^{1}

^{1}

^{1}

^{*}

An investigation of the influence of the relief of a planet on the global circulation of the Earth’s atmosphere is an important problem. Beyond doubt, mountains affect the global circulation of the troposphere, however, their influence on the global circulation of the stratosphere and mesosphere is not evident. In the present study, to investigate the influence of the relief of a planet on the global circulation of the Earth’s stratosphere and mesosphere, the non-hydrostatic mathematical model, developed earlier in the Polar Geophysical Institute, is utilized. Calculations were made for two distinct cases. The relief of the planet was taken into account for the first case. Unlike, the Earth’s surface was assumed to be smooth for the second case. Simulations were performed for the winter period in the northern hemisphere (January). Simulation results, obtained for both considered cases, are qualitatively similar at the levels of stratosphere and mesosphere, however, some noticeable distinctions exist. The horizontal domains exist, where the simulated horizontal and vertical components of the neutral wind velocity, obtained for two considered cases, differ noticeably at the levels of the stratosphere and mesosphere. Some of these horizontal domains are not connected with positions of mountains at the Earth’s surface. On the contrary, some of these horizontal domains are situated above mountains.

An investigation of the planetary wind system of the Earth’s atmosphere is a very important problem. It is well known that the human activity and health are considerably influenced by the atmospheric processes. Furthermore, cyclonic storms and hurricanes can produce tremendous damage and numerous fatalities. Unfortunately, many of the details of the formation of the planetary wind system of the Earth’s atmosphere are still unresolved. To investigate features of the planetary wind system of the Earth’s atmosphere not only the experimental and theoretical but also computational studies may be applied. It can be noted that several general circulation models of the Earth’s lower and middle atmosphere have been developed during the last four decades (e.g., see [

The study of the effect of the relief of a planet on the global circulation of the Earth’s atmosphere is close to investigations of surface-atmosphere interaction (for example, see [

In the present study, to investigate how the relief of a planet can affect the formation of the large-scale global circulation of the stratosphere and mesosphere, the non-hydrostatic mathematical model of the planetary wind system of the Earth’s atmosphere, developed recently in the Polar Geophysical Institute (PGI), is utilized.

The utilized mathematical model may be considered as a combination of two distinct mathematical models, developed earlier in the PGI. The first mathematical model, pertaining to this combination, 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. [

The second mathematical model, developed earlier in the PGI, is a limited area non-hydrostatic numerical model of the wind system of the Earth’s lower atmosphere which has been described in the paper of Belotserkovskii et al. [

It may be emphasized that both of mentioned mathematical models, developed earlier in the PGI, are non-hydrostatic numerical models of the wind system of the Earth’s atmosphere. Furthermore, both of mentioned mathematical models do not take into account the relief of a planet, with the Earth’s surface being smooth. On the contrary, in the mathematical model, applied in the present study, a planetary surface can contain mountains.

The mathematical model, applied in the present study, does not utilize the pressure coordinate equations of atmospheric dynamic meteorology, in particular, the hydrostatic equation. Instead, the vertical component of the air 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 velocity are obtained by means of a numerical solution of the generalized Navier-Stokes equation. Consequently, the applied mathematical model of the planetary wind system of the Earth’s atmosphere is non-hydrostatic.

In the applied 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. These equations are analogous to those applied in the mathematical models, described in the papers of Mingalev et al. [

It can be noted that, in the utilized 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 [

In general, the applied mathematical model is based on numerical solving of non-simplified gas dynamic equations and produces three-dimensional time- dependent distributions of the wind components, temperature, air density, water vapor density, concentration of micro drops of water, and concentration of ice particles. The model takes into account heating/cooling of the air due to absorption/emission of infrared radiation, as well as due to phase transitions of water vapor to micro drops of water and ice particles. The finite-difference method is applied for solving the system of governing equations, with numerical schemes, used in the mathematical model, having been presented in the study of Mingalev et al. [

Detailed description of the mathematical model, applied in the present study, may be found in the paper of Chetverushkin et al. [

To study how the relief of a planet can affect the formation of the large-scale global circulation of the Earth’s stratosphere and mesosphere, simulation results have been obtained for two distinct cases. The relief of the planet is taken into account for the first case (

initial moment, the neutral gas density at the lower boundary and air temperature in all simulation domain were taken from the NRLMSISE-00 empirical model [

After initial moment, three-dimensional global distributions of the gas dynamic parameters of the atmosphere, obtained for two considered cases and calculated with the help of the mathematical model, changed essentially. In the course of time, the calculated global distributions of the gas dynamic parameters of the atmosphere of the Earth acquire a tendency to fluctuate, with the period of the fluctuations being close to one day. Thus, establishing of the stable daily variations of the gas dynamic parameters came true. Consequently, daily variations of the gas dynamic parameters, conditioned by the rotation of the Earth around its axis, may be reproduced by the applied mathematical model of the global wind system.

We shall present the results of simulation, corresponding to the moment of 20.00 UT, which were obtained after the period of establishing the stable daily variations of the gas dynamic parameters. The global distributions of the gas dynamic parameters, calculated with the help of the mathematical model for two considered cases, are shown in Figures 2-7, with the coordinate systems in these figures being the same as in

The global distributions of the vector of the simulated horizontal component of the neutral wind velocity at the altitude of 20 km, obtained for both considered cases, are presented in

Nevertheless, some distinctions are present. Namely, the horizontal domain exists where the horizontal velocities, obtained for the case, correspondent to taking into account the relief of a planet, are more than those, obtained for the case, correspondent to smooth planetary surface. This horizontal domain is situated at latitudes close to −60˚ and at longitudes close to 70˚. It turns out that, in this horizontal domain, the vertical velocities, obtained for the case, correspondent to taking into account the relief of a planet, are more than those, obtained for the case, correspondent to smooth planetary surface (

In the vicinity of the South Pole, the downward vertical velocities, obtained for the case, correspondent to taking into account the relief of a planet, are less than those, obtained for the case, correspondent to smooth planetary surface

(

In

−60˚ and at longitudes close to −110˚, for both considered cases. Another cyclonic vortex exists, whose center is situated at latitudes close to −60˚ and at longitudes close to 40˚, for both considered cases.

However, some noticeable distinctions are present. In particular, the maximal module of the horizontal wind velocity, obtained for the first case when the relief of the planet is taken into account, is more than that, obtained for the second case when the planetary surface is assumed to be smooth.

The global distributions of the calculated parameters, obtained for both considered cases at the altitude of 60 km, are shown in

that the global distributions of the calculated parameters, obtained for both considered cases, are qualitatively similar. The horizontal domain exists where the horizontal velocities, obtained for both considered cases, have increased values. This horizontal domain is situated at latitudes close to 60˚ and at longitudes close to −150˚. It turns out that, in this horizontal domain, the vertical velocities, obtained for both considered cases, are downward (

Distinctions of the global distributions of the calculated parameters are present in

that, in this horizontal domain, the vertical velocities are downward. Unlike, such horizontal domain is absent for the second case when the planetary surface is assumed to be smooth. It can be noted that the biggest island Greenland is situated under this horizontal domain at the Earth’s surface (

It can be noticed that the existing hydrostatic general circulation models of the atmosphere (in particular, [

when the vertical component of the neutral wind velocity at the levels of the mesosphere and lower thermosphere can be as large as several tens of meters per second [

Fortunately, the mathematical model, applied in the present study, can describe the global neutral wind system under disturbed conditions, when the vertical component of the neutral wind velocity at the levels of the middle atmosphere can be rather large, due to the fact that the model is non-hydrostatic. From the simulation results, obtained in the present study, we can see that the simulated upward and downward vertical components of the neutral wind velocity can achieve values of a few m/s at the levels of the mesosphere. Such values of the upward and downward vertical components of the neutral wind velocity are unachievable for hydrostatic general circulation models.

There is not a shadow of doubt that the relief of a planet influences the global circulation of the Earth’s troposphere. Really, many Earth’s mountains can achieve the heights of some kilometers. However, the question about influence of the relief of a planet on the global circulation of the Earth’s stratosphere and mesosphere is not simple. In the present study, the mathematical model of the planetary wind system of the Earth’s atmosphere, developed recently in the PGI, was applied to investigate how the relief of a planet can affect the formation of the large-scale global circulation of the stratosphere and mesosphere.

The applied 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 . The relief of a planet is taken into account by the applied mathematical model. The mathematical model produces three-dimensional time-dependent distributions of the gas dynamic parameters of the atmosphere.

To investigate the influence of the relief of a planet on the global circulation of the Earth’s stratosphere and mesosphere, calculations were made for two distinct cases. The relief of the planet was taken into account for the first case. Unlike, the Earth’s surface was assumed to be smooth for the second case.

Simulation results indicated that the applied mathematical model of the global wind system reproduces daily variations of the gas dynamic parameters, conditioned by the rotation of the Earth around its axis. It turned out that the global distributions of the simulated horizontal and vertical components of the neutral wind velocity, obtained for both considered cases, are qualitatively similar at the levels of stratosphere and mesosphere.

However, the simulated global distributions of the gas dynamic parameters display some noticeable distinctions. At the levels of stratosphere and mesosphere, the horizontal domains exist where the simulated horizontal and vertical components of the neutral wind velocity, obtained for two considered cases, differ conspicuously. Some of these horizontal domains are not connected with positions of mountains at the Earth’s surface. On the contrary, some of these horizontal domains are situated above mountains.

Thus, it was established with the help of mathematical modeling that the relief of the planet ought to influence conspicuously on the global circulation of the Earth’s stratosphere and mesosphere for the winter period in the northern hemisphere.

It can be noticed that the applied mathematical model was able to simulate the noticeable effect of the relief of a planet on the global circulation of the Earth’s stratosphere and mesosphere due to the fact that the model is non-hydrostatic.

This work was partly supported by Grant No. 17-01-00100 from the Russian Foundation for Basic Research. The authors would like to thank the reviewers for helpful suggestions that led to improvement in the original manuscript.

Mingalev, I.V., Orlov, K.G. and Mingalev, V.S. (2017) Numerical Modeling of the Influence of the Relief of a Planet on the Global Circulation of the Earth’s Stratosphere and Mesosphere. Atmospheric and Climate Sciences, 7, 496-510. https://doi.org/10.4236/acs.2017.74036