Appraisal of Statistical Predictability under Uncertain Inputs: SST to Rainfall

Abstract

Climatic variables that are used as inputs in hydrologic models often have large measurement uncertainties that are mostly ignored in hydrologic applications because of lack of appropriate tools. This study develops a set of algorithms to engage uncertainty information in three of the most common statistical procedures applied on climatic data, namely correlation (BaNCorr), principal component analysis (VBaNPCA), and regression (VNRVM). These new algorithms are developed within a common framework of Bayesian learning, and together they provide a comprehensive tool to account for uncertainty in various stages of model development. The developed algorithms are first tested and compared with traditional methods and state-of-the-art algorithms on synthetic data. Practical application of the proposed algorithms is demonstrated by developing a seasonal prediction model for all India summer monsoon rainfall by using sea surface temperature (SST) data and associated measurement errors as inputs. The results suggest that incorporating measurement errors in hydrologic models improves their prediction performance and provides better assessment of their predictive capabilities.