Dispersion of Groundwater Age in an Alluvial Aquifer System

Abstract

[1] Interpretation of groundwater ages typically rests on assumptions of minimal mixing of different water ages in the water samples. The effects of three-dimensional, geologic heterogeneity on groundwater mixing and tracer concentrations, however, have not been evaluated. In this study, we use a series of 10 detailed geostatistical realizations along with high-resolution numerical groundwater flow and contaminant transport simulation to model distributions of groundwater ages and chlorofluorocarbon (CFC) ages at wells within a heterogeneous stream-dominated alluvial fan aquifer system. Results show that groundwater reaching a well in the heterogeneous aquifer system typically consists of a wide distribution of groundwater ages (often spanning >50 years), even over short (

Full text

Dispersion of groundwater age in an alluvial aquifer system
Gary S. Weissmann,
1
Y. Zhang, Eric M. LaBolle, and Graham E. Fogg
2
Hydrologic Sciences, University of California, Davis, California, USA
Received 28 August 2001; revised 9 April 2002; accepted 25 April 2002; published 18 October 2002.
[1]Interpretation of groundwater ages typically rests on assumptions of minimal mixing
of different water ages in the water samples. The effects of three-dimensional, geologic
heterogeneity on groundwater mixing and tracer concentrations, however, have not been
evaluated. In this study, we use a series of 10 detailed geostatistical realizations along with
high-resolution numerical groundwater flow and contaminant transport simulation to
model distributions of groundwater ages and chlorofluorocarbon (CFC) ages at wells
within a heterogeneous stream-dominated alluvial fan aquifer system. Results show that
groundwater reaching a well in the heterogeneous aquifer system typically consists of a
wide distribution of groundwater ages (often spanning >50 years), even over short (<1.5
m) screened intervals. Additionally, simulated arithmetic mean groundwater ages do not
correspond to mean ages estimated from simulated CFC concentrations. Results
emphasize the potential ambiguity of ‘‘mean’’ groundwater ages estimated from
environmental tracer concentrations in typically heterogeneous geologic systems. The
significant dispersion of groundwater ages also implies that ultimate, maximum effects of
nonpoint source, anthropogenic contamination of groundwater may not be reached until
after many decades or centuries of gradual decline in groundwater quality. INDEX TERMS:
1829 Hydrology: Groundwater hydrology; 1832 Hydrology: Groundwater transport; KEYWORDS:
heterogeneity, groundwater age, environmental tracer, chlorofluorocarbons, transport, modeling
Citation: Weissmann, G. S., Y. Zhang, E. M. LaBolle, and G. E. Fogg, Dispersion of groundwater age in an alluvial aquifer system,
Water Resour. Res.,38(10), 1198, doi:10.1029/2001WR000907, 2002.
1. Introduction
[2] The use of environmental tracers, such as chlorofluor-
ocarbons (CFCs), tritium/helium-3, and carbon-14, for age
dating groundwater has made it possible to estimate mean
ages of groundwater pumped from wells [e.g., Solomon and
Sudicky, 1991; Solomon et al., 1992; Hackley et al., 1992;
Plummer et al., 1993; Busenberg et al., 1993; Cook et al.,
1995; Johnston et al., 1998; Varni and Carrera, 1998;
Plummer and Sprinkle, 2001]. In concept, groundwater
age dates provide important information on sources and
timing of recharge and vulnerability of aquifers to contam-
ination. An age date of 40 years, for example, might suggest
that surface contaminant sources that have only existed for
20 years could not be present in the 40-year-old water.
Accordingly, there is growing interest among regulatory
agencies in using groundwater age dates to map suscepti-
bility of groundwater systems to contamination.
[3] Many papers state or imply that the validity of the
age-dates is suspect if dispersion and/or long screened
intervals create significant mixing of ages [Walker an d
Cook, 1991; Mazor and Nativ, 1992; Goode, 1996; Varni
and Carrera,1998;To m p s o n e t a l . , 1999; Bethke and
Johnson, 2002]. Hinkle and Snyder [1997] noted that
mixing a small portion of younger water that contains
CFC with older water that is CFC-free will result in
reporting of a CFC age date that is between 1944 and the
date of recharge of the modern water in the mixture, even if
the water sample consists of a low percentage of younger
water. Thus groundwater ages determined from CFC data
may not represent the weighted mean age of groundwater
where mixing is significant. Varni and Carrera [1998]
presented similar results indicating this influence of mixing
to be true for any environmental tracer in a heterogeneous
aquifer. Though several writers have indicated that the
influence of heterogeneity and groundwater mixing due to
hydrodynamic dispersion might produce uncertainty in
environmental tracer-based age date results [Busenberg
and Plummer, 1992; Dunkle et al., 1993; Reilly et al.,
1994; Johnston et al., 1998; Varni and Carrera, 1998;
Burow et al., 1999; Tompson et al., 1999], the magnitude
of this effect is largely unknown. It is often assumed,
however, that age dating of waters from short screened
intervals (1 m) will eliminate significant mixing of differ-
ent groundwater ages from different depths.
[4]Bethke and Johnson [2002] used the age-mass
equation of Goode [1996] to analytically model effects
of mass transfer between regional aquifer and aquitard
layers. They showed that for very long times of transport,
a conservative environmental tracer that undergoes advec-
tion, dispersion, and diffusion (Brownian motion) will, in
the limit, become distributed among the aquitard and
1
Now at Department of Geological Sciences, Michigan State University,
East Lansing, Michigan, USA.
2
Also at Department of Geology, University of California, Davis,
California, USA.
Copyright 2002 by the American Geophysical Union.
0043-1397/02/2001WR000907$09.00
16 -1
WATER RESOURCES RESEARCH, VOL. 38, NO. 10, 1198, doi:10.1029/2001WR000907, 2002

aquifer materials in direct proportion to the relative vol-
umes of those materials. Because diffusive mass transfer
into the aquitards must be balanced by diffusive mass
transfer out of the aquitards, mean groundwater ages in the
aquifers can be substantially older than ages that would be
indicated by a simple piston displacement model for the
aquifer alone.
[5] The purpose of our work is to examine the role of
dispersion on groundwater age dates in an alluvial aquifer
complex containing typical heterogeneity in hydraulic con-
ductivity. While Bethke and Johnson [2002] examined
steady state effects of age mixing among aquifer and
aquitard layers, wherein diffusion is the dominant transport
process in the aquitards, we examine the effects of advec-
tion, dispersion, and diffusion in a multiscale model of
heterogeneity containing multiple hydrostratigraphic units,
some of which are dominated by diffusion. Bethke and
Johnson’s [2002] analysis is most applicable for under-
standing potential age mixing of old groundwaters (say,
>10,000 yr) dated by radiometric tracers that have reached a
steady state in terms of mass transfer between tight aqui-
tards and the aquifers. In contrast, the present study applies
more to dating of younger groundwaters with environmental
tracers that have not migrated long enough or far enough to
have reached equilibrium in terms of mass exchange among
the various hydrostratigraphic units.
[6] We also explore whether, as often suggested in the
age-date literature, the age distribution is appropriately
narrow when the screened interval is small. The literature
contains limited quantitative evaluations of these assump-
tions with field data or with models [e.g., Varni and Carrera,
1998; Tompson et al., 1999]. In particular, effects of dis-
persion due to heterogeneity and mixing due to well screen
length on age dates has, to our knowledge, never been
investigated in typically complex alluvial materials.
2. Study Area
[7] We tested the effects of heterogeneity on groundwater
age distributions in the Kings River Alluvial Fan aquifer
system, located southeast of Fresno, California (Figure 1).
The Kings River deposited a stream-dominated alluvial fan
where it exits the Sierra Nevada into the San Joaquin Valley,
thus the aquifer consists of a highly heterogeneous mix of
lithologies ranging from cobble to mud (i.e., silt and clay)
[Weissmann, 1999; Weissmann and Fogg, 1999; Weissmann
et al., 2002]. Five hydrofacies were recognized within this
aquifer system based on core descriptions. These include, in
decreasing order of hydraulic conductivity, gravel, sand,
muddy sand, mud, and paleosol [Burow et al., 1997;
Weissmann, 1999; Weissmann and Fogg, 1999]. Addition-
ally, stratigraphic studies show that the aquifer consists of
five depositional sequences, where each sequence consists
of a heterogeneous composite of the gravel, sand, muddy
sand, and mud hydrofacies, and each sequence is bounded
by laterally continuous unconformities marked by the pale-
osol hydrofacies [Weissmann, 1999; Weissmann and Fogg,
1999; Weissmann et al., 2002].
[8]Burow et al. [1999] reported collection of CFC
samples in 1994 and 1995 from several discrete intervals
within the Kings River alluvial fan. Twenty multilevel
nested sampling wells at six locations (B1, B2, B2.5, B3,
B4, and B5) were used for this sampling. CFC-based age
dates indicate that groundwater ages range between 2 and
>55 years at the time of this 1994-95 sampling (Table 1).
3. CFC Age Dating Method
[9] Age dating of groundwater with CFC is based on
correlation of variable atmospheric tracer concentrations
through time to tracer concentrations in the groundwater
at sampling locations. For instance, CFC-11 (CCl
3
F) and
CFC-12 (CCL
2
F
2
) concentrations in the atmosphere have
steadily increased since the 1940s (Figure 2) [Elkins et al.,
1993, 1999; Plummer et al., 1993]. CFCs are soluble in
water, and the CFC concentration in water (C
CFC
) is related
to the atmospheric CFC partial pressure by Henry’s Law
CCFC ¼KCFC;TPCFC ð1Þ
where K
CFC,T
is the Henry’s Law constant for the CFC
compound at temperature, T, and P
CFC
is the atmospheric
partial pressure of the CFC compound [Warner and Weiss,
1985; Plummer et al., 1993]. Assuming meteoric water
recharged to the groundwater is at equilibrium with the
atmosphere with respect to the CFCs, estimates of CFC
partial pressure in the atmosphere at time of recharge can be
obtained from groundwater sample CFC concentrations by
application of equation (1). A groundwater age is estimated
by relating this estimated past CFC partial pressure to
historic CFC atmospheric concentrations shown in Figure 2
[Plummer et al., 1993; Busenberg et al., 1993].
[10] Several assumptions in estimating groundwater ages
from CFC data are outlined by Plummer et al. [1993],
including (1) the recharge temperature is known, (2) col-
lection procedures do not allow contact with the atmosphere
or other sources of CFCs, (3) no local sources of CFC
contamination in the groundwater exist outside of the
background atmospheric levels, and (4) groundwater con-
centrations are not significantly affected by hydrodynamic
dispersion, thus piston-type transport of the tracer can be
used to approximate tracer movement in the groundwater
system.
4. Modeling Heterogeneity, Groundwater Flow,
and Environmental Tracer Transport
[11] The modeling approach used to understand the
influence of heterogeneity on groundwater ages and CFC
concentrations at a well was accomplished in three steps: (1)
model the heterogeneity through application of transition
probability geostatistics within a sequence stratigraphic
framework [Weissmann and Fogg, 1999], (2) simulate
steady state groundwater flow using a block-centered finite
difference model, and (3) estimate water travel time from
the water table to wells using backward-in-time random
walk particle tracking [Uffink, 1989; Fogg et al., 1999;
LaBolle et al., 2000]. The following sections outline this
approach.
4.1. Modeling Heterogeneity
[12] To simulate the heterogeneous distribution of hydrof-
acies within the Kings River alluvial fan aquifer system, we
used a transition probability geostatistics approach [Carle
and Fogg, 1996; Carle et al., 1998; Weissmann et al.,
1999]. Weissmann and Fogg [1999] describe application
16 -2 WEISSMANN ET AL.: DISPERSION OF GROUNDWATER AGE

of this approach to the Kings River Alluvial Fan study area.
The following discussion is a brief summary of the geo-
statistical work.
[13] In the transition probability geostatistical approach,
transition probabilities between categorical data (e.g.,
hydrofacies) are measured in the vertical and horizontal
directions and a Markov chain model is fit to these
measured results. The 3-D Markov chain model is then
used in sequential indicator simulation followed by simu-
lated annealing to produce realizations of the subsurface
heterogeneity. Importantly, ‘‘soft’’ or interpreted geologic
information, such as facies mean lengths, global facies
proportions, and facies juxtaposition relationships, can be
incorporated into the Markov chain model of spatial vari-
ability [Carle et al., 1998]. Because close-spaced data are
plentiful in the vertical direction from core and geophysical
well logs, fitting a model to measured vertical transition
probabilities is straightforward. To estimate the more diffi-
cult horizontal components of the Markov chain model, we
analyzed C-horizon textures from soil surveys in a geologic
Figure 1. A map showing the study area location southeast of Fresno, California. The six USGS well
nest locations are indicated in the study area boundaries (modified from Burow et al. [1999]).
WEISSMANN ET AL.: DISPERSION OF GROUNDWATER AGE 16 -3

depositional systems context, as described in Weissmann et
al. [1999] and Weissmann and Fogg [1999].
[14] To deal with the nonstationarity created by the multi-
ple stratigraphic sequences and to represent discontinuity
across the unconformity boundaries, we modeled each strati-
graphic sequence separately [Weissmann and Fogg, 1999].
Additionally, the paleosol hydrofacies marks the laterally
continuous unconformity surface and was formed over the
exposed fan surface on the other four hydrofacies; therefore
the paleosols were modeled separately and later overprinted
on the simulated geology of each sequence. Assembly of
conditional simulation results for each sequence together
with the paleosols resulted in a nonstationary, multiscale
model of heterogeneity [Weissmann and Fogg, 1999].
[15] The three-dimensional cell size of 100 m, 200 m, and
0.5 m in the depositional strike, depositional dip, and
vertical directions, respectively, was selected using two
criteria: (1) these lengths are significantly less than the
mean lengths of each facies [Weissmann and Fogg, 1999]
and (2) sufficiently large to avoid computational limitations
during groundwater flow simulation. The overall dimen-
sions of the simulated region are 6300 15,000 100.5 m
in the depositional strike, depositional dip, and vertical
directions, respectively.
[16] A series of 10 equally probable realizations were
developed for this study. Figure 3 shows one realization of
the Kings River Alluvial Fan hydrostratigraphy used in the
groundwater flow and random walk particle tracking sim-
ulations described in the following sections.
4.2. Groundwater Flow Simulation
[17] A three-dimensional steady state modeling approach
was used to simulate groundwater flow conditions in the
aquifer with the finite difference code MODFLOW-96
[McDonald and Harbaugh, 1988; Harbaugh and McDo-
nald, 1996]. The study area was discretized into approx-
imately 950,000 cells within a simulation grid of overall
dimensions of 6300 15,000 100.5 m in the depositional
strike, depositional dip, and vertical directions, respectively,
from the geostatistical realizations. The constant cell dimen-
sions from the geostatistical realizations (100 200 0.5
m) were used for the numerical flow simulation grid.
Table 1. Reported CFC Age Dates From USGS Wells Within the Study Area Compared to Mean Simulated CFC Age Dates for the 10
Realizations From This Study
a
Well and Screen Number Screen Midpoint
Elevation,
m amsl
Simulated Residence
Time, years
Reported CFC Ages,
years
Simulated CFC Ages, years
Mean SD CFC-11 CFC-12 CFC-11 CFC-12
Mean SD Mean SD
B1-1 85.2 22.4 11.3 20 8 20.6 8.7 20.7 9.1
B1-2 58.7 a a 38 41 a a a a
B1-3 28.2 a a 37 48 a a a a
B2-1 84.3 31.6 14.7 16 2 14.0 3.7 13.7 3.8
B2-2 81.8 33.3 16.1 8 4 14.4 3.9 14.1 3.9
B2-3 68.1 57.2 12.5 22 18 26.7 4.5 27.8 4.8
B2.5-1 64.2 81.0 32.2 31 39 33.6 12.0 34.9 12.4
B2.5-2 52.9 144.6 64.8 29 32 49.9 6.0 51.1 4.6
B3-1 85.2 17.7 9.6 6 3 9.7 2.2 9.4 2.3
B3-2 72.1 34.2 11.7 b 16 17.3 3.1 17.5 2.9
B3-3 54.1 87.0 37.7 32 33 32.6 5.5 34.4 6.4
B3-4 46.5 96.9 38.9 29 41 38.1 7.8 40.5 8.9
B3-5 25.8 a a 35 >55 a a a a
B4-1 81.2 18.8 9.2 7 2 10.9 3.3 10.7 3.6
B4-2 70.0 43.6 16.3 b b 18.7 2.2 18.9 2.5
B4-3 48.9 104.4 33.1 b b 36.4 3.9 39.5 4.7
B4-4 25.4 124.7 39.0 b 30 45.3 4.0 49.3 4.0
B5-1 78.2 23.9 18.3 14 6 14.3 7.7 14.5 8.0
B5-2 54.4 52.1 18.1 26 25 25.4 4.9 26.4 5.5
B5-3 20.9 124.5 32.4 b b 49.7 4.8 52.2 3.1
a
Also included are simulated mean ages of groundwater at selected wells. Reported CFC ages are from Burow et al. [1999]. Here a indicates that
significant particles through upgradient boundary (>15%), and therefore groundwater age was indeterminate; b indicates that measured CFC-based age
dates were not reported by Burow et al. [1999].
Figure 2. Atmospheric concentrations of CFC-11 and
CFC-12 since 1940. Concentration values between 1940
and 1977 are from Busenberg et al. [1993]. Concentration
values between 1977 and 1994 were taken from the NOAA/
CMDL Niwot Ridge Station, Colorado, as reported by
Elkins et al. [1999].
16 -4 WEISSMANN ET AL.: DISPERSION OF GROUNDWATER AGE

[18] Hydraulic conductivity (K) was assigned to each cell
based on the simulated hydrofacies determined by the
geostatistical realization for each scenario. Values used for
K of each hydrofacies (Table 2) were estimated from
pumping test, slug test, laboratory core measurements, and
literature estimates for similar lithologies [Burow et al.,
1999; Weissmann, 1999].
[19] General head boundary conditions [McDonald and
Harbaugh, 1988] were used in the modeling to simulate
inflow and outflow through the lateral and basal boundaries
of the model. Hydraulic head values were defined for these
boundaries using a general gradient of 0.002 parallel to the
stratigraphic dip direction. Minor adjustments to the boun-
dary head values were made along the stratigraphic dip
boundaries to account for local gradient variability reported
in water-elevation maps of the study area [Fresno Irrigation
District, 1993]. No vertical gradient was assigned because
measured vertical gradients in the area are small and
variable in both upward and downward directions [Burow
et al., 1999]. The boundary condition for the top of the
model represents constant recharge to the water table at a
rate of 150 mm/year [Burow et al., 1999].
[20] Groundwater pumpage was not included in the
model for two reasons: (1) the previous characterization
and modeling study of the same area [Burow et al., 1999]
showed no perturbations in hydraulic head suggestive of
significant pumping influence on horizontal or vertical
gradients and (2) wells in the area are not metered. The
main effect of pumping would be to increase downward
groundwater velocities, yet measured heads in the USGS
well nests show no pervasive, downward gradients. Leakage
out of the lower boundary of the model into deeper, finer-
grained alluvial materials may, in fact, be compensating for
lack of specified pumpage in the model. Effects of pumpage
on general characteristics of the local groundwater age
Figure 3. Geostatistical realization 5 from the Kings River Alluvial Fan system.
Table 2. Hydraulic Conductivity Values Assigned to the Five
Hydrofacies
Hydrofacies K, m/s
Gravel 1 10
2
Sand 1 10
3
Muddy sand 1 10
5
Mud 1 10
6
Paleosol 1.3 10
7
Figure 4. Measured hydraulic head [from Burow et al.,
1999] plotted against simulated mean hydraulic head at 20
monitoring well locations for the 10 realizations. Data
points show mean results and error bars show the range of
values from the 10 realizations.
WEISSMANN ET AL.: DISPERSION OF GROUNDWATER AGE 16 -5

distributions is expected to be minimal, but should be
investigated in future studies.
[21] Figure 4 shows the simulated steady state hydraulic
head at the midpoint of the 20 well screens plotted against
measured head for these locations from Burow et al. [1999].
The average root-mean square error in head at the 20
measuring points for the 10 realizations is 2.41 meters, with
r
2
value of near 1. Although modeled head values do not
exactly match the measured values, simulated head values
are close and the flow simulations preserved both the
variability in vertical gradients and the overall observed
horizontal gradients within the study area.
[22] The measured heads indicate no pervasive trend in
vertical hydraulic gradients [Burow et al., 1999], but rather
shifting gradients from upward to downward, apparently
due to flow around lenticular heterogeneities in three-
dimensions. The simulated heads exhibit similar behavior,
except at location B4, where the model tends to have
downward gradients. In addition to flow simulations
through the heterogeneous realizations, we simulated flow
through a homogeneous K field for comparison purposes.
Anisotropic values for K of 3.6 10
4
m/s, 4.3 10
4
m/
s, and 1.7 10
5
m/s for the depositional strike, deposi-
tional dip, and vertical directions, respectively, were esti-
mated from effective K properties of the geostatistical
realizations. Effective K values in all three directions were
determined through simulation of flow in the strike, dip, and
vertical directions, as described by Weissmann [1999].
Similar boundary conditions to those previously described
were used for these ‘‘homogeneous’’ simulations.
4.3. Particle Tracking Simulation Approach
[23] Transport simulations employed a random-walk par-
ticle tracking method (RWPM), described by LaBolle et al.
[1998, 2000]. Application of the RWPM to simulate the
forward-time advection-dispersion equation (ADE) models
future particle distributions, with density representing solute
concentration given knowledge of past distributions. When
applied to simulate the backward-time ADE, the RWPM
equation models past particle locations, with density repre-
senting probability given that future positions are known
[Uffink, 1989; Fogg et al., 1999; Neupauer and Wilson,
1999]. This procedure accurately models transport in a
heterogeneous porous media, where sharp contrasts exist
between lithologies. Details of the RWPM are described by
Uffink [1989], LaBolle et al. [1996, 1998, 2000], and
LaBolle and Fogg [2001], and are summarized in this
section.
[24] In this approach, we assume that transport is
described by an ADE of the form:
@nc
@t¼@vic
@xi
þ@
@xi
nDij
@c
@xj
 ð2aÞ
Dij ¼aTv
jj
þD0
d

dij þaLaT
ðÞvivjv
jj=ð2bÞ
where cis the concentration, vis pore water velocity, D
ij
is
a dispersion tensor, nis effective porosity, D
d
0
is the
molecular diffusivity in a porous media, d
ij
is the Dirac
delta function, and a
L
and a
T
are longitudinal and
transverse dispersivities, respectively. The dependent vari-
able of (2a) can be replaced with the conditional probability
p(x,t|s,y), where c(x,t)=p(x,t) = p(x,t|s,y)p(s,y) with initial
condition [Arnold, 1974]
lim
t!spx;tjy;sðÞ¼dxyðÞ ð3Þ
where xis the final location of the particle at time tand yis
the initial location of the particle at time s. The form of the
backward-time ADE for constant nis given by the adjoint
of (2a) [Arnold, 1974]
@p
@s¼vi
@p
@yi
@
@yi
Dij
@p
@yj
 ð4aÞ
lim
s!tpx;tjy;sðÞ¼dxyðÞ ð4bÞ
The diffusion operator is said to be self-adjoint because it
takes the same form in both the forward and backward
processes. The advection term is not self-adjoint unless the
velocity is divergence free, in which case (4a) is equivalent
to
@p
@s¼@vip
@yi
@
@yi
Dij
@p
@yj
 ð5Þ
In reference to the forward equation, pin the backward
equation (5) is evolving in sfrom some final time to some
initial time. If, for convenience, one reverses time in (5) such
that positive values of strepresent evolution backward in
time, the backward ADE (5) simply takes the form of the
forward ADE (2a) with the velocity reversed. Both
equations are based on conditional probabilities. The
backward equation gives information on locations where
contaminants may have originated in the past [Uffink, 1989;
Fogg et al., 1999]. This backward-time ADE was used to
compute the ages of groundwater entering a monitoring well
from travel time between the well screen and water table.
[25] Parameter values required for the RWPM include
velocities calculated from the flow simulations, molecular
diffusivities, effective porosity, and longitudinal and trans-
verse dispersivities. The molecular diffusivity (D
d
0
)was
estimated from
D0
d¼Dd
t2ð6Þ
where D
d
is the diffusion coefficient in a liquid [Grathwohl,
1998] and tis tortuosity defined as
t¼Le
Lð7Þ
where L
e
is the flow path length and L is the straight-line
distance [Carman, 1956; Grathwohl, 1998; Fetter, 1999].
Using D
d
=210
9
m
2
/s, an average of diffusion
coefficients for common ions cited by Domenico and
Schwartz [1998], and a tortuosity of 1.7 [Carman, 1956], D
d
0
was estimated to be approximately 6.9 10
10
m
2
/s. An
effective porosity value of 0.33 was applied for these
simulations.
[26]LaBolle [1999] and LaBolle and Fogg [2001]
showed that simulation results are insensitive to the value
16 -6 WEISSMANN ET AL.: DISPERSION OF GROUNDWATER AGE

of local-scale a
L
. This is true because the spreading due to
longitudinal dispersion is insignificant compared to that
caused by the hydrofacies-scale heterogeneity that is cap-
tured in the geostatistical simulations. Furthermore, the
particular random walk particle algorithm that accurately
balances mass across sharp interfaces runs faster when
dispersivity is isotropic. Dispersivity was therefore treated
as isotropic, with a
L
=a
T
= 0.04 m, a value similar in
magnitude to reported transverse dispersivities at field sites
similar to the scale of our cells [e.g., Freyberg,1986;
Sudicky, 1986; Garabedian et al., 1991; Farrell et al.,
1994; Mallants et al., 2000]. Because some uncertainty in
this value exists, we conducted sensitivity runs with aset to
0.1 and 0.01 m. These simulations showed minimal effects
on the results reported here (Figure 5).
4.4. Numerical Simulation of Groundwater Ages
[27] To assess the age distribution of water entering a well
screen, we simulated backward-in-time release of 5000
particles from a discrete point located at the midpoint of
17 monitoring well screens at various depths in the study
area (Table 1). Thus these simulations reflect groundwater
age distributions at a discrete point in the aquifer. Particles
in these simulations represent parcels of water of various
ages. Using the steady state velocity fields along with the
backward-time particle tracking approach previously
described, the travel times for particles between these
monitoring well screen midpoints and the water table were
simulated for each of the 10 heterogeneous realizations and
the homogeneous system. Because the backward-moving
particles reach the water table at various times, the results of
this procedure produces probability distribution of ground-
water residence time at a well (Figure 6). Average residence
time of groundwater reaching each well screen was calcu-
lated as the arithmetic mean of particle travel times
(Table 1). Assuming that CFC atmospheric concentrations
are the same as vadose zone air concentrations, and that
water recharged at the water table is in equilibrium with this
Figure 5. Sensitivity results of simulated CFC-based age estimates for 10 realizations using a
T
= 0.01,
0.04, and 0.1 m for (a) CFC-11 ages at well B1-1, (b) CFC-12 ages at well B1-1, (c) CFC-11 ages at well
B4-2, and (d) CFC-12 ages at well B4-2.
WEISSMANN ET AL.: DISPERSION OF GROUNDWATER AGE 16 -7

concentration, this residence time should be equivalent to
the CFC-based groundwater age.
[28] In several groundwater residence time simulations, a
significant number of particles left the simulation through
the upgradient boundary, never reaching the water table.
Therefore we could not directly determine the residence
time of those particles. Instead, we estimated their residence
times by adding the estimated residence time based on a
relationship between particle age and depth in the system. A
depth versus residence time relationship was determined by
averaging simulated groundwater residence time at several
depths along the downgradient boundary (Figure 7). This
depth versus residence time relationship carries much
uncertainty for several reasons, including (1) upgradient
geology may be significantly different since this will
include the apex region of the alluvial fan and thus be
dominated by a greater percentage of coarse-grained mate-
rial; and (2) heterogeneity within a system, as shown by this
research, causes significant variance around the depth
versus residence time relationship at any depth. However,
even with these potential sources of error for these particles,
the overall influence of these particles is minimal for most
wells and simulations (Figure 6) since these particles
represent water with residence times >55 years and would
thus contain no CFC. This assumption allows a means of
estimating the full distribution of groundwater residence
Figure 6. Simulated groundwater residence time distributions from the midpoint of selected well
screens for each of the 10 realizations: (a) B1-1, (b) B4-1, (c) B4-2, (d) B5-1, and (e) B5-2. Dashed
portions of the residence time distribution curves indicate that >10% of the particles required estimation
of groundwater residence times using the depth versus residence time relationship of Figure 7. The thick
dashed line shows simulated residence times assuming a homogeneous aquifer system. See color version
of this figure at back of this issue.
16 -8 WEISSMANN ET AL.: DISPERSION OF GROUNDWATER AGE

time while maintaining a simulation space small enough to
conduct the numerical experiments within a reasonable
amount of time.
[29] Simulated CFC age dates were obtained by finding
in Figure 2 the reported atmospheric CFC concentration
values (C
CFC,p
) corresponding to residence time of each
particle. A total CFC concentration was estimated at each
well using
CCFC ¼P
Np
CCFC;p
Np
ð8Þ
where N
p
is the number of particles. The resulting
‘‘simulated CFC-age’’ of groundwater was estimated by
determining the year in Figure 2 that corresponds to this
calculated CFC concentration at the well. In this applica-
tion, we assume that the temperature at recharge depth
remains constant over the length of time simulated in order
to honor Henry’s Law.
5. Results
5.1. General Observations
[30] Simulations of groundwater residence time distribu-
tions show that groundwater tapped by each well consists of
a wide mix of water with various residence times, even
though the particles were released from points in space rather
than from the entire 1.5-m-long well screens (Table 1 and
Figure 6). A high degree of residence time distribution
variability between the 10 different realizations was
observed (Figure 6) and is also reflected in standard devia-
tion of residence times computed for the various scenarios
(Table 1). This variability reflects the uncertainty inherent to
our conditional simulations of heterogeneity in the system.
Even with this uncertainty, most curves associated with a
well retain similar shape and breadth of age distribution.
[31] With the exception of Well B1-1 and Well B5-1, the
broad age distributions and their asymmetry indicate that
non-Fickian dispersion caused by facies-scale heterogeneity
is significant. In the case of Wells B1-1, most simulated age
results agree fairly closely with the normal age distribution
produced under homogeneous conditions (Figure 6a). In the
Well B1-1 simulations that display this normal distribution,
the particles traveled primarily through one hydrofacies type
with minor excursions into other hydrofacies. Simulations
that produced a broader residence time distribution (e.g.,
realizations 4, 6, and 10) were the result of particles
traveling through several hydrofacies between the well
screen and water table. Similar responses were observed
in simulations conducted from Well B5-1, where all but four
of the simulations showed Fickian response related to
transport through primarily one hydrofacies. Therefore the
residence time distribution shape appears to be highly
dependant on the degree of heterogeneity encountered by
the tracer.
[32] Simulated CFC-based groundwater ages favorably
match measured CFC-based groundwater ages reported by
Burow et al. [1999] (Figure 8 and Table 1), with some
anomalies that are explainable. Simulated CFC-based
groundwater ages are generally slightly older than reported
CFC ages, especially for ages from CFC-12. This may stem
from the lack of regional pumping in our simulations that
would potentially draw a greater proportion of younger
water to the deeper screened intervals in the model.
5.2. Anomalies
[33] Only simulation results for wells B2-2, B2.5-2, B3-4,
and B4-4 show noticeably greater CFC ages than those
reported by Burow et al. [1999]. Sample measurement error,
possibly caused by CFC contamination of the sample (thus
producing an artificially young age result since concentra-
tions would be increased), may explain some of these
discrepancies. For example, the measured groundwater
age from CFC-12 for Well B4-4 is 29.5 yrs, which is
inconsistent with the lack of detectable tritium [Burow et
al., 1999] and the depth of this well. Furthermore, 1,2-
Dibromo-3-Chloropropane (DBCP) and nitrate concentra-
tions, contaminants determined to be associated with
younger groundwater [Burow et al., 1999], along with
specific conductance in groundwater sampled from this well
suggest that the water from this well is older than 29.5 yrs
[Burow et al., 1999]. Finally, each of the 10 simulated ages
from the 10 geostatistical realizations for Well B4-4 is older
than measured value (Table 1). The discrepancy between
measured and modeled age may also be related to a problem
with the geostatistical representation of heterogeneity at that
location since simulated vertical gradients at location B4
were consistently downward in contrast to the measured
gradients at that location. Burow et al. [1999], however,
noted that some of the samples from the study site were
probably contaminated with CFC-11 or CFC-12.
[34] Discrepancies between our simulated groundwater
ages and observed CFC ages were also noted in the CFC-11
age dates for well B3-4. The simulated CFC-11 ground-
water age of 38.1 years is greater than the observed 29 years
for CFC-11 in this well. However, the simulated CFC-12
Figure 7. Estimated residence time versus depth relation-
ship for the study area produced by estimating groundwater
residence times for cells along the downgradient boundary
of the study area.
WEISSMANN ET AL.: DISPERSION OF GROUNDWATER AGE 16 -9

age of 40.5 favorably matches the observed 41-year CFC-12
age date. Additionally, the age trend between Wells B3-1,
B3-2, B3-3, B3-4, and B3-5 show the expected tendency of
increasing age with depth at the B3 location, and the
measured B3-4 age date appears to be too young to fit this
trend. Burow et al. [1999] indicate that CFC-11 is more
susceptible to microbial transformation, however this was
not thought to be a dominant factor affecting CFC-11
concentrations due to low organic content and well-oxy-
genated groundwater. Additionally, CFC-12 is less likely
than CFC-11 to be contaminated by sampling [Bartolino,
1997]. Burow et al. [1999] assigned a recharge date to this
older value from CFC-12 data. Our results suggest this older
age date is more appropriate.
[35] Finally, the measured CFC-11 age of water in Well
B2-2 (8 years) is less than that observed in Well B2-1 (16
years), indicating that the deeper aquifer holds younger
water at the B2 location. This same phenomenon was
reported for measured ages at Well B2.5-1 and Well B2.5-
2. None of the simulations within the 10 realizations
reflected this reversed groundwater age, thus simulated
CFC-11 and CFC-12 ages are greater than the measured
values. These age discrepancies may be either due to
contamination of the CFC samples, thus producing a
younger age date, or presence of short-circuit flow paths
close to wells B2 and B2.5 in the field but not in the model.
5.3. Simulated CFC Age and the Mean Age
[36] In order to assess whether CFC ages reflect the mean
groundwater age of a sample in a heterogeneous aquifer, we
compared the simulated CFC age results to the simulated
overall mean groundwater residence time at a well
(Figure 9). Simulated CFC-based age dates are consistently
lower than the actual mean residence time of the simulated
samples. This is because the CFC age dating cannot differ-
entiate ages of water older than 55 years. Therefore it
appears that CFC-based ages do not typically reflect the
mean age of the groundwater in a typically heterogeneous
alluvial system. This result supports similar observations by
Varni and Carrera [1998], Tompson et al. [1999], and
Bethke and Johnson [2002].
6. Discussion and Conclusions
6.1. Residence Time Dispersion and Mean Age
[37] The simulated residence time distributions (Figure 6
and Table 1) exhibit substantial variance and positive skew-
ness (tailing), with some water ‘‘samples’’ containing water
ages ranging from 5 – 10 yrs to >100 yrs. The resulting CFC
age dates represent biased sampling of these distributions,
thereby underestimating actual mean age. The bias increases
with mean age (Figure 9), owing to the growth in residence
time variance with mean age.
[38] The substantial variance of residence times is caused
primarily by spatially variable groundwater velocities that
are inherent to the three-dimensional, heterogeneous allu-
vial system (Figure 3). Mixing of residence times along the
sampling interval is not a significant factor here because the
well screens are short (1.5 m). The tailing behavior is
caused by presence of very low-K units (paleosols and
muds) in which relatively slow advection and diffusion
dominate transport [LaBolle and Fogg, 2001].
[39] The results clearly illustrate how representation of
groundwater age by a single date can be misleading. Only
when the flow paths are relatively short, as in the case of
wells B1-1 and B5-1, does the groundwater residence
time distribution approximate a normal distribution with
small variance for some realizations of the heterogeneity
Figure 8. Mean simulated CFC-based groundwater ages plotted against measured CFC-based
groundwater ages reported by Burow et al. [1999] for (a) CFC-11 and (b) CFC-12. Ranges around the
mean show the range of simulated CFC-based ages within the 10 realizations.
16 -10 WEISSMANN ET AL.: DISPERSION OF GROUNDWATER AGE

(Figure 6), and, thus only in these cases will simulated CFC
ages reasonably correspond to the mean groundwater ages.
[40] Even if the age date technique is capable of unbiased
sampling, interpretation of the field measured ages can be
confounded by the broad range of ages within the sample.
For example, the notion that an age date of, say, 40 years is
always indicative of less vulnerability to recent, anthropo-
genic contamination than an age of 20 years is flawed. If the
source of contamination began 30 years ago, depending on
the groundwater residence time distributions, the 40-year
water could contain as much or more water that is younger
than 30 years as the 20-year water. Furthermore, if the age
of a water is estimated to be very old (e.g., thousands of
years), the tailing phenomenon could have the effect of
including very young water in the same sample. Such
extreme tailing of residence times is consistent with Bethke
and Johnson’s [2002] analysis, which indicates that diffu-
sion induced tailing can cause mixing of young and very old
waters locally within an aquifer. Even without diffusion-
induced tailing, it is expected that regional groundwater
flow systems would commonly include both old water that
has traveled great distances and younger water that enters
the regional aquifer system via leakage or preferential,
vertical flow through discontinuities in confining beds.
Groundwater pumpage would accelerate the downward
flow of relatively young water and enhance the mixing of
disparate groundwater ages. Future research should be
directed at assessing potential age dispersion and age
sampling bias for a variety of environmental tracers and
aquifer systems.
[41] The hypothesis that CFC-based age dates represent
an average age appears to be with little merit for all but the
most simple flow systems involving relatively young
(<55 years) groundwater. Several writers have indicated
that this may be the case [e.g., Walker and Cook, 1991;
Mazor and Nativ, 1992; Goode, 1996; Varni and Carrera,
1998; Fogg et al., 1999; Tompson et al., 1999; Bethke and
Johnson, 2002]. The present study models the full residence
time distributions, thereby quantifying and elucidating the
potential errors and ambiguities for a highly characterized,
heterogeneous system.
[42] The bias problem in age dating techniques that
preferentially detect the relatively young waters (e.g., CFC
and tritium-based methods) could be evaluated more
directly with an age dating technique that works well for
groundwater ages in the intermediate range (e.g.,<1000 yr).
While techniques exist for dating much older waters (e.g.,
14
C,
36
Cl), no techniques are available for dating the
intermediate range. Clearly, intermediate-age dating techni-
ques are needed.
6.2. Implications for Groundwater Quality
Sustainability
[43]Fogg et al. [1999] simulated dispersion of ground-
water residence times in a regional-scale (45 km) analysis
of a portion of the Salinas Valley. Similarly, their results
indicated significant dispersion of groundwater residence
time within simulated water ‘‘samples,’’ with residence
times in individual ‘‘samples’’ often ranging from 10 to
>500 yrs. Their model indicated such mixing over most of
the Salinas Valley study area, which receives nonpoint
source contaminant (nitrate) loading primarily from fertil-
izer sources. Fogg et al. [1999] pointed out a weighty
implication of such extreme mixing - that wells exhibiting
contamination today in alluvial aquifers similar to the
Salinas Valley (e.g., San Joaquin Valley, basin and range
aquifers, Gulf Coast aquifers, etc.) commonly derive only a
fraction of their production from the waters that are young
Figure 9. Simulated mean groundwater residence times plotted against mean simulated CFC-based
groundwater ages from the 10 realizations for (a) CFC-11 and (b) CFC-12. The error bars show the
ranges of simulated groundwater residence times and CFC ages for each of the 10 realizations.
WEISSMANN ET AL.: DISPERSION OF GROUNDWATER AGE 16 -11

enough to be contaminated. Thus, if the sources of recalci-
trant contaminants (nitrates and salinity in the Salinas Valley
case) have not diminished appreciably since their introduc-
tion starting in the 1940s and 1950s, one can expect steadily
declining water quality many decades into the future, even
if the sources are reduced or eliminated today. In other
words, if the groundwater contamination that we see today
in the Salinas Valley is due only to contamination of that
fraction of the water pumped by wells that has been exposed
to anthropogenic contaminants, this fraction will increase
for many decades or centuries into the future, leading to
gradually rising concentrations at the wellhead. Because of
the slow response time of basin-scale groundwater quality
in deep, alluvial systems like the Salinas and San Joaquin
Valleys, this degradation would be virtually irreversible on
the scale of decades to centuries.
[44] Such a scenario has played out with respect to
pesticide contamination in the Kings River fan aquifer
[Burow et al., 1999], where use of the chemical DBCP
circa 1950– 1972 has left a legacy of contamination in wells
up through the present. DBCP concentrations in this system
appear to have been declining in recent years owing to
chemical transformation and/or recycling of groundwater
through pumpage and reapplication for irrigation. The
average groundwater residence times in this comparatively
thin, coarse-grained system are young relative to many other
portions of the San Joaquin Valley and many other alluvial
basins. Thus the contamination and subsequent recovery of
groundwater quality in the Kings River fan aquifer system
within 30 to >50 yrs can be considered relatively fast. It is
likely that sources of contamination in finer-grained aquifer
systems (e.g., west side of the San Joaquin Valley) where
the time constants for transport are much greater have not
yet had full impact on deeper aquifers.
[45] The present study was conducted in part to inves-
tigate the age dispersion processes in greater detail, with
much more detailed hydrostratigraphic characterization and
a more carefully calibrated model, including some valida-
tion with measured CFC-based ages. Much like the results
of Fogg et al. [1999], we find significant dispersion of ages
within individual water ‘‘samples,’’ albeit for less regional
length and timescales. Thus the work of this study reinfor-
ces the conclusions of Fogg et al. [1999] regarding ground-
water sustainability in the presence of nonpoint source,
recalcitrant contaminants.
[46] Such trends in groundwater quality can only be
detected through very long-term monitoring, which is
typically rare. Although groundwater hydrologists and
managers intuitively know that groundwater quality
changes can be very slow, there is a strong tendency to
stop monitoring water quality when certain chemical con-
stituents show little variation for several months or years.
Although data on long-term water quality trends are rare,
some of the available data show an alarming consistency
with the above hypothesis regarding long-term degradation
of groundwater quality. For example, Dubrovsky et al.
[1998, p. 17] show average groundwater nitrate concen-
trations rising steadily from the 1950s through the 1980s
and 1990s in the eastern San Joaquin Valley. Such data
together with our improved understanding of groundwater
residence time dispersion suggest that in many basins we
may presently be viewing only the ‘‘early breakthrough’’ of
this centuries long ‘‘tracer test.’’ Continued long-term water
quality monitoring and process investigation are therefore
paramount.
[47]Acknowledgments. This research was supported by the Coop-
erative State Research Service, U.S. Department of Agriculture, under
agreement 93-38420-8792, the National Science Foundation (EAR-98-
70342), University of California Water Resources Center (W-901), Occi-
dental Chemical Company, the U.S. EPA (R819658) Center for Ecological
Health Research at U.C. Davis, NIEHS Superfund Grand (ES-04699),
University of California Toxic Substances Teaching and Research Program,
and Lawrence Livermore National Laboratory. Although the information in
this document has been funded in part by the United States Environmental
Protection Agency, it may not necessarily reflect the views of the Agency
and no official endorsement should be inferred. We benefited greatly from
discussions with Karen Burow, Steve Carle, and Thomas Harter and from
comments on the manuscript from Karen Burow. Comments by two
anonymous reviewers and the associate editor also led to significant
improvements to the manuscript.
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WEISSMANN ET AL.: DISPERSION OF GROUNDWATER AGE 16 -13

Figure 6. Simulated groundwater residence time distributions from the midpoint of selected well
screens for each of the 10 realizations: (a) B1-1, (b) B4-1, (c) B4-2, (d) B5-1, and (e) B5-2. Dashed
portions of the residence time distribution curves indicate that >10% of the particles required estimation
of groundwater residence times using the depth versus residence time relationship of Figure 7. The thick
dashed line shows simulated residence times assuming a homogeneous aquifer system.
WEISSMANN ET AL.: DISPERSION OF GROUNDWATER AGE
16 -8