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Methods
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We numerically simulated groundwater age in a wide range of steady-state, regional-scale (1-
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100s km) groundwater systems (see Table S1 for range of parameter values). We simulate mean
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groundwater age mass as a tracer subject to advection, diffusion and dispersion using a yearly
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production of one unit of conservative solute within the fluid (Bethke and Johnson, 2002; Goode,
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1996; Voss and Wood, 1994). Over 1000 simulations were conducted with SUTRA, a US
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Geological Survey numerical groundwater model that uses the finite element method (Voss,
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2002). Recently, the full distribution of groundwater age (Cornaton, 2011) and the moments of
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age distribution (Ginn et al., 2009) have been quantified but we focus on mean age that represent
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first-order patterns of groundwater age within a basin. The model domain consists of a
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rectangular cross-section of a generic basin with an imposed linear hydraulic gradient at the
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upper boundary and no flow boundaries on all other sides (Figure 1b). The basin contains three
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layers, an upper aquifer, a low permeability unit and a lower aquifer. Each unit is assumed to be
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homogeneous and isotropic. Parameters other than permeability such as diffusivity and porosity
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are kept constant within the whole domain. Values of dispersivity at the regional scale are
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uncertain (Freeze and Cherry, 1979). We chose to assign the dispersivity at the minimum value
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that allows numerical stability, and we studied the effect of dispersivity on groundwater ages in a
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separate set of model simulations (Figure S3). Longitudinal dispersivity is set to one fourth of the
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local element dimension (αL = 5m) and transversal dispersivity at one tenth of longitudinal
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dispersivity(Voss, 2002) (αT = 0.5m). We explored the effects of a large range of values of the
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key parameters that control groundwater age, including the permeability of the low-permeability
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unit (k2) and the high permeability unit (k1), basin size and aspect ratio, hydraulic gradient and
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lateral continuity of the low-permeability layer. The continuity of the low-permeability unit is
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defined as the lateral extent of the low-permeability unit divided by the total length of the basin,
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and the layer is equally cut off at the recharge and discharge ends. The parameter ranges
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(Table S1) are intended to capture the variability observed in natural hydrogeological systems.
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We define ‘high age zone’ as a zone within the low permeability layer where the maximum
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groundwater age is at least twice that of surrounding water. The width of this high age zone was
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determined as the horizontal distance where the groundwater age is more than half the maximum
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age (Figure S4b). If groundwater age remained above 50% of the maximum on one side of the
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layer, we considered that the high age zone did not form (Figure S4a, S4c) which excludes cases
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where the whole low permeability unit has a higher groundwater age. The value of 50% of the
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maximum age is arbitrary; other cut offs such as 90% were also examined and result in similar
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patterns of high age zones. In many simulations, groundwater age also is high in the discharge-
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side of the domain within and below the low permeability layer (i.e. lower left hand corner of
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Figure 2c). This is the natural result of longer flow paths and has been documented previously
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(Jiang et al., 2010), but is not considered as a high age zone, since the zone is not surrounded on
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both sides by younger water.
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Table S1. Overview of parameter values.
Parameter
Range of variation
Related figure
Permeability k1 of the aquifer
k1 = 10-8 m² to 10-17 m²
Figure 2, Figure 3
Permeability k2 of the low-permeability unit
k2 = 10-8.5 m² to 10-20 m²
Figure 2, Figure 3
Hydraulic gradient
0.001, 0.005, 0.01, 0.1
Figure 2
Depth of the low-k layer
0.1 to 0.9
Figure 4a
Thickness of the low-k layer
0.05 to 0.95
Figure 4b
Continuity of the low-k layer
0.05 to 1
Figure 4c
Length of the basin L
1 to 100 km
Figure 4d
Depth of the basin Z
100 m to 10km
Figure 4d
Aspect ratio of the basin
1:1 to 1:100
Figure 4e
Porosity
0.1, 0.3
All figures with n = 0.3
except for Figure S5.
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Longitudinal dispersivity αL
5, 50, 500 m
Figure S3
Transversal dispersivity αT
0.005, 0.05, 0.5, 5, 50 m
Figure S3
Horizontal grid spacing
20 m
Vertical grid spacing
5m
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Table S2. Parameter values for Figure 2a-c.
Parameter
Value
Permeability k1 of the aquifer
k1 = 10-13 m²
Permeability k2 of the low-permeability unit
(a) k2 = 10-14 m², (b) k2 = 10-15.4 m²,
(c) k2 = 10-16 m²
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Hydraulic gradient
0.01
Depth of the low-k layer
0.5
Thickness of the low-k layer
0.2
Continuity of the low-k layer
1
Length of the basin L
10 km
Depth of the basin Z
1 km
Porosity
0.3
Longitudinal dispersivity αL
5m
Transversal dispersivity αT
0.5 m
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Table S3. Parameter values for Figure 3.
Parameter
Value
Permeability k1 of the aquifer
k1 = 10-8 m² to 10-18 m²
Permeability k2 of the low-permeability unit
k2 = 10-8.5 m² to 10-18 m²
Hydraulic gradient
0.01
Depth of the low-k layer
0.5
Thickness of the low-k layer
0.2
Continuity of the low-k layer
1
Length of the basin L
10 km
Depth of the basin Z
1 km
Porosity
0.3
Longitudinal dispersivity αL
5m
Transversal dispersivity αT
0.5 m
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Table S4. Parameter values for Figure 4.
Parameter
Value
Permeability k1 of the aquifer
k1 = 10-13 m²
Permeability k2 of the low-permeability unit
k2 = 10-14 m² to 10-16 m²
Hydraulic gradient
0.01
Depth of the low-k layer
(a) 0.1 to 0.9
Thickness of the low-k layer
(b) 0.05 to 0.95
Continuity of the low-k layer
(c) 0.05 to 1
Length of the basin L
(d) 1 to 100 km
Depth of the basin Z
(e) 100 m to 10km
Aspect ratio of the basin
(e) 1:1 to 1:100
Porosity
0.3
Longitudinal dispersivity αL
5m
Transversal dispersivity αT
0.5 m
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Details on why high age zones form (with figures)
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Our results suggest that two mechanisms lead to the formation of a zone of high groundwater
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ages. First, high age zones are caused by mixing of groundwater from flow paths that travel
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through only the upper two layers and flow paths that travel through all three layers. For a wide
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range of permeabilities of the low permeability unit (k2), the groundwater velocity in the lower
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aquifer is high enough for the groundwater to travel faster than the groundwater flowing only
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through the overlying low-permeability unit (Figure S1). Upward flow of the younger
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groundwater near the discharge zone leads to rejuvenation of groundwater age within the low-
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permeability unit. High age zones are formed upgradient of the intersection of flow paths going
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through the lower aquifer and the low-permeability unit, and through the low-permeability unit
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only. Second, the high age zones are controlled by the flow velocities in the low-permeability
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unit (Figure S2). The lowest velocities are found near the middle of the basin and coincide with
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the location of the high age zone.
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Which of these two mechanisms is dominant controls the location of the high age zone and is
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predictable from the permeability contrast between the aquifer and the low-permeability unit. At
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low permeability contrasts the velocity is relatively constant over most of the low-permeability
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unit, and the high age zone is mainly controlled by the rejuvenation of groundwater below the
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discharge zone due to upflowing groundwater from the lowest aquifer (Figure S2a). At high
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permeability contrast the location of the high age zone follows the narrow zone of low flow
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velocities that is located in the middle of the basin (Figure S2b-c). Model simulations confirm
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that high age zones are not necessarily stagnation points, zones where groundwater velocity is
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zero or/and flow is in opposite directions (Jiang et al., 2011). In our model simulation flow
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velocities maintain values of 10-4 m/yr or higher (Figure S2). However, high age zones develop
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in areas of low velocities.
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Figure S1. The permeability of the low-permeability unit controls the velocity of the lower
aquifer. Distribution of velocity (m/yr) within the aquifer under a 0.01 hydraulic gradient for
sedimentary rocks (k1 = 10-13 m²) and a layer permeability of (a) k2 = 10-14 m², (b) k2 = 10-15.4 m²
and (c) k2 = 10-16 m².
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Figure S2. High age zones are not hydraulic stagnation points. Cross-section of groundwater
age (blue) and velocity (red) at the middle of the low-permeability unit under a 0.01 hydraulic
gradient for sedimentary rocks (k1 = 10-13 m²) and a layer permeability of (a) k2 = 10-14 m², (b) k2
= 10-15.4 m² and (c) k2 = 10-16 m².
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Figure S3. Zones of high groundwater age are common for diverse values of dispersivity.
Location of high age zone vs. k2 for sedimentary rocks (k1 = 10-13 m²) under a gradient of 0.01
with a longitudinal and transversal dispersivity of (a) αL = 5 m and αT = 0.5 m, (b) αL = 50 m
and αT = 5 m, and (c) αL = 5 m and αT = 0.005 m.
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Figure S4. Determination of high age zone location. Cross-section of groundwater age and
location of maximum age (xmax) and points where groundwater age is 50% of the maximum (x1 <
xmax < x2) at the middle of the low-permeability unit under a 0.01 hydraulic gradient for
sedimentary rocks (k1 = 10-13 m²) and a layer permeability of (a) k2 = 10-13.6 m², (b) k2 = 10-14 m²
and (c) k2 = 10-16.4 m². High age zone forms in case b but not in cases a and c.
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Figure S5. Location of zones of high groundwater age for a 0.1 porosity. (a-c). Distribution
of groundwater age within the aquifer under a 0.01 hydraulic gradient for sedimentary rocks (k1
= 10-13 m²) and a layer permeability of (a) k2 = 10-14 m², (b) k2 = 10-15.4 m² and (c) k2 = 10-16 m².
(d-f). Location of high age zone vs. k2 for sedimentary rocks (k1 = 10-13 m²) under a gradient of
(d) 0.1, (e) 0.01 and (f)0.001. (g-i). Location of high age zone vs. k2 for unconsolidated
sediments (k1 = 10-11 m²) under a gradient of (g) 0.1, (h) 0.01 and (i) 0.001. Circles represent the
location of the maximum groundwater age; lines represent the area where groundwater ages are
higher than 50% of the maximum age. For each case, simulations have been run for values of k2
from k1 to 10-18 m². Values not specified mean that a high age zone does not form for this set of
parameters.