Sensitivity and out‐of‐sample error in continuous time data assimilation
Sensitivity and out‐of‐sample error in continuous time data assimilation
复制标题
连续时间数据同化中的灵敏度和样本外误差
DOI：
10.1002/qj.940
复制
发表时间：
2011
影响因子：
8.9
通讯作者：
I. Szendro
中科院分区：
文献类型：
--
作者：
J. Bröcker;I. Szendro
数据同化指的是找到一个规定的动态模型的轨迹的问题，以这样一种方式，模型的输出（通常是模型状态的一些函数）遵循给定的时间序列的观测。然而，通常情况下，这两个要求不能同时得到满足——如果轨迹不偏离所提出的模型方程，跟踪观测是不可能的，而遵守模型则需要偏离观测。因此，数据同化面临着一个权衡。在这篇文章中，数据同化对观测扰动的敏感性被确定为控制权衡的参数。建立了灵敏度与样品外误差之间的关系，从而可以在工作条件下计算样品外误差。最小样本外误差被提议作为一个标准，以设置适当的灵敏度和解决所讨论的权衡。考虑了两种数据同化方法，即变分数据同化和牛顿助推，也称为同步。数值算例验证了该方法的可行性。版权所有©2011英国皇家气象学会
Data assimilation refers to the problem of finding trajectories of a prescribed dynamical model in such a way that the output of the model (usually some function of the model states) follows a given time series of observations. Typically though, these two requirements cannot both be met at the same time–tracking the observations is not possible without the trajectory deviating from the proposed model equations, while adherence to the model requires deviations from the observations. Thus, data assimilation faces a trade‐off. In this contribution, the sensitivity of the data assimilation with respect to perturbations in the observations is identified as the parameter which controls the trade‐off. A relation between the sensitivity and the out‐of‐sample error is established, which allows the latter to be calculated under operational conditions. A minimum out‐of‐sample error is proposed as a criterion to set an appropriate sensitivity and to settle the discussed trade‐off. Two approaches to data assimilation are considered, namely variational data assimilation and Newtonian nudging, also known as synchronization. Numerical examples demonstrate the feasibility of the approach. Copyright © 2011 Royal Meteorological Society