Comparison of regression and kriging techniques for mapping the average annual precipitation of Turkey

Abstract

Accurate mapping of the spatial distribution of annual precipitation is important for many applications in hydrology, climatology, agronomy, ecology and other environmental sciences. In this study, we compared five different statistical methods to predict spatially the average annual precipitation of Turkey using point observations of annual precipitation at meteorological stations and spatially exhaustive covariate data (i.e. elevation, aspect, surface roughness, distance to coast, land use and eco-region). The methods compared were multiple linear regression (MLR), ordinary kriging (OK), regression kriging (RK), universal kriging (UK), and geographically weighted regression (GWR). Average annual precipitation of Turkey from 1970 to 2006 was measured at 225 meteorological stations that are fairly uniformly distributed across the country, with a somewhat higher spatial density along the coastline. The observed annual precipitation varied between 255mm and 2209mm with an average of 628mm. The annual precipitation was highest along the southern and northern coasts and low in the centre of the country, except for the area near the Van Lake, Keban and Ataturk Dams. To compare the performance of the interpolation techniques the total dataset was first randomly split in ten equally sized test datasets. Next, for each test data set the remaining 90% of the data comprised the training dataset. Each training dataset was then used to calibrate and apply the spatial prediction model. Predictions at the test dataset locations were compared with the observed test data. Validation was done by calculating the Root Mean Squared Error (RMSE), R-square and Standardized MSE (SMSE) values. According to these criteria, universal kriging is the most accurate with an RMSE of 178mm, an R-square of 0.61 and an SMSE of 1.06, whilst multiple linear regression performed worst (RMSE of 222mm, R-square of 0.39, and SMSE of 1.44). Ordinary kriging, UK using only elevation and geographically weighted regression are intermediate with RMSE values of 201mm, 212mm and 211mm, and an R-square of 0.50, 0.44 and 0.45, respectively. The RK results are close to those of UK with an RMSE of 186mm and R-square of 0.57. The spatial extrapolation performance of each method was also evaluated. This was done by predicting the annual precipitation in the eastern part of Turkey using observations from the western part. Results showed that MLR, GWR and RK performed best with little differences between these methods. The large prediction error variances confirmed that extrapolation is more difficult than interpolation. Whilst spatial extrapolation benefits most from covariate information as shown by an RMSE reduction of about 60mm, in this study covariate information was also valuable for spatial interpolation because it reduced the RMSE with on average 30mm.