An evaluation of two statistical downscaling models for downscaling monthly precipitation in the Heihe River basin of China

The stepwise regression model (SRM) is a widely used statistical downscaling method that could be used to establish a statistical relationship between observed precipitation and predictors. However, the SRM cannot reflect the contributions of predictors to precipitation reasonably, which may not be the best model based on several possible competing predictors. Bayesian model averaging (BMA) is a standard inferencing approach that considers multiple competing statistical models. The BMA infers precipitation predictions by weighing individual predictors based on their probabilistic likelihood measures over the training period, with the better-performing predictions receiving higher weights than the worse-performing ones. Furthermore, the BMA provides a more reliable description of all the predictors than the SRM, leading to a sharper and better calibrated probability density function (PDF) for the probabilistic predictions. In this study, monthly precipitation at fifteen meteorological stations over the period of 1971-2012 in the Heihe River basin (HRB), which is located in an arid area of Northwest China, was simulated using the Bayesian model averaging (BMA) and the stepwise regression model (SRM), which was then compared with the observed datasets (OBS). The results showed that the BMA produced more accurate results than the SRM when used to statistically downscale large-scale variables. The multiyear mean precipitation results for twelve of the fifteen meteorological stations that were simulated by the BMA were better than those simulated by the SRM. The RMSE and MAE of the BMA for each station were lower than those of the SRM. The BMA had a lower mean RMSE (- 13.93%) and mean MAE (- 14.37%) compared with the SRM. The BMA could reduce the RMSEs and MAEs of precipitation and improve the correlation coefficient effectively. This indicates that the monthly precipitation simulated by the BMA has better consistency with the observed values.