Physical Oceanography, Vol.
3, September, 2011 (Ukrainian Original No.
3, May–June, 2011)
MATHEMATICAL MODELING OF MARINE SYSTEMS
RECONSTRUCTION OF THE SURFACE TEMPERATURE FIELDS ACCORDING
TO THE FRAGMENTARY DATA OF REMOTE SENSING
E. F. Vasechkina
We propose a gap-filling method for the data of remote sensing of the hydrophysical and biological
characteristics of the water surface. The proposed method of reconstruction is based on the representa-
tion of the fields of surface characteristics as the sums of certain numbers of empirical orthogonal func-
tions (EOF) making the largest contributions to the total variance of the field. According to the frag-
mentary data obtained as a result of processing of the satellite images for the summer season, we con-
struct estimates of the mean field and of the four-dimensional space covariance function of the surface
temperature of the Black Sea. The coefficients of expansion are computed by the method of least
squares or determined with the help of a genetic searching algorithm. The results of numerical experi-
ments show that the proposed method is quite promising for applications in the problems of gap filling
in the available satellite data.
Keywords: satellite data, space covariance function, empirical orthogonal functions.
The application of the data obtained from the satellites opens broad possibilities for the investigations of the
three-dimensional dynamics of the fields of physical and/or biological characteristics of the surface layers of the
sea. However, the value of these data significantly decreases by the presence of a large number of gaps, “white
spots,” in the satellite images caused mainly by the presence of clouds over the sea. There are various ap-
proaches to the solution of this problem. However, we consider a method based on the expansion of the fields in
a basis of empirical orthogonal functions. This method is well studied and used in the hydrophysical investiga-
tions since 1950s [1, 2]. The prospects of its application to the analyzed problem are connected with the high
rate of convergence of the expansions in empirical orthogonal functions (EOF) and, hence, with a relatively
small number of coefficients required for the reconstruction of the fields. Various aspects of the application of
the method of reconstruction of the data based on the systems of EOF are studied in the works performed by the
researchers of the Department of Systems Analysis of the Marine Hydrophysical Institute of the Ukrainian Na-
tional Academy of Sciences [3–6]. The accumulated results reveal the applicability of the proposed approach to
the problem of processing of the satellite data. Clearly, in the case of clouds covering almost the entire area of
the sea, it is impossible to reconstruct the missing data. However, there exists a significant part of the data array
of observations which becomes suitable for the problems of monitoring or as boundary conditions in model cal-
culations after the procedure of reconstruction.
Marine Hydrophysical Institute, Ukrainian National Academy of Sciences, Sevastopol, Ukraine; e-mail: email@example.com.
Translated from Morskoi Gidrofizicheskii Zhurnal, No.
48–65, May–June, 2011. Original article submitted January 19, 2010; revi-
sion submitted March 10, 2010.
0928–5105/11/2103–0195 © 2011 Springer Science+Business Media, Inc. 195