Mapping spatio-temporal variables: The impact of the time-averaging window width on the spatial accuracy

Spatial mapping of variables that vary in space and time is a common procedure in many research fields. Very often it is of interest to map the time-average or time-integration of the variable over the whole period of interest. Normally, such a map is produced by spatially interpolating the whole period averages of the observed data. An alternative option is to first spatially interpolate narrow time slice averages of the variable and then sum the resultant maps. This paper discusses the latter option, and the accuracy of the spatio-temporal variable interpolation as a function of the width of the time-averaging window. Theoretically, using a linear and data-value independent operator to interpolate a complete data set (i.e. without missing data), the accuracy is independent of the width of the time-averaging window. However, using a nonlinear or a data-value dependent interpolation operator, and/or in the presence of missing data, the accuracy of the interpolation can vary with the averaging window width. The concept is demonstrated using a set of half-hourly SO2 concentrations measured at 20 monitoring stations in Haifa Bay area, Israel, during the years 1996–2002. Cross-validated interpolation accuracy measures calculated for this data set vary significantly with the time-averaging window width, showing a clear minimum at daily averaging. The results and their general implications for the interpolation of spatio-temporal variables are discussed.