Assimilation of data in the imitative modeling of environmental processes by the method of minimizing corrective perturbations

Abstract

The on-line correction of the vector of a dynamic model state variable by direct or indirect measurements is a well-known problem of the theory of automatic control. It is called the problem of data assimilation. Ecological models require specific approaches to this problem in comparison to traditional methods used in hydrometeorology. The main difference is that there are only rare observations on a limited number of indirect characteristics. The paper presents an original approach to data assimilation for such cases. The main idea is inclusion an additional term to the initial system, which describes the random external influences that are not counted in the ideal model. Further, one can find a form of these perturbations that minimizes the weighted sum of their integrated power and the norm of deviations of the observed and theoretical characteristics at moments of measurement. Then the choice of weighting factor allows us for comparative confidence to be reflected between the theoretical model and actual measurements. Thus, the formal statement of the problem is written down as a problem of optimal control. Examples of application of the proposed method for several simple models are given. In the problem of the uniform motion of a material point, an analytical solution can be obtained which, nonetheless, yields rather interesting results. The problem of data assimilation for the Lotka—Volterra model has been solved numerically. It is shown that the proposed method of “minimal perturbation” leads to the least “traumatic” correction of the ideal model in comparison with the available alternative approaches; i. e., adaptive parameter identification or backdating adjustment of the initial state. Refs 7. Figs 2.