论文标题
用于数据同化和预测的多模型集合Kalman滤波器
A multi-model ensemble Kalman filter for data assimilation and forecasting
论文作者
论文摘要
数据同化（DA）旨在最佳地结合部分和嘈杂的模型预测和观察结果。多模型DA概括了Kalman滤波器的变异或贝叶斯公式，我们证明它也是最小方差线性无偏估计器。在这里，我们根据此框架制定并实施了多模型集合Kalman滤波器（MM-ENKF）。 MM-ENKF可以以流动依赖的方式将DA和预测的多个模型集合结合在一起。它使用自适应模型误差估计来为单独的模型和观测值提供矩阵值的权重。我们使用Lorenz96模型将此方法应用于各种情况，以进行说明。我们的数值实验包括具有参数误差，不同分辨率量表和不同保真度的多个模型。与概率和确定性误差指标相比，MM-ENKF与最佳模型以及未加权的多模型集合相比会大大减少误差。
Data assimilation (DA) aims to optimally combine model forecasts and observations that are both partial and noisy. Multi-model DA generalizes the variational or Bayesian formulation of the Kalman filter, and we prove that it is also the minimum variance linear unbiased estimator. Here, we formulate and implement a multi-model ensemble Kalman filter (MM-EnKF) based on this framework. The MM-EnKF can combine multiple model ensembles for both DA and forecasting in a flow-dependent manner; it uses adaptive model error estimation to provide matrix-valued weights for the separate models and the observations. We apply this methodology to various situations using the Lorenz96 model for illustration purposes. Our numerical experiments include multiple models with parametric error, different resolved scales, and different fidelities. The MM-EnKF results in significant error reductions compared to the best model, as well as to an unweighted multi-model ensemble, with respect to both probabilistic and deterministic error metrics.
