Horizontal Structure of Hemispheric Forecast Error Correlations for Geopotential and Temperature

Abstract

A detailed study of hemispheric forecast-error (f.e.) statistics for the operational Canadian large-scale forecast model was made in preparation for reparameterization of the correlation function used in the data assimilation step of the forecast cycle. The choice of an appropriate function type for geopotential height and temperature f.e. lag-correlation representations was a major concern. A number of possible functional representations, both isotropic and anisotropic, were considered, and the goodness-of-fit of the various candidate functions to correlations computed from observed f.e. data were compared. The following special form of the second-order autoregressive function was adopted as the function of choice: (1 + c|s|)e?c|s|, where |s| is geographic location separation. An examination of f.e. correlation structure on a regional basis revealed large differences from region to region. Latitudinal, pressure-level, and seasonal dependencies of the statistical structure of constant pressure-surface height and temperature f.e. were also examined. Temperature f.e. correlations were found to have significantly narrower structure than the corresponding height f.e. correlations. In general, the width of the structure functions for both height and temperature f.e. was found to decrease with increasing latitude and with decreasing pressure. The extrapolated height correlations at zero separation were found to decrease significantly with pressure, indicating that the ratio of height prediction error to height observation error also decreases with pressure. An examination of the seasonal dependence of the f.e. correlation structure at 500 mb indicated that it was relatively small. Implications for operational forecasting with periodic adjustment of the objective analysis scheme are discussed.