The assimilation of past data in dynamical analysis. II

Systems for continuous data assimilation are presented and discussed. The balanced barotropic equation is used as an example of a dynamical (evolution) equation. In the first method, geopotential height data are assimilated into the model's computation, as the data become available, without any modification. It turns out that this leads to intolerable growth of error, suggesting the necessity of filtering the input information or alleviating discrepancies between the newly injected data and the prediction fields. In the second method, an optimal assimilation is attempted by applying adequate weights to the input data, which minimize statistically the mean-square difference between the estimate and the true solution. The analysis result is acceptable. But the magnitude of the error reduction is comparable to that of the previous synthesis analysis discussed in Part I of this paper. In the assimilation process we employed, the quality of the analysis seems to be determined by the characteristics of the measurements, i.e., density, distribution and magnitude of error, and also by the rate of inherited error growth in the dynamical prediction.