Tóth problems can be applied to multiple scales ranging from hyporic zones of
streams on the meter-scale to hillslopes on the hundred-meter-scale to large basins on
the kilometer-scale (Cardenas, 2008; Wörman et al., 2006). Determining a proper cell
size for a specific-scale numerical groundwater flow model is of great importance. In
this paper, the method used by Goderniaux et al., (2013) is adopted. Details regarding
this method could be found in the work of Goderniaux et al. (2013), Ijjasz-Vasquez
and Bras (1995) and Montgomery and Foufoula-Georgiou (1993). According to Fig.
S1, the first-order catchment area of the Dosit River Watershed is identified to be
348300 m2. Consequently, the cell size for the numerical groundwater flow model is
chosen to be 500 m (Fig. S2-a).
Due to the limited distribution area and relatively thin thickness, the Luohandong
(K1lh) sandstone, the Tertiary (E) mudstone and the Quaternary (Q) sediment can be
lumped into the underlying Huanhe (K1h) sandstone. Therefore, vertically, the
numerical model is roughly discretized into two layers representing the Huanhe (K1h)
and the Luohe (K1l) sandstones, respectively. Bottom elevations of these two layers,
which are interpolated by numerous deep boreholes in the Ordos Plateau, could be
obtained from Hou et al. (2008) (Fig. S3). In order to elaborately depict the vertical
movement of groundwater flow, the numerical model is vertically refined into 9 layers
(Fig. S2-b). Note that the top layer is relatively thicker than others as to minimize the
possibility of the existence of drying cells during the calculation.
Precipitation is the most important groundwater recharge component of the study
site (human activities are not considered). Recharge Package of MODFLOW
(Harbaugh, 2005) is chosen to describe this process. Recharge rate is obtained by
multiplying the infiltration coefficient by the annual precipitation. According to the
field infiltration experiments conducted nearby, the infiltration coefficient is 0.28
(Hou et al., 2008). Evapotranspiration (EVT) is one of the main groundwater
discharge processes of the study site. EVT Package of MODFLOW (Harbaugh, 2005)
is chosen to describe this process. Elevation of EVT surface is defined by the
topography. Maximum EVT rate is obtained by multiplying the experiment coefficient,
0.475 (Hou et al., 2008), by the annual potential EVT. Extinction depth of EVT is
referred to lithology as 2.8 m (Hou et al., 2008). Since the Dosit River is mainly
supplied by groundwater, a drain boundary (Harbaugh, 2005) is prescribed to the river
network. The first-order catchment is used as a threshold to obtain the river network
(Fig. S2-a). Drain hydraulic conductance is given a large value to let groundwater
fluently flow out. Drain elevation derives from the topography.
It was reported that the hydraulic conductivity of the Huanhe (K1h) sandstone
decreases with depth (Hou et al., 2008; Jiang et al., 2012). In the numerical model, the
exponential decay model used by Jiang et al. (2012) is adopted to fit this relationship.
The decay exponent is 0.0022 m-1 according to Jiang et al. (2012). The horizontal
hydraulic conductivity of the Huanhe (K1h) sandstone at the ground surface should be
calibrated. The thickness of the Luohe (K1l) sandstone is limited, and its hydraulic
conductivity does not substantially change with depth. Therefore, a constant
horizontal hydraulic conductivity is assigned to the Luohe (K1l) sandstone. Porosities
of the Huanhe (K1h) sandstone and the Luohe (K1l) sandstone were reported to be
19.26% and 18.86%, respectively (Hou et al., 2008; Jiang et al., 2012).
Values of horizontal hydraulic conductivities and anisotropic ratios (Kx/Kz or
Ky/Kz) of the Huanhe (K1h) sandstone and the Luohe (K1l) sandstone are estimated
during calibration. Available data for calibration are: (1) water levels of 539 shallow
domestic wells, which were partly measured during a field investigation in the years
of 2012 to 2013 and partly collected from the topographic maps; (2) water levels and
14C ages of groundwater from different depths of borehole B2. Borehole B2 is located
at the center of the Dosit River Watershed. In borehole B2, the packer system was
used to measure the hydraulic head and to sample groundwater from three sections
(i.e., the upper part of the Huanhe (K1h) sandstone, the lower part of the Huanhe (K1h)
sandstone and the Luohe (K1l) sandstone).
Fig. S4-a gives the comparison between the simulated hydraulic heads and the
measured values of the 539 shallow domestic wells. As shown in Fig. S4-a, there is a
good agreement with a correlation coefficient of 0.99. For different sections in
borehole B2, comparisons between the measured hydraulic heads and 14C ages and
the simulated values are shown in Figs. S4-b and S4-c. The simulated hydraulic heads
generally mimic the vertical variation of hydraulic head in borehole B2 (Fig. S4-b).
The simulated groundwater ages locate in the scope bounded by the two measured 14C
ages (Fig. S4-c). After calibration, the horizontal hydraulic conductivity of the
Huanhe (K1h) sandstone at the ground surface is 0.4 m/d; the horizontal hydraulic
conductivity of the Luohe (K1l) sandstone is 0.55 m/d; anisotropic ratios are both 100.
Groundwater of the Dosit River Watershed generally flows from surface-water
divides and discharges at the Dosit River. The spatial distribution of the water table
depth (WTD) could be obtained by subtracting the water table from the topography. It
shows that the maximum WTD can be as deep as 150 m, which is about 30% of the
maximum elevation difference of the topography (Fig. S5).
Fig. S1 Log-log diagram of averaged slope versus contributing area for the Dosit
River Watershed. Original data (grey points) are binned to average the slope (red
X: 3. 48 3e + 05
Contributing area (m2)
Fig. S2 Discretization of the numerical groundwater flow model of the Dosit River
Watershed in the planar view (a) and the cross section view (b).
Fig. S3 Bottom elevations of the Huanhe (K1h) sandstone (a) and the Luohe (K1l)
sandstone (b) of the Ordos Plateau (modified from Hou et al. (2008))
Fig. S4 (a) Comparison of measured and simulated hydraulic heads of the 539
domestic wells of the Dosit River Watershed. Comparison of measured and simulated
hydraulic heads (b) and groundwater ages (c) of different sections in borehole B2.
Fig. S5 Topography (a), simulated water table (b) and water table depth (WTD) of the
Dosit River Watershed.
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