Journal cover Journal topic
Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
Journal topic

Journal metrics

IF value: 1.558
IF1.558
IF 5-year value: 1.475
IF 5-year
1.475
CiteScore value: 2.8
CiteScore
2.8
SNIP value: 0.921
SNIP0.921
IPP value: 1.56
IPP1.56
SJR value: 0.571
SJR0.571
Scimago H <br class='widget-line-break'>index value: 55
Scimago H
index
55
h5-index value: 22
h5-index22
Volume 21, issue 1
Nonlin. Processes Geophys., 21, 187–199, 2014
https://doi.org/10.5194/npg-21-187-2014
© Author(s) 2014. This work is distributed under
the Creative Commons Attribution 3.0 License.

Special issue: Ensemble methods in geophysical sciences

Nonlin. Processes Geophys., 21, 187–199, 2014
https://doi.org/10.5194/npg-21-187-2014
© Author(s) 2014. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 05 Feb 2014

Research article | 05 Feb 2014

Diagnostics on the cost-function in variational assimilations for meteorological models

Y. Michel Y. Michel
  • Météo-France and CNRS, CNRM-GAME, UMR3589, Toulouse, France

Abstract. Several consistency diagnostics have been proposed to evaluate variational assimilation schemes. The "Bennett-Talagrand" criterion in particular shows that the cost-function at the minimum should be close to half the number of assimilated observations when statistics are correctly specified. It has been further shown that sub-parts of the cost function also had statistical expectations that could be expressed as traces of large matrices, and that this could be exploited for variance tuning and hypothesis testing.

The aim of this work is to extend those results using standard theory of quadratic forms in random variables. The first step is to express the sub-parts of the cost function as quadratic forms in the innovation vector. Then, it is possible to derive expressions for the statistical expectations, variances and cross-covariances (whether the statistics are correctly specified or not). As a consequence it is proven in particular that, in a perfect system, the values of the background and observation parts of the cost function at the minimum are positively correlated. These results are illustrated in a simplified variational scheme in a one-dimensional context.

These expressions involve the computation of the trace of large matrices that are generally unavailable in variational formulations of the assimilation problem. It is shown that the randomization algorithm proposed in the literature can be extended to cover these computations, yet at the price of additional minimizations. This is shown to provide estimations of background and observation errors that improve forecasts of the operational ARPEGE model.

Publications Copernicus
Download
Citation