On the relationship between flood and contributing area

Abstract

Although it is well known that the vast majority of the time only a portion of any watershed contributes run‐off to the outlet, this extent is rarely documented. Also, the power law form of the streamflow and contributing area (Q‐Ac) relationship has been known for a half century, but it is uncommon for it to be quantified, and time series of contributing area extensive enough to calculate its frequency distribution are almost non‐existent. Data from the Canadian Prairies, where there are extensive estimates of contributing area during the median annual flood, imply that the power law coefficient for any Q‐Ac curve is a function of flow magnitude and return period. These data also suggest that regional flood frequency curves are a construct of Q‐Ac curves from individual basins. This paper will discuss research that attempted to reproduce the Q‐Ac curves for the La Salle River Watershed with a semidistributed numerical hydrological model, MESH‐PDMROF. The model simulated streamflow reasonably well (Nash Sutcliffe values = 0.62) compared with published examples of comparable models applied in the region. Estimates of the coefficient and exponent of the Q‐Ac power law function ranged from 0.08–0.14 and 0.9–1.12, respectively. These exponent values were lower than those of regional flood frequency curves and support the theory that regional flood frequency curves are a construct of Q‐Ac curves. Simulations of the area contributing to the median annual flood were lower (0.3) than those derived from independent topographic analysis (0.9) described in earlier literature though there is uncertainty in both these estimates. This uncertainty was extended across the flood frequency distribution and may be too large to definitively verify the study hypothesis.

Mechanisms of Cold Region Hydrologic Change to Recent Wetting in a Northern Glaciated Landscape

“…The depressional storage was finally filled by mid‐June of 2013 when the snowmelt and ROS streamflow recessed substantially. The FA ( FA = 0.5) contribution to 2013 MCB flood is comparable to FA reported by Spence and Mengistu (2019) for median flood in the La Salle River Basin. Extreme evaporation in depressions during two previous water years (2011 and 2012) and delayed melting (in 2013) in some upstream subbasins due to heavy snow accumulation resulted in poor connectivity during 2013.…”

“…Wetland depressions and their number, size, spatial distribution, and effective contributing area are responsible for lack of streamflow response to increased precipitation in the NGP region (Ehsanzadeh et al, 2012; Spence & Mengistu, 2019). The glaciated prairie landscape includes innumerable topographically closed wetland depressions of variable size and depth created by past continental ice sheets (Zhang et al, 2009).…”

Empirical modelling of snow cover duration patterns in complex terrains of Italy

“…In that way, a varying exponent not only provides a parsimonious description of the process under study, but it is also a generic mechanism governing the process. In particular, lower exponent values of mean areal response (compared to the response obtained at a single site) suggest that they are a construct (smoothing approximation) from individual sites (e.g., Spence and Mengistu 2019).…”

Multi-Decadal Variability in the Snow-Cover Reconstruction at Parma Observatory (Northern Italy, 1681–2018 CE)

“…In particular, the η exponent does not only provide a parsimonious description of the process under study, but it is also a generic mechanism governing the process. In particular, higher exponent values obtained at a single site (compared to mean areal response) suggest that they can be regarded as a method to downscale areal (smoothed out) approximations to finer units (e.g., Spence and Mengistu, 2019).…”