## 1. Introduction

Interpolation is a way of reconstructing continuous fields from variables measured at point locations. This is no straightforward operation and one of the main difficulties is to select the method that provides the best estimates. Two families of methods have come to stand out for the quality of their results: the methods of kriging and regression. Given the statistical constraints associated with them, these methods are not interchangeable and do not yield optimal results in all cases. Kriging is better suited when variables are strongly spatially autocorrelated, where, for temperatures, say, a gentle topography engenders regular thermal gradients. Conversely, regression yields better results where, again for the example of temperatures, their spatial variation is dictated by prominent relief. The two methods may be concatenated and results are often improved by kriging the residuals of a regression. The criteria for choosing from among these possibilities are not always obvious even when the geographical sectors in question appear homogeneous.

Matters are further complicated where plains and mountains lie side by side over areas of some size (Joly *et al.*, 2010). This is the case in a multidisciplinary research project to estimate the ‘price of climate’ across France. Continuous climatic information across the entire country was required so that economic and climatic data could be matched. As climatic data are sporadic, they had to be interpolated by relating the response variables, those for climate, and the explanatory variables (latitude, longitude, and environmental data on relief and land cover). To investigate this issue, we tested three global methods of interpolation: regression, kriging, and regression followed by kriging of residuals. Then we compared the findings with results from a fourth method based on local interpolation. The results of the experiment are presented here.

Section 2 describes the data used. Section 3 presents the main features of the four methods. The principle behind the local interpolation method is described in detail from a set of data on sunshine duration; this variable was chosen because it was recorded at just 111 weather stations, thus simplifying our exposition. In Section 4, the entire approach is applied to temperature measured at 651 stations to compare the findings from all four methods. The standard deviation of residuals is used for this. Section 5 relates to the specific developments of the local interpolation method, i.e. the mapping of the coefficient of determination, the Pearson correlation coefficient, and the parameter estimate for each of the explanatory variables included in a geographical information system (GIS). This additional information is a fundamental contribution to climatology that is specifically interested in the study of local climate. This provides insight into the factors behind the spatial distribution of climatic phenomena.