Abstract
Abstract. 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.
Highlights
Runoff is a very important component in the terrestrial water budget in terms of both its magnitude and temporal variability (Hagemann and Dumenil, 1998; Pan et al, 2012)
We choose the University of Washington (UW) routing model (Lohmann et al, 1996, 1998), which is a relatively simple linear routing model developed for coupling with land surface models (LSMs), and it has been calibrated, implemented and validated in many large-scale streamflow studies (Mitchell et al, 2004; Nijssen et al, 1997)
The UW routing model is fully contained in Eq (8), and, in short, the streamflow at a gauge point is nothing but the sum of runoff from all contributing pixels in all possible lag times weighted by the overall impulse response function (IRF)
Summary
Runoff is a very important component in the terrestrial water budget (precipitation, evapotranspiration, runoff, and soil/snow water storage) in terms of both its magnitude and temporal variability (Hagemann and Dumenil, 1998; Pan et al, 2012). The question for our study is how to bridge the gap between streamflow and runoff in both time and space, i.e. to derive the spatial fields of runoff from streamflow measurements at gauging points, such that our water budget analysis or any related studies are no longer limited by the gap between the two This requires us to invert the routing process and invent a way to realize the streamflow-torunoff conversion. The streamflow values are always correlated in time as a result of the time integration nature of the routing process, and that implies the unknown runoff fields across multiple time steps need to be solved together, which dramatically increases the size of the estimation problem (number of simultaneous unknowns) For these above reasons, we look for a linear routing model to invert such that the most efficient methods for linear systems like Kalman filters/smoothers (Anderson and Moore, 1979; Kalman, 1960) can be applied.
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