Theoretical link between rainfall and flood magnitude

Abstract

The rainfall-run-off convolution integral is analytically solved for several models for the elementary hydrograph. These solutions can be combined with available rainfall frequency analyses to predict flood flows along streams for different recurrence intervals, using no free parameters for gauged streams and one estimable parameter for ungauged streams. Extreme discharge magnitudes at gauged sites can be typically estimated within a factor of two of actual records, using no historical data on extreme flows. The flow predictions reproduce several important characteristics of the flood phenomenon, such as the slope of the regression line between observed extreme flows and basin area on the conventional logQ versus logA plot. Importantly, for the models and data sets investigated, the storm duration of greatest significance to flooding was found to approximate the intrinsic transport timescale of the particular watershed, which increases with basin size. Thus, storms that deliver extraordinary amounts of rainfall over a particular time interval will most greatly activate basins whose time constants approximately equal that interval. This theoretical finding is supported by examination of the regional hydrological response to the massive storms of September 14, 2008, and April 28-30, 2017, which caused extraordinary record flooding of basins of about 5-100 km 2 and 500-4,000 km 2 , respectively, but produced few records in basins that were larger or smaller than those ranges.

Dynamics of River Flood Waves below Hydropower Dams and Their Relation to Natural Floods

“…For unimpounded Missouri river basins, b in days is empirically proportional to 0.0135 times the square root of basin area in square km [36]. The rough estimate for peak velocity approximates 1.5 times the reciprocal of this number, or about 100 km/d.…”

“…Equations (7a,b) differ only in the upper limit of integration. Criss [36] provides a solution to this pair of integrals using the normalized form of Equation ( 5) as the unit response function for a situation where the perturbation F τ represents the rate of water delivery to the watershed, assumed to be constant from time zero up to time τ, and zero thereafter. These solutions can simulate streamflow variations caused by steady rainfall delivered over a stated interval, but they can also be used to simulate the flow downstream of a hydropower dam, which releases a high flow (Q i ) for a discrete period and then shuts down power production.…”

“…Equations (7a,b) differ only in the upper limit of integration. Criss [36] provides a solution to this pair of integrals using the normalized form of Equation ( 5) as the unit response function for a situation where the perturbation Fτ represents the rate of water delivery to the watershed, assumed to be constant from time zero up to time τ, and zero…”