Doing Hydrology Backwards—Analytic Solution Connecting Streamflow Oscillations at the Basin Outlet to Average Evaporation on a Hillslope

Abstract

The concept of doing hydrology backwards, introduced in the literature in the last decade, relies on the possibility to invert the equations relating streamflow fluctuations at the catchment outlet to estimated hydrological forcings throughout the basin. In this work, we use a recently developed set of equations connecting streamflow oscillations at the catchment outlet to baseflow oscillations at the hillslope scale. The hillslope-scale oscillations are then used to infer the pattern of evaporation needed for streamflow oscillations to occur. The inversion is illustrated using two conceptual models of movement of water in the subsurface with different levels of complexity, but still simple enough to demonstrate our approach. Our work is limited to environments where diel oscillations in streamflow are a strong signal in streamflow data. We demonstrate our methodology by applying it to data collected in the Dry Creek Experimental Watershed in Idaho and show that the hydrology backwards principles yield results that are well within the order of magnitude of daily evapotranspiration fluctuations. Our analytic results are generic and they encourage the development of experimental campaigns to validate integrated hydrological models and test implicit parameterization assumptions.

Keywords

• dynamical systems
• surface hydrology
• hillslope model
• model inversion