Critical evaluation of stable isotope mixing end-members for estimating groundwater recharge sources: case study from the South Rim of the Grand Canyon, Arizona, USA

This study is focused on groundwater along the South Rim of the Grand Canyon (Fig. 1). The study area encompasses the Coconino Plateau north to south from the South Rim to the San Francisco Peaks (SF Peaks), respectively, and east to west from the Little Colorado River to Mohawk Canyon, respectively, where surface elevation ranges from approximately 530–3,850 m (m) above North American Vertical Datum of 1988 (NAVD88). The primary units of South Rim hydrogeology are layered Paleozoic sedimentary rock intersected by a complex system of faults and fractures (Haynes and Hackman 1978; Billingsley and Hampton 2000; Billingsley et al. 2006; Billingsley et al. 2007). Most groundwater is found in the shallow sandstone Coconino aquifer and the deep carbonate Redwall-Muav aquifer, separated by the thick Supai Group of fine-grained sandstone and mudstone. A minor aquifer is present in the underlying Proterozoic rock (Metzger 1961; Cooley 1976). Groundwater generally flows from south to north and discharges at springs along the South Rim or directly to the Colorado River (Hart et al. 2002; Bills et al. 2007).

A recharge area was estimated to constrain δ²H and δ¹⁸O of precipitation data representative of recharge to South Rim springs and wells (Fig. 1). Without detailed maps of groundwater levels, the recharge area was based on surface watersheds (Steeves and Nebert 1994), land-surface elevation, regional geology, ground-based knowledge of spring location and geologic formations, and previously reported groundwater potentiometric surfaces (Hart et al. 2002; Bills et al. 2007). The entire Little Colorado River drainage basin was not included in the recharge area. Two groundwater sites for which this is most relevant (Blue Spring and GC-1 well) were located on the west side of the river, where substantially more precipitation occurs, implying limited recharge from east of the river would be captured. Further, the upper head waters of the Little Colorado River cover a vast area that is likely not representative of the recharge captured at the majority of springs and wells, and inclusion would have likely biased results of this work. More detailed delineation of recharge areas for individual springs is unwarranted given the available data.

Climatic data were compiled for weather stations—Fig. 1 and Table S1 of the electronic supplemental material (ESM1)—as 30-year normal (1981–2010) monthly total precipitation and snowfall (National Climatic Data Center; NOAA 2018). An approximation of the average snow water equivalent (SWE; depth of water (mm) if snow was completely melted) was estimated as follows. The ‘observed’ SWE was calculated as monthly total precipitation divided by monthly snowfall for the three coldest months (Dec, Jan, Feb). Sites with an unreasonable average ‘observed’ SWE (>50%) for the 3-month period or did not have snowfall data (WNM, PS, PR, GRCAA, and DMR; Fig. 1) were excluded from average SWE. Snowfall in the warmer winter months (May, Apr, Nov) likely has a higher SWE meaning the contribution of snowfall to total precipitation might be underestimated for those months. The fraction of winter (Nov–Apr) precipitation was calculated as the contribution of precipitation during the winter months to the total annual precipitation amount.

Observed δ²H and δ¹⁸O in precipitation and precipitation amount data (Table S2 of the ESM1) were compiled from the Global Network of Isotopes in Precipitation (GNIP; IAEA 2018), Waterisotopes Database (WID 2019) and from Beisner et al. (2016). Evaporative effects on observed δ²H and δ¹⁸O were investigated through deuterium excess values (d-excess = δ²H – 8 × δ¹⁸O; Dansgaard 1964). Grids of predicted mean monthly δ²H and δ¹⁸O in precipitation (Bowen 2018) were precipitation weighted using 30-year (1981–2010) mean monthly precipitation (PRISM Climate Group 2012) to account for the spatial variability of precipitation across the study area. δ²H and δ¹⁸O grids were resampled to match the resolution and cell extent of the precipitation dataset prior to the calculation. Precipitation weighting of gridded δ²H and δ¹⁸O was conducted on a cell-by-cell basis. Gridded data were subset using the estimated recharge area boundaries to calculate the respective mean modeled δ²H and δ¹⁸O monthly and seasonal end-members. Mixing end-member δ²H and δ¹⁸O were calculated for observed and modeled data on a precipitation-amount-weighted basis for elevation and seasonal groups as:where δ_wgt is the weighted mean isotopic value for the respective grouping, δ_i is the individual isotopic ratio, p_i is the related precipitation amount, and p_t is the total precipitation amount for the respective grouping. A pooled standard deviation was calculated for each respective weighted mean. The definition of seasons, for winter as November through April and summer as May through October were based on the climatic data compiled for this study, seasonal weather patterns in northern Arizona (group 3 in Figs. 3 and 4 of Tulley-Cordova et al. 2018), and observed δ²H and δ¹⁸O in precipitation relative to groundwater. For the purpose of this study, high and low elevation groups were separated by collection site elevation above or below 2,000 m above NAVD88, respectively. This elevation breakpoint was chosen based on clear differences in observed long-term precipitation data above and below 2,000 m.

Groundwater data were collected for this study between 2016 and 2018 by US Geological Survey (USGS) and National Park Service (NPS) staff following standard procedures (Gibs et al. 2012; Radtke et al. 2002; Ritz and Collins 2008; Rounds and Wilde 2012; Rounds et al. 2013; Skrobialowski 2016; USGS 2006, 2019a; Wilde et al. 2014; Wilde 2002, 2004, 2006). Stable isotope analysis was conducted by dual-inlet isotope-ratio mass spectrometry (δ²H, VG Micromass 602; δ¹⁸O, modified DuPont 491) at the USGS Reston Stable Isotope Laboratory, USA (Révész and Coplen 2008a, b). Previously published groundwater isotopic data—Zukosky 1995, Monroe et al. 2005, Bills et al. 2007, the National Water Information System database (NWIS; USGS 2019b)—were compiled (Table S3 of ESM1 and Fig. S1 of the ESM2) to investigate the temporal variability of groundwater δ²H and δ¹⁸O and expand the analysis of South Rim groundwater. Surface-water data were compiled from Wagner (1987), Waterisotopes Database (WID 2019), and NWIS (USGS 2019b) to constrain an end-member that might better represent recharge from surface run-off (Table S4 of the ESM1). Surface-water sites clearly and mainly derived from groundwater discharge were excluded.

Statistical analysis was used to identify differences in mean values, verify the relationship between δ²H and δ¹⁸O and explanatory variables, and evaluate trends in δ²H and δ¹⁸O to refine the conceptual model. Statistical difference in means were evaluated using nonparametric Wilcoxon test assuming unequal variance for nonweighted δ²H and δ¹⁸O arithmetic mean end-members and a Welsh test assuming nonnormal distribution for weighted end-members. Monotonic correlations between δ²H and δ¹⁸O and elevation, precipitation amount, and longitude were tested using Spearman’s ρ. The statistical significance of correlation and difference in means values (H₀ = difference in means is equal to 0) was tested at the 95% confidence interval (α = 0.05). Statistical analysis was conducted in R programming language (R Core Team 2018) using the base ‘stats’ package for hypothesis testing as wilcox.test and calculating correlation as cor.test(method = “spearman”) and the ‘weights’ package (Pasek et al. 2018) for the Welsh test as wtd.t.test(bootse = TRUE). Isotopic ratios in precipitation and groundwater were compared to independent explanatory variables (precipitation amount, elevation, longitude, groundwater age) using an ordinary least square regression (OLSR). Relationships between individual and seasonal weighted δ²H and δ¹⁸O and elevation were assessed in R as lm(weights = precipitation amount). Goodness of model fits were assessed using the square of Pearson’s correlation coefficient (R²). Statistical significance of regression fit and/or slope was evaluated at the 95% confidence level (α = 0.05). A local meteoric water line (LMWL), groundwater line (GWL), and surface-water line (SWL) were calculated by reduced major axis (RMA) regression (Crawford et al. 2014) as appropriate for this analysis since both variables are independent and have associated error. Precipitation weighting of the LMWL was not conducted as there was only a very weak observed relationship between δ²H and δ¹⁸O and precipitation amount (see section ‘Precipitation amount’). A total of 12 surface-water samples of δ²H and δ ¹⁸O were available (Table S4 of the ESM1)—Lake Mary and Lake Marshall southeast of the San Francisco Peaks near WCNM weather station, Volunteer Wash near the southwest base of the San Francisco Peaks, and the Little Colorado at Cameron approximately located between WNM and Blue Spring (Fig. 1)—were used to calculate the SWL.

The fraction of recharge sourced from winter precipitation (F_win; fraction winter) for a given groundwater sample was calculated using a precipitation weighted isotopic mass balance model described by Jasechko et al. (2014) as:where δ_gw is the measured isotopic ratio in groundwater, δ_s is the precipitation weighted mean isotopic ratio of summer precipitation or surface water, and δ_w is the precipitation-weighted-mean-isotopic ratio of winter precipitation. F_win was calculated for both δ²H and δ¹⁸O. Uncertainty in F_win was calculated following Phillips and Gregg (2001) as:where σ is the respective standard deviation for each component. The σ of groundwater is taken to be the analytical uncertainty (1‰ for δ²H, 0.2‰ for δ¹⁸O; Révész and Coplen 2008a, b). This is an underestimate of analytical uncertainty for groundwater data reported by Zukosky (1995). The σ of weighted seasonal end-members (δ_s and δ_w) were taken to be the standard deviation of the nonweighted values of δ²H and δ¹⁸O in precipitation for the given season. The method of uncertainty estimation described by Genereux (1998) provided similar results; Eq. (3) was adopted in this study for clarity in notation. Mixing model inputs and complete model outputs are provided in Table 1 and in ESM1. Table S3 of ESM1 is also reported in a USGS ScienceBase Data Release (Solder 2020).

Two important caveats to the δ²H and δ¹⁸O mixing model is the potential error in end-members associated with (1) evaporative concentration of isotopes in precipitation prior to recharge (i.e., enrichment; Stewart 1975) and (2) groundwater recharged under a different climatic regime where δ²H and δ¹⁸O in precipitation differed from modern values. In this study, the effects of evapoconcentration and paleoclimate cannot be disentangled from the seasonal signal on a sample-by-sample basis; yet, the drivers of the variations are central to identifying recharge sources in the study area.

To constrain the effect of evaporated waters on estimates of F_win, a mean and weighted mean δ²H and δ¹⁸O of surface water and summer precipitation, respectively, were calculated. The mean δ²H and δ¹⁸O of surface water was calculated by taking the average of three measurements reported by Wagner (1987), collected close in space and time, as a single value to include in the average of the remaining values to avoid biasing the limited surface-water dataset (n = 5). As summer precipitation was less influenced by secondary evaporation, calculated values of F_win using the precipitation end-member represent a minimum value.

The effect of paleoclimatic variation was investigated by plotting δ²H and δ¹⁸O versus mean ages reported by Solder et al. (2020) for select sites. Site selection criteria included (1) estimated groundwater ages greater than a few thousand years and not indicated to have a large component of modern water (i.e., low tritium (³H) and high terrigenic He (⁴He_terr); Solder et al. 2020), (2) locations can be used to construct a hypothetical flow path (i.e., not necessarily physically valid but representative of increasing groundwater age down hydraulic gradient), and (3) sites were not likely to have captured substantial groundwater from shallow aquifers. Indications of mixtures of modern (< a few 100 years) and paleo-recharge (>10,000 years) is the most common factor limiting data that could be used for the comparison (see Solder et al. 2020). Statistical analysis of correlation and fitted OLSRs were used to evaluate the relationship between δ²H and δ¹⁸O and groundwater age.

Climatic data compiled for long-term weather stations show precipitation falls entirely as rain between May and November and there are distinct seasonal peaks in total precipitation (Fig. 2a) associated with winter low pressure systems and the summer North American Monsoon. Winter season precipitation does not fall entirely as snow in the study area with SWE totals tending to be less than total precipitation (Fig. 2a). Total annual precipitation and snowfall are correlated with elevation (Fig. 2b) where higher elevations receive more precipitation. The fraction of total annual precipitation that falls during winter months does not change significantly with elevation (Fig. 2b), so although higher elevations receive more precipitation, overall there is not an elevational bias to seasonal precipitation amounts.

Observed δ²H and δ¹⁸O in precipitation ranged from −158.2 to 11.2‰ and −20.4 to 7.6‰, respectively, and plot along the global meteoric water line (GMWL; Craig 1961) except for some data falling below the line (i.e., low d-excess), which tend to occur for samples with high values of δ²H and δ¹⁸O (Fig. 3, Table S2 of the ESM1). Mean monthly and seasonal modeled precipitation data show a similar trend to the observed data but fall closer to the GMWL than the LMWL with high d-excess observational data being the source of disagreement (Fig. 3).

In total, individual measurements of δ²H and δ¹⁸O (n = 167) were available for 50 groundwater (springs and wells) sample locations in the study area (Table 3 and Table S3 of the ESM1; Fig. 3). Groundwater δ²H varied from −71 to −114‰ with a mean and standard deviation of −88.8 ± 5.4‰ and groundwater δ¹⁸O varied from −8.5 to −15.9‰ with a mean and standard deviation of −11.92 ± 0.83‰. Of the 50 total groundwater sample sites, repeat sampling was conducted at 40 locations (Table S3 of the ESM1). The relative percent error from repeat data indicates δ²H and δ¹⁸O varied at a given site by less than 1.1% on average. Two sites with long-term records, Indian Garden Spring (n = 11 over 24 years) and Monument Spring (n = 11 over 20 years), show relative percent change in δ²H of 0.9% and 1.9% and in δ¹⁸O of 0.5 and 1.4%, respectively. Two available samples of δ²H and δ¹⁸O from JT Spring are significantly different even though the samples were collected less than a month apart (Table 3 and Table S3 of the ESM1). It is suspected that the earlier sample, with a more enriched δ²H and δ¹⁸O, may have been in error (more likely that sampling error would result in a more enriched sample), but it cannot be ruled out that the variability in δ²H and δ¹⁸O is real and additional data collection is needed. In general, no seasonal variations of δ²H and δ¹⁸O were observed in groundwater except at Canyon Mine Well and Salt Creek Spring (Table S3 of the ESM1). A statistically significant correlation was found between sample month and δ¹⁸O at Canyon Mine well (Spearman’s ρ = 0.96, p-value = 0.002, n = 6) and between sample month and δ²H, δ¹⁸O at Salt Creek Spring (Spearman’s ρ = −0.95, −0.98, respectively, p-value <0.001, n = 7). The long period of record over which samples were collected at these sites (24 and 22 years, respectively) and the limited sample sizes mean the correlation has little statistical power but does provide context for mixing model results for those sites.

Groundwater δ²H and δ¹⁸O generally cluster together and fall along the GMWL, with a clear evaporative signal (values farther falling to the right of the GMWL) at more enriched values of δ²H and δ¹⁸O (Fig. 3). Surface-water samples δ²H ranged from 0.5 to −11.8‰ with a mean and standard deviation of −8 ± 4.1‰ and δ¹⁸O ranged from −23.1 to −86.8 with a mean and standard deviation of −65 ± 20‰ (n = 12; Fig. 3; Table S4 of the ESM1). Mean δ²H and δ¹⁸O in surface water after correction for sampling bias used for calculating F_win was −38.3 ± 18.03 and − 2.4 ± 1.08, respectively (Fig. 3). Observed summer precipitation and surface-water means and the modeled winter precipitation means constrain the majority of groundwater data, whereas the observed winter precipitation mean does not.