Variational procedures for determining the parameters of the transfer model based on measurement data
UDC
51.37EDN
FWFVSEDOI:
10.31429/vestnik-22-4-31-36Abstract
Due to the intensive development of technical capabilities for obtaining satellite information on the state of the ocean and seas, the creation of methods and algorithms for processing such information, the development of methods for mathematical modeling of water dynamics and concentrations of impurities of various nature, it is necessary to create and use reliable procedures for assimilating such information in numerical models. There are different approaches to solving this problem. These are dynamic stochastic methods for correcting the obtained solution and variational algorithms for assimilating measurement data by determining model parameters. Such parameters make it possible to determine model estimates of concentration fields consistent not only with the measurement data, but also with the model itself. This alignment occurs by minimizing the corresponding forecast quality functionality and integrating the model itself. When implementing the dynamic-stochastic approach, there are difficulties in correctly determining the error covariance matrix, and in the case of using the second one, with nonlinear constraints imposed by the model, it is necessary to perform linearization on the assimilation interval used. When solving the problem of identifying the input parameters of the passive impurity transfer model, there is no problem of finding a global minimum. This is due to the convexity of the quality functional itself and the linearity of constraints that do not change the convexity of the overall functional. Such identification procedures are based on solving related problems and implementing iterative algorithms for finding optimal parameters based on measurement data. The uniqueness of the solution of the adjoint problem, the linearity of the constraints, and hence the convexity of the overall functional, allows us to determine the necessary parameters. Such parameters in the problem of passive impurity transfer can be the initial data, the fluxes of matter on the bottom and surface, the power of point sources, the sedimentation rate of the impurity, the coefficients of turbulent diffusion and velocity fields. The paper describes a technique for variational identification of input parameters for a passive impurity transfer model when assimilating measurement data for a finite time. Similar procedures are being built for the case of time-distributed measurement data.
Keywords:
model of transport, passive admixture, identification, adjoint task, minimizationFunding information
The work was carried out within the framework of the state assignment on topic No. FNNN-2024-0016 "Study of the spatio-temporal variability of oceanographic processes in the coastal, coastal and shelf zones of the Black Sea under the influence of natural and anthropogenic factors based on contact measurements and mathematical modeling" (code "Coastal research").
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