by Michel, Y.

Abstract:

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.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

Reference:

Michel, Y., 2013: Estimating deformations of random processes for correlation modelling: methodology and the one-dimensional caseQuarterly Journal of the Royal Meteorological Society, 139, 771-783.

Bibtex Entry:

@Article{Michel2013, Title = {Estimating deformations of random processes for correlation modelling: methodology and the one-dimensional case}, Author = {Michel, Y.}, Journal = {Quarterly Journal of the Royal Meteorological Society}, Year = {2013}, Number = {672}, Pages = {771-783}, Volume = {139}, Abstract = {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.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}, Copublication = {1: 1 Fr}, Doi = {10.1002/qj.2007}, ISSN = {1477-870X}, Keywords = {wavelet, covariance, texture, data assimilation, background error}, Owner = {hymexw}, Publisher = {John Wiley \& Sons, Ltd.}, Timestamp = {2016.01.07}, Url = {http://dx.doi.org/10.1002/qj.2007} }