预测不确定性量化的机器学习技术的评估

产生准确的天气预报和对其不确定性的可靠量化是一个公开的科学挑战。到目前为止，集合预报是最成功的方法，可以产生相关的预报和对其不确定性的估计。集合预报的主要局限性是计算成本高，难以捕捉和量化不同的不确定性来源，特别是那些与模型误差有关的不确定性。在这项工作中，我们进行了概念验证的模型实验，以检查训练有素的ANN的性能，以预测系统的修正状态和仅使用单一确定性预测作为输入的状态不确定性。我们比较了不同的训练策略：一种是以集合预测的平均值和分布为目标的直接训练，另一种是以确定性预测为目标的间接训练策略，其中不确定性是从数据中隐含学习的。对于最后一种方法，我们提出并评估了两种可供选择的损失函数，一种是基于数据观察的可能性，另一种是基于误差的局部估计。在不同的准备时间和有无模型错误的情况下，对网络的性能进行了检验。使用Lorenz'96模型的实验表明，ANNs能够模仿集合预报的一些特性，如过滤最不可预测的模式和对预报不确定性的状态量化。此外，ANNs在存在模型误差的情况下提供了一个可靠的预测不确定性的估计。

原文题目：Evaluation of Machine Learning Techniques for Forecast Uncertainty Quantification

原文：Producing an accurate weather forecast and a reliable quantification of its uncertainty is an open scientific challenge. Ensemble forecasting is, so far, the most successful approach to produce relevant forecasts along with an estimation of their uncertainty. The main limitations of ensemble forecasting are the high computational cost and the difficulty to capture and quantify different sources of uncertainty, particularly those associated with model errors. In this work proof-of-concept model experiments are conducted to examine the performance of ANNs trained to predict a corrected state of the system and the state uncertainty using only a single deterministic forecast as input. We compare different training strategies: one based on a direct training using the mean and spread of an ensemble forecast as target, the other ones rely on an indirect training strategy using a deterministic forecast as target in which the uncertainty is implicitly learned from the data. For the last approach two alternative loss functions are proposed and evaluated, one based on the data observation likelihood and the other one based on a local estimation of the error. The performance of the networks is examined at different lead times and in scenarios with and without model errors. Experiments using the Lorenz'96 model show that the ANNs are able to emulate some of the properties of ensemble forecasts like the filtering of the most unpredictable modes and a state-dependent quantification of the forecast uncertainty. Moreover, ANNs provide a reliable estimation of the forecast uncertainty in the presence of model error.