Propagating Uncertainty in Climate Data for Hydrologic Prediction

Understanding the impact of climate change and its variability on regional hydrology is predicated, to a large extent, on availability of long records of high quality climate data. Although recent advances in satellite technology have improved our observation capabilities, past records come from traditional in situ measurements that have large associated uncertainties. Further, the uncertainties in historical observations vary significantly over space and in time. The information on uncertainty that is available with latest datasets is vastly ignored in the hydrologic literature. Since any relationship linking hydrologic and climatic variables is underpinned by historical data, ignoring this uncertainty information can be misleading. In this study, a methodology is developed to incorporate the observation, uncertainty in climate data for hydrologic prediction by combining Bayesian learning theory and the concepts of robust optimization. A Bayesian variant of principal component analysis is used to propagate uncertainties in observations to derive a new representation of data with reduced dimensionality. Robust optimization is then used to obtain the parameters of the prediction model, a linear support vector machine in this case, by accounting for the uncertainty in data representation. The developed methodology is applied to make long-range prediction of Indian summer monsoon rainfall (ISMR) by capturing dynamic relationships between ISMR and sea surface temperature. The advantages of incorporating observation uncertainties for hydrologic predictions are discussed in the light of results obtained.