1. Introduction
Headwater basins are recognized as being critically important for generating runoff that is captured in reservoirs and used for irrigation and municipal water supplies. As climate change progresses, precipitation in subalpine regions will occur more frequently as rain rather than snow, which could have drastic impacts on stream flow and on groundwater recharge. Snowpack in the Sierra Nevada of California allows for slow melting and gradual groundwater recharge in basins; however, as more precipitation occurs as rain, more limited opportunity for groundwater recharge is likely to cause increased run-off as overland flow [
1,
2,
3,
4,
5]. Groundwater is essential to the area as it provides baseflow to Martis Creek during the dry summer months, which is critically important for maintaining stream ecosystem health. Discharge that ends earlier in the summer or fall as a result of climate change or of groundwater pumping that continues into the summer and fall will put stress on the baseflow of the stream. Groundwater discharge to the stream also moderates stream temperature, especially in the late summer and fall, which is essential to the viability of the fish population in the stream [
6,
7,
8,
9,
10].
Groundwater influx to streams is difficult to quantify, but changes in groundwater influx due to pumping will be regulated in California under the Sustainable Groundwater Management Act [
11]. Lower order streams like Martis Creek are typically not gauged and gaining and losing reaches are not known. Geochemical methods like the one described here offer an alternative to physical measurements like stream gauging and to modeling methods that may be associated with high uncertainty.
A number of studies have used
222Rn as a tracer of groundwater influx in streams and a few of those used introduced tracers to determine the degassing constant in order to quantify groundwater influx to the river [
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32]. Most current studies utilizing
222Rn as a tracer use complementary methods to examine groundwater source, age of groundwater, or flowpath. Some studies use physical parameters such as flow measurements [
12,
13,
14,
15,
16], temperature [
14,
15,
17,
18], or electrical conductivity [
14,
17,
18,
19] in addition to
222Rn to better constrain locations of groundwater inflow. Another method is to use multiple naturally occurring tracers, such as major ions [
20],
4He [
20,
21],
87Sr/
86Sr [
15,
20,
22], Cl [
14,
20,
23,
24], and thoron [
25], among others, to increase accuracy in groundwater inflow calculations. There have been few studies that use introduced tracers as a way to better characterize the system, though NaCl, propane [
26], and SF
6 [
16,
18,
27,
30] have been used successfully. Multitechnique approaches give a more complete picture of the interaction between groundwater and surface water [
24] and lower prediction error for groundwater inflow [
16]. For instance, resolutions of groundwater inflow rates can be as low as 5 mm/day for electrical conductivity and ion tracers and 2 mm/day for radon [
28].
In this study, we identified reaches of Martis Creek with groundwater discharge by measuring the concentration of naturally occurring
222Rn and introduced xenon (Xe). Radon-222 is a radioactive (half-life 3.8 days) gaseous daughter product in the
238U decay series that accumulates in groundwater. Cox et al. [
33] also used
222Rn as a tracer of groundwater influx in Squaw Creek in the nearby Olympic Valley. However, in that study, the degassing constant had to be estimated based on prior studies in similar streams. The introduction of a Xe tracer in this study allows direct quantification of the degassing parameter. Additional studies, such as those performed by Clark et al. [
34] and Benson et al. [
35], have used introduced tracers such as
3He and SF
6 to examine gas exchange rates. In this study, groundwater influx is determined by two independent methods: geochemically (using
222Rn as a tracer) and physically (using measured stream discharge). The goals of the study are to compare these methods, and to quantify groundwater discharge in an area where climate change is likely to affect both groundwater recharge and runoff.
4. Discussion
The change in flux of a dissolved gas with distance downstream is a balance between the flux into the stream from groundwater and hyporheic zone sediments and the flux out of the stream due to evaporation losses, degassing (volatilization), decay, and losses to the hyporheic zone, as represented by the equation [
27]
where, at time
t,
Q is stream discharge (m
3/day),
I is influx (m
3/day),
ci is the initial
222Rn activity (pCi/L) of groundwater discharge to the stream,
c is
222Rn activity (pCi/L) at location
x,
w is the mean stream width (m),
E is the evaporation rate (m/day),
k is the degassing constant (m/day),
d is the mean stream depth (m),
λ is the radioactive decay constant (day
−1) for
222Rn,
γ is the production rate for
222Rn (pCi/L/day) within the hyporheic zone,
is the porosity of sediments in the hyporheic zone,
h (m) is the thickness of the hyporheic zone, and
th is the mean residence time of water (day) within the hyporheic zone [
27].
Since the time the stream water takes to go from the tracer injection point to the end of the stream survey is negligible compared to the half-life of
222Rn, the term
can be eliminated. Additionally, if production in the hyporheic zone is effectively zero (as demonstrated later in this section), the concentration of
222Rn activity in the hyporheic zone porewater will be equal to that in the stream water, and the equation may be simplified by eliminating the last two terms
[
33]. The equation may be further simplified if evaporation is neglected, which, in the case of Martis Creek, is appropriate, since the creek experiences minimal evaporation over the short study reach. Stream width
w varies from 117 to 658 cm, and the evaporation rate
E for streams the size of Martis Creek is estimated to be between 10
−3 and 10
−2 m/day. Measured
222Rn activities
c vary from 27 pCi/L to 169 pCi/L. In that case, the term
is negligibly small, which leaves
Rearranging terms to solve for
I gives
which is used to calculate the groundwater influx (
I) to Martis Creek. Stream discharge (
Q), gas transfer velocity (
k), mean stream width (
w), and stream
222Rn activity (
c) were all measured, while groundwater
222Rn activity (
ci) was estimated to be 400 pCi/L (
Table 3). To evaluate the uncertainty on the estimated groundwater discharge patterns, additional analyses were performed with groundwater
222Rn activities of 200 pCi/L or 800 pCi/L.
Groundwater inflow for each of the 50 sections was estimated by minimizing the difference between the measured and modeled
222Rn concentrations. Simultaneously, the xenon concentration was modeled in the stream, decreasing due to gas exchange between the stream and the atmosphere and dilution by groundwater discharge. The xenon concentration at the first xenon survey location (MC04) was fixed at 44 nanomol/L. Stream discharge was fixed to the measured stream discharge (4380 m
3/day) at MC-01, 11 m upstream of the xenon injection location. Stream flow upstream of MC-01 was calculated by subtracting the estimated groundwater inflow. This approach also allowed for the effective gas exchange coefficient (
kw) to be optimized, considering xenon dilution by groundwater inflow. The objective
O for the optimization was the sum of squared differences between the measured and modeled
222Rn and xenon concentrations, divided by the measurement uncertainty:
Figure 3 shows the resulting modeled
222Rn and Xe concentrations in Martis creek, together with the measured concentrations. The Xe concentrations are mostly well captured by the model, and are within the measurement uncertainty (8%). Differences between modeled and measured concentrations indicate variation in stream morphology resulting in variable gas exchange velocities along the 1 km stretch under investigation.
Measured 222Rn concentrations are generally well captured by the forward model. Measured 222Rn concentrations show stronger decreases than the model in the first 500 m of the investigated stretch, upstream of the Xe introduction. These decreases could indicate that the gas exchange rate was higher in this section. Modeled 222Rn concentrations with either 400 pCi/L or 800 pCi/L as groundwater 222Rn concentration do not capture the increase between 250 and 200 m before the Xe injection location and predict no groundwater increase over the interval. If a groundwater 222Rn concentration of 200 pCi/L is assumed, groundwater contributions are predicted between −325 m and −250 m, as discussed further below. Also, downstream of the Xe injection location, there appear to be sections where 222Rn decreases more rapidly over short intervals than the smooth decrease of Xe over larger intervals. As a consequence, the estimated groundwater discharge could be too low. These nuances show the importance of an introduced tracer constraint on the gas exchange rate. The optimized gas transfer velocity k (2.16 m/day) is at the low end of the range previously estimated, considering a stream width w of 3.5 m.
Although Xe and
222Rn show roughly similar, exponentially decreasing patterns, the calculations indicate that some groundwater influx is required at locations throughout the study reach to maintain observed
222Rn levels. Groundwater influxes are estimated at the location of Xe injection (0–35 m, 15 m
3/day/m), 250 m downstream (8 m
3/day/m for 26 m), and more gradually between 320 and 500 m (0–3 m
3/day/m). A small influx of 4 m
3/day/m is captured at 955 m. These groundwater influx locations are identified as independent of the groundwater
222Rn concentration
ci. The magnitude of groundwater inflow is inversely related to the assumed groundwater
222Rn concentration. The uncertainty of the stream flow measurements is such that neither the highest nor the lowest groundwater
222Rn concentration can be rejected as unlikely (
Figure 4). If a groundwater
222Rn concentration of 200 pCi/L is assumed, the optimization procedure finds a solution with significant groundwater inflow between −400 and −180 m along this stretch of Martis Creek. Flow measurements are not available to confirm this result.
To evaluate the contribution of the hyporheic zone to the
222Rn budget of the stream, let us assume that the groundwater influx is negligible. In this special case, the
222Rn concentration is given by Equation (8) (Equation (10) in [
27]):
The
222Rn concentration in the stream then depends on the production rate for
222Rn within the hyporheic zone (
γ), the thickness of the hyporheic zone (
h), the porosity of sediments in the hyporheic zone (
= 0.4), the radioactive decay constant for
222Rn (
λ = 0.18 day
−1), the mean residence time of water within the hyporheic zone (
th), the degassing constant (
k = 2.16), and the mean stream depth (
d = 0.16). The average of the measured hyporheic zone
222Rn production rates is 180 pCi/L/d. The thickness of the hyporheic zone (
h) and the residence time of water in the hyporheic zone are unknown. Assuming a thickness equal to the stream depth (0.16 m) and an infinitely short residence time (which yields the highest hyporheic zone contribution) results in an equilibrium
222Rn concentration in the stream of 5 pCi/L. Assuming that the thickness of the hyporheic zone is four times larger results in a stream concentration of 20 pCi/L. The dependence of the hyporheic zone contribution to the stream water concentration is illustrated in
Figure A5. We conclude that the hyporheic zone contribution is relatively minor compared with the measured
222Rn concentrations in the stream (27–169 pCi/L).
The groundwater influx “hot spots” would be difficult to identify using physical flow measurements, as it would not be practical to measure discharge over the spatial scale and with the accuracy necessary to ascertain the level of spatial detail afforded by the 222Rn results. While deployment of an extrinsic tracer may not be practical in many situations, measurement of 222Rn is relatively easy and inexpensive, and allows identification of reaches where groundwater influx is occurring on a scale pertinent for ecological considerations.
The modeled cumulative stream flow increases from 4380 m
3/day at the injection location to 5175 m
3/day at a distance 1 km downstream (
Figure 4). The calculated influx of groundwater is equivalent to 18% of the initial stream flow if a groundwater
222Rn concentration of 400 pCi/L is assumed. Lower (200 pCi/L) or higher (800 pCi/L) groundwater
222Rn concentrations result in higher (28%) or lower (11%) influxes of groundwater, respectively. Although the calculated groundwater influx values in this reach (800 m
3/day) are within the uncertainty ranges of the stream flow measurements made at various locations on August 15 and 16, the influx represents a critical portion of the annual discharge, as the importance of the persistence of the influx into the late summer and fall cannot be overstated. The presence of deep pools that act as refugia for fish and the moderating effect of groundwater discharge on temperature are recognized as controls on species distribution and total biomass [
6,
7,
8,
9,
10].
These results indicate that influx of groundwater to the stream is heterogeneous and related to topographic or morphologic stream features. The study reach is within the transition of the stream from being well shaded, with a relatively steep gradient (2–3%), and little anthropogenic alteration to having no overstory, with a low gradient (<1%), and nearby features including a golf course and housing development. The meadow area within and downstream of the study reach has been altered by historical land use practices and, to a lesser extent, by current recreational activities.
Another significant transition is the degree of incision and preponderance of eroded banks within the study reach compared with within the upstream reach, where bank stability is bolstered by outcrops and boulders. Within the study reach, the pool and riffle morphology likely plays a role in streambed sediment distribution and re-aeration of
222Rn, but observations of individual pools and riffles during the experiment did not correlate with locations of groundwater input (e.g., between 200–350 m and at 950 m) in an obvious manner. However, stream incision can cause an increase in the hydraulic gradient and result in groundwater drainage from the riparian sediments [
46], and this likely plays a role in the spatial variability in groundwater discharge along Martis Creek.