Volume 18, Issue 4

We developed nonhydrostatic three-dimensional models of the ocean boundary layer and the atmospheric boundary layer, which can reproduce large-scale (comparable to mixed layers thickness) eddy structures induced by both thermal convection and surface wind stress. The models are integrated into a coupled model of interacting boundary layers. Interaction between the models is due to the exchange of momentum, heat and moisture fluxes through the water-air interface. When constructing the models we use the methodology of large-eddy simulation. It supposes that large-scale eddies which play a significant part in the momentum, heat and salinity (or moisture) transport inside the boundary layers are described explicitly. To take into account small-scale (with spatial scales smaller than the mesh size of the model) isotropic turbulence we use parameterizations relating the energy of sub grid motions to the characteristics of slower processes. The systems of differential equations in the models consist of the Reynolds-type equations for describing the evolution of momentum, heat and salinity (or moisture), the equation of incompressible fluid continuity, and equations of state for sea water and damp air. To close the system of equations we use additional evolution equations of the turbulent kinetic energy of small-scale eddies and the dissipation rate of turbulent energy. We carried out a number of numerical experiments with the obtained models in which we succeeded in reproducing the motions similar to eddies observed in the atmosphere and the ocean.

We propose an algorithm for estimating the coefficients of the parabolic equation on the basis of observational data. The solution of the problem is based on the probabilistic representation of the solution of the parabolic equation and its parametric derivatives as the functional of the solution to the system of stochastic differential equations (SDEs).

A new version of the global ocean general circulation model with σ -coordinates is presented. The modelled area approximates the whole World ocean basin from the coast of Antarctica to the North Pole. The model is designed for very long integration periods. Accordingly the numerical techniques applied are very efficient, using implicit timestepping and operator splitting methods. The model is driven at the surface by wind-stress and by restoring temperature and salinity to the observed annual cycle. The cyclo-stationary solution of the model is shown to depend on the initial conditions even after many thousand years of integration. Four different solutions are briefly reported in this paper. The existence of multiple equilibria has been reported previously only under mixed boundary conditions. The key mechanismof the multiple equilibria is nonlinear deep convection processes. Numerical experiments show that global mean values of temperature and salinity are rather important parameters affecting the quasi-equilibrium state.

Using variational information assimilation, we propose the method of dynamic probabilistic numerical investigation of the climatic sensitivity of atmospheric processes to their long-term perturbations in given regions. We use the known representation of the atmosphere climate as a statistical ensemble of possible realizations of space-time meteoelement fields. In essence, we propose an algorithm for the approximate numerical modelling of conditionally distributed realizations by variational information assimilation methods using a numerical model of atmosphere hydrothermodynamics.

The variable resolution in latitude was implemented in the 3D global semi-Lagrangian finite difference numerical weather prediction model SL-AV. The implementation of the variable resolution is demonstrated by one of the model blocks, where the velocity field is reconstructed from vorticity and divergence. This block includes the solution of the Poisson equations on the sphere. Then this approach is validated in the context of a shallow-water model on the sphere by the set of standard tests. The results of the series of five-day forecasts by the 3D model show the benefit of using the variable resolution version of the model for three-day forecasts over Russia.