Statistical downscaling plays an important role in reducing the uncertainty in regional-scale climate change studies. A major assumption of all statistical downscaling studies is the stationarity in the relationship identified from the historical observations. This assumption is difficult to validate since the future is truly unknown. The proposed methodology tries to overcome the limitations of this assumption by considering global physics that drive the regional climate to select the predictors to develop the statistical relationship. Since the statistical model is developed with climatic processes as a background, it can be said with higher confidence that the modelled relation would remain sound for the future as well. The proposed methodology is divided into two stages. In the first stage, a Relevance Vector Machine model is developed using historical observed global predictors that are identified to have teleconnections with the regional climate predictand. The spatial downscaling of this regional predictand has been done on a monthly scale. The bias associated with the downscaled predictand is removed by separating the anomalies from the prediction and adding that to the historical mean of the observed data. This monthly series is further disaggregated into daily series using a weather generator. The non-stationarity in the climate projections is accommodated in the weather generator and more regional features of the climate is integrated into the predictand in this stage. The proposed methodology is validated by downscaling rainfall over a river basin in India and its performance is analysed. The downscaled data is seen to reproduce characteristics of daily rainfall like consecutive wet days, the number of rainy days, wet spell duration, and dry spell duration with a bias of less than 10%.