Mesoscale numerical modeling of the boundary atmospheric layer adapted to the north-western Black Sea region. Part 1. Mathematical problem formulation

E. V. Ivanova

doi:10.31481/uhmj.24.2019.01

E. V. Ivanova

DOI: https://doi.org/10.31481/uhmj.24.2019.01

Keywords: three-dimensional model; boundary layer; parametrization; turbulence; meteorological parameters; cloudiness; heat and water balance

Abstract

The article presents a complete mathematical formulation of the problem of the boundary layer of the atmosphere and the interacting surface layers of the soil with the active layer of the sea adapted to the North-Western Black Sea Region through the inclusion of the coastline shape, relief elevation angles and climatic characteristics of soil moisture. The numerical model is a three-dimensional, unsteady, hydrostatic model with one- or two-parameter closure. The paper presents a detailed description of the applied sub-grid processes parameterizations such as cloudiness in the lower tier, flows of short- and long-wave radiation throughout thickness of the boundary layer and near the Earth, antigradient migration for basic meteorological variables in the presence of neutral or weakly stable stratification, components of water, heat and radiation balance, phase transitions of moisture in the atmosphere, and different parameterizations of turbulent processes used in the model. The possibilities of the model include description of neutral and stable boundary layers with consideration of the kinetic energy of vertical velocity fluctuations instead of the kinetic energy of longitudinal and transverse velocity fluctuations. Identification of the type of the boundary layer at a particular point in time is estimated using values of the Richardson number. In addition, in case of convective conditions presence, parameterization of dry convection and wet-convective adaptation may be implemented. At the boundaries of "free boundary layer – surface or near-water layer of air, air-soil and air-water" certain bonding conditions are to be set to ensure continuity of meteorological parameters or their flows. On the upper boundary of the free boundary layer actual values of meteorological parameters and necessary parameters, or corresponding values from the global atmospheric model are to set. At the lower boundary of the deep soil layer the invariance of the vertical temperature gradient of the active layer of the sea – the value of temperature which is equal to the value of the latter according to its climatic values in the considered season of the year is to be set. The presented model is the first approximation in numerical modeling of the boundary layer over the adapted territory and is designed for studying the thermodynamic structure of the boundary layer of the adapted territory, as well as for identifying the breeze effects over the terrain.

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