Numerical Methods of Modeling Atmospheric Circulation and Its Physical Processes

Numerical Methods of Modeling Atmospheric Circulation and Its Physical Processes

Copyright: © 2018 |Pages: 107
DOI: 10.4018/978-1-5225-2636-0.ch008
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Abstract

The last decades are characterized by significant progress in the development and operational use of modern numerical hydrodynamic methods of the Earth's weather and climate. This was made possible primarily due to modern understanding of the laws governing the basic physical and thermodynamic processes in the atmosphere and the emergence of more advanced mathematical models and effective methods of their implementation. In this chapter, we develop new numerical techniques used to solve the non-stationary problem of general circulation of the atmosphere with a prehistory and the problem of planetary weather forecast.
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A Brief Overview

The existing prediction models are classified according to the type of meteorological processes, specifics of their mathematical realization of the forecast period, as well as the size of the territory for which they are formulated. Until 1980 the operational weather services of the developed countries have focused on models of global forecasting of synoptic processes, despite some evidence that the quality of such forecasts remained almost constant. The increased interest in global models is explained, first of all, by political reasons and that they allow significant simplifications of the model equations and the use of effective methods of their numerical solution.

To implement a global model with a local high resolution with limited computing resources requires the use of efficient numerical methods. We will measure efficiency as the time that a single processor takes for the integration of model equations for one hour of the model time at a predetermined level of atmospheric circulation reproduction error. Of course, it is desirable that the methods used have an internal parallelism permitting efficient implementation on modern parallel computers.

The accuracy and efficiency of the existing numerical methods depend on the dimension of the problem. Choosing the best solution method is a difficult task as the purpose (accuracy) and means (cost) are contradictive to each other. Despite the constant improvement of computers, problems of accuracy and efficiency of numerical methods for solving problems of the circulation of the atmosphere remain valid today.

Currently, there are widely known various modifications of approaches to the numerical solution of the Navier-Stokes equations that are the basis of hydrodynamic models of atmospheric circulation. They can be divided into the following groups:

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