Square Root and Perturbed Observation Ensemble Generation Techniques in Kalman and Quadratic Ensemble Filtering Algorithms
Square Root and Perturbed Observation Ensemble Generation Techniques in Kalman and Quadratic Ensemble Filtering Algorithms
复制标题
卡尔曼和二次系综滤波算法中的平方根和扰动观测系综生成技术
DOI：
10.1175/mwr-d-12-00117.1
复制
发表时间：
2013
影响因子：
3.2
通讯作者：
W. Campbell
中科院分区：
文献类型：
--
作者：
D. Hodyss;W. Campbell
摘要本工作的主要目标是提出一种新的平方根集合生成技术，该技术与最近发展的基于卡尔曼的线性回归算法的扩展相一致，使得它们可以执行非线性多项式回归（即，在平均更新方程中包含二次非线性项），并适用于地球科学中的集合数据同化。在此过程中，作者提出了平方根理论和摄动观测（有时被称为随机）集成生成的数据同化算法的统一，配置为执行线性（卡尔曼）回归以及二次非线性回归。在三变量洛伦兹模型以及用于模拟剪切层不稳定性的非线性模型中，探讨了具有两种集成生成技术的线性和非线性回归算法的性能。
AbstractThe main goal of this work is to present a new square root ensemble generation technique that is consistent with a recently developed extension of Kalman-based linear regression algorithms such that they may perform nonlinear polynomial regression (i.e., includes a quadratically nonlinear term in the mean update equation) and that is applicable to ensemble data assimilation in the geosciences. Along the way the authors present a unification of the theories of square root and perturbed observation (sometimes referred to as stochastic) ensemble generation in data assimilation algorithms configured to perform both linear (Kalman) regression as well as quadratic nonlinear regression. The performance of linear and nonlinear regression algorithms with both ensemble generation techniques is explored in the three-variable Lorenz model as well as in a nonlinear model configured to simulate shear layer instabilities.