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 representation of the fields of surface characteristics as the sums of certain numbers of empirical orthogonal functions (EOF) making the largest contributions to the total variance of the field. According to the fragmentary data obtained as a result of processing of the satellite images for the summer season, we construct 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 experiments show that the proposed method is quite promising for applications in the problems of gap filling in the available satellite data.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 approaches 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 investigations 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 National Academy of Sciences [3][4][5][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 calculations after the procedure of reconstruction.