# Yann MICHEL, Météo France and CNRS

## Modelling spatial correlations for observation errors with Lanczos: application to SEVIRI and RADAR data

##### Coauthors

S. Guedj#### Abstract:

The observation error covariance matrix is mostly specified as diagonal in operational NWP. Yet, recent applications of the Desroziers diagnostics have shown that observation errors may be spatially correlated, in particular for water-vapour channels of the SEVIRI instrument and for Doppler radial winds. Those observations are assimilated at high resolution into the operational AROME system from Météo-France that runs at kilometric scale. Thus it is probably important to take into account those correlations.

The problem of spatially correlated observation errors is mostly numerical. Indeed with conventional minimisation schemes we have to specify the inverse covariance matrix, which is difficult to handle when observation locations are not structured. Among the scheme, one was proposed by M. Fisher and relies on the modelling of the observation covariance matrix through interpolation then approximate inversion using the truncated Lanczos algorithm.

We illustrate the method with real data from SEVIRI and RADAR observations, using recent estimates from the Desroziers diagnostics. In particular, we show that truncated the Lanczos algorithm leads to erroneous long range correlations. The modelled variances are also affected by truncation error. With observations vectors of size about 10^3-10^4, we show that several hundreds of eigenpairs are typically needed to obtain a good approximation. This questions the computational relevance of this method when observations are assimilated at higher spatial density.