Construction and application of covariance functions with variable length‐fields
Construction and application of covariance functions with variable length‐fields
复制标题
变长域协方差函数的构造与应用
DOI：
--
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
S. Pawson
中科院分区：
文献类型：
--
作者：
G. Gaspari;S. Cohn;Jing Guo;S. Pawson
本文着重于直接在物理空间中构建由长度场参数化的三维协方差函数，并应用这些函数来改进戈达德地球观测系统第4版（GEOS - 4）数据同化系统中准两年一次振荡（QBO）的表示。协方差函数是通过将具有不同定长尺度的自协方差函数集合与其相关的交叉协方差函数融合得到的。这种构造产生具有长度尺度的协方差函数，这些协方差函数可以在空间域的任何有限分区上任意变化。这些函数的一个简单而又激励人心的应用是长度尺度仅在垂直方向上变化的情况。本文构造的具有可变长度字段的协方差函数类将被称为多层，以便与此应用相关联。多水平协方差函数扩展了众所周知的单水平协方差函数，仅依赖于恒定的长度尺度。给出了熟悉的一阶和三阶自回归协方差在三维中的推广，分别提供了在零分离下具有零导数和四个连续导数的多层协方差。给出了在零分离处具有两个连续导数的多级分段有理协方差。多级幂律协方差是用所有阶的连续导数构造的。附加的多层协方差函数是用单层和多层协方差函数的舒尔积构造的。采用具有较大对流层至平流层长度场梯度的多变量、多水平幂律协方差，从热带平流层下层的稀疏无线电探空风观测中重现QBO。该协方差模型与同化实验的细节一起描述。新的协方差模型比基线GEOS‐4系统的多变量、多层次协方差模型更能有效地表征与QBO相关的垂直风切变。版权所有©2006英国皇家气象学会
This article focuses on construction, directly in physical space, of three‐dimensional covariance functions parametrized by a length‐field, and on an application of these functions to improve the representation of the Quasi‐Biennial Oscillation (QBO) in the Goddard Earth Observing System, Version 4 (GEOS‐4) data assimilation system. The covariance functions are obtained by fusing collections of auto‐covariance functions having different constant length‐scales with their associated cross‐covariance functions. This construction yields covariance functions with length‐scales that can vary arbitrarily over any finite partition of the spatial domain. A simple, and also motivating application of these functions is to the case where the length‐scale varies in the vertical direction only. The class of covariance functions with variable length‐fields constructed in this article will be called multi‐level to associate them with this application. The multi‐level covariance functions extend well‐known single‐level covariance functions depending only on a constant length‐scale. Generalizations of the familiar first‐and third‐order autoregressive covariances in three dimensions are given, providing multi‐level covariances with zero and four continuous derivatives at zero separation, respectively. Multi‐level piecewise rational covariances with two continuous derivatives at zero separation are also provided. Multi‐level power‐law covariances are constructed with continuous derivatives of all orders. Additional multi‐level covariance functions are constructed using the Schur product of single‐ and multi‐level covariance functions. A multi‐variate, multi‐level power‐law covariance with a large troposphere‐to‐stratosphere length‐field gradient is employed to reproduce the QBO from sparse radiosonde wind observations in the tropical lower stratosphere. This covariance model is described along with details of the assimilation experiments. The new covariance model is shown to represent the vertical wind shear associated with the QBO much more effectively than the multi‐variate, multi‐level covariance model in the baseline GEOS‐4 system. Copyright © 2006 Royal Meteorological Society