Supplemental material for the paper:
Use of nested flow models and interpolation techniques for science-based
management at the Sheyenne National Grassland, North Dakota, USA.
M.A. Gusyev1,2, H. M. Haitjema2, C.P. Carlson3 and M.A. Gonzalez4
1: GNS Science, Lower Hutt 5010, New Zealand
Phone: +64-4-570-4396; Fax: +64-4-570-4600; e-mail: m.gusyev@gns.cri.nz
2: School of Public and Environmental Affairs, Indiana University, Bloomington, IN,
47405, USA
3: USDA Forest Service, Washington, D.C., 20250-0003, USA
4: National Riparian Service Team, Bureau of Land Management, Prineville,
OR, 97754, USA
Abstract
Noxious weeds threaten the Sheyenne National Grassland (SNG) ecosystem and
herbicides have been used for control. To protect groundwater quality, the herbicide
application is restricted to areas where the water table is less than 10 ft (3.05 m)
below the ground surface in highly permeable soils, or less than 6 ft (1.83 m) below
the ground surface in low permeable soils. A local MODFLOW model was extracted
from a regional GFLOW analytic element model and used to develop depth-togroundwater maps in the SNG that are representative for the particular time frame of
herbicide applications. These maps are based on a modeled groundwater table and a
digital elevation model (DEM). The accuracy of these depth-to-groundwater maps is
enhanced by an Artificial Neural Networks (ANN) interpolation scheme that reduces
residuals at 48 monitoring wells. The combination of groundwater modelling and
ANN improved depth-to-groundwater maps, which in turn provided more informed
decisions about where herbicides can or cannot be safely applied.
Note: For consistency some of the discussions below overlap with those in the journal
article.
Background information regarding the Sheyenne National Grassland
The Sheyenne National Grassland (SNG) is a part of the US Forest Service (USFS)
Dakota Prairie Grasslands and contains the largest publicly owned tract of the
Northern Tallgrass Prairie ecosystem. The SNG contains many of the rare, threatened,
and endangered species of the Northern Region of the USFS, which encompasses
Montana, North Dakota, and parts of Idaho and South Dakota. The SNG is located in
Ransom and Richland counties of southeastern North Dakota. The SNG
administrative boundary is shown in purple and dark green in Figure S1, with the
Forest Service-managed portion shown as dark green. The SNG occupies an area of
70,000 acres (283.27 km2) between 46034'N – 46019'N and 97028'W – 97005'W.
Underlying the SNG is the Sheyenne Delta Aquifer (SDA), which consists of sand
and gravels, and overlies low permeability silt, diamicton, and clay deposits (Baker
1967; Baker and Paulson 1967; Klausing 1968; Bluemle 1979; Armstrong 1982; Fritz
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2001). The Sheyenne River, which traverses through the SNG, and the Wild Rice
River, which is located south of the SNG, are the main streams draining the SDA. The
Maple River, located north of the SNG, affects groundwater levels in that area of the
SNG, but does not directly drain it. There are riverine, ponded, emergent, and forested
types of freshwater wetlands identified on the SNG from the National Wetlands
Inventory (NWI) maps (US Fish and Wildlife Service 2006).
The SNG ecosystem is threatened by leafy spurge (Euphorbia esula) and other weeds,
which have spread across the unit (USDA Forest Service 2007). To contain the
spread of these weeds the USFS has resorted, in part, to the use of herbicides, such as
tordon and imazapic (USDA Forest Service 2007). However, herbicide application is
restricted to limit the potential for groundwater contamination. Specifically, the Forest
Service forbids herbicide application in areas where the water table is less than 10 ft
(3.05 m) below the ground surface in highly permeable soils or less than 6 feet below
the ground surface in low permeability soils (USDA Forest Service 2007).
Figure S1. The edge of the purple and dark green areas depicts the administrative
boundary of the McLeod tract of the Sheyenne National Grassland (SNG), with the
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dark green areas with white shading showing the publicly owned lands managed by
the USFS Dakota Prairie Grasslands, ND. The light green area is the extent of the
Sheyenne Delta Aquifer (SDA) and the nearby Milnor Channel aquifer. The dark red
squares are the active wells in the SDA. The dashed red curve indicates the area of a
regional GFLOW model and the red box indicates the area of the local MODFLOW
model.
Regional GFLOW model
The purpose of the regional groundwater model is to provide the regional setting for a
more detailed local model of the SNG. The Analytic Element Method (AEM) model
GFLOW (Haitjema 1995) was used to represent the regional flow domain. In the
AEM a solution to the groundwater flow problem is obtained by superposition of
many (hundreds in this case) elementary analytic solutions (analytic elements) such as
pumping wells and streams. These wells and streams are represented in the AEM
model by point-sinks and line-sinks, respectively (Strack and Haitjema 1981a).
Aquifer heterogeneities are represented by zones of differing aquifer properties
(Strack and Haitjema 1981b). GFLOW is a gridless single-layer Dupuit-Forchheimer
model that is especially suitable for representing large-scale groundwater systems
with locally detailed conjunctive surface-groundwater interactions (Haitjema 1995;
Hunt 2006).
The area of the regional model includes the SDA, the Milnor Channel Aquifer, and
nearby low permeability deposits in Ransom, Richland, Sargent, and Cass counties in
ND. The model domain is enclosed by a no-flow boundary since almost no interaction
is anticipated with the low permeability formations that surround it (see the black
polygon around the model area in Figure S2). The major rivers in the modelled area,
such as the Sheyenne, Wild Rice, and Maple, were included in the model domain by
strings of line-sinks with a specified head. The Wild Rice River, Maple River and
perennial streams are included as line-sinks with a stream bottom resistance (blue
lines in Figure S2). The line-sinks representing the Sheyenne River did not include a
bottom resistance (green lines in Figure S2). Instead, the low permeability river
channel of the Sheyenne River was represented by low hydraulic conductivity zones
Z3 and Z4 that were adjusted during model calibration. Some of the smaller streams
or creeks are included in the model by using a conjunctive surface water and
groundwater solution process (brown lines in Figure S2). These streams may or may
not receive groundwater in the model, depending on the recharge rate applied. If they
are found to fall dry during the model solution process, they are automatically
removed from the groundwater flow solution. The aquifer thickness in the model is
arbitrarily set to 100 ft (30.48 m) as measured from the aquifer bottom, but the actual
saturated thickness of the aquifer depends on the elevation of the unconfined water
table, which will always remain below the model aquifer top. The variations in the
aquifer bottom, b, from 940 ft (286.51 m) to 1050 ft (320.04 m) above MSL, and
hydraulic conductivity, k, from 7 (2.13 m/day) to 400 ft/day (121.92 m/day), were
obtained from available literature and field data and included in the model as discrete
zones of differing aquifer properties (orange polygons in Figure S2). Aquifer base and
hydraulic conductivity values were inferred from numerious bored logs obtained from
the North Dakota State Water Commission (NDSWC) database (NDSWC, 2011). The
model is steady state with an average recharge rate of 3.94 inches/year (0.1 m/year).
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The groundwater recharge of 3.94 inches/year (0.1 m/year) is 18.7% of the average
annual precipitation of 21.07 inches/year (0.54 m/year) for a data record of 1881-2000
at the Fargo Airport about 50 miles (80 km) from the SNG (Godon and Godon, 2002).
The regional GFLOW model has 32 pumping wells that were abstracting groundwater
in 2009 from SDA (NDSWC, 2011). The pumping rate for these wells was calculated
by distributing the reported amount of withdrawn groundwater over 365 days. Using
NDSWC database, 100 monitoring wells with discontinuous groundwater level
measurements between 1977 and 2010 were selected for purposes of model
calibration. For our steady state model, each monitoring well is assigned a
groundwater level which is an average value calculated from the existing time series
of data for that well.
The modeling results are presented in Figure S2 in the form of a contour map of
groundwater elevations. These groundwater heads range from 920 ft (280.42 m) to
1095 ft (333.76 m) above MSL with a 5-ft (1.52-m) contour interval. The difference
between the modeled and the measured groundwater heads in observation wells are
indicated in the figure by triangles. Red downward pointing triangles indicate that the
modeled head is too low, whereas green upward pointing triangles indicate modeled
heads that are too high. The size of the triangles of the labelled outliners in Figure S2
indicates the magnitude of the monitoring well residuals in the model. The modeled
groundwater heads and the monitoring well data are generally within 6 ft (1.83 m),
but with some outliers ranging between -10.6 ft (-3.23 m) and +8.5 ft (+2.59 m) that
are shown on the see bottom of Figure S2. The model calibration was accomplished
by a manual trial-and-error calibration in combination with a sensitivity analysis for
hydraulic conductivity using PEST (Doherty 2010). Hydraulic conductivity values for
zones Z0 through Z9, see Figure S2, were included in the PEST sensitivity
simulations. The highest relative sensitivity was for zone Z5 with a value of 6.22.
The hydraulic conductivity of zones Z0 and Z5 had relative sensitivity values of 3.72
and 3.14, respectively. The relative sensitivities values were 1.01 for Zone Z4, 1.89
for Zone Z6, 1.17 for Z9 and less than 0.7 for zones Z1, Z2 and Z3 and suggest low
sensitivity of model results to hydraulic conductivity (Doherty 2010).
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Figure S2. The regional GFLOW model. Streams are modeled by strings of line-sinks
(blue, green, or brown lines). Zones of differing aquifer properties are delineated by
orange lines and have labels with aquifer bottom, b, (286.51 m) to 1050 ft (320.04 m)
above MSL, and hydraulic conductivity, k, from 7 ft/day (2.13 m/day) to 400 ft/day
(121.92 m/day). Pumping wells are indicated by purple crossed circles. The
potentiometric head contours (dotted lines) have an interval of 5 ft (1.52 m) and range
from 920 ft (280.42 m) to 1095 ft (333.76 m) above MSL. Monitoring wells are
depicted by small green and red triangles for too high or too low modeled heads,
respectively. Differences between modeled and observed groundwater heads range
between -10.6 ft (-3.23 m) and +8.5 ft (+2.59 m) and are generally within 6 ft (1.83
m).
Local MODLFOW model
We constructed a single layer MODFLOW model (McDonald and Harbaugh 1988) of
the SNG area (red box in Figure S1). The MODFLOW model has 1,000 by 1,000 grid
cells that are 98.4 ft (30 m) on a side. The perimeter boundary conditions for the
model were obtained from the regional GFLOW model by using GFLOW's
MODFLOW extract feature (Hunt et al. 1998; Hunt 2006). The hydraulic
conductivity and aquifer bottom elevation data from GFLOW were also transferred to
MODFLOW. For the land elevation, we aggregated DEM10 elevation data to a
MODFLOW cell size and used it to define the aquifer top in MODFLOW. In Figure
S3 we show the MODFLOW groundwater head contours with a 5 ft (1.52 m) interval
for an annual average recharge rate of 3.94 inches/year (0.1 m/year). The
MODFLOW model contains 48 monitoring wells incorporated from the 100
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monitoring wells in the regional GFLOW model. The numbers near the monitoring
wells show the residuals with observed water levels. The same monitoring wells are
later used for developing depth-to-groundwater maps. The color flood in Figure S3
indicates the land surface elevations in MODFLOW that vary between 930 ft (283.46
m) (blue) and 1100 ft (335.28 m) (red) above MSL. The groundwater head that comes
within 3 ft (0.91 m) or in some locally confined areas is above land surface places
may indicate wetland conditions.
To assess how well our model could predict wetland locations we compared our
modeling results to the National Wetlands Inventory (NWI) map (U.S. Fish and
Wildlife Service 2006). In Figure S4 (a) we show an image of NWI mapped wetlands
in the SNG area, whereas in Figure S4 (b) we show where our MODFLOW model
predicts groundwater elevations that are within 3 ft (0.91 m) of the land surface (or
above it). We constructed Figure S4 (a) by aggregating the NWI shapefile polygons
into the grid of the local MODLFOW model with 98.4 ft (30 m) on a side. We
compared both the matrix of wetland and non-wetland cells in Figure S4 (a) and
Figure S4 (b) in the SNG area and found that 73% of wetland cells coincided with
MODFLOW cells that had a groundwater level of 3 ft (0.91 m) or less below the land
surface. Aggregating the NWI shapefile polygons into a grid of 3,000 by 3,000 grid
cells with 32.8 ft (10 m) on a side and comparing it with results of MODFLOW
model resulted in 70% of coincided cells. Thus 27-30% of the wetland cells occur in
places where the water table is more than 3 ft (0.91 m) below the land surface in the
MODFLOW model. Conversely, the MODFLOW simulation shows a few areas
where depth-to-groundwater is less than 3 ft (0.91 m), where the NWI does not show
wetlands. Note that wetlands are defined by more than one parameter; in addition to
depth-to-groundwater a wetland must also have certain characteristic vegetation and
hydric soils; two conditions that are not represented by the MODFLOW model.
Overall, the wetland patterns in Figure S4 (a) and (b) are quite similar. In some areas
the groundwater table exceeds the land surface to form wetlands that contain surface
water. However, these surface waters are not sufficiently interconnected to cause
(appreciable) surface water flow towards any of the streams. In fact, we attempted to
model surface water flow in these wetlands by adding a model layer above the land
surface with a very high transmissivity. Any water above the land surface, therefore,
was allowed to flow under conditions of very low resistance. This modification,
however, did not noticeably affect the groundwater heads, hence we proceeded with
the single layer MODFLOW model used to produce Figure S3 and Figure S4 (b).
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Figure S3. Groundwater elevation contours in the local MODFLOW model of the
SNG area. The unsigned black and negative red numbers indicate monitoring wells
where the modeled head is too low and too high, respectively. The land surface
elevations are presented as a color flood and vary between 930 ft (283.46 m) (blue)
and 1100 ft (335.28 m) (red) above MSL. The small blue box indicates the modeling
area in Figure 3 (a) presented in the manuscript.
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Figure S4. Wetland areas obtained from NWI (a) and depth-to-groundwater less than
3 ft (0.91 m) in the MODFLOW model for average recharge conditions (b). The area
shown is the same as the MODFLOW model area shown in Figure S3.
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