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Assimilation

With increasingly complexity and diversity in both measurements and models of the systems being measured, there is great interest in developing flexible and efficient means of combining all possible sources of information. The research uses a Bayesian approach, in which it is assumed that the a priori probability distributions of errors in the observations and the model forcing terms are known. The analysis can then be taken as the field which maximises the joint probability distribution function. This approach leads to a penalty function which must be minimised to find the analysis. If the error probability distribution functions are not known, a penalty function can be constructed by analogy and used on an ad hoc basis. In the latter case, the parameters which would ideally be determined from the probability disributions must be tuned to obtain smooth and physically reasonable results. An analysis system must be able to smooth noisy data, interpolate sparse data, and infer variables which are not directly measured. The approach used here imposes the model equations as a soft constraint.