Diagnostic Analysis of Bank Storage Effects on Sloping Floodplains

Abstract

Stream bank storage effects during floods have received limited attention, despite the significant role of such floods in aquifer water budgets. One reason is the complexity of geometry of the problem, which commonly has been treated numerically. Using a simple model in a domain with moving boundary, a semianalytical solution for bank storage effects is proposed to account for stream stage hydrograph, floodplain slope, and aquifer parameters. The results extend classic solutions by Cooper and Rorabaugh (1963, https://doi.org/10.3133/wsp1536J) for idealized vertical streambanks but applied to realistic floodplain cross sections. The accuracy of the semianalytical solution is verified by a one‐dimensional numerical method and compared to a vertical two‐dimensional variably saturated‐flow numerical model. Comparison indicates that a robust solution is valid for diagnostic analyses of modeling bank storage effects on floodplains. The semianalytical solution is applied to laboratory experiments as well. The results indicate that the present solution provides reasonable estimates of peak timing and head of groundwater flow response in the sloping bank during varying stream stage.

On River‐Aquifer Exchange Flow With Irregular and Semipervious Bank

“…Instead of using the linearized BEQ, Jiang and Tang (2015) and Tang et al (2016) solved the nonlinear 1-D BQE by exploiting a decomposition method which separates the nonlinear BQE into a linear equation and a head correction equation to derive approximate analytical solutions of BQE with a sloping surface water-groundwater boundary. Liang et al (2020) proposed a semi-analytical solution which can be used to analyze the responses of bank storage to any variation in river stage under the situation of single or multiple bank slopes.…”

“…where D is often called the aquifer hydraulic diffusivity, (L 2 T −1 ), C represents the riverbank conductance, (T −1 ). In the following, we will develop a new semi-analytical solution by solving Equations 8-10 using the similar procedures of Liang et al (2020).…”

“…The hydraulic conductivity of the aquifer K a = 10 m d −1 is used and this value is identical as the saturated horizontal K a of the 2-D numerical model. The value of specific yield of the aquifer S y is taken as the difference between θ s and θ r , and is generally reasonable for the sandy aquifer (Johnson, 1967;Liang et al, 2020). Some discrepancies occur between the solutions of the new 1-D and the 2-D numerical models, and are attributed to the following two reasons (Liang et al, 2020).…”

“…The value of specific yield of the aquifer S y is taken as the difference between θ s and θ r , and is generally reasonable for the sandy aquifer (Johnson, 1967;Liang et al, 2020). Some discrepancies occur between the solutions of the new 1-D and the 2-D numerical models, and are attributed to the following two reasons (Liang et al, 2020). First, the vertical flow occurs in the 2-D numerical model while the river stage rising and falling, and the presented 1-D model only considered the dominantly horizontal flow.…”

“…For a river bounded by an irregular bank, as stage fluctuates, the free water surface of the river spreads/shrinks in the horizontal direction over the irregular bank (Figure 1). The horizontal extension/ shrinkage of river water surface can closely affect the exchange flow between the river and its adjacent aquifer, but it can not be captured by the conventional vertical bank approximation (Doble et al, 2012;Liang et al, 2020). For example, by undertaking numerical simulations of variably saturated aquifers with rivers bounded by a sloping bank, Doble et al (2012) and Li et al (2008aLi et al ( , 2008b and Liang et al (2020) indicated that the temporally horizontal extension/shrinkage of river water surface over nonvertical banks can greatly increase the bank infiltration rate, storage volume and the head responses of an aquifer to its adjacent surface water level fluctuations compared with the conventionally assumed vertical banks.…”