Complexity-based robust hydrologic prediction: extension of statistical learning theory to conceptual hydrological models

The applications of statistical learning theory (SLT) in hydrology have been either in the form of Support Vector Machines and other complexity regularized machine learning algorithms that learn and predict input-output patterns such as rainfall-runoff time series or of identifying optimal complexity of low order models such as k nearest neighbour models to predict hydrological time series such as streamflow. The regularization of model complexity offers a way to identify minimal complexity of a model to accurately predict a time series of interest. However such applications often assume that the modelled residual are independent of each other. This limits its application to conceptual hydrological models where residuals are often auto-correlated. This paper applies recent results of risk bounds for time series forecasting and SLT approaches to dynamical system identification to conceptual hydrological models, offering a means to identify optimal complexity of conceptual models and complexity regularised streamflow predictions based on it.

Basins from CAMELS data set are used to demonstrate the effect of regularizing the problem of hydrological model calibration on streamflow prediction over unseen data. SAC-SMA and SIXPAR (a lower order version of SACSMA) are used as model examples. Preliminary results show that prediction uncertainty bounds are narrower if regularization does not improve the performance of a calibrated model over unseen data. This effect is stronger in drier basins than in humid ones. Also, as expected, this effect is stronger when training data size is small and holds for both SACSMA and SIXPAR.