Inverse streamflow routing
The process whereby the spatially distributed runoff (generated through saturation/infiltration excesses, subsurface flow, etc.) travels over the hillslope and river network and becomes streamflow is generally referred to as "routing". In short, routing is a runoff-to-streamflow process, and the streamflow in rivers is the response to runoff integrated in both time and space. Here we develop a methodology to invert the routing process, i.e., to derive the spatially distributed runoff from streamflow (e.g., measured at gauge stations) by inverting an arbitrary linear routing model using fixed interval smoothing. We refer to this streamflow-to-runoff process as "inverse routing". Inversion experiments are performed using both synthetically generated and real streamflow measurements over the Ohio River basin. Results show that inverse routing can effectively reproduce the spatial field of runoff and its temporal dynamics from sufficiently dense gauge measurements, and the inversion performance can also be strongly affected by low gauge density and poor data quality.
The runoff field is the only component in the terrestrial water budget that cannot be directly measured, and all previous studies used streamflow measurements in its place. Consequently, such studies are limited to scales where the spatial and temporal difference between the two can be ignored. Inverse routing provides a more sophisticated tool than traditional methods to bridge this gap and infer fine-scale (in both time and space) details of runoff from aggregated measurements. Improved handling of this final gap in terrestrial water budget analysis may potentially help us to use space-borne altimetry-based surface water measurements for cross-validating, cross-correcting, and assimilation with other space-borne water cycle observations.