A Scalable Approach to Fusing Spatiotemporal Data to Estimate Streamflow via a Bayesian Network

Flow of water through stream networks directly impacts flooding and transport of sediments and pollutants in watershed systems. Hence, knowledge of streamflow is critical for water management and mitigation of flooding and drought events. Unfortunately, spatially dense networks of in situ streamflow measurements are generally unavailable and would be prohibitively expensive to deploy and maintain. Thus, a data fusion framework is needed that utilizes available data to predict streamflow. Observed data in spatial (e.g., topography and land cover), temporal (e.g., streamflow and groundwater levels), and spatiotemporal domains (e.g., rainfall) impact streamflow. Some of these quantities can be obtained from remote sensing imagery; however, combining such disparate data types using traditional data fusion methods is problematic. Physically based hydrologic models have been used to predict streamflow but often with significant uncertainty because numerous assumptions are made for many unmeasured input and parameter values. Traditional Bayesian inference approaches suffer from superlinear increases in computational complexity as the number of data sets to be fused grows. In this paper, a scalable spatiotemporal approach based on Bayesian networks (BNs) is presented for estimating streamflow. An information-theoretic methodology based on conditional entropy is employed to quantify the impact of adding nodes in the BN in terms of information gained. The framework offers the flexibility of embedding knowledge from hydrologic models calibrated for the study area by introducing them as additional nodes in the network, thereby improving prediction accuracy. Posterior probabilities of estimates and the associated entropy provide valuable information on the quality of predictions and also offer directions for future watershed instrumentation.