Vertical Covariance Localization for Satellite Radiances in Ensemble Kalman Filters

Abstract

A widely used observation space covariance localization method is shown to adversely affect satellite radiance assimilation in ensemble Kalman filters (EnKFs) when compared to model space covariance localization. The two principal problems are that distance and location are not well defined for integrated measurements, and that neighboring satellite channels typically have broad, overlapping weighting functions, which produce true, nonzero correlations that localization in radiance space can incorrectly eliminate. The limitations of the method are illustrated in a 1D conceptual model, consisting of three vertical levels and a two-channel satellite instrument. A more realistic 1D model is subsequently tested, using the 30 vertical levels from the Navy Operational Global Atmospheric Prediction System (NOGAPS), the Advanced Microwave Sounding Unit A (AMSU-A) weighting functions for channels 6-11, and the observation error variance and forecast error covariance from the NRL Atmospheric Variational Data Assimilation System (NAVDAS). Analyses from EnKFs using radiance space localization are compared with analyses from raw EnKFs, EnKFs using model space localization, and the optimal analyses using the NAVDAS forecast error covariance as a proxy for the true forecast error covariance. As measured by mean analysis error variance reduction, radiance space localization is inferior to model space localization for every ensemble size and meaningful observation error variance tested. Furthermore, given as many satellite channels as vertical levels, radiance space localization cannot recover the true temperature state with perfect observations, whereas model space localization can.

Operational implementation of a hybrid ensemble/4D‐Var global data assimilation system at the Met Office

“…For non-local observations such as satellite radiances, Campbell et al (2010) show that model space localization is superior to the observation-space localization schemes typically used with the ensemble Kalman filter, such as that of Houtekamer and Mitchell (2001).…”

Tests of different flavours of EnKF on a simple model

“…Campbell et al (2010) noted that localization performed in observation space does not work correctly for vertically integrated observations. Other methods to perform localization in the LETKF have been proposed (Bishop and Hodyss, 2009) and these methods may not suffer from these deficiencies.…”

A GSI-Based Coupled EnSRF–En3DVar Hybrid Data Assimilation System for the Operational Rapid Refresh Model: Tests at a Reduced Resolution

“…A variational framework used by the hybrid scheme also makes it easier to include additional equation constraints in the cost function (e.g., Ge et al 2012;Kleist et al 2009b). Furthermore, for observations whose forward operators are nonlocal, such as those of satellite radiance data, the state-space-based covariance localization used in the hybrid formulation is potentially advantageous (Campbell et al 2010). As suggested by Lorenc (2003) and Buehner et al (2010a, b), both (traditional) 3DVar and 4DVar can be formulated to use the ensemble covariance with the extended control variable method, and we call such ensemble-variational formulations En3DVar and En4DVar, 2 respectively, or EnVar in general.…”