The behavior of forecast error covariances for a Kalman filter in two dimensions
The behavior of forecast error covariances in a fairly realistic setting is demonstrated via a Kalman filter algorithm. It is used to assimilate simulated data from the existing radiosonde network, from the demonstration network of 31 Doppler wind profilers in the central U.S., and from hypothetical radiometers located at five of the profiler sites. Some theoretical justification of the hypothesis advanced by Phillips (1982), and the hypothesis is used to formulate the model error covariance matrix required by the Kalman filter. The results show that assimilating the profiler wind data leads to a large reduction of forecast/analysis error in heights as well as in winds, over the profiler region and also downstream, when compared with the results of assimilating the radiosonde data alone. The forecast error covariance matrices that the Kalman filter calculates to obtain this error reduction differ considerably from those prescribed by the optimal interpolation schemes that are employed for data assimilation at operational centers.