论文标题
随机参数化与VARX过程
Stochastic parameterization with VARX processes
论文作者
论文摘要
在这项研究中，我们研究了一种数据驱动的随机方法，以参数化原型多尺度动力学系统（Lorenz '96（L96）模型）中的小规模特征。我们建议使用带有外源变量（VARX）的矢量自回归过程对小规模特征进行建模，并根据给定的样本数据估算。为了减少VARX的参数数量，我们对其系数矩阵施加了对角线结构。我们将VARX应用于2层L96模型的两种不同配置，一种具有通用参数选择，可为L96模型变量提供单形式不变的概率分布，一种具有非标准参数提供三型分布。我们通过各种统计标准表明，提出的VARX在单峰配置方面表现良好，同时将参数数量保持在模型变量数量中。我们还表明，通过允许致密的（非二元）VARX协方差矩阵，参数化对非常具有挑战性的三峰L96配置进行了准确的性能。
In this study we investigate a data-driven stochastic methodology to parameterize small-scale features in a prototype multiscale dynamical system, the Lorenz '96 (L96) model. We propose to model the small-scale features using a vector autoregressive process with exogenous variable (VARX), estimated from given sample data. To reduce the number of parameters of the VARX we impose a diagonal structure on its coefficient matrices. We apply the VARX to two different configurations of the 2-layer L96 model, one with common parameter choices giving unimodal invariant probability distributions for the L96 model variables, and one with non-standard parameters giving trimodal distributions. We show through various statistical criteria that the proposed VARX performs very well for the unimodal configuration, while keeping the number of parameters linear in the number of model variables. We also show that the parameterization performs accurately for the very challenging trimodal L96 configuration by allowing for a dense (non-diagonal) VARX covariance matrix.
