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Localization of satellite data
When processing satellite information about various geophysical fields, it may be necessary to convert the fields of values averaged by pixels by satellite device into fields of local values on the output geographical grid. Sometimes it is necessary to inverse the transformation of the local values on the grid into a set of pixel integrals. Compact finite-difference schemes provide a higher accuracy order than classical explicit algorithms. In order to convert one type of field into another, it is sufficient to solve a system of linear algebraic equations (SLAE) with a sparse matrix. The transformations are not exact for an arbitrary field, and lead to errors that depend on the grid step and the wave spectrum of the interpolated fields. These errors for different algorithms are compared using the Fourier analysis. The comparison confirms the advantage of compact algorithms for a wide spectral range of waves. The advantage of the compact algorithms is also observed for Gaussian formulas, but in some special way. The grid knots for such formulae are not equidistantly spaced. Additional difficulties in converting one type of field to another exist in the vicinity of the boundary of the computational domain V. Modification of these algorithms is necessary here. For many geophysical problems, the spectral energy distribution of the interpolated fields is known a priori if these fields are interpreted as random. It is useful to apply this a priori information for interpolation to minimize the probabilistic error for a given type of field. Compact finite-difference schemes for these problems also provide minimal error
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