Abstract
Abstract. Ensemble forecasting has gained popularity in the field of numerical medium-range weather prediction as a means of handling the limitations inherent to predicting the behaviour of high dimensional, nonlinear systems, that have high sensitivity to initial conditions. Through small strategical perturbations of the initial conditions, and in some cases, stochastic parameterization schemes of the atmosphere-ocean dynamical equations, ensemble forecasting allows one to sample possible future scenarii in a Monte-Carlo like approximation. Results are generally interpreted in a probabilistic way by building a predictive density function from the ensemble of weather forecasts. However, such a probabilistic interpretation is regularly criticized for not being reliable, because of the chaotic nature of the dynamics of the atmospheric system as well as the fact that the ensembles of forecasts are not, in reality, produced in a probabilistic manner. To address these limitations, we propose a novel approach: a possibilistic interpretation of ensemble predictions, taking inspiration from fuzzy and possibility theories. Our approach is tested on an imperfect version of the Lorenz 96 model and results are compared against those given by a standard probabilistic ensemble dressing. The possibilistic framework reproduces (ROC curve, resolution) or improves (ignorance, sharpness, reliability) the performance metrics of a standard univariate probabilistic framework. This work provides a first step to answer the question whether probability distributions are the right tool to interpret ensembles predictions.
Highlights
As a result of its chaotic dynamics, the prediction of the atmospheric system is sensitive to the limited resolution in the initial conditions (ICs), discrepancies introduced by measurement error, computational truncation and an incomplete description of the system’s dynamics
We have presented a possibilistic framework which allows us to interpret ensemble predictions without the notion of member density, or additivity that proved to be incoherent with the conditions in which Ensemble prediction systems (EPS) were built
Preliminary results show that such a framework can be used to reproduce the probabilistic performances (ROC curves, resolution) and even slightly improve some of them
Summary
As a result of its chaotic dynamics, the prediction of the atmospheric system is sensitive to the limited resolution in the initial conditions (ICs), discrepancies introduced by measurement error, computational truncation and an incomplete description of the system’s dynamics (closure problem). By design (limited EPS size, biased sampling of ICs) and by context (flow-dependent regime error, strongly nonlinear system) they do not represent the true probabilities of the system at hand (Legg and Mylne, 2004; Orrell, 2005; Bröcker and Smith, 2008) This is all the more true for extreme events, that, for dynamical reasons, cannot be associated to a high density of ensemble members; such events result from nonlinear interactions at small scales, which cannot be reproduced in number in a limited-size EPS (Legg and Mylne, 2004). If generic strategies for post-processing globally improves the skill for common events, they tend to deteriorate the results for extreme events (Mylne et al, 2002) The latter are for predictability reasons, less susceptible to be associated to a high density of ensemble members (Legg and Mylne, 2004).
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