A simple iterative method for estimating evapotranspiration with integrated surface/subsurface flow models

•A simple iterative method is derived to estimate evapotranspiration.•The convergence of the method was achieved with a reasonable number of iterations.•The method could be valuable in hydrologic systems with scarce observational data.

SummaryThis work presents an iterative, water balance based approach to estimate actual evapotranspiration (ET) with integrated surface/subsurface flow models. Traditionally, groundwater level fluctuation methods have been widely accepted and used for estimating ET and net groundwater recharge; however, in watersheds where interactions between surface and subsurface flow regimes are highly dynamic, the traditional method may be overly simplistic. Here, an innovative methodology is derived and demonstrated for using the water balance equation in conjunction with a fully-integrated surface and subsurface hydrologic model (HydroGeoSphere) in order to estimate ET at watershed and sub-watershed scales. The method invokes a simple and robust iterative numerical solution. For the proof of concept demonstrations, the method is used to estimate ET for a simple synthetic watershed and then for a real, highly-characterized 7000 km2 watershed in Southern Ontario, Canada (Grand River Watershed). The results for the Grand River Watershed show that with three to five iterations, the solution converges to a result where there is less than 1% relative error in stream flow calibration at 16 stream gauging stations. The spatially-averaged ET estimated using the iterative method shows a high level of agreement (R2 = 0.99) with that from a benchmark case simulated with an ET model embedded directly in HydroGeoSphere. The new approach presented here is applicable to any watershed that is suited for integrated surface water/groundwater flow modelling and where spatially-averaged ET estimates are useful for calibrating modelled stream discharge.