Data Assimilation by Statistical Interpolation of Forecast Error Fields

An operational method of combining observations with short-period forecasts of the same quantities is described. The method amounts to performing an interpolation in the field of apparent forecast errors, as defined by the available observations, by a linear least-squares technique similar to Gandin's. Statistics on the errors of observation and prediction are required. The spatial autocorrelations of the forecast error depend on the particular forecast model employed, the forecast period, etc. Those statistics necessary for the assimilation of synoptic data with four-level baroclinic 12-hr forecasts have been derived. They appear to be approximately homogeneous and isotropic and to vary slowly with season. Asynoptic data can be handled by allowing for variations with forecast period. Some practical problems in the determination of empirical statistics are discussed.