Beyond probabilities: A possibilistic framework to interpret ensemble predictions and fuse imperfect sources of information,Quarterly Journal of the Royal Meteorological Society

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Beyond probabilities: A possibilistic framework to interpret ensemble predictions and fuse imperfect sources of information
Quarterly Journal of the Royal Meteorological Society ( IF 3.0 ) Pub Date : 2021-07-24 , DOI: 10.1002/qj.4135
Noémie Le Carrer ₁ , Scott Ferson ₂

Affiliation

Ensemble forecasting is widely used in medium-range weather predictions to account for the uncertainty that is inherent in the numerical prediction of high-dimensional, nonlinear systems with high sensitivity to initial conditions. Ensemble forecasting allows one to sample possible future scenarios in a Monte-Carlo-like approximation through small strategical perturbations of the initial conditions, and in some cases stochastic parametrization schemes of the atmosphere–ocean dynamical equations. Results are generally interpreted in a probabilistic manner by turning the ensemble into a predictive probability distribution. Yet, due to model bias and dispersion errors, this interpretation is often not reliable and statistical postprocessing is needed to reach probabilistic calibration. This is all the more true for extreme events which, for dynamical reasons, cannot generally be associated with a significant density of ensemble members. In this work we propose a novel approach: a possibilistic interpretation of ensemble predictions, taking inspiration from possibility theory. This framework allows us to integrate in a consistent manner other imperfect sources of information, such as the insight about the system dynamics provided by the analogue method. We thereby show that probability distributions may not be the best way to extract the valuable information contained in ensemble prediction systems, especially for large lead times. Indeed, shifting to possibility theory provides more meaningful results without the need to resort to additional calibration, while maintaining or improving skills. Our approach is tested on an imperfect version of the Lorenz '96 model, and results for extreme event prediction are compared against those given by a standard probabilistic ensemble dressing.

中文翻译：

超越概率：解释集成预测和融合不完美信息源的可能性框架

集合预报广泛用于中期天气预报，以解决对初始条件高度敏感的高维非线性系统数值预报中固有的不确定性。集合预测允许人们通过初始条件的小战略扰动，以及在某些情况下大气-海洋动力学方程的随机参数化方案，以类似蒙特卡罗的近似方式对可能的未来情景进行采样。结果通常通过将集成转换为预测概率分布以概率方式解释。然而，由于模型偏差和分散误差，这种解释通常不可靠，需要进行统计后处理才能达到概率校准。对于极端事件来说更是如此，由于动态原因，通常不能与大量的合奏成员相关联。在这项工作中，我们提出了一种新方法：从可能性理论中汲取灵感，对集合预测进行可能性解释。该框架使我们能够以一致的方式整合其他不完善的信息来源，例如模拟方法提供的关于系统动力学的洞察力。因此，我们表明概率分布可能不是提取集合预测系统中包含的有价值信息的最佳方式，尤其是对于大提前期。事实上，转向可能性理论提供了更有意义的结果，而无需求助于额外的校准，同时保持或提高技能。我们的方法在 Lorenz '96 模型的不完美版本上进行了测试，

更新日期：2021-09-06

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