An Analysis of River Bank Slope and Unsaturated Flow Effects on Bank Storage

1 An Analysis of River Bank Slope and Unsaturated Flow Effects on Bank Storage Rebecca Doble1, Philip Brunner2,3, James McCallum2,4, and Peter G. Cook2,4,5 Abstract Recognizing the underlying mechanisms of bank storage and return flow is important for understanding streamflow hydrographs. Analytical models have been widely used to estimate the impacts of bank storage, but are often based on assumptions of conditions that are rarely found in the field, such as vertical river banks and saturated flow. Numerical simulations of bank storage and return flow in river-aquifer cross sections with vertical and sloping banks were undertaken using a fully-coupled, surface-subsurface flow model. Sloping river banks ◦ were found to increase the bank infiltration rates by 98% and storage volume by 40% for a bank slope of 3.4 from ◦ horizontal, and for a slope of 8.5 , delay bank return flow by more than four times compared with vertical river banks and saturated flow. The results suggested that conventional analytical approximations cannot adequately be ◦ used to quantify bank storage when bank slope is less than 60 from horizontal. Additionally, in the unconfined aquifers modeled, the analytical solutions did not accurately model bank storage and return flow even in rivers with vertical banks due to a violation of the dupuit assumption. Bank storage and return flow were also modeled for more realistic cross sections and river hydrograph from the Fitzroy River, Western Australia, to indicate the importance of accurately modeling sloping river banks at a field scale. Following a single wet season flood event of 12 m, results showed that it may take over 3.5 years for 50% of the bank storage volume to return to the river. Introduction saline, bank storage can provide a fresh source of ground- Bank storage is an important hydrological process. water to streams for sustained periods of time following It can reduce flood intensity at downstream sites as the flow events. flood hydrograph peak is reduced and delayed because Analytical models are widely used for estimating the event water is stored within the saturated and unsatu- dynamics of bank storage. Cooper and Rorabaugh (1963) rated zones of the alluvial aquifer. Bank storage then provided analytical solutions for changes in watertable, sustains flow in streams for some time after flood events as flow, and bank storage occurring from a single flood wave the stream stage recedes. Where regional groundwater is oscillation in both finite and semi-infinite aquifers with a vertical river bank. They showed that in infinite aquifers, the return flow from bank storage after the flood wave has passed is very slow, with 50% of the bank storage volume 1 Corresponding author: Water for a Healthy Country, National returned to the river after 1.3 flood wave periods (t = τ) Research Flagship, CSIRO Land and Water, Adelaide, SA, Australia; [email protected] and 90% returned after 18 flood wave periods. Rorabaugh 2School of Chemistry, Physics and Earth Sciences, Flinders (1964) then used these models to estimate changes in bank University, Adelaide, Australia. storage and groundwater contribution to streamflow for 3Centre for Hydrogeology and Geothermics, University of the Bitterroot River basin in Montana, USA. This included Neuchatel,ˆ Switzerland. groundwater recharge from irrigation and precipitation. 4National Centre for Groundwater Research and Training, Adelaide, SA, Australia. Hall and Moench (1972) applied the convolution 5Water for a Healthy Country, National Research Flagship, equation to solve for groundwater flow and head varia- CSIRO Land and Water, Adelaide, SA, Australia. tions due to stream perturbations for four idealized cases 2 of finite and semi-infinite aquifers with and without semi- could not determine how these variables affected the rate pervious stream banks. This allowed input flood pulses of return flow. of an arbitrary shape to be used. Moench et al. (1974) McCallum et al. (2010) modeled solute dynamics then used the convolution equation to model channel loss during bank storage and return flow for confined and and base flow resulting from a reservoir release in cen- unconfined aquifers and rivers with vertical banks, includ- tral Oklahoma. On the basis of this method, Hunt (1990) ing single wave and multiple streamflow wave events. used a perturbation approach to calculate an approximate They observed vertical head gradients present in the unsat- flood-routing solution for the coupled groundwater and urated models due to the pressure head moving more open channel flow equations in order to apply the bank quickly in the deep part of the aquifer than at the water storage effects discussed in the study by Moench et al. table. As a result, they suggested that it was important to (1974) longitudinally down a river. model the unsaturated zone near the stream environment Limitations to the above-mentioned bank storage to accurately simulate the bank storage process. The study models include assumptions of homogeneity, valid also showed that including the unsaturated zone reduced Dupuit-Forchheimer conditions, fully penetrating streams, the magnitude of the return flow peak compared with mod- vertical river banks, and bank storage return under els that assume saturated flow conditions. saturated conditions. These conditions are rarely found For the conceptual approach of MODFLOW 2000 in the field, as highlighted by Sharp (1977). From our (Harbaugh et al., 2000), it is assumed that the stream is a best knowledge, all of the analytical solutions are based rectangular shape with vertical banks and flux exchange on these assumptions. A quantitative assessment of most through the stream bed. To model rivers with sloping of these assumptions, however, has so far not been banks, it would be necessary to create a stepped river carried out. profile with localized fine discretization, or use a depth Whiting and Pomeranets (1997) modeled return flow dependent conductance term, which may be possible with after an instantaneous river stage reduction from alluvial the SFR2 package of MODFLOW (Niswonger and Prudic, aquifers using a two-dimensional (2-D) numerical model 2005). with a free surface watertable and partially penetrating This paper explores the implications of assuming a river. For the widest floodplain scenario presented, results vertical river bank and not allowing for variable satura- were similar to those of Cooper and Rorabaugh (1963) and tion for calculations of bank storage fluxes and the return Rorabaugh (1964), with depletion of bank storage taking flow. Generic simulations use a regular cosine-wave vari- over 7 months for 50% of the water to drain from the ation in the river level and a triangular-shaped river to bank for a sand aquifer. Recently, Chen and Chen (2003) explore the role of bank slope on bank storage processes. and Chen et al. (2006) modeled streamflow infiltration and Additional simulations using more realistic river hydro- bank storage changes in a partially penetrating stream graph and floodplain geometries have been modeled on due to stage fluctuations using the numerical groundwa- the Fitzroy River in Western Australia. ter model, MODFLOW. They noted changes in the rate of infiltration and baseflow as a response to a series of param- eters, including river hydrographs, hydraulic conductivity Conceptualization and Model Development of the streambed and the underlying aquifer, and regional groundwater gradients. Both of these studies assumed ver- Generic Simulations tical river banks, and did not explicitly model unsaturated Generic simulations of a river-aquifer transect per- zone processes using the full Richards Equation. pendicular to the river were developed, based on the The first study to look at the impacts of sloping semi-infinite aquifer example in the study by Cooper river banks was done by Li et al. (2008a). Dimensionless and Rorabaugh (1963), but additionally including unsatu- numerical simulations were undertaken to quantify bank rated subsurface and surface flow domains. Rather than a storage in variably saturated, homogeneous, anisotropic vertical bank for the stream-aquifer interface, the model aquifers with fully penetrating rivers with variable bank domain included a sloping section (Figure 1). Bank stor- slopes, as a result of a simulated flood event using the age and return flow in a river with a straight, but sloping model described by Boufadel et al. (1999). The study bank could then be simulated, allowing for direct com- determined that bank storage was an increasing func- parison with the Cooper and Rorabaugh (1963) analytical tion of the rate of stream level rise, that smaller domain solution. We initially model changes in head in the river aspect ratios (or smaller bank slope) resulted in larger following a cosine river stage input. Flow in the river is bank storage volumes due to a larger bank surface area not simulated, but represented using a specified head for a given river stage. They also included an unsaturated boundary in the surface water domain. zone, showing that materials with a low capillary suction The problem to be modeled involved both resulted in higher volumes of bank storage. Also using surface-water and porous media domains, therefore the dimensionless numerical relationships, Naba et al. (2002) fully-coupled, surface-subsurface flow model HydroGeo- and Li et al. (2008b) modeled similar problems associated Sphere (Therrien et al., 2006) was used. HydroGeoSphere with seepage flows and tidal seawater-groundwater inter- simultaneously solves the diffusion-wave approximation actions. The model used did not, however, consider the of the Saint Venant equation for surface water flow, return flow of bank storage into the river, and therefore and the Richards’ equation governing three-dimensional 3 (a) (b) Figure 1. Bank cross sections used in the study with (a) vertical and (b) sloping river/aquifer interfaces (not to scale). Bank angle (α) is defined in degrees from a horizontal plane. Actual aquifer dimensions are 4 m thick and 250 m long. (3-D) unsaturated/saturated subsurface flow with a phys- equation: ical coupling between the two domains.

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