Estimation of Three-Dimensional Error Covariances. Part II: Analysis of Wind Innovation Vectors

The method of statistical analysis of wind innovation (observation minus forecast) vectors is refined upon the work of Hollingsworth and Lönnberg (HL). The new refinements include (i) improved spectral representations of wind forecast error covariance functions, and (ii) simplified and yet more rigorously constrained formulations for multilevel analysis. The method is applied to wind innovation data over North America from the Navy Operational Global Atmospheric Prediction System (NOGAPS). The major products of the analysis include (i) wind observation error variance and vertical correlation, (ii) wind forecast error covariances as functions of height and horizontal distance, (iii) their spectra as functions of height and horizontal wavenumber, and (iv) partitioned vector wind error variances and correlation structures for the large-scale and synoptic-scale components and for the rotational and divergent components of synoptic scale. The results are compared with HL, showing a 20% overall reduction in wind forecast errors and a slight reduction in wind observation errors for the NOGAPS data in comparison with the European Centre for Medium-Range Weather Forecasts (ECMWF) global model data 16 years ago. The spatial structures of the estimated observation and forecast error correlation functions are found to be roughly comparable to those in HL.