RUSSIAN JOURNAL OF EARTH SCIENCES VOL. 8, ES6004, doi:10.2205/2006ES000216, 2006

1. Introduction

[2]  In our paper, we formulate the principles of using computational tools to solve applied problems of tsunami oriented to the support of decisions by managers in critical situations [Shokin and Chubarov, 1999].

[3]  From hereon we shall use term "tsunami" to denote the entire complex of catastrophic impacts caused by the waves in the basins and adjacent territories of the coast. The nature and spectral characteristics of these waves are usually associated with long surface gravity tsunami waves.

[4]  Similarly to other natural and anthropogenic catastrophes, tsunamis pass three stages in their development: stage before crisis, crisis, and stage after crisis.

[5]  Each of these stages is characterized by its duration, spatial scale, localization, and specific impact on the population involved in the crisis. Each stage requires specific methods of control and formulation of the list of problems, the important place in the solution of which is occupied by the methods of computational modeling. Specific limitations are imposed on mathematical models, numerical algorithms, technologies of calculation, character and volume of the results, means of their presentation (including visualization) means, protocols, and addressing of their spreading.

[6]  Leaving a number of provisions formulated above without consideration for a certain period of time we shall discuss the requirements, which the computational tools should satisfy. These tools are allowed by the scientific community for determining the vital characteristics of tsunami that are impossible or difficult to obtain using alternative sources (field studies, laboratory experiment, historical search, analytical methods, etc.).

[7]  These requirements should determine the technologies of developing mathematical models, creating numerical algorithms, methods of processing the numerical results, field and historical data, means of visualization and user interfaces, their programming realization, testing of mathematical models, algorithms, and programs.

[8]  It is assumed that the recommendations of the international community would be exclusively granted to those systems whose development, testing, documentation, and guidelines of use would satisfy the coordinated requirements.

[9]  Such approach is not new. It operates successfully for a long time in the development of algorithmic and programming software in the fields related to the solution of problems influencing the health, safety, and life of people, reliability of creating and application of high risk constructions (medicine, avionics, navigation, etc.).

[10]  Let us formulate the list of applied problems solved during each of the stages of tsunami.

[11]  The context of the problems listed above is determined, first, by the mandatory list formulated and accepted by the community of experts, and second, by additional list prepared by the crisis managers involved in specific work with account for the regional and local peculiarities of protected territories and specific crisis situation.

[12]  A set of mathematical models, algorithms of calculation and programs is defined depending on the peculiarities mentioned above and formulation of the problems. Two extreme technologies of calculations, and the third one, which is a symbiosis of the first two are possible.

[13]  1. Calculations are carried out locally by the personnel using software tools, which were obtained in advance and thoroughly documented. The personnel were specially trained and received the required certificates. This method has obvious advantages and not less obvious disadvantages.

[14]  Advantages. The work is carried out locally. Some parameters of the problems, models, and algorithms can be determined in a flexible manner with adjustment to the observed physical conditions. The major part of the customers is located locally, which decreases the load on telecommunication systems.

[15]  Disadvantages. The necessity to perform extremely complicated work in the conditions of chaos and mess, which appears in the crisis situations. Impossibility to enlist the services of the specialists in mathematics, hydrodynamics, computational algorithms, visualization and interpretation of the results including the authors of the applied mathematical models, algorithms and programs. Impossibility of using powerful computational devices increasing the accuracy of calculations, their properties of detailed work, and speed of solving the problems. Unreliability of telecommunication channels needed to obtain large volumes of information (bathymetry, topography of the land surface, characteristics of underlying surface), and wide spreading of the results.

[16]  2. Solution of the problems including processing of the results at special centers certified by the community for performing the corresponding works. The advantages and disadvantages of this approach are exactly opposite to those listed for the first approach.

[17]  3. Finally, the third, combined approach, when different problems are solved in different places. Realization of this approach requires certain additional work to structure the problems and reflect this structure to the corresponding structure of specialized centers of calculation. Good perspectives are opened for optimizing the works, information flows, and databases. The general efficiency of the works increases.

[18]  Now, let us discuss the computational tool, which is a result of the interaction of several objects:

[19]  Mathematical model with a set of parameters (hydrodynamic: initial data, bathymetry, form of the boundaries, topography of the land, roughness of the surface, wind tension, coefficients of turbulent viscosity, etc., and mathematical values of "virtual" properties, and those specified in deduction of equations);

[20]  Computational algorithm, which approximates the equations of the mathematical model with its parameters of spatial and temporal discretization, scheme and artificial viscosity and dispersion, with "additional" boundary conditions, etc.;

[21]  Algorithm of preprocessing, which modifies a number of hydrodynamic parameters for their adjustment to the peculiarities of the computational algorithm (recalculation to alternative grids, modification of boundaries, interpolation, etc.);

[22]  Algorithm of calculation controlling, which monitors irregular situations during the calculations (especially during long-term modeling) such as loss of stability and others, and introduces necessary changes (automatically or by means of the user interface) in the parameters of the computational algorithm (up to changing the model and algorithm) and provides the specified accumulation of the results for further processing and interpolation as well as ensures operative presentation of critically important information about the dynamics of the modeled phenomenon or computational process, etc.;

[23]  Algorithms of post processing, which process the results of modeling, calculated the necessary functionals of the solution, provides visualization of high quality, and if necessary transmits automatically generated messages of necessary volume and character to the specified telecommunication channels. The same algorithms perform selection and sorting of the information for further analysis, its archiving and transmission for long-term storage to the information databases. Most likely, this list can be supplemented, and no doubt presented in more detail.

[24]  The problems of application of the methods of computational modeling, appearing in the solution of applied tsunami problems are related to the peculiarities of the corresponding software tools.


RJES

Citation: Shokin, Yu. I., L. B. Chubarov, Z. I. Fedotova, S. A. Beizel, and S. V. Eletsky (2006), Principles of numerical modeling applied to the tsunami problem, Russ. J. Earth Sci., 8, ES6004, doi:10.2205/2006ES000216.

Copyright 2006 by the Russian Journal of Earth Sciences

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