Combining dynamical and statistical ensembles

Abstract

A prediction accompanied by quantitative estimates of the likely forecast accuracy is inherently superior to a single "best guess" forecast. Such estimates can be obtained by "dressing" a single forecast using historical error statistics. Dressing ensemble forecasts is more complicated, as one wishes to avoid double counting forecast errors due, for example, to uncertainty in the initial condition when that uncertainty is explicitly accounted for by the ensemble (which has been generated with multiple initial conditions). The economic value of dressed forecasts has been demonstrated by previous studies. This paper presents a method for dressing ensembles of any size, thus enabling valid comparisons to be made between them. The method involves identifying the "best member" of an ensemble in a multidimensional forecast space. The statistics of the errors of these best members are used to dress individual forecasts in an ensemble. The method is demonstrated using ECMWF ensemble forecasts, which are compared with the ECMWF high-resolution best guess forecasts. It is shown that the dressed ECMWF ensembles have skill relative to the dressed ECMWF best guess, even at the maximum lead time of the ECMWF forecasts (10 days). The approach should be applicable to general ensemble forecasts (initial condition, multi-model, stochastic model etc.), allowing better informed decisions on forecast aquisition and forecast system development.

Addressing model uncertainty in seasonal and annual dynamical ensemble forecasts

“…More sophisticated methods of obtaining an estimate of the forecast probability distribution function (PDF) from the ensemble have been proposed (e.g. Roulston and Smith, 2003;Stephenson et al, 2005), but given the limited sample size of long-range forecasts a simple, frequentist, non-parametric approach has been used.…”

Ensemble forecasting and data assimilation: two problems with the same solution?

“…Other approaches (DelSole andHou, 1999, Kaas et al, 1999) rely on empirical methods to reduce the errors using past observations. Yet another method, known as "dressing" adds random perturbations to the ensemble forecasts in order to reproduce the observed error covariance with the ensemble (Roulston andSmith, 2003, Wang andBishop, 2004). It is possible that the Ensemble Kalman Filtering approach will also be able to handle efficiently model errors by augmenting the model variables with a relatively small number of parameters associated with model errors, and using the observations to estimate the optimal value of their time-varying coefficients.…”

How much does simplification of probability forecasts reduce forecast quality?

“…More sophisticated methods to obtain the full forecast probability distribution function from the ensemble have been proposed (e.g. Roulston and Smith, 2003;Stephenson et al, 2005), but given the limited sample size of seasonal forecasts, a simple, frequentist, non-parametric approach has been used. For long-range forecasts such as those used in this study, the thresholds are usually defined in terms of percentiles of the climatological distribution.…”