Mapping of temperature variables in Israel: a comparison of different interpolation methods

Abstract

Interpolating values of climate variables from measurement stations to large areas is important in a variety of disciplines. Each of the 38 climate observation stations in the Israel area represents an average area of 725 km 2 . Therefore it is important to minimize the extent of interpolation errors by using a suitable interpolation method. In this study we compared the performance of 2 local interpolation methods, Spline and Inverse Distance Weighting (IDW), with the performance of multiple regression models. These interpolation methods were applied to 4 temperature variables: mean daily temperature of the coldest month (January), mean daily temperature of the warmest month (August), the lowest mean monthly minimum temperature (January) and the highest mean monthly maximum temperature (June). Spline and IDW models with a range of parameter settings were applied to eleva- tion detrended temperature data. The multiple regression models were based on geographic longitude, latitude and elevation and included terms of first and second order. Two methods of variable selection (Stepwise, Forced Entry) were used to construct 2 regression models for each temperature variable. Accuracy was assessed by a one-left-out cross validation test. Mean daily temperature variables proved more predictable than mean monthly extreme temperature variables. Mean daily temperature vari- ables were predicted more accurately by using a regression model, whereas mean monthly extreme temperature variables were somewhat better predicted by a local interpolation method. The Spline interpolator predicted more accurately than IDW for the 2 summer temperature variables, while IDW performed better for the winter temperature variables. Combining multiple regression and local inter- polation methods improved prediction accuracy by about 5% for the extreme temperature variables but did not effect the prediction of mean daily temperatures. Errors in the estimation increased with the use of local interpolation methods in areas where neighboring data were not 'local enough' to show micro-climatic influences. Where the data supported strong short-range climatic factors (such as the cooling effect of the Mediterranean Sea on the shoreline in summer), local methods were more effec- tive than regression models, which became complicated and tended to over extrapolate. These findings suggest that in some instances simple overall regression models can be as effective as sophisticated local interpolation methods, especially when dealing with mean climatic fields.