In Chapters 4 and 5, we considered a system hydrodynamics equations and boundary conditions that constitute the mathematical basis of the circulation models of the atmosphere of a scale. They contain terms describing sources (sinks) of mass and energy involved in the phase transformation of atmospheric moisture and radiative processes in the system atmosphere – the Earth. Direct inclusion of these microscale and mesoscale processes in the atmospheric circulation model is inappropriate as: 1) this leads to an increase in the total number of grid points in the decision area, and 2) not all these processes can be described by precise differential equations.
TopParameterization Of The Interaction Of The Atmosphere With The Underlying Surface
The interaction of the atmosphere with the underlying surface occurs through the physical processes of the boundary layer. Regarding the atmosphere, the latter is a “sink” of the momentum and the “source” of heat and moisture. At the same time, atmospheric processes themselves significantly affect the structure of the boundary layer. However, the models take into account its properties only with a certain degree of approximation as possibilities of description of the boundary layer in the atmospheric circulation models are limited. These options depend on the time and spatial scales of the simulated atmospheric processes and phenomena.
In the simulation of the general circulation of the atmosphere and long-range weather forecasting, it is important to consider the dissipation of the average amount of motion in the boundary layer, as well as heat and moisture flow from the planetary boundary layer. At the same time, for the calculation of dynamic processes in mesoscale systems, the boundary layer associated with the topography and thermal heterogeneity of the underlying horizontal surface, and the spatial variability of surface turbulence play especially an important role. Therefore, the creation of numerical models of atmospheric circulation of various types of different resolution in both vertical and horizontal makes demands on adequate description of the boundary layer. Unfortunately, there is no well-founded answer to the question, what are details necessary to consider the boundary layer in the models, and what is a sensitivity of different scale to a method for its disclosure.
The main way to account the interaction of the atmosphere with the underlying surface in the given numerical model is implemented based on the method of parameterization of the planetary boundary layer (PBL) of the atmosphere.
Small-scale turbulence may be the most significant in layers with significant gradients of wind speed, temperature, and humidity, i.e., in the atmospheric boundary layer. The height h in the case of PBL neutral stratification can be approximately estimated by equating the orders of magnitude of the forces of turbulent viscosity and the Coriolis force,
.
It follows that 
. More detailed assessment based on the definition of h as a size of the layer in which the direction of the actual and geostrophic wind is different, lead to h≈1km.
Designate the vertical turbulent flows of momentum of the horizontal components of the wind speed 
by 
and 
, and turbulent flow of heat and moisture by 
and 
respectively, i.e.,
,
.
We confine ourselves to the PBL. We assume that 
, and replace the values 
, 
, 
, 
, 
by finite differences with emphasis on their values when 
and 
. The result is: