Four-Dimensional Variational Data Assimilation and Sensitivity of Ocean Model State Variables to Observation Errors

Abstract

The use of Four-Dimensional variational (4D-Var) data assimilation technology in the context of sea dynamics problems, with a sensitivity analysis of model results to observation errors, is presented. The technology is applied to a numerical model of ocean circulation developed at the Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences (INM RAS), with the use of the splitting method and complemented by 4D-Var data assimilation with covariance matrices of background and observation errors. The variational data assimilation involves iterative procedures to solve inverse problems so as to correct sea surface heat fluxes for the model under consideration. An algorithm is formulated to study the sensitivity of the model outputs, considered as output functions after assimilation, to the observation errors. The algorithm reveals the regions where the output function gradient is the largest for the average sea surface temperature (SST) in a selected area, obtained by assimilation. In the numerical experiments, a 4D variational problem of SST assimilation for the Baltic Sea area is solved.