COMPARISON OF TWO DATA ASSIMILATION METHODS USED TO ACCOUNT FOR OPEN BOUNDARIES IN SEA AREA HYDROTHERMODYNAMICS MODELING

The problems of modeling hydrothermodynamics of particular sea and coastal areas are of current interest, since the results of this modeling are often used in many applications. One of the methods allowing to take into account open boundaries and bring the simulation results closer to real data is the variational assimilation of observational data. In this paper the following approach is considered: it is supposed that there are observational data at a certain moment in time; the problem is considered as an inverse problem, in which the functions of fluxes across the open boundary are treated as additional unknowns. Comparison of methods for reconstructing unknown functions in boundary conditions at an open boundary using sea level and velocity observational data in a number of numerical experiments for a region of a simple shape is carried out.

Processing and assimilation of observation data for the hydrodynamics model of the Black Sea and the Sea of Azov

This work is aimed at using the marine data of the Shared Use Centre (SUC) “IKI-Monitoring” in the variational assimilation procedures of the Informational Computational System (ICS) “INM RAS - Black Sea”. SUC “IKI - Monitoring” is a tool for obtaining remote sensing observations on the Earth state. In the paper observation data information is given, data processing procedures are described, algorithms for the assimilation of the information received and several specific features of the numerical model used are presented. Results of the variational assimilation of two sets of observation data are presented and discussed. Numerical experiments have confirmed the possibility of using incomplete data from satellites in the problems of modelling the sea area.

Randomised preconditioning for the forcing formulation of weak constraint 4D-Var

<p>There is growing awareness that errors in the model equations cannot be ignored in data assimilation methods such as four-dimensional variational assimilation (4D-Var). If allowed for, more information can be extracted from observations, longer time windows are possible, and the minimization process is easier, at least in principle. Weak constraint 4D-Var estimates the model error and minimizes a series of linear least-squares cost functions using the conjugate gradient (CG) method; minimising each cost function is called an inner loop. CG needs preconditioning to improve its performance. In previous work, limited memory preconditioners (LMPs) have been constructed using approximations of the eigenvalues and eigenvectors of the Hessian in the previous inner loop. If the Hessian changes signicantly in consecutive inner loops, the LMP may be of limited usefulness. To circumvent this, we propose using randomised methods for low rank eigenvalue decomposition and use these approximations to cheaply construct LMPs using information from the current inner loop. Three randomised methods are compared. Numerical experiments in idealized systems show that the resulting LMPs perform better than the existing LMPs. Using these methods may allow more efficient and robust implementations of incremental weak constraint 4D-Var.</p>