Well the mystery surrounding the origins of this equation has been at least partially resolved. It is clearly presented in Stephenson and Doblas-Reyes "Statistical methods for interpreting Monte Carlo ensemble forecasts" Tellus 2000 (as the first author pointed out to me last week), who attribute the result to Epstein 1969 and Leith 1974. The attribution seems a little unclear to me, as these earlier papers both present a large number of equations relating to the evolution of forecast ensembles of specific systems, whereas this identity is fully general irrespective of the ensemble generation. However it is not in doubt that it is well known by lots of people and dates to the origins of ensemble methods in weather prediction, even though it has perhaps been subsequently forgotten by some (and apparently never known in climate science, or indeed numerous other fields).
2 comments:
I was wondering if I drew the right conclusion from the post on the Multi-Model Mean (MMM) and if the following might illustrate your point better. Take the models and the observations and arbitrarily choose one of the model results. Take the multi-model mean of the rest of models and the observations. See how that new MMM compares to the new "truth", the model results that were held back. The comparison should be as good as that of the original MMM to the observations if I read your posts correctly.
Yes, that's correct, I think. Of course this idea is a bit of an approximation, it will depend exactly what you use as the observations.
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