Mathematical, methodological questions concerning the spatial interpolation of climate elements

摘要

The paper focuses on the basic mathematical and theoretical questions of spatial interpolation of meteorological elements. Nowadays, in meteorology the most often applied procedures for spatial interpolation are the geostatistical interpolation methods built also in GIS software. The mathematical basis of these methods is the geostatistics that is an exact but special part of the mathematical statistics. However, special meteorological spatial interpolation methods for climate elements also exist, such as Gandin optimum interpolation as well as the MISH method developed at the Hungarian Meteorological Service in the last few years. These meteorological interpolation methods are also based on the mathematical statistical theory. Therefore, the basic type of the interpolation formulas applied by the geostatistical and meteorological methods are similar. One of our intentions is to present some comparison of the various kriging formulas, such as ordinary, universal, regression, residual, detrended, etc., ones. In general, these formulas can be derived from the multiple linear regression formula by using the generalized-least-squares estimation for certain unknown parameters. But the main difference between the geostatistical and meteorological interpolation methods can be found in the amount of information used for modeling the necessary statistical parameters. In geostatistics, the usable information or the sample for modeling is only the system of predictors, which is a single realization in time, while in meteorology we have spatiotemporal data, namely the long data series which form a sample in time and space as well. The long data series is such a speciality of the meteorology that makes possible to model efficiently the statistical parameters in question.