THE IMPROVEMENT OF THE NUMERICAL MODEL OF THE GLOBAL WIND SYSTEM OF THE ATMOSPHERE BY TAKING INTO ACCOUNT THE RELIEF OF A PLANET I.V. Mingalev1, K.G. Orlov1, V.S. Mingalev1, V.M. Chechetkin2, O.V. Mingalev1 1Polar Geophysical Institute, Apatity, Russia 2Keldysh Institute o fApplied Mathematics, Moscow, Russia Abstract. The non-hydrostatic mathematical model of the global wind system of the atmosphere, developed recently in the Polar Geophysical Institute, is improved by taking into account the relief of a planet. In the previous version of the mathematical model, the planetary surface was assumed to be a smooth spheroid. In the new version of the mathematical model, a planetary surface can contain mountains and depressions. A planetary surface is approximated by using one of the existing digital maps of the surface relief of a planet. The new version of the mathematical model is based on the numerical solution of the system of gas dynamic equations in the layer surrounding the Earth globally and stretching from the ground up to the altitude of 75 km, with the internal energy equation for the atmospheric gas being taken into account. In troduc tion During the last decade, in the Polar Geophysical Institute (PGI), two non-hydrostatic mathematical models of the wind system in the Earth’s atmosphere have been developed. The first model enables to calculate three-dimensional global distributions of the zonal, meridional, and vertical components of the neutral wind and neutral gas density in the layer surrounding the Earth globally over the height range from the ground to 120 km. The characteristic feature of this model is that the internal energy equation for the atmospheric gas is not included in the system of governing equations. Instead, the global temperature field is supposed to be a given distribution, i.e. the input parameter of the model, and obtained from one of the existing empirical models. This mathematical model has been applied in order to investigate numerically how various geophysical conditions influence on the formation of the global wind system of the Earth’s troposphere, stratosphere, mesosphere, and lower thermosphere [Mingalev et al., 2014a and references therein]. The second mathematical model is a limited area mathematical model of the wind system of the lower atmosphere, with the internal energy equation for the atmospheric gas being included in the system of governing equations. The model produces three-dimensional distributions of the atmospheric parameters in the height range from 0 to 15 km over a limited region of the Earth's surface. This regional model has been applied in order to investigate numerically the mechanisms responsible for the formation of large-scale vortices, in particular cyclones and anticyclones, in the Earth’s troposphere [Mingalev et al., 2014b and references therein]. Recently, the second mathematical model has been improved by enlarging the three-dimensional simulation domain [Mingalev et al., 2015], with the new version of the second mathematical model having been become global. In the new version of the second mathematical model, the internal energy equation for the atmospheric gas is included in the system of governing equations and written by using a relaxation approach. This version of the mathematical model enables to calculate the global wind system and heat regime in the layer surrounding the Earth globally and stretching from the ground up to the altitude of 75 km, with the planetary surface being approximated by a smooth spheroid. It may be sawn that the new version of the second mathematical can be considered as a combination of the first and second mathematical models pointed out in the beginning of the present Section. This new version of the second mathematical model may be named as a self-consistent mathematical model of the global wind system and heat regime of the planet’s atmosphere. It can be noted that analogous self-consistent mathematical models have been developed for simulations of the behavior of the atmospheres of Venus and Titan [Mingalev et al., 2012; 2015]. The purpose of the present work is an improvement of the self-consistent mathematical model of the global wind system and heat regime of the Earth’s atmosphere by taking into account the relief of a planet. M athem atical model In the present study, the new version of the self-consistent mathematical model of the global wind system and heat regime of the Earth’s atmosphere is described. In the new version of the self-consistent mathematical model, the atmospheric gas is considered as a mixture of air and water vapor, in which two types of precipitating water (namely, water microdrops and ice microparticles) can exist. The system of governing equations contains the “P hysics o fAuroral P henom ena”, Proc. X XXV in A nnual Sem inar, Apatity, pp. 184-187, 2 0 1 5 © K ola Science Centre, Russian Academy o f Science, 2015 Polar Geophysical Institute 184

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