Groundwater–Surface Water Interaction—Analytical Approach

Abstract

Modelling of water flow in the hyporheic zone and calculations of water exchange between groundwater and surface waters are important issues in modern environmental research. The article presents the Analytical Hyporheic Flux approach (AHF) permitting calculation of the amount of water exchange in the hyporheic zone, including vertical water seepage through the streambed and horizontal seepage through river banks. The outcome of the model, namely water fluxes, is compared with the corresponding results from the numerical model SEEP2D and simple Darcy-type model. The errors of the AHF model, in a range of 11–16%, depend on the aspect ratio of water depth to river width, and the direction of the river–aquifer water exchange, i.e., drainage or infiltration. The AHF model errors are significantly lower compared to the often-used model based on vertical water seepage through the streambed described by Darcy’s law.

Modelling of Groundwater–Surface Water Interaction Applying the Hyporheic Flux Model

“…The approach suggested by Nawalany et al [25] adds a lateral term in the interaction between river and aquifer called the recharge/discharge bank. Figure 2 shows the adaptation of the equation of Nawalany et al [25] to the MODFLOW scheme. This approach implemented in MODFLOW takes into consideration the river as a seepage boundary condition with the package RECHARGE.…”

“…D a i,j is the thickness of the aquifer beneath river sediments cell location (i,j) (L), W r is the half-width of the river (L), and W rs is the half-width of river sediments (L). Applying the assumptions of Nawalany et al [25] in this domain, it is possible to establish the relationships described in Equations 1and 2, where…”

“…On the other side, the flow in subdomain P.2, i.e., in the part of the aquifer under the river bottom sediments of P.4, is also described by the Laplace equation for y ∈ [0, Wr], z ∈ [0, Da]. Nawalany et al [25] determined Equations 3and 4.…”

“…This document will present a new analytical model-the Analytical Hyporheic Flux model (AHF). The model allows estimating the seepage at river banks through a riverbed using a simplified geometry [25].…”

“…The AHF model allows calculating the amount of water exchange in the hyporheic zone, including both vertical water seepage through the streambed and seepage through riverbanks. The analytical model assumes a simplified rectangular geometry of the river bed cross-section [25].…”