Predictor selection for streamflows using a graphical modeling approach

Streamflows are influenced by various hydroclimatic variables in complex ways. Accurate prediction of monthly streamflows requires a clear understanding of the dependence patterns among these influencing variables and streamflows. A graphical modeling technique, employing conditional independence, is adopted in this study to quantify the interrelationships between streamflows and a suite of available hydroclimatic variables, and to identify a reduced set of relevant variables for parsimonious model development. The nodes in the undirected graph represent relevant variables, and the strengths of the connections among the variables are learnt from the data. The graphical modeling approach is compared to the state-of-the-art method for predictor selection based on partial mutual information. For a synthetic benchmark dataset and a watershed in southern Indiana, USA, the graphical modeling approach shows more discriminating results while being computationally efficient. Along with artificial neural networks and time series models, results of the graphical model are used for formulating a variational relevance vector machine to predict monthly streamflows and perform probabilistic classification of hydrologic droughts in the watershed being studied. The parsimonious models developed for prediction at different lead times performed as well as the non-parsimonious models during both the calibration and testing periods. Drought forecasting for the study watershed at 1-month lead time was performed using the two selected predictors—soil moisture and precipitation anomalies alone, and the model performance was evaluated. The graphical model shows promise as a tool for predictor selection, and for aiding parsimonious model development applications in statistical hydrology.