Physical Oceanography, Vol. 19, No. 6, 2009
MATHEMATICAL MODELING OF MARINE SYSTEMS
ASSIMILATION OF THE DATA OF OBSERVATIONS AND ADAPTIVE
PREDICTION OF THE NATURAL PROCESSES
I. E. Timchenko and E. M. Igumnova
We propose a dynamical model for the prediction of random components of natural processes.
The model is based on the system concept of adaptive balance of causes (ABC-model) and con-
tains dynamic equations for the coefficients of influence adapted to the correlations existing in
the predicted processes. To improve the accuracy of predictions, we consider two possible
schemes of assimilation of the data of observations in the equations of the ABC-model, namely,
the Kolmogorov and Kalman schemes. Both schemes are oriented toward the application of
sample correlation coefficients for the prediction of time series of measurements and, hence, take
into account the nonstationarity of actual natural processes. We present some examples of pre-
diction of the simulated time series clarifying the algorithms of assimilation of the data of obser-
vations. A conclusion is made that the methods of systems modeling and adaptive prediction of
random processes by the ABC-method are quite promising.
The development of dynamic models of natural processes aimed at prediction of the values of these pro-
cesses at certain times in the future is one of the principal applied problems of geophysical investigations. The
natural processes are fairly complicated objects for simulation because parallel with deterministic components
they, as a rule, include random components. The application of the general methods of the theory of random
functions to the construction of prognostic models enables one to estimate the statistics of the errors of predic-
tions relative to the data of observations and use this information for the improvement of the quality of predic-
tions. This forms a basis for the assimilation of the data of observations [1, 2] in the models of natural processes
which plays an important role in the construction of scenarios of the development of processes running in the in-
tegral ecological-economic systems of marine media [3, 4] and in the natural economic systems of the coastal
zone of the sea .
In the integral description of marine systems, the prognostic models proposed by Kolmogorov  and Kal-
man  are used especially extensively. In these models, the future values of a process are formed by its past
values under the influence of correlations either regarded as known from observations or determined from the
dynamic equations specially deduced for this purpose. The mean value of a process at a future time conditional
relative to the observations of the process in the past is regarded as the optimal (in accuracy) prognostic estimate
of this process. A sufficiently full list of problems dealing with probabilistic algorithms of assimilation of the
data of oceanological observations can be found in [8–13].
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol, Ukraine.
Translated from Morskoi Gidrofizicheskii Zhurnal, No.
47–70, November–December, 2009. Original article submitted July 10,
2008; revision submitted August 7, 2008.
0928-5105/09/1906–0379 © 2009 Springer Science+Business Media, Inc. 379