From ensemble forecasts to predictive distribution functions

JOCHEN BRCKER, LEONARD A. SMITH
2008 Tellus: Series A, Dynamic Meteorology and Oceanography  
Original citation: Bröcker, Jochen and Smith, Leonard A. (2008) From ensemble forecasts to predictive distribution functions. Tellus series A: dynamic meteorology and oceanography, 60 (4). pp. 663-678. A B S T R A C T The translation of an ensemble of model runs into a probability distribution is a common task in model-based prediction. Common methods for such ensemble interpretations proceed as if verification and ensemble were draws from the same underlying distribution, an assumption not
more » ... assumption not viable for most, if any, real world ensembles. An alternative is to consider an ensemble as merely a source of information rather than the possible scenarios of reality. This approach, which looks for maps between ensembles and probabilistic distributions, is investigated and extended. Common methods are revisited, and an improvement to standard kernel dressing, called 'affine kernel dressing' (AKD), is introduced. AKD assumes an affine mapping between ensemble and verification, typically not acting on individual ensemble members but on the entire ensemble as a whole, the parameters of this mapping are determined in parallel with the other dressing parameters, including a weight assigned to the unconditioned (climatological) distribution. These amendments to standard kernel dressing, albeit simple, can improve performance significantly and are shown to be appropriate for both overdispersive and underdispersive ensembles, unlike standard kernel dressing which exacerbates over dispersion. Studies are presented using operational numerical weather predictions for two locations and data from the Lorenz63 system, demonstrating both effectiveness given operational constraints and statistical significance given a large sample. Ensemble interpretation methods generally differ due to the different families of distribution functions employed in building the ensemble interpretation and the way it is actually built. Both aspects are discussed in this paper. As to the different families of distribution functions, two particular approaches are considered here. The first one is referred to as kernel dressing and consists of replacing individual ensemble members by kernel functions. In the second approach, the ensemble is replaced by a parametrized distribution function, where the parameters of the distribution function have to be represented as functions of the original ensemble. This approach will be referred to as distribution fit or DF interpretation. 1,2 Both approaches typically involve parameters which have to be determined. Approaches to build the ensemble interpretation method differ in what the ensemble is taken to represent. In the simplest case, 1 In fact, kernel dressing and DF interpretation are not really distinct, as a sum of kernel functions can be interpreted as a special family of distribution functions, the centres of the kernel being part of the parameters. But when speaking of DF interpretations, we usually have somewhat more common families of distributions in mind, like Gaussian, Weibull or exponential distributions. 2 The term distribution fitting is used by, for example, Wilks (2006) .
doi:10.1111/j.1600-0870.2008.00333.x fatcat:djyql5fvkbhmnmjejn6jonjyzi