“P hysics o f Auroral Phenom ena", Proc. XXXVIII A n n u a l Sem inar, A patity, pp. 181-183, 2 0 1 5 © Kola Science Centre, Russian Academy o f Science, 2015 Polar Geophysical Institute SELF-CONSISTENT NUMERICAL MODELING OF THE GLOBAL WIND SYSTEM AND HEAT REGIME OF THE LOWER AND MIDDLE ATMOSPHERE I.V. Mingalev1, K.G. Orlov1, V.M. Chechetkin2, V.S. Mingalev1, O.V. Mingalev1 1Polar Geophysical Institute, Apatity, Russia 2Keldysh Institute o fApplied Mathematics, Moscow, Russia Abstract. The regional non-hydrostatic mathematical model of the wind system of the Earth’s lower atmosphere, developed earlier in the Polar Geophysical Institute, is improved by enlarging the three-dimensional simulation domain, with the new version of the mathematical model becoming global. In the new version of the mathematical model, the internal energy equation for the atmospheric gas is written by using a relaxation approach. The finite- difference method is applied for solving the system of governing equations. The new version of the mathematical model produces three-dimensional time-dependent global distributions of the gas dynamic parameters of the lower and middle atmosphere of the Earth. Thus, self-consistent numerical modeling of the global wind system and heat regime of the Earth’s lower and middle atmosphere is allowed by the new version of the mathematical model. Introduction Earlier, in the Polar Geophysical Institute, two non-hydrostatic mathematical models of the wind system in the Earth's atmosphere have been developed. The first model is the non-hydrostatic model of the global neutral wind system in the Earth’s atmosphere which has been described in the papers of Mingalev I. and Mingalev V. [2005] and Mingalev et al. [2007]. This model enables to calculate three-dimensional global distributions of the zonal, meridional, and vertical components of the neutral wind and neutral gas density over the height range from the ground to 120 km, with whatever restrictions on the vertical transport of the neutral gas being absent. 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 model has been utilized in order to simulate the global circulation of the middle atmosphere for various geophysical conditions [Mingalev et al., 2014a and references therein]. The second mathematical model is a regional mathematical model of the wind system of the lower atmosphere which has been described in the paper of Belotserkovskii et al., [2006], 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. The mechanisms responsible for the formation of large-scale vortices in the Earth’s troposphere, in particular cyclones and anticyclones, have been investigated with the help of this model [Mingalev et al., 2014b and references therein]. The purpose of the present work is an improvement of the latter mathematical model by enlarging the three- dimensional simulation domain, with the new version of the mathematical model becoming global. Mathematical model In the present paper, the new version of the mathematical model of the wind system of the Earth’s lower and middle atmosphere is described. It may be noticed that this new version of the mathematical model can be considered as a combination of two mathematical models pointed out in the previous Section. In the new version of the 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 equations of continuity for air and for the total water content in all phase states, momentum equations for the zonal, meridional, and vertical components of the air velocity, and energy equation. In the new version of the mathematical model, the internal energy equation for the atmospheric gas is written by using a relaxation approach, in which a heating / cooling rate of the atmospheric gas in various chemical-radiational processes is supposed to be straightly proportional to the difference between the real temperature of the atmospheric gas and an equilibrium temperature of the atmospheric gas. The latter equilibrium temperature may be given by utilizing the global temperature field, obtained from one of the existing empirical models, for example, from the NRLMSISE-00 empirical model [Picone et al., 2002]. Furthermore, the mathematical model is non-hydrostatic, that is the model does not include the pressure coordinate equations of atmospheric dynamic meteorology, in particular, the hydrostatic equation. Instead, the vertical component of the atmospheric gas velocity is obtained by means of a numerical solution of the appropriate momentum equation, with whatever simplifications of this equation being absent. Thus, three components of the air 181

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