Physical Oceanography, Vol. 17, No. 4, 2007
MATHEMATICAL MODELING OF MARINE SYSTEMS
DYNAMIC MODEL OF INTEGRATED PROCESSES IN THE ECOSYSTEM OF
THE NORTHWEST SHELF OF THE BLACK SEA
I. E. Timchenko,
V. A. Zhorov,
E. M. Igumnova,
and I. P. Lazarchuk
For the ecosystem of the northwest shelf of the Black Sea studied as an example, we construct a
dynamic model of the integrated processes of development of phyto- and zooplankton, larvae,
and fish and the variations of the concentrations of biogenic elements and detritus. The data of
many-year observations over these processes are generalized and the scheme of genetic relations
between these processes is proposed. By the method of adaptive balance of causes, we establish
the dynamic model equations of the ecosystem. It is proposed to use the method of analytic hier-
archy process for the estimation of the coefficients of the model with regard for the degree of in-
fluence of external and internal factors on the dynamics of the ecosystem. Some examples of an-
alysis of various scenarios of the development of integrated processes running in the ecosystem
are presented and their comparison with the data of many-year observations in this region is per-
The process of construction of a dynamic model of marine ecosystems includes a series of consecutive
steps. In the first step, it is necessary to formulate the main purpose of modeling, collect all available data re-
lated to the problem, and combine these data into two verbal models—a model of the ecosystem and a model of
the environment. The term “verbal models of ecosystems” stands for the systematized data on phyto- and zoo-
plankton, fish larvae, fishes, other biological objects, and their responses to the external actions. These are the
empirical models created by the experts and based on the data of observations and the experience accumulated as
a result of the comparison of scientific hypotheses with the observed facts.
In the second stage, it is necessary to construct the schemes of genetic relations for each of the indicated
two verbal systems. They are often called conceptual models . A model of this sort must contain all pro-
cesses in the ecosystem of principal importance for the purposes of modeling, as well as all significant mutual
influences of these processes. The system of influences in the conceptual models inevitably forms a hierarchy of
causes and effects of the phenomena. Thus, the influence of the environment occupying a higher level in the hi-
erarchy serves as a source (cause) of changes in the ecosystem.
The adequate conceptual model concentrating the results of mental analysis of the experts predetermines
the success of the third (final) stage of modeling aimed at the development of a formal dynamic model of the
ecosystem. Only formal models enable one to use computers as powerful means of investigation of the pro-
cesses running in the ecosystem. Thus, simulating the external actions upon the ecosystem, one can study its re-
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol.
Translated from Morskoi Gidrofizicheskii Zhurnal, No.
48–69, July–August, 2007. Original article submitted March 2, 2006;
revision submitted March 24, 2006.
0928-5105/07/1704–0223 © 2007 Springer Science+Business Media, Inc. 223