Stage-dependent hydraulic and hydromorphologic properties in stream networks translated into response functions of compartmental models

Abstract

► A distributed non-uniform quasi-steady routing model was developed and applied. ► The travel time within the stream network was derived as a function of discharge. ► A non-linear relationship between travel time distributions and discharge was shown. ► The stage dependent travel time was used to parameterize a hydrological model. ► Predictions were improved using this parameterization, particularly for peak flows. A distributed non-uniform routing model was constructed and applied to two stream networks in southern Sweden to investigate the effects of stage, topology and morphology on advective travel times within the stream networks. Using particle-tracking, we found markedly non-linear relationships between travel time distributions and discharge for both catchments under a range of hydraulic conditions, represented by discharges comprising percentiles between 30 and 99.9 extracted from the discharge data set for the two catchments in this study. The travel time distributions from the particle tracking were used to numerically parameterise the response function of a lumped hydrological model, which resulted in improvements, particularly in the prediction of high flows. A sensitivity analysis was performed on the routing procedure, particularly regarding the choice of Manning’s friction coefficient and the choice of generic cross-sectional areas along the two stream networks showing that the uncertainty in routing parameters did not have a major effect on the final hydrograph. The new parameterisation performed better than the conventional model in every modelled case. A theoretical demonstration shows that correct descriptions of streamflow processes becomes more important with increased watershed scale, because the travel time within the stream network relative to the travel time on hillslopes increases with the watershed scale. The topology and topography of the stream network were shown to be the major factors influencing the network averaged travel time. These results demonstrate that physically based response functions (and model parameters) can be superior to compartmental model parameters that are based on numerical calibration and that are extrapolated to account for conditions during hydrological extremes.