A Weighted Linear Regression Model for Precipitation Spatial Interpolation in Altiplano and Mountain Area

Abstract

Precipitation is evidently influenced by the terrain in the altiplano and mountain areas,in which the common methods,such as Inverse Distance Weighted(IDW),Kriging Statistics and Polynomial Approximation,can't effectively estimate the actual spatial distribution of precipitation.Elevation is a significant factor in precipitation and,on a given mountain slope, precipitation typically increases with elevation.Accordingly,a local weighted linear regression model(WLR) is introduced attempting to accurately interpolate precipitation in the altiplano and mountain areas.The linear regression of precipitation versus elevation for spatial interpolation method is implemented in ArcGIS 9.0 software using VBA programming.The weight of each precipitation observation is calculated by the distance between the estimated point and the observation point.Case study of precipitation interpolation in northwestern Texas shows that:(1) WLR model is better than the common methods such as Kriging and IDW in terms of MAE and RMSE of cross validation in altiplano and mountain areas for specific precipitation periods.(2) Due to the seasonal characteristics of the precipitation distribution,the precision of WLR interpolation varies in different periods of precipitation;compared with the common methods,the WLR model is better than IDW and Kriging methods for August precipitation data and has no evident difference for January data.(3) In the complex terrain area,the WLR model has evident advantages over the common approaches,and in the relatively flat area the model matches the IDW method.Considering that precipitation is influenced by more geographic factors such as mountain slope,aspect and wind direction,it is expected to develop a multiple linear regression model for precipitation interpolation in the future studies.