Estimating and including observation-error correlations in data assimilation

Usually in data assimilation with geophysical systems, the observation-error covariance matrix R is assumed to be diagonal for simplicity and computational efficiency, although there are studies indicating that several types of satellite observations contain significantly correlated errors. This study brings to light the impact of the off-diagonal terms of R in data assimilation. The adaptive estimation method of Li et al., which allows online estimation of the observation-error variance using innovation statistics, is extended to include off-diagonal terms of R. The extended method performs well with the 40-variable Lorenz model in estimating non-diagonal observation-error covariances. Interestingly, the analysis accuracy is improved when the observation errors are correlated, but only if the observation-error correlations are explicitly considered in data assimilation. Further theoretical considerations relate the impact of observing systems (characterized by both R and an observation operator H) on analysis accuracy. This analysis points out the importance of distinguishing between observation-error correlations (i.e. non-diagonal R) and correlated observations (i.e. non-orthogonal H). In general, observations with a non-diagonal R carry more information, whereas observations with a non-orthogonal H carry less information, but it turns out that the combination of R and H is essential: more information is available from positively (negatively) correlated observations with negatively (positively) correlated errors, resulting in a more accurate analysis.

[1]  Niels Bormann,et al.  Estimates of spatial and interchannel observation‐error characteristics for current sounder radiances for numerical weather prediction. I: Methods and application to ATOVS data , 2010 .

[2]  R. J Keeler,et al.  Observational error covariance matrices for radar data assimilation , 2000 .

[3]  K. Emanuel,et al.  Optimal Sites for Supplementary Weather Observations: Simulation with a Small Model , 1998 .

[4]  G. Evensen.  Sequential data assimilation with a nonlinear quasi‐geostrophic model using Monte Carlo methods to forecast error statistics , 1994 .

[5]  Nancy Nichols,et al.  Correlated observation errors in data assimilation , 2008 .

[6]  E. Kalnay,et al.  Simultaneous estimation of covariance inflation and observation errors within an ensemble Kalman filter , 2009 .

[7]  Mark Buehner,et al.  Interchannel error correlation associated with AIRS radiance observations : Inference and impact in data assimilation , 2007 .

[8]  Geir Evensen,et al.  The Ensemble Kalman Filter: theoretical formulation and practical implementation , 2003 .

[9]  R. Daley.  Estimating Model-Error Covariances for Application to Atmospheric Data Assimilation , 1992 .

[10]  J. Whitaker,et al.  Ensemble Data Assimilation without Perturbed Observations , 2002 .

[11]  Jeffrey L. Anderson,et al.  A Monte Carlo Implementation of the Nonlinear Filtering Problem to Produce Ensemble Assimilations and Forecasts , 1999 .

[12]  Paul Poli,et al.  Diagnosis of observation, background and analysis‐error statistics in observation space , 2005 .

[13]  Istvan Szunyogh,et al.  Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter , 2005, physics/0511236.

[14]  E. Lorenz.  Predictability of Weather and Climate: Predictability – a problem partly solved , 2006 .

[15]  Jean-Noël Thépaut,et al.  The Spatial Structure of Observation Errors in Atmospheric Motion Vectors from Geostationary Satellite Data , 2003 .

[16]  Clive D Rodgers,et al.  Inverse Methods for Atmospheric Sounding: Theory and Practice , 2000 .

[17]  Niels Bormann,et al.  Estimates of spatial and interchannel observation‐error characteristics for current sounder radiances for numerical weather prediction. II: Application to AIRS and IASI data , 2010 .