Interpolation of temperature data for improved weather forecasts

Abstract: To create weather forecasts at the Swedish Meteorological and Hydrological Institute (SMHI), it is needed to interpolate the temperature from the observation stations into a grid with 2.5 km between each point. Since the observed temperatures are known and without error, they should be held fix even after the interpolation. Usually, there is a strong relationship between temperature and elevation which needs to be accounted for in the interpolation method. In this study, regression kriging was investigated and compared to inverse distance weighted interpolation (IDW). Different choices to be made within regression kriging were investigated to optimize the method and the results were evaluated using leave-one-out cross validation for many different sets of data. The result was that regression kriging always had a smaller mean square error than IDW, as long as there were no violation of the required assumptions. If there were, regression kriging can lead to large errors and can therefore not be used. To avoid violating the assumptions, the regression part of regression kriging needs to be accurate enough. This might require more information than only the latitude and longitude coordinates and the elevation, which is what was known in this study.