The Geometry of Model Error
The Geometry of Model Error
复制标题
模型误差的几何
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
Leonard A. Smith
中科院分区：
文献类型：
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作者：
K. Judd;C. Reynolds;T. Rosmond;Leonard A. Smith
摘要研究了天气预报模型等复杂确定性非线性系统中模型误差的性质。预报系统包括两个组成部分，预报模型和数据同化方法。后者将对现实的观察的集合投射到模型状态中。根据数据投影和吸引流形的模型的几何性质，可以理解模型误差的关键特征。模型误差可分解为两个组成部分：投影误差和方向误差，前者可被理解为在给定数据投影的情况下模型的吸引子位于错误的位置，后者可被理解为与现实向模型空间的投影相比，模型在错误方向上移动的轨迹。这项研究引入了一些新的工具和概念，包括阴影滤镜、因果和非因果阴影分析，以及各种几何诊断。描述了预测误差和模型误差的各种性质。
Abstract This paper investigates the nature of model error in complex deterministic nonlinear systems such as weather forecasting models. Forecasting systems incorporate two components, a forecast model and a data assimilation method. The latter projects a collection of observations of reality into a model state. Key features of model error can be understood in terms of geometric properties of the data projection and a model attracting manifold. Model error can be resolved into two components: a projection error, which can be understood as the model’s attractor being in the wrong location given the data projection, and direction error, which can be understood as the trajectories of the model moving in the wrong direction compared to the projection of reality into model space. This investigation introduces some new tools and concepts, including the shadowing filter, causal and noncausal shadow analyses, and various geometric diagnostics. Various properties of forecast errors and model errors are described ...