Modeling Wind-Driven Circulation in Lake Balaton

Shanahan, P., Harleman, D.R.F., & Somlyody, L. (1981). Modeling Wind-Driven Circulation in Lake Balaton. IIASA Collaborative Paper. IIASA, Laxenburg, Austria: CP-81-007

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Abstract

This paper reports the results achieved to date in a program of research to develop and apply mathematical computer models of water quality in shallow lakes. The portion of the research which is the specific topic of this paper is the development, testing and trial application of a transient three-dimensional model of wind-driven circulation. The results are presented in the context of an application to Lake Balaton in Hungary, a large yet very shallow lake.

The paper presents a review of the mathematical formulation of the circulation problem and the major methods used in computer models of wind-driven circulation. Detailed examinations of the model assumptions and parameters are also included. A description of the application lake follows and a three-dimensional model appropriate to shallow lakes is proposed and derived. This model is examined for consistency with Lake Balaton's characteristics, and the important need for congruence with an eventual coupled biogeochemical model of the water quality is described and investigated. The requirement that the length and time scales of the hydrodynamic model and the biogeochemical model be consistent with each other and with the processes of interest in the lake is stressed.

The proposed circulation model employs a Galerkin technique to compute the vertical velocity profile using a depth-dependent vertical eddy viscosity. The parameters for this model are determined by calibration using simple hypothetical seiche simulations as a standard. It is found that the function specified for the vertical eddy viscosity is a crucial determinant of the model response. The resulting model and calibration are then successfully verified with historical events on Lake Balaton. A detailed examination of the results of one of these event simulations explores aspects of the model predictions pertinent to the mass transport of water quality constituents. Conclusions of the paper include identification of the need to improve the representation of mass transport in existing models of Balaton's water quality and an agenda for future development of a coupled hydrodynamic-biogeochemical water quality model.

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