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Supplementary material to "On the use of late-time peaks of residence time distributions for the characterization of hierarchically nested groundwater flow systems"

  • Yellow River Engineering Consulting Co., Ltd. (YREC)
Supplementary material
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
Y: 0.01175
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.
Cardenas, M.B., 2008. Surface water-groundwater interface geomorphology leads to
scaling of residence times. Geophys Res Lett, 35(8): L08402.
Goderniaux, P., Davy, P., Bresciani, E., Dreuzy, J.R., Borgne, T., 2013. Partitioning a
regional groundwater flow system into shallow local and deep regional flow
compartments. Water Resour Res, 49(4): 2274-2286.
Harbaugh, A.W., 2005. MODFLOW-2005, the US Geological Survey modular
ground-water model: the ground-water flow process. US Department of the
Interior, US Geological Survey Reston, VA, USA.
Hou, G.C. et al., 2008. Groundwater Investigation in the Ordos Basin [in Chinese].
Geological Publishing House, Beijing, China.
Ijjasz-Vasquez, E.J., Bras, R.L., 1995. Scaling regimes of local slope versus
contributing area in digital elevation models. Geomorphology, 12(4): 299-311.
Jiang, X.W. et al., 2012. A quantitative study on accumulation of age mass around
stagnation points in nested flow systems. Water Resour Res, 48(12): W12502.
Montgomery, D.R., Foufoula-Georgiou, E., 1993. Channel network source
representation using digital elevation models. Water Resour Res, 29(12):
Wörman, A., Packman, A.I., Marklund, L., Harvey, J.W., Stone, S.H., 2006. Exact
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arbitrary surface topography. Geophys Res Lett, 33(7): L07402.
ResearchGate has not been able to resolve any citations for this publication.
Full-text available
The distribution of groundwater fluxes in aquifers is strongly influenced by topography, and organized between hillslope and regional scales. The objective of this study is to provide new insights regarding the compartmentalization of aquifers at the regional scale and the partitioning of recharge between shallow/local and deep/regional groundwater transfers. A finite-difference flow model was implemented, and the flow structure was analyzed as a function of recharge (from 20 to 500 mm/yr), at the regional-scale (1400 km2), in three dimensions, and accounting for variable groundwater discharge zones; aspects which are usually not considered simultaneously in previous studies. The model allows visualizing 3-D circulations, as those provided by Tothian models in 2-D, and shows local and regional transfers, with 3-D effects. The probability density function of transit times clearly shows two different parts, interpreted using a two-compartment model, and related to regional groundwater transfers and local groundwater transfers. The role of recharge on the size and nature of the flow regimes, including groundwater pathways, transit time distributions, and volumes associated to the two compartments, have been investigated. Results show that topography control on the water table and groundwater compartmentalization varies with the recharge rate applied. When recharge decreases, the absolute value of flow associated to the regional compartment decreases, whereas its relative value increases. The volume associated to the regional compartment is calculated from the exponential part of the two-compartment model, and is nearly insensitive to the total recharge fluctuations.
Full-text available
The stagnant zones in nested flow systems have been assumed to be critical to accumulation of transported matter, such as metallic ions and hydrocarbons in drainage basins. However, little quantitative research has been devoted to prove this assumption. In this paper, the transport of age mass is used as an example to demonstrate that transported matter could accumulate around stagnation points. The spatial distribution of model age is analyzed in a series of drainage basins of different depths. We found that groundwater age has a local or regional maximum value around each stagnation point, which proves the accumulation of age mass. In basins where local, intermediate and regional flow systems are all well developed, the regional maximum groundwater age occurs at the regional stagnation point below the basin valley. This can be attributed to the long travel distances of regional flow systems as well as stagnancy of the water. However, when local flow systems dominate, the maximum groundwater age in the basin can be located around the local stagnation points due to stagnancy, which are far away from the basin valley. A case study is presented to illustrate groundwater flow and age in the Ordos Plateau, northwestern China. The accumulation of age mass around stagnation points is confirmed by tracer age determined by 14C dating in two boreholes and simulated age near local stagnation points under different dispersivities. The results will help shed light on the relationship between groundwater flow and distributions of groundwater age, hydrochemistry, mineral resources, and hydrocarbons in drainage basins.
[1] We know little regarding how geomorphological features along the surface-groundwater interface collectively affect water quality and quantity. Simulations of surface water-groundwater exchange at increasing scales across bed forms, bars and bends, and basins show that groundwater has a power-law transit time distribution through all these features, providing a purely mechanistic foundation and explanation for temporal fractal stream chemistry. Power-law residence time distributions are almost always attributed to spatial variability in subsurface transport properties- something we show is not necessary. Since the different geomorphological features considered here are typical of most landscapes, fractal stream chemistry may be universal and is a natural consequence of water exchange across multifaceted interfaces.
Methods for identifying the size, or scale, of hillslopes and the extent of channel networks from digital elevation models (DEMs) are examined critically. We show that a constant critical support area, the method most commonly used at present for channel network extraction from DEMs, is more appropriate for depicting the hillslope/valley transition than for identifying channel heads. Analysis of high-resolution DEMs confirms that a constant contributing area per unit contour length defines the extent of divergent topography, or the hillslope scale, although there is considerable variance about the average value. In even moderately steep topography, however, a DEM resolution finer than the typical 30 m by 30 m grid size is required to accurately resolve the hillslope/valley transition. For many soil-mantled landscapes, a slope-dependent critical support area is both theoretically and empirically more appropriate for defining the extent of channel networks. Implementing this method for overland flow erosion requires knowledge of an appropriate proportionality constant for the drainage area-slope threshold controlling channel initiation. Several methods for estimating this constant from DEM data are examined, but acquisition of even limited field data is recommended. Finally, the hypothesis is proposed that an inflection in the drainage area-slope relation for mountain drainage basins reflects a transition from steep debris flow-dominated channels to lower-gradient alluvial channels.
1] It has been long known that land surface topography governs both groundwater flow patterns at the regional-to-continental scale and on smaller scales such as in the hyporheic zone of streams. Here we show that the surface topography can be separated in a Fourier-series spectrum that provides an exact solution of the underlying three-dimensional groundwater flows. The new spectral solution offers a practical tool for fast calculation of subsurface flows in different hydrological applications and provides a theoretical platform for advancing conceptual understanding of the effect of landscape topography on subsurface flows. We also show how the spectrum of surface topography influences the residence time distribution for subsurface flows. The study indicates that the subsurface head variation decays exponentially with depth faster than it would with equivalent two-dimensional features, resulting in a shallower flow interaction. Citation: Wörman, A., A. I. Packman, L. Marklund, J. W. Harvey, and S. H. Stone (2006), Exact three-dimensional spectral solution to surface-groundwater interactions with arbitrary surface topography, Geophys. Res. Lett., 33, L07402, doi:10.1029/2006GL025747.
Four scaling regimes are observed in Digital Elevation Models (DEMs) when the average local slope is calculated for pixels grouped according to the values of the contributing area. Threshold criteria, proposed by various researchers to identify the extent of the channel network, are examined relative to the slope-area scaling diagram. The scaling response observed in DEMs is reproduced with a landscape evolution and channel network growth model originally developed by Willgoose et al. (1989). The threshold criterion proposed in this model is a useful tool to separate two different slope-area scaling regimes observed in DEM data.
Groundwater Investigation in the Ordos Basin
  • G C Hou
Hou, G.C. et al., 2008. Groundwater Investigation in the Ordos Basin [in Chinese].