Nonparametric Statistical Downscaling of Temperature, Precipitation, and Evaporation in a Semiarid Region in India

The climate impact studies in hydrology often rely on climate change information at fine spatial resolution. Because general circulation models (GCMs) operate on a coarse scale, the output from a GCM has to be downscaled to obtain the information relevant to hydrologic studies. In this paper, downscaling models are developed using the state-of-the-art nonparametric method $K$-Nearest Neighbor ($K$-NN) approach, with an emphasis on optimal choice in selection of nearest neighbors for obtaining simultaneous projections of mean monthly maximum and minimum temperatures ($T_{\max }$ and $T_{\min }$) as well as monthly precipitation and pan evaporation to lake-basin scale in a semiarid region that is considered to be a climatically sensitive region in India. The performance of the $K$-NN approach was evaluated based on several statistical performance indicators. A comparison of $K$-NN has been made with a linear multiple regression (LMR)-based downscaling model. Also, the prevailing view in the literature regarding optimal choice of selection of nearest neighbors is checked with different perturbations. A simple multiplicative shift was used for correcting predictand values. The $K$-NN-based models are found to be superior to LMR-based models, and, subsequently, the $K$-NN-based model is applied to obtain future climate projections of the predictands. An increasing trend is observed for $T_{\max }$ and $T_{\min }$ for A1B, A2, and B1 scenarios, and the precipitation is projected to increase in the future for A2 and A1B scenarios, whereas no trend has been observed for pan evaporation in future.