The abstract of master's thesis

"Numerical analysis of the mathematical models of weather forecast"

Made by A.B.Ivaschenko

Content
• Introduction
• The purposes and tasks of the work
• New scientific result
• Practical value
• The List of unsolved problems and questions
• The current and planned results on the subject
• The Conclusion and summary

• Introduction

The rapid development of computing machinery in the last decades events has allowed to use widely the mathematical methods in theoretic researchs of the world ocean, atmosphere and climate.

At present the number of numerical algorithms for solving the problems of weather forecasting and general circulation of atmosphere are available. However it is necessary to note that equations of hydrodynamic atmospheric processes are so complex that there is still a need for the development of more qualitative algorithm that are able to describe with high accuracy the wide spectrum of problems in dynamic meteorology and weather forecasting. Development of qualitative algorithm for these problems is closely connected with the problem of aproximation of equations and the stability of differential schemes, which in general are the main problems in designing new numerical algorithms.

• The purposes and tasks of the work

ЦThe Purposes of the work are:

• analysis of mathematical models of weather forecast;
• solving problems of meteorology with the use of splitting methods;
• development of software, based on splitting methods.

The tasks of master’s thesis are:

• Search in the Internet and in literature for information on mathematical models, describing the dynamics of the atmosphere, and on the numerical methods for solving the problem of weather forecasting.
• Study of the numerical methods which are used in solving systems of partial differential equations (differential schemes, splitting method, and others)
• Definition of the methods that are the most efficient for modeling and solving the problem on computer.
• Analysis of software allowing to forecast climate and weather changes.
• Search for and collection of the input data for the weather forecasting model.
• The development of the software that will allow to do weather forecasts.

• New scientific result

The problem of weather forecasting was a subject of deep study particularly in postwar years. Starting from work of I. A. Kibel in 1940, in which the hydrodynamics theory of the short-term weather forecast was formulated for the first time. These developped extensively both in former USSR, and abroad. The works of I. A. Kibel, E. N. Blinova, A. M. Obuhov, M I. Yudin, N. I. Bulev and G. I. Marchuk, K. Hinkelman and others have brought about a number of new original target settings, and development of electronic computing machinery created the solid base for further improvement of hydrodynamics theory of weather forecasting and theory of the climate, which have got the essential development in works of E. Minc, F. Tomson, E. Lorenc, F. Shuman, A. Kasahara and others. New more efficient and universal methods such, as the "box-method" of Kurihara and Brayn, the splitting method, designed by G.I. Marchuk, came to take the place of traditional algorithms of numerical solving of problems of atmosphere dynamics. These new approaches allow to include the problem of the hydrodynamyc forecast as an example of the solution of difficult problems in mathematical physics with the help of the methods of modern computing mathematics.

• Practical value

The reference sources and results of the master’s thesis will be useful, first of all, for those who are working at meteorological centres, concerning with short-term weather forecasting.

Data about weather and its forecast have a great importance in many branches of economy, especially in civil aviation, construction, agriculture and even in sea - everywhere, where planning or undertaking of some actions and projects depends directly on weather conditions. So the work can turn out to be useful for many branches of economy.

Also the results of the work can be successfully used by individual meteorological posts both for making weather forecast and for comparing and checking the results of others weather forecasting models.

• The List of unsolved problems and questions

• Limitation in computing powers;
• The problem of choosing the most efficient models analysis
• The questions of model stability and inexactness of numerical forecasts, which appear in consequence of:
• incompletenesses of the physical scheme of the forecast, inexact account of some factors in the schemes that can influence on weather;
• insufficient amount or insufficient accuracy of observed data at the initial moment of the forecast;
• use of approximate methods of solving partial differential equations.

• The current and planned results on the subject

The current results:

• literture on mathematical modeling of climate and methods of solving the problems weather forecast have been studied;
• models of atmosphere circulations have been studied;
• the idea behind the splitting method for solving complex systems of differential equations have been studied;
• иthe capabilities of mathematical packages (such, as MatLab, MathCad) as for modeling and simulation of the weather forecasts have been studied.

The following works are to be carried out:

• further collection of information on mathematical models of the climate and numerical weather forecasts;
• choosing a model and methods of its solution, target settings, choosing software tools in the field of information technology;
• making the software allowing to produce weather forecasts.

• The Conclusion and summary

Though scientists concern with mathematical modeling of the climate and weather forecasting for a long time, the problem arising in this field have not lost their topicality even today. To my opinion, the problem of numerical weather forecast is quite complex and, hence, very interesting. So, I hope, my study of all details and problems of climate modeling and numerical weather forecast will not be limited by the frameworks of my master’s thesis.