The effect of station density in geostatistical prediction of air temperatures in Sweden: a comparison of two interpolation techniques

Abstract

Sparse coverage of meteorological stations reporting climatic variables is a key challenge in generating spatially continuous temperature data set because sparse coverage of stations is known to introduce uncertainty in the interpolation of temperature and related data sets. Consequently, development of methods to improve the accuracy of interpolated surfaces based on sparsely distributed point measurements has been an area of active research in geospatial studies. In this study, we assessed and compared Empirical Bayesian Kriging (EBK) and EBK Regression Kriging (EBKRP) interpolation techniques in terms of their accuracy under varying sampling density scenarios using monthly maximum temperature normals (1991–2020) for the entire area of Sweden as a case study. The EBK family of geostatistical interpolation methods are touted to have a generally higher interpolation accuracy over other interpolation techniques especially when sample data is sparse or locally non-stationary. Here, seven sampling density scenarios were created which ranged from 1 sample per 63,614 km2 to 1 sample per 634,350 km2, representing both low and high sampling density situations. The accuracy assessment was based on five robust prediction performance indices including mean error, mean absolute error, mean square error, root mean square error and Pearson correlation R, obtained from independent validation /cross-validation operation. The results show that generally, prediction accuracy was positively related to sampling density and sampling density accounted for 85% – 87% of interpolation accuracy as indicated in the RMSE and MAE for both EBK and EBKRP techniques. However, even though sampling density increased linearly, the rate of change in accuracy from one sampling density scenario to the next was not constant nor linear. A rapid increase (jump) in accuracy was noted when transiting from 40–60% sampling density scenario, but the rate remained fairly stable before and after 40% and 60%, respectively. For equivalent sampling density set-ups, EBKRP consistently performed better than EBK in all the accuracy metrics and EBKRP is generally considered to be about 40% better than EBK. Generally, the two interpolation techniques produced very low prediction bias at all the sampling density scenarios investigated. Our study suggests that potential effect of low sampling density and non-stationarity of sample data can be significantly reduced and, depending on the desired level of accuracy, EBK and EBKRP could produce reasonably accurate prediction surfaces even in a widely varying sampling densities settings. This is especially true for continuous and slowly varying phenomena such as temperature and similar variables.