Data interpolation using Kohonen networks

Physical data interpolation is a common issue in geosciences. For many variables of interest, the measurements are often sparse and irregularly distributed in time and space. Analyzing the data usually requires a numerical model, which samples the data on a regular grid. Mapping irregular measurements on a regular grid is done by interpolation, which aims to generalize, but not to create, information. A popular method to map geophysical data is kriging. This method, based on the hypothesis that the measurements are realizations of a random variable, has been proven to be optimal under certain conditions. It requires solving a system of linear equations at each point where the interpolation must be done, which might be computationally heavy. The paper proposes an original interpolation method based on Kohonen networks. The method is applied to the problem of building a surface-temperature climatology in the Mediterranean Sea. The method performs very well, combining an accuracy comparable with usual kriging methods with a shorter computing time, and is especially efficient when a great amount of data is available. The paper is organized as follows. Section 2 recalls the backgrounds of kriging techniques. Section 3 describes the adaptation of self-organizing maps to the spatial interpolation problem. The results of actual data interpolation in an oceanographic problem are presented and discussed. The last section draws conclusions and perspectives.