Estimation of three-dimensional error covariances. Part I: Analysis of height innovation vectors

The statistical analysis of innovation (observation minus forecast) vectors is one of the most commonly used techniques for estimating observation and forecast error covariances in large-scale data assimilation. Building on t he work of Hollingsworth and Lonnberg, the height innovation data over Nort h America from the Navy Operational Global Atmospheric Prediction System (N OGAPS) are analyzed. The major products of the analysis include (i) observa tion error variances and vertical correlation functions, (ii) forecast erro r autocovariances as functions of height and horizontal distance, (iii) the ir spectra as functions of height and horizontal wavenumber. Applying a mul tilevel least squares fitting method, which is simpler and more rigorously constrained than that of Hollingsworth and Lonnberg, a full-space covarianc e function was determined. It was found that removal of the large-scale hor izontal component, which has only small variation in the vertical, reduces the nonseparability. The results were compared with those of Hollingsworth and Lonnberg, and show a 20% overall reduction in forecast errors and a 10% overall reduction in observation errors for the NOGAPS data in comparison with the ECMWF global model data 16 yr ago.