On the Relationship Between Flood and Contributing Area

Abstract. While it is well known that the vast majority of the time only a portion of any watershed contributes runoff to the outlet, this extent is rarely documented. The power-law form of the streamflow and contributing area (Q-A_c) relationship has been known for a half century, but it is uncommon for it to be quantified or its controls evaluated. In this study a semi-distributed hydrological model (MESH-PDMROF) that can simulate contributing area and streamflow was employed to compare contributing area and flood frequency distributions in a southern Manitoba, Canada catchment and test the hypothesis that the relationship between a catchment’s floods and contributing area is a power function that influences the form of regional flood-area relationships. The model simulated streamflow reasonably well (Nash Sutcliffe values = 0.62). Modelled estimates of the area contributing to the mean annual flood were much lower (0.3) than those derived from independent topographic analysis (0.9) described in earlier literature, even after bias and error corrections. Estimates of the coefficient and exponent of the Q-A_c power law function ranged from 0.08–0.14 and 0.9–1.12, respectively. Lower exponent values of regional flood frequency curves suggest they are a construct of Q-A_c curves from individual basins. The non-linear nature of this relationship implies any contributing area change will have a profound impact on flood magnitude. The mean annual flood of the major river in this region, the Red, has increased 33 % since 1987. Applying the coefficient and exponent ranges above suggests this is associated with an expansion in contributing areas of 29–38 %. There are implications for the attribution of causes and mitigation of nutrient transport from regional watersheds. However, how physiography and land and water management could change Q-A_c power law exponents is poorly known and MESH-PDMROF does not provide explicit estimates of the spatial distribution of contributing area. These are areas encouraged for future research.