is key since they provide boundary conditions for the downscaling.


Hence, there is a need for a strong and continued coordination between the downscaling groups so that more scientists contribute to building such ensembles.


Also, while CORDEX has been strong on regional climate modelling, the new RifS community needs additional new expertise. Perhaps a stronger presence of statisticians is a good thing. And while the downscaled results from large ensembles can provide a basis for a risk analysis, there is also another way to provide regional information for society: stress-testing.


  1. C. Deser, R. Knutti, S. Solomon, and A.S. Phillips, “Communication of the role of natural variability in future North American climate”, Nature Climate Change, vol. 2, pp. 775-779, 2012.

  2. A. Mezghani, A. Dobler, R. Benestad, J.E. Haugen, K.M. Parding, M. Piniewski, and Z.W. Kundzewicz, “Subsampling Impact on the Climate Change Signal over Poland Based on Simulations from Statistical and Dynamical Downscaling”, Journal of Applied Meteorology and Climatology, vol. 58, pp. 1061-1078, 2019.

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