Geographically weighted regression based quantification of rainfall–topography relationship and rainfall gradient in Central Himalayas

Abstract

ABSTRACTModelling of the relationship between rainfall and topography is important for precipitation mapping in mountainous regions. Global regression techniques like ordinary least square (OLS) assume that the relationship is uniform across the study area. In complex terrains like the Himalayas, the rainfall–topography relationship is non‐stationary and can be better modelled using local geographically weighted regression (GWR) technique that incorporates spatial heterogeneity. This study quantifies the spatial variability of relationship strength between rainfall and the topography of Central Himalayas, India, using GWR model. Further, the variation in rainfall gradient of the study area was derived from the modelled rainfall‐elevation relationship. The topographic parameters of elevation (E), slope (S) and terrain ruggedness index (TRI) computed from digital elevation model were considered for the analysis. For exploring the effect of stratification on the relationship study, the rainfall data were grouped into lowland and upland data based on terrain homogeneity. With higher coefficient of determination (R2), GWR showed improved result over OLS for all the cases. For annual rainfall, GWR(E) (R2 = 0.53), GWR(S) (R2 = 0.79) and GWR(TRI) (R2 = 0.60) estimated the best result for complete, lowland and upland, respectively. As compared to OLS, the coefficient of determination was higher by 90, 22.5 and 18%, respectively. The annual rainfall gradient derived from regression parameters of the model ranged from 1.33 mm m−1 (R2 = 0.53) in northwest to zero in southeast as against a constant value of 0.14 mm m−1 obtained from OLS model. For the subdivided region, annual rainfall gradient ranged from 1.2 to 1.7 mm m−1 in lowland and 0.3 to 0.6 mm m−1 in upland. The study demonstrates that scaling down from global OLS to local GWR model decreases the unexplained variance in the rainfall–topography relationship significantly. The result obtained from the stratification of study region proved that the clustering of data in mountainous region has the potential for improving the predictability of rainfall.