Estimation of Three-Dimensional Error Covariances. Part I: Analysis of Height Innovation Vectors

Abstract

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 the work of Hollingsworth and Lönnberg, the height innovation data over North America from the Navy Operational Global Atmospheric Prediction System (NOGAPS) are analyzed. The major products of the analysis include (i) observation error variances and vertical correlation functions, (ii) forecast error autocovariances as functions of height and horizontal distance, (iii) their spectra as functions of height and horizontal wavenumber. Applying a multilevel least squares fitting method, which is simpler and more rigorously constrained than that of Hollingsworth and Lönnberg, a full-space covariance function was determined. It was found that removal of the large-scale horizontal component, which has only small variation in the vertical, reduces the nonseparability. The results were compared with those of Hollingsworth and Lönnberg, 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.