Taking into account the rank of a member within the ensemble for probabilistic forecasting based on the best member method

Optimal use of an atmospheric forecast typically requires some information on its sharpness and reliability. Outputs from an ensemble prediction system (EPS) can be used to estimate both characteristics, but on the other hand do not prove to be very useful probabilistic forecasts, mainly because the forecasts are not perfectly reliable: they can be biased and typically do not display enough variability, thus leading to an underestimation of the uncertainty. Different approaches have been proposed recently to build reliable probabilistic forecasts from such ensembles, including Bayesian model averaging, the Bayesian processor of output and the best member method, which is by far the simplest to implement. The best member method relies on a simple resampling scheme: individual members of an ensemble are "dressed" with an error distribution derived from a database of past errors made by the "best" member of the ensemble, where the best member of an ensemble forecast is defined as the ensemble member which described best the observed state of the atmosphere for this forecast, with respect to a given norm. It has however been shown by stochastic simulations that the best member method can lead both to underdispersive and overdispersive ensembles. A modified version of the best member method has recently been proposed, where the variance of the error distribution is scaled so as to obtain ensembles which display the desired variance. This approach however fails in cases where the undressed ensemble members are already overdispersive. We propose to overcome this difficulty by dressing and weighing each member differently, depending on its rank within the ensemble. This method leads to forecasts which not only have the right amount of variance both for underdispersive and overdispersive EPS, but which also have better tail behaviour.