Regression-based air temperature spatial prediction models: an example from Poland

Abstract

A Geographically Weighted Regression – Kriging (GWRK) algorithm, based on the local Geographically Weighted Regression (GWR), is applied for spatial prediction of air temperature in Poland. Hengl’s decision tree for selecting a suitable prediction model is extended for varying spatial relationships between the air temperature and environmental predictors with an assumption of existing environmental dependence of analyzed temperature variables. The procedure includes the potential choice of a local GWR instead of the global Multiple Linear Regression (MLR) method for modeling the deterministic part of spatial variation, which is usual in the standard regression (residual) kriging model (MLRK). The analysis encompassed: testing for environmental correlation, selecting an appropriate regression model, testing for spatial autocorrelation of the residual component, and validating the prediction accuracy. The proposed approach was performed for 69 air temperature cases, with time aggregation ranging from daily to annual average air temperatures. The results show that, irrespective of the level of data aggregation, the spatial distribution of temperature is better fitted by local models, and hence is the reason for choosing a GWR instead of the MLR for all variables analyzed. Additionally, in most cases (78%) there is spatial autocorrelation in the residuals of the deterministic part, which suggests that the GWR model should be extended by ordinary kriging of residuals to the GWRK form. The decision tree used in this paper can be considered as universal as it encompasses either spatially varying relationships of modeled and explanatory variables or random process that can be modeled by a stochastic extension of the regression model (residual kriging). Moreover, for all cases analyzed, the selection of a method based on the local regression model (GWRK or GWR) does not depend on the data aggregation level, showing the potential versatility of the technique.