Revised Interpolation Statistics for the Canadian Data Assimilation Procedure: Their Derivation and Application

Abstract

The first part of this paper presents the results of a study of the structure of the observed residuals, or differences, between radiosonde data and the short-range forecasts that are used as trial fields in an operational hemispheric data assimilation scheme. The study is based on fitting appropriate functional representations to horizontal correlations of observed height and wind residuals. Rather than represent the height residuals by the sum of a degenerate second-order autoregressive function and an additive constant to account for long-wave error, as in a previous study, we use a representation consisting of a sum of two degenerate third-order autoregressive functions of the form (1 + cr + c2r2/3) exp(−cr), where r represents radial distance. For the wind residuals, we use the functional form that follows by geostrophy. In addition to examining the structure of the horizontal and vertical correlations, we also present other statistics relating to the performance of the data assimilation procedure, such as vertical profiles of the magnitude of the observed wind and height residuals for various regions. In the second part of the paper, the results of the study are used as a basis for specifying interpolation statistics for the objective analysis. To evaluate the impact of the new interpolation statistics, various objective measures of analysis performance are examined and parallel 48-h forecasts are performed. It is found that significant improvements result when the new interpolation statistics are used in the data assimilation procedure.