Non‐stationary modelling framework for rainfall interpolation in complex terrain

Abstract

ABSTRACTThe knowledge of rainfall‐elevation relationship forms an important input for modelling the orographic rainfall in mountainous areas. The conventional regression and geostatistical techniques assume the rainfall and elevation relationship to be constant; however, in complex terrain these exhibit non‐stationarity in their relationship. This study proposes a novel spatial rainfall modelling framework, stratified geographically weighted regression‐residual kriging (s‐GWRK) that integrates the benefit of spatially clustered data as an input, local‐scale model and incorporation of spatial correlation structure of residuals. The application of the framework is demonstrated in Indian Himalayas of Uttarakhand region with two spatial clusters of normal annual rainfall data, lowland and upland, based on natural clustering technique. The performance of the proposed model is compared with ordinary co‐kriging (OCK), ordinary least square regression (OLS), geographically weighted regression (GWR) and geographically weighted regression kriging (GWRK) that incorporates elevation as predictor variable. Model evaluation shows that s‐GWRK performed best with root mean square error (RMSE) of 153.98 and index of agreement (d) of 0.92. OLS performed least with RMSE of 461.2 and d value of 0.32. OCK using elevation as auxiliary variable performed better than OLS with RMSE of 454.7 and d value of 0.53. The predictive capability of s‐GWRK was validated using the data collected from rain gauge network in the mountainous terrain of Ashburton in New Zealand and Bhutan. An improvement of 30% and 55% in RMSE was observed compared to OCK for Ashburton and Bhutan respectively. For Uttarakhand, Ashburton and Bhutan, the positive rainfall lapse rate derived from GWR model of rainfall‐elevation relation, ranged from 0.01–1.3, 0.2–1.43 and 0.09–0.4 mm m−1.