Estimating deformations of random processes for correlation modelling: methodology and the one‐dimensional case. (17th September 2012)

• Record Type: Journal Article
• Authors: Michel, Y.
• Is Part Of: Quarterly journal of the Royal Meteorological Society. Volume 139:Number 672(2013:Apr.)
• Page Start: 771
• Page End: 783
• Publication Date: 2012-09-17
• Subjects: Meteorology -- Periodicals; 551.5
• DOI: 10.1002/qj.2007
• Languages: English
• ISSNs: 0035-9009

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>We introduce the use of spatial deformations for the modelling of background‐error correlations in data assimilation with large dimensions of the state variable. Usually, the background‐error covariance matrix is split into standard deviations and correlations. In this framework, a proposal is made to model the correlations as the space deformation of a stationary correlation model. The 'shape from texture' approach introduced in the computer vision community is an algorithm that estimates the relative deformation gradient and relies on a continuous wavelet analysis. It is also shown that it is possible to estimate the deformation gradient from a simple length‐scale diagnosis and both approaches are compared. Then, a change of coordinate is derived from the numerical integration of the deformation gradient, opening the path to build the approximate correlation model.</p> <p>Many variational data‐assimilation schemes use a square‐root form to construct the background‐error covariance matrix and it is shown how the deformation can be easily included in such a formulation. This approach is of interest in allowing for objective geographical inhomogeneities of the structure functions. The deformed matrix is of slightly reduced rank, but this can be compensated for by a regularization. There is no need for additional normalization as is the case when one models correlations with wavelet frames or recursive filters. The algorithm has a similar computational cost to these two other approaches. Results are illustrated with real data from one‐dimensional temperature forecast errors produced by an operational atmospheric model. Copyright © 2012 Royal Meteorological Society</p> </abstract>