Applying non-parametric Bayesian networks to estimate maximum daily river discharge: potential and challenges

Non-parametric Bayesian networks (NPBNs) are graphical tools for statistical inference widely used for reliability analysis and risk assessment and present several advantages, such as the embedded uncertainty quantification and limited computational time for the inference process. However, their implementation in hydrological studies is still scarce. Hence, to increase our understanding of their applicability and extend their use in hydrology, we explore the potential of NPBNs to reproduce catchment-scale hydrological dynamics. Long-term data from 240 river catchments with contrasting climates across the United States from the Catchment Attributes and Meteorology for Large-sample Studies (CAMELS) data set will be used as actual means to test the utility of NPBNs as descriptive models and to evaluate them as predictive models for maximum daily river discharge in any given month. We analyse the performance of three networks, one unsaturated (hereafter UN-1), one saturated (hereafter SN-1), both defined only by hydro-meteorological variables and their bivariate correlations, and one saturated network (hereafter SN-C), consisting of the SN-1 network and including physical catchments' attributes. The results indicate that the UN-1 network is suitable for catchments with a positive dependence between precipitation and discharge, while the SN-1 network can also reproduce discharge in catchments with negative dependence. The latter can reproduce statistical characteristics of discharge (tested via the Kolmogorov–Smirnov statistic) and have a Nash–Sutcliffe efficiency (NSE) ≥0.5 in ∼40 % of the catchments analysed, receiving precipitation mainly in winter and located in energy-limited regions at low to moderate elevation. Further, the SN-C network, based on similarity of the catchments, can reproduce discharge statistics in ∼10 % of the catchments analysed. We show that once a NPBN is defined, it is straightforward to infer discharge and to extend the network itself with additional variables, i.e. going from the SN-1 network to the SN-C network. However, the results also suggest considerable challenges in defining a suitable NPBN, particularly for predictions in ungauged basins. These are mainly due to the discrepancies in the timescale of the different physical processes generating discharge, the presence of a “memory” in the system, and the Gaussian-copula assumption used for modelling multivariate dependence.