Statistical Analysis of Innovation Vectors

The statistical analysis of innovation (observation minus forecast) vectors is the most common, and currently the most accurate, technique for estimating observation and forecast error covariances in large scale data assimilation. Following the work of Hollingsworth and Lonnberg (1986, HL86), the technique is further developed in spectral representations of wind forecast error covariance functions based on the classic theory of two-dimensional homogeneous turbulence. The technique is applied to geopotential and wind innovation data over North America for a 3-month period from the Navy Operational Global Atmospheric Prediction System (NOGAPS). The major products of the analysis include (i) observation error variances as functions of height, (ii) forecast error auto-covariances and cross-covariances as functions of height and horizontal distance and their spectra as functions of height and horizontal wavenumber, and (iii) forecast error geostrophy measured, at each height and horizontal wavenumber, by the ratio between the geopotential-streamfunction cross-covariance spectrum and the streamfunction power spectrum. The results will be presented and compared with HL86 at the conference.