A geomorphic perspective on discharge–area relationships

It 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.