Quantifying spatio-temporal stream-aquifer exchanges: upscaling local measurements to watershed-scale predictions

We present a physically-based upscaling approach for estimating spatially-distributed stream-aquifer exchanges at the watershed scale. The approach relies on local measurements, geostatistical analysis and integrated surface-subsurface numerical modeling. First, we estimate local properties in the hyporheic zone at the point scale ( 1m). The estimation is based on local in situ-measurements consisting in the coupling of vertically-distributed temperature timeseries and hydraulic head differential timeseries (mini-LOMOS). Using a Bayesian inverse modeling approach, we derive the statistical distributions of hydrological and thermal parameters at a number of distinct locations distributed along the hyporheic corridor. We then study the spatial distribution of hydraulic conductivity along the hyporheic corridor. Using geostatistical tools, we derive a spatial law describing its variability along the hyporheic corridor. To that end, we use the Matern covariance function as a general formulation of spatial correlation between parameters at any two locations. Finally, the spatial distribution of hydraulic conductivity in the hyporheic zone can be simulated along the entire hydrographic network, honoring the geostatistical spatial law and conditionally on local parameter inversions. The spatial distribution of the hyporheic zone properties can then be integrated in a numerical hydrological model simulating coupled surface and subsurface flow at the watershed scale and exchanges through the stream-aquifer interface. Spatially-distributed stream-aquifer exchanges can then be estimated at the watershed scale, accounting for regional geology (through the numerical model) and local-scale heterogeneity of hyporheic properties (through geostatistical modeling). We demonstrate this upscaling strategy on the 48-km² Avenelles basin, France. This upscaling approach from the local to the watershed scale could be applied in further studies to quantify the consequences of local physical processes on watershed-scale water availability and quality.