Environmental Engineering Reference
In-Depth Information
beds are represented by active model layers,
flow through the beds to the aquifer is calcu-
lated by the model according to Equation (
3.8
).
When confining beds and other overlying layers
are not actively represented in a model, vertical
flux to the aquifer may be represented as a con-
stant or head-dependent flux, as described in
this section. Groundwater modelers commonly
refer to this flux as recharge. In the terminology
introduced in
Section 1.2
, flow through confin-
ing layers to an aquifer is referred to as inter-
aquifer flow instead of recharge. Regardless of
terminology, this flux is often an important
source of water for the aquifer. For modeling
purposes, flux through a confining layer can
be simulated as diffuse recharge by using the
Recharge Package of MODFLOW-2005. Inverse
groundwater-flow modeling is a useful tool for
estimating interaquifer flow.
Stoertz and Bradbury (
1989
) described a pro-
cedure that uses a groundwater-flow model to
calculate recharge at every water-table cell. A
water-table map was drawn by hand for the
model domain and superimposed on a two-
dimensional horizontal grid. The mapped
water-table elevation at each nodal location
was assigned to that node. All nodes were set as
constant head boundaries. MODFLOW was then
used to simulate groundwater flow. Because all
cells were constant head, no new head values
were calculated, but fluxes between cells were
calculated by the model. Net flux through each
cell is equal to the difference between outflow
to adjacent cells and inflow from adjacent cells.
The net flux must be balanced by flow into the
cell from the constant head boundary, which is
by definition recharge. In addition to water lev-
els, the method requires estimates of hydraulic
conductivity and aquifer thickness. The method
is perhaps of most use in a qualitative sense,
identifying areas of recharge and discharge,
and in that sense the method may be useful
for aquifer vulnerability studies. Quantitative
estimates of recharge by this method are prob-
lematic because calculated recharge rates are
linearly related to hydraulic conductivity; if
hydraulic conductivity is doubled, the calcu-
lated recharge is also doubled. This method has
been used in a number of studies (Hunt
et al
.,
1996
; Gerla,
1999
; Lin and Anderson,
2003
). Lin
et al
. (
2009
) developed a GIS application that
uses a similar approach for estimating recharge
and discharge rates; their approach has more
flexibility because it is not constrained by a
MODFLOW grid.
The analytic-element method (AEM) is an
alternative to the finite-difference and finite-
element methods for solving the groundwa-
ter-flow equation (Haitjema,
1995
). The AEM
uses superposition of an analytical solution to
Equation (
3.8
) to determine head values at any
point in the simulated domain; hence, a spatial
grid is not required. The AEM is generally not
capable of capturing the fine-scale complexities
that can be incorporated into a model such as
MODFLOW, but AEM models are relatively easy
to set up, and they can serve as useful tools for
calibrating more complex models (Hunt
et al
.,
1998
). Dripps
et al
. (
2006
) demonstrated how an
AEM model can be used in conjunction with a
parameter estimation code to derive estimates
of recharge in a small watershed in northern
Wisconsin. Model calibration was based on
matching simulated base flow with annual
average base flow as determined by streamflow
hydrograph separation (
Section 4.5
) for four
streamflow gauge sites for 5 years. Steady-state
conditions were assumed for each year. Using
best estimates of recharge, simulated base flows
were within 5% of measured values.
Example: Truckee Meadows, Nevada
In one of the first examples of automatic cali-
bration of a groundwater-flow model, Cooley
(
1979
) used regression techniques to calibrate
a steady-state groundwater-flow model of
Truckee Meadows in the Reno-Sparks area of
Nevada. Water levels in 59 observation wells
were used for model calibration. The model
domain was divided into 13 regions that were
assumed to have uniform aquifer transmis-
sivity and net recharge rate (recharge minus
groundwater evapotranspiration). Optimum
values for 22 model parameters (6 head bound-
aries, 4 transmissivities, 1 streambed conduct-
ance, and 11 recharge rates) were determined.
Overall model fit was good (R
2
> 0.99), but large
standard errors of recharge estimates, some in
