Forested hillslope water budget uncertainty: understanding the pathway from precipitation to biota to stream discharge

Hillslopes provide the necessary scale for linking the hydrological processes that connect precipitation to stream discharge, making them ideal for improving our mechanistic understanding of local water budgets. Critical mechanisms affecting hillslope water flow include surface terrain, subsurface flow paths, and biota. These mechanisms are represented conceptually through the use of water budgets; however, it is important that such models are informed by data, and quantify the uncertainty in simulated hydrological fluxes. Our study site in southeast Wyoming is a montane riparian area hosting a loosing stream. Analyses from the water budget analysis conducted over a week's time indicates an ET flux of 3.5 mm/day, stream discharge of -4.1 mm/day, soil moisture depletion of 0.6 mm/day, and loss of 1.2 mm/day to groundwater recharge. We are testing a phenomenological‏ hillslope water budget model against this data that describes uncertainty associated with hydraulic fluxes through the use of a spatially-explicit Bayesian hierarchy. Data to be integrated include transient, 3D estimates of soil moisture using electrical resistivity tomography (ERT) and ground water monitoring, evapotranspiration through Bowen ratio and Granier sap flux sensors, and stream flow measurements. We model the flow of water in each component acknowledging four sources of error: 1) uncertainty in the flux measurements, 2) uncertainty in driving forces, 3) uncertainty in scaling, 4) uncertainty in the process itself. This uncertainty will be carried throughout, affecting other water budget processes, and eventual probabilistic estimates of stream discharge. Our goals for this work include 1) identifying which hydrological processes are associated with the highest amount of uncertainty, 2) proposing ways in which uncertainty associate with such processes could be reduced, and 3) providing more accurate probabilistic predictions of hydraulic fluxes when compared to traditional frequentist approaches. Considering that water budgets are never free of error,, including a Bayesian hierarchical infrastructure elucidates which sources of uncertainty are largest and provide probabilistic statements on how to reduce the uncertainty.