Physical Oceanography, Vol.
APPLICATION OF THE GENETIC ALGORITHM TO THE PROBLEM OF
RECONSTRUCTION OF MISSING DATA
E. F. Vasechkina and V. D. Yarin
We study the problem of reconstruction (interpolation and extrapolation) of the vertical profiles
of hydrochemical and hydrobiological elements according to incomplete sets of data with simul-
taneous filtration of short-period components based on expansions in empirical orthogonal func-
tions. The genetic algorithm is used to compute the coefficients of expansion of profiles with
We present the results of processing the data arrays on oxygen, chlorophyll A, and
biogenic elements collected in the Black Sea in 1982–1993. The mean error of reconstruction of
the profiles enables us to conclude that the proposed method has considerable advantages over
the conventional approaches.
In testing ecological models, the problem of insufficiency of available data of observations is quite urgent
despite the vast amount of accumulated data. This is explained by the irregularity and fragmentary character of
measurements, whereas a model requires a certain uniform collection of data for its verification. At the same
time, the typical situation encountered in oceanology in processing the data of contact measurements is con-
nected with the presence of only several points in the profiles of some parameters of the marine environment
(this is true mainly for hydrochemical and hydrobiological data), and the number of depths with missing data of-
ten exceeds the number of depths with available information. In this case, it is impossible to use statistical
methods for the reconstruction of the profile, and the linear (or spline) interpolation gives too large errors. As a
result, the station is simply excluded from the database.
In the present work, we propose to reconstruct these
poorly defined profiles by the method of empirical orthogonal functions (EOF) and genetic algorithms (GA),
which are now widely used in various fields of science and engineering.
The method of expansion of fields in empirical orthogonal functions has been successfully applied in geo-
physics for a long period time due to its obvious advantages. Thus, it is characterized by the rapid convergence
of series in systems of empirical orthogonal functions as compared with all other orthogonal bases and the possi-
bility of low-parameter representation and “natural” filtration of fields. By using the method of empirical or-
thogonal functions, we can efficiently reconstruct missing data if the total data array is sufficiently rich. Numer-
ous works [1–5] were devoted to this problem and the accumulated results show that this approach can be re-
garded as quite promising. Parallel with reconstruction of missing data, the application of expansions in empiri-
cal orthogonal functions gives a natural procedure for the filtration of data and simplifies the problem of extrap-
olation. This simplification is connected with separation of space and time variability as a result of the expan-
sion of a predicted variable in empirical orthogonal functions, i.e., the problem of prediction of the dynamics of
a two-dimensional field is reduced to the problem of prediction of time-dependent series for the coefficients of
expansion. Any realization of the observed field ft(,)x can be represented in the form
ft(,)x = ftf t(,) (,)xx−
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol. Translated from Morskoi Gidrofizicheskii Zhurnal,
30–39, July–August, 2002. Original article submitted December 12, 2000; revision submitted February 8, 2001.
200 0928-5105/02/1204–0200 $27.00 © 2002 Plenum Publishing Corporation