A geomorphic perspective on discharge–area relationships

Abstract

AbstractIt is well‐documented that the discharge‐area power‐law scaling exponent (θ) can be much lower than 1 during peak flow periods. A physical explanation for this phenomenon is generally given with the help of the channel network width function, which represents pure surface flow (PSF). When PSF ceases to dominate, θ is expected to increase due to the increasing contribution of mixed surface sub‐surface flow (MSSF) and approach 1. However, to our knowledge, no study thus far has conducted a systematic investigation of the variation of θ. In this study, we use a channel network morphology‐based routing model that considers both PSF and MSSF to investigate the variation of θ across the streamflow spectrum. The model captures the increasing trend of θ quite well during recession periods, attributable to the growing dominance of MSSF. We also demonstrate that the analysis of the discharge‐area scaling is further complicated by several factors, including spatio‐temporal variation of rainfall. The uniqueness of the model is that it suggests θ to assume values much greater than 1 because the flow in smaller basins decreases at a higher rate during late recession periods. Demonstrating this effect using observed data is difficult since obtaining sufficiently long recession curves is practically challenging. However, the predicted trend of θ is well supported by observed data when we perform percentile‐based discharge‐area scaling analysis. Our results thus indicate the possibility that a basin is not merely a sum of its hillslopes, with far‐reaching consequences for modelling hydrological and ecological phenomena.