2.3 Numerical Modeling
We numerically simulated all flume runs in HydroGeoSphere to visualize
longer duration flow paths moving through the subsurface (Aquanty Inc.
2015; Brunner & Simmons, 2012). The model domain mirrors our flume
dimensions of 1.2 m wide, 9.0 m long, and 0.1 m deep. We defined the
base and sides of the model as no-flow boundaries to represent the
bottom and sides of the flume environment. At the upstream boundary of
the flume domain, a specified inflow flux was assigned to simulate the
stepped spillway. At the downstream outlet, a critical depth boundary
condition was given to match flume observations.
The HydroGeoSphere model solves wave approximations of the Saint Venant
equation for surface flow, the Richards equation for subsurface flow,
and the advection-dispersion-diffusion equation for groundwater age. The
surface flow equation is solved on a 2-D finite-element mesh stacked
upon the subsurface grid. The surface of the model domain was
discretized with an unstructured, triangular mesh with maximum element
length of 2.0 cm. For comparison, the grain diameter of flume sediments
ranges up to 17 mm, therefore choosing a finer mesh would have been
inconsistent with the concept of a porous continuum. The subsurface
domain of our model is discretized into ten vertical layers. The three
near-surface sediment layers represent the gravel and coarse sand top
coat layer of the flume and are assigned element heights of 0.005 m and
hydraulic conductivity of 2.5×10-3 m/s. The deeper
seven mesh layers represent the underlying coarse sand layer and are
assigned an element height of 0.028 m and hydraulic conductivity of
8.9×10-5 m/s. Sediment hydraulic properties are
consistent with Wilhelmsen et al. (2021) (Table 3). Logjams were
simulated as a porous medium with varying permeability (Table 3) to test
the effect of this parameter on hyporheic flow and subsurface transient
storage. The hydraulic conductivity of the more permeable logjam(s) is 1
m/s, while the value for less permeable logjam(s) is 0.5 m/s. It is
important to note that because we treat the jams as a porous medium, we
also chose to include flow paths through the jams as part of
“subsurface” transient storage.
For each simulation in HydroGeoSphere, we visualized subsurface flow
paths in Tecplot. We also visualized groundwater age throughout the
subsurface, which was computed using the groundwater age mass-transport
equation embedded in HydroGeosphere. Groundwater age is similar in
concept to a residence time and includes the effects of both advection
and dispersion (Therrien et al. 2006). We calculated this age only for
visualization purposes, as it could not be used to construct residence
time distributions because of the zero-age boundary condition at the
bottom of the water column. To compute residence time distributions in
the subsurface, we released particles at the water-sediment or water-jam
interface and analyzed the flux-weighted residence times of the
9000-18000 particles that returned to the surface water. From the
flux-weighted residence time distribution, we calculated the mean travel
time in the subsurface and the skew. It is important to note that the
model-derived mean travel time in the subsurface is not directly
comparable with the flume-derived mean travel time, as the former only
considers travel due to advection in the subsurface, while the latter
considers salt transport due to advection and dispersion in the surface
and subsurface. We report both values, as both represent different
aspects of solute travel through the interconnected stream-groundwater
system. Similarly, skew in the
model-derived hyporheic residence time distribution is not directly
comparable with skew in the salt breakthrough curve. We report both
values to quantify the weighting of longer solute residence times (in
one case, for the entire flume system, and in the other case, for the
hyporheic zone specifically). We also calculated average hyporheic
fluxes for each simulation. Model parameters are included in Table 3 and
more on the governing equations is in the Supplemental Information.
Table 2. Flume and numerical model runs with discharge and
logjam characteristics (number of jams and permeability). All runs were
conducted in flume and numerically simulated unless otherwise noted.
Replicates were run for all flume trials.