Streamflow Reconstruction in the Upper Missouri River Basin Using a Novel Bayesian Network Model

Abstract

A Bayesian model that uses the spatial dependence induced by the river network topology, and the leading principal components of regional tree ring chronologies for paleo‐streamflow reconstruction is presented. In any river basin, a convergent, dendritic network of tributaries come together to form the main stem of a river. Consequently, it is natural to think of a spatial Markov process that recognizes this topological structure to develop a spatially consistent basin‐scale streamflow reconstruction model that uses the information in streamflow and tree ring chronology data to inform the reconstructed flows, while maintaining the space‐time correlation structure of flows that is critical for water resource assessments and management. Given historical data from multiple streamflow gauges along a river, their tributaries in a watershed, and regional tree ring chronologies, the model is fit and used to simultaneously reconstruct the full network of paleo‐streamflow at all gauges in the basin progressing upstream to downstream along the river. Our application to 18 streamflow gauges in the Upper Missouri River Basin shows that the mean adjusted R2 for the basin is approximately 0.5 with good overall cross‐validated skill as measured by five different skill metrics. The spatial network structure produced a substantial reduction in the uncertainty associated with paleo‐streamflow as one proceeds downstream in the network aggregating information from upstream gauges and tree ring chronologies. Uncertainty was reduced by more than 50% at six gauges, between 6% and 50% at one gauge, and by less than 5% at the remaining 11 gauges when compared with the traditional principal component regression reconstruction model.

Informing Seasonal Proxy‐Based Flow Reconstructions Using Baseflow Separation: An Example From the Potomac River, United States

“…Records of tree growth have been used to reconstruct short‐term precipitation events (e.g., Howard & Stahle, 2020) and such records most likely contain a strong stormflow signal. The spatial correlation of flow in snowpack driven basins has been shown to have significant skill in predicting downstream gages (Ravindranath et al., 2019) and similarly, independent seasonal reconstructions may add skill from temporal persistence. It is likely that there are locations where both baseflow and stormflow could be reconstructed separately if utilizing both EW and LW records of multiple species.…”

“…The extrapolation of warm season streamflow signal in tree rings has also been shown to have skill on bi‐weekly to monthly scales (Sauchyn & Ilich, 2017; Stagge et al., 2018). Although significant work has been done to improve our understanding of the predictor variables of tree‐ring based streamflow reconstruction, including predictor selection (Ho et al., 2016; Saito et al., 2008; Strange et al., 2019), standardization techniques (Meko et al., 2015), and the application of Bayesian modeling (Devineni et al., 2013; Ravindranath et al., 2019), less attention has been given to the target variable to be reconstructed—the instrumental streamflow data.…”

“…application of Bayesian modeling (Devineni et al, 2013;Ravindranath et al, 2019), less attention has been given to the target variable to be reconstructed-the instrumental streamflow data.…”

A Bayesian Hierarchical Network Model for Daily Streamflow Ensemble Forecasting

“…In order to model the daily streamflow at n ‐2 locations simultaneously, the model structure takes advantage of the feature of the river network by treating the streamflow processes as a spatial Markov process (Ravindranath et al., 2019). Flow at a downstream gauge, i , on day t is dependent on: flow at the most immediate ( i +1) or second most immediate ( i +2) upstream feeder gauge at day t−k with ( k represents the lead time of the forecast); precipitation and other hydrometeorological variables that represent local inputs to the streamflow between the streamflow gauges.…”

“…Our research in this paper is motivated by the need for a daily streamflow modeling framework on a river network for potential use in real-time forecasting, that can capture the space-time dependence structure, and robust estimation of uncertainties. To this end, we develop a novel Bayesian Hierarchical Network Model (BHNM) inspired by the framework proposed in Ravindranath et al (2019). We demonstrate this framework by its application to model and predict daily summer monsoon (July-August) streamflow at three gauges in the Narmada River Basin network in central India.…”