Physical Oceanography, Vol. 14, No. 5, 2004
MATHEMATICAL MODELING OF MARINE SYSTEMS
PREDICTION OF NATURAL PROCESSES BY THE METHOD OF ADAPTIVE
BALANCE OF CAUSES
I. E. Timchenko and E. M. Igumnova
The problem of estimation of the future values of processes is studied as a problem of their adap-
tation to the known data of observations in the past. The method of adaptive balance of causes
(ABC-method) is used for the construction of a dynamic model of the coefficients of influence.
This model enables one to compute the current values of these coefficients according to the cur-
rent correlation matrix determined as a result of reanalysis of the observed processes. We pro-
pose an ABC-model with variable coefficients of influence guaranteeing the optimal (from the
viewpoint of accuracy) prediction of natural processes and present an example of its application.
The method of adaptive balance of causes is used for the simulation of complex systems representable as
collections of numerous processes interacting both with each other and with the ambient medium . It is based
on the assumption that the processes running inside the system are consequences of the action of external factors
upon the system. The system responds to variable external actions preserving the state of dynamic balance with
the external forces. In this case, the processes are adjusted (adapted) to each other. The analyzed method (also
called the ABC-method) can be regarded as a development of the well-known method of system dynamics exten-
sively used for the simulation of genetic relations in economics and many other fields dealing with control over
complex systems .
The results of investigations demonstrate that the ABC-method can be successfully applied to the simula-
tion of marine ecosystems [3, 4]. As an important advantage of this method, we can mention the fact that the
equations of the model of an ecosystem take a unified form, which significantly simplifies their construction.
Furthermore, there exists a possibility to obtain statistical estimates of the coefficients in these equations as a re-
sult of the reanalysis of archival data about the simulated processes. In numerous cases, this property of the
method enables us to avoid the necessity of specifying the coefficients of the models heuristically, i.e., the neces-
sity of using expert estimates for this purpose (as a rule, these are hypotheses based on laboratory experiments)
If the time series of the data of observations of natural processes are available, then it is not difficult to per-
form the current reanalysis of their statistical characteristics: single-point and two-point moments of the probab-
ility distributions. Then the current (partial) elements of the correlation matrix serve as a basis for the evaluation
of the variable (as functions of time) coefficients taking into account the genetic relations between the processes.
Since the coefficients are computed via the elements of the correlation matrix, one can expect that the scales of
their variability are significantly larger than the scales of variability of the processes themselves. This opens a
possibility to predict the values of the processes for certain periods of time in the future. Note that the term of
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol. Translated from Morskoi Gidrofizicheskii Zhurnal,
53–63, September–October, 2004. Original article submitted February 18, 2003.
0928-5105/04/1405–0303 © 2004 Springer Science+Business Media, Inc. 303