Data assimilation with correlated observation errors: experiments with a 1-D shallow water model

Abstract

A B S T R A C T Remote sensing observations often have correlated errors, but the correlations are typically ignored in data assimilation for numerical weather prediction. The assumption of zero correlations is often used with data thinning methods, resulting in a loss of information. As operational centres move towards higher-resolution forecasting, there is a requirement to retain data providing detail on appropriate scales. Thus an alternative approach to dealing with observation error correlations is needed. In this article, we consider several approaches to approximating observation error correlation matrices: diagonal approximations, eigendecomposition approximations and Markov matrices. These approximations are applied in incremental variational assimilation experiments with a 1-D shallow water model using synthetic observations. Our experiments quantify analysis accuracy in comparison with a reference or 'truth' trajectory, as well as with analyses using the 'true' observation error covariance matrix. We show that it is often better to include an approximate correlation structure in the observation error covariance matrix than to incorrectly assume error independence. Furthermore, by choosing a suitable matrix approximation, it is feasible and computationally cheap to include error correlation structure in a variational data assimilation algorithm.

Data assimilation of GNSS zenith total delays from a Nordic processing centre

“…Methods have been developed to account for serially correlated errors (Järvinen et al, 1999), but there is certainly room for improvement regarding spatially correlated errors, although some general research within this area has been carried out (Lin et al, 2000;Liu and Rabier, 2002;Bormann and Bauer, 2010;Stewart et al, 2013). Some studies have focused on GNSS ZTD observations (Kleijer, 2001;Stoew, 2004;Eresmaa and Järvi-nen, 2005), but the handling of the correlated observation errors is still an active area of research. GNSS ZTD observations processed by the NGAA centre have been used within the MetCoOp forecasting system, aiming at improving short-range forecasts of, in particular, moisture, clouds and precipitation.…”

Diagnosing Horizontal and Inter-Channel Observation Error Correlations for SEVIRI Observations Using Observation-Minus-Background and Observation-Minus-Analysis Statistics

“…Inter-channel correlations have been calculated for observations from satellite instruments such as the Atmospheric Infrared Sounder (AIRS) and Infrared Atmospheric Sounding Interferometer (IASI) using the Desroziers et al diagnostic [12][13][14][15][16]. The literature shows that inter-channel observation errors are correlated and that including these errors in the assimilation leads to improved analysis accuracy, better forecast skill score and the inclusion of more observation information content [6,[16][17][18][19]. As a result, the assimilation of correlated inter-channel errors for IASI observations is now operational at the Met Office.…”

Improving the ensemble transform Kalman filter using a second-order Taylor approximation of the nonlinear observation operator

“…Hunt et al (2007) extended the ETKF method to deal with a general nonlinear observation operator using the cost function. In addition to the reduction of computational cost compared with EnKF, another advantage of the ETKF proposed by Hunt et al (2007) is that it can assimilate observations with strongly nonlinear observation operators (Chen et al, 2009) and with spatially correlated observation errors (Stewart et al, 2013).…”