Ensemble forecasting has become popular in weather prediction to reflect the uncertainty about high-dimensional, nonlinear systems with extreme sensitivity to initial conditions. By means of small strategical perturbations of the initial conditions, sometimes accompanied with stochastic parameterisation schemes of the atmosphere–ocean dynamical equations, ensemble forecasting aims at sampling possible future scenario and ideally at interpreting them in a Monte-Carlo-like approximation. Traditional probabilistic interpretations of ensemble forecasts do not take epistemic uncertainty into account nor the fact that ensemble predictions cannot always be interpreted in a density-based manner due to the strongly nonlinear dynamics of the atmospheric system. As a result, probabilistic predictions are not always reliable, especially in the case of extreme events. In this work, we investigate whether relying on possibility theory, an uncertainty theory derived from fuzzy set theory and connected to imprecise probabilities, can circumvent these limitations. We show how it can be used to compute confidence intervals with guaranteed reliability, when a classical probabilistic postprocessing technique fails to do so in the case of extreme events. We illustrate our approach with an imperfect version of the Lorenz 96 model and demonstrate that it is promising for risk-averse decision-making.

中文翻译：

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可能是极端的，可能不是：可能性理论是规避风险决策的途径吗？

集合预报已在天气预报中变得流行，以反映对初始条件极其敏感的高维非线性系统的不确定性。通过初始条件的小的战略性扰动，有时伴随着大气-海洋动力学方程的随机参数化方案，集合预测旨在对可能的未来情景进行采样，并在理想情况下以类似蒙特卡罗的近似解释它们。集合预报的传统概率解释没有考虑到认知不确定性，也没有考虑到由于大气系统的强非线性动力学，集合预测不能总是以基于密度的方式解释的事实。因此，概率预测并不总是可靠的，尤其是在极端事件的情况下。在这项工作中，我们研究了依赖可能性理论（一种源自模糊集理论并与不精确概率相关的不确定性理论）是否可以规避这些限制。我们展示了如何使用它来计算具有保证可靠性的置信区间，当经典概率后处理技术在极端事件的情况下无法这样做时。我们用 Lorenz 96 模型的不完美版本来说明我们的方法，并证明它有利于规避风险的决策。我们展示了如何使用它来计算具有保证可靠性的置信区间，当经典概率后处理技术在极端事件的情况下无法这样做时。我们用 Lorenz 96 模型的不完美版本来说明我们的方法，并证明它有利于规避风险的决策。我们展示了如何使用它来计算具有保证可靠性的置信区间，当经典概率后处理技术在极端事件的情况下无法这样做时。我们用 Lorenz 96 模型的不完美版本来说明我们的方法，并证明它有利于规避风险的决策。