Volume 26, Issue 2

A mathematical model of the dynamics of oceans and seas is considered subject to tide-forming forces. The methods of description of tide-forming forces are discussed. Based on the variational data assimilation of satellite altimetry data, a solution algorithm for the inverse problem of reconstruction of ‘self-attraction’ forces and a method for approximate solution of this problem are proposed. The numerical study of the effect of tide-forming forces on the World Ocean dynamics is performed.

Semiexplicit and explicit finite-difference schemes for the multilayer quasigeostrophic model of ocean dynamics with time-dependent forcing are considered. The existence of the uniform attractor is established for each of the schemes. It is proved that when the mesh size decreases, the attractors of the schemes lie in an arbitrarily small neighbourhood of the actual attractor of the model.

A model of the joint circulation of the North Atlantic, the Arctic Ocean, and the Bering Sea is presented with the resolution of 0.25° in latitude and longitude. The numerical technique of solving this problem and the organization of numerical experiments are described. Numerical calculations have been performed using this model for the period of 1958–2006. The results are compared with observation data and with the results of simulation by other models. Model estimates of the evolution of the Atlantic water incoming into the Arctic basin through the Fram Strait and the Barents Sea are presented. A positive trend of Atlantic water incoming into the Arctic basin through the Fram Strait is revealed. The evolution of the fresh water layer thickness in the Beaufort Gyre is considered. Three periods of increased thickness correlated with increased anticyclonic vorticity are pointed out: 1960s, 1980s, and the period from 1999 until now. The evolution of the anticyclonic vorticity is ahead of the changes in the fresh water layer thickness by 1.75 years. Long-term positive trends of fresh water layer thickness and the anticyclonic field vorticity in the Beaufort Gyre have been observed from the middle of 1970s. This period is characterized by a negative model trend of the ice area in the Arctic, which corresponds to observation data.

The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition function. The optimal solution error is considered through the errors of input data (background and observation errors). The optimal solution error covariance operator is approximated by the inverse Hessian of the auxiliary (linearized) data assimilation problem, which involves the tangent linear model constraints. We show that the derivative of the inverse Hessian with respect to the exact solution may be treated as the measure of nonlinearity for analysis error covariances in variational data assimilation problems.

The σ -model of the general ocean circulation is described in the paper, its numerical implementation and the parallelization method for massively parallel computing systems are considered. The method called two-dimensional domain decomposition implemented by the MPI technology is used. The efficiency of the code was tested on the ‘Lomonosov’ supercomputer at the Moscow University using a geographic ocean grid with the resolution of 0.5° × 0.25°.

The problem of four-dimensional variational initialization of velocity, temperature, and salinity fields in the World Ocean is considered. The ocean dynamics equations are written in the generalized σ -system of coordinates on a sphere with arbitrary positions of coordinate poles. The World Ocean model has the spatial resolution 2.5° × 2°× 33. The computational north pole is shifted onto the continent to the point (60° E, 60.5° N), the south pole coincides with the geographic one. The numerical experiments consist of two stages. At the first stage, we perform the calculations of the direct World Ocean circulation model for the period of 3000 years. On the ocean surface we specify the climatic atmospheric forcing constructed from the averaged CORE data from the period 1958–2004 with the discreteness of 6 hours. At the second stage, the problem is solved in the ‘variational initialization – forecast’ mode. The calculation interval equals 1 year, the solution obtained at the first stage is taken as the initial condition. After the initialization, the calculation of the direct model in the forecast mode is performed up to the end of the current month of the year. The mean monthly fields of temperature and salinity from the Argo buoys data for year 2008 are used as assimilated observation data. The results of the calculations show that observation data assimilation leads to a noticeable improvement of treatment characteristics. The model values approach the observations, and the solution adequately reflects the observed structure of natural fields.