Introduction

Approximately 25% of the Earth’s population relies on karst-hosted groundwater (Ford and Williams 2007). In mountainous regions with extensive carbonate bedrock, “alpine karst aquifers” host the majority of groundwater, and are sensitive to changing recharge and precipitation patterns due to climate change (Ozyurt 2008; Moral et al. 2008; Goldscheider and Neukum 2010; Zeng et al. 2012; Frondini et al. 2014)—for example, approximately 50% of the population of Austria, including its capital, Vienna, relies on water from such aquifers (Savio et al. 2019). However, because of difficult accessibility, alpine karst aquifers have received little attention, and almost exclusively in the Alps (Chen and Goldscheider 2014; Filippini et al. 2018; Gremaud et al. 2009; Lauber and Goldscheider 2014). In fact, the only studies of alpine karst in North America were conducted in the Canadian Rocky Mountains in the 1980s (Ford 1983; Smart 1983, 1988). Furthermore, no studies of such aquifers have been conducted in arid to semiarid regions, such as the western United States, where water supplies in these aquifers may be adversely impacted by the effects of climate change. The Bear River Mountains of northern Utah are an excellent field laboratory to improve the understanding of groundwater recharge and movement in alpine karst aquifers.

The north–south trending Bear River Range in northern Utah is located in the Rocky Mountain province of the western United States, bounded on the west by Cache Valley that hosts the city of Logan and other communities (Fig. 1). It contains an alpine karst aquifer system that sustains the baseflow of the Logan River (Gooseff et al. 2005; Kolesar et al. 2005), the largest stream in the range. A number of springs drain into the Logan River, one of which, Dewitt Spring, is the primary source of water for the city of Logan (Spangler 2001), the largest city in Cache Valley. The eastern margin of Cache Valley hosts a highly productive aquifer system (Bjorklund and McGreevy 1971), later termed the principal aquifer by Robinson (1999), that is recharged in part by the Logan River.

Fig. 1
figure 1

a Location of the study area in the USA. b Topography of Cache Valley and the Bear River Range in northern Utah (UT) and southern Idaho (ID). The principal aquifer is shown as small white lines. The coordinate system is UTM Zone 12 N

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Nearly 7,600 m of Paleozoic marine limestones, dolostones and interbedded siliciclastic deposits comprise the bedrock geology of the Bear River Range (Williams 1948, 1958; Francis 1972). Quartzites and shales separate thick carbonate aquifer units and likely act as aquicludes (Dover 1995). The East Cache fault, a Basin-and-Range normal fault, cuts the west limb of the NNE-trending, south-plunging, Sevier-age Logan Peak syncline (Williams 1948; McCalpin 1989, 1994; Evans and Oaks 1996; Evans et al. 1996). The syncline (Fig. 2) funnels groundwater flow south to seven primary springs draining limestone- and dolostone-aquifer units adjacent to the Logan River (Fig. 2). The spring discharges range from 0.03 to 0.71 m3/s (Mundorff 1971; Spangler 2001).

Fig. 2
figure 2

Location of the Logan Peak syncline, and springs, streams and dye traces in Logan Canyon, Bear River Range (Spangler 2001; Bahr 2016)

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Dissolution of carbonate minerals can enhance the permeability of fractures, bedding planes and pore space in karst aquifers, with most flow typically occurring in solution-enhanced conduits and most storage occurring interstitially if enhanced pore space is present (White 2003). The resulting flowpath architecture may adhere to one of three conceptual karst flow models (Fig. 3): (flowpath a) a single-porosity model assumes that all groundwater moves through conduits on the order of days to weeks; (flowpath b) a double-porosity model adds an intermediate velocity component (years to decades) that moves along less-enhanced fractures; and (flowpath c) a triple-porosity model adds a third component of slow velocity (hundreds to thousands of years) that moves through solution-enhanced pore space.

Fig. 3
figure 3

Schematic of single, double and triple porosity conceptual models (after White 2003). Subsurface white areas are void space

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Dye traces in the Bear River Range indicate that groundwater flow along bedding planes and solution-enhanced fractures can cross topographic divides and drop up to 300 m, spending as little as 2–4 weeks in the subsurface (Spangler 2001, 2012; Bahr 2016). Bright (2009) used tritium data to identify possible decadal residence times for springs in the eastern Bear River Range. This bimodal age distribution aligns with that observed in a low-relief karst aquifer in Florida (Katz et al. 2009). Kolesar et al. (2005) and Neilson et al. (2018) both inferred the possibility for zones of slow karst development based on major-ion data of the Logan River and major tributary springs. Whereas matrix-dominated flowpaths of this type are documented in low-relief karst aquifers, geochemical lines of evidence used in alpine systems rarely address natural processes or anthropogenic solutes that confound interpretation. The presence or absence of groundwater with long (centennial to millennial) residence times has significant implications for water resource sensitivity to a variable climate.

The purposes of this study are to develop a conceptual model of the alpine karst aquifer system in the Bear River Range, and to increase the understanding of alpine karst aquifers in general by quantifying water–rock interactions and residence times. The new data reported here include major ion chemistry, oxygen and hydrogen stable isotope ratios (δ18O and δ2H values), stable isotope ratios of dissolved inorganic carbon (δ13C values), and tritium (3H) and chlorofluorocarbon (CFC) concentrations from the seven springs, as well as the δ18O of snow cores from 17 locations. These data are used to: (1) determine if springs have geochemical signatures that relate to specific hydrogeologic flowpaths, and if average spring discharge magnitudes indicate open-system (high discharge) or closed-system (low discharge) dissolution of calcite and dolomite; (2) calculate carbonate mineral saturation indices to ascertain whether geochemical signatures are controlled by dissolution processes or instead impart flowpath-specific fingerprints; (3) assess whether springs drain groundwater in equilibrium with contemporary atmospheric values reflective of short (weeks to months) or indicate longer (decadal or older) residence times; and (4) determine if snowpack isotopic values can be used to estimate groundwater recharge elevation for these springs. The data reported here were collected in March, May and November of 2017.

Materials and methods

Field chemical parameters

Temperature, pH, electrical conductivity (EC), dissolved oxygen (DO) and carbonate alkalinity were measured in the field at all seven springs during all three chemical sampling excursions. A YSI-30 m was used to measure temperature and EC during the first two excursions, but was replaced by a YSI EcoSense EC 300A meter for the third excursion. An Orion 2013A pH meter, a Hanna HI 9142 dissolved-oxygen meter, and a Hach model AL-AP MG-L alkalinity test kit were used to measure pH, DO and alkalinity, respectively, during all three field excursions. Total alkalinity also was measured by laboratory colorimetric titration to reduce error (±0.05 mg/L as HCO3) over the Hach field test kit (±20 mg/L as HCO3). Only the results from the laboratory titrations are reported here.

Major ion analysis

Samples for major ion analysis were collected from each spring during low-flow (4 March 2017) and high-flow (31 May 2017) conditions. Samples were collected in November 2017 only at Benchmark, China Row, Spring Hollow (2 November) and Dewitt (3 November) Springs. Chemically clean polyethylene bottles were prerinsed, filled with filtered (0.45 μm) sample water, and acidified with 1:1 trace-metal-grade nitric acid to a pH less than 2 (Wilde 2008). Samples for anion (chloride and sulfate) analysis were collected in glass bottles without acidification or filtering. All samples were refrigerated prior to analysis. Cation and anion analyses were performed at Utah State University (USU) Geochemistry Lab and the USU Water Research Lab using a Thermo X Series 2 Quadrupole inductively-coupled plasma mass spectrometer (ICP-MS) and a Dionex ion chromatograph (IC) to ±0.1 and 1.1 mg/L accuracy, respectively. The unacidified, unfiltered samples were also titrated for alkalinity as bicarbonate with 0.02 N sulfuric acid and Bromo Blue indicator to ±0.05 mg/L accuracy at the USU Geochemistry Lab.

O, H and C stable isotope ratios

Samples for O and H stable-isotope analysis were collected on 4 March and 31 May 2017 in chemically clean, clear glass bottles and refrigerated prior to analysis. Samples for C stable-isotope analysis were collected at the same time and in the same manner as O and H samples, but in amber glass bottles with no headspace to minimize aquatic biological-fractionation due to microbial activity (Mook 2001).

Snow samples for O and H stable isotopes were collected in March 2017 with a custom 10-ft (3.05 m) PVC toothed snow coring tool. The tool was driven through the snowpack until the soil was reached. The core then was cleaned of soil, ejected into a 1-gal plastic bag until melted, transferred to a chemically clean, clear glass bottle and refrigerated until analysis. Cores were collected over a range of elevations (1,543–2,393 m asl) where the snowpack was pristine and unaltered by remobilization via wind or anthropogenic activity.

Analyses for O, H and C stable isotope ratios were performed at the USU Stable Isotope Lab using a Thermo Scientific Delta V Advantage isotope-ratio mass spectrometer (IRMS) with a Gasbench II peripheral. The stable-isotope values were corrected for temporal drift and linearity effects as appropriate using in-house standards and calibrated to international standards and are reported using delta notation in per mille (‰). The δ18O and δ2H values of water and snow are reported +0.06 and 2.0‰, respectively, versus Vienna Standard Mean Ocean Water (VSMOW). The δ13C values of dissolved inorganic carbon (DIC) are reported +0.1‰ versus Vienna Pee Dee Belemnite (VPDB). To quantify the statistical relationship of δ18O values to elevation and location (“rainout” distance), bulk-snowpack stable-isotope values were assessed with analysis-of-variance. Linear regression was used to estimate a local elevation gradient, in ‰ per 100 m, after James et al. (2000). Precision for a data-dense δ18O elevation gradient is on the order of ±0.5‰ (Brooks et al. 2012).

Tritium and chlorofluorocarbon sampling and analyses

Two low-discharge springs (Benchmark, China Row) and two high-discharge springs (Dewitt, Spring Hollow) on either side of the Logan River were sampled for 3H and CFCs on 2 November (Benchmark, China Row and Spring Hollow) and 3 November (Dewitt) 2017. Tritium samples were collected in chemically clean 1-L Nalgene bottles such that no bubbles remained after pre-rinsing with spring water (Solomon 2017). Samples were transported overnight to Brigham Young University (BYU) and analyzed to a precision of ±0.1 TU and a detection limit of 0.3 TU using a Quantulus ultra-low-level liquid-scintillation counter after electrolytic enrichment (S. Nelson, Brigham Young University, written communication, 2017).

Chlorofluorocarbon samples were collected in accordance with USGS GDL (2017), using a peristaltic pump with Viton and copper tubing extended to the base of a 4-oz Boston-type glass bottle within a 1-gal stainless-steel container. The container was allowed to overflow such that a minimum of one gallon flushed through the sample bottle. The bottle then was capped (foil-lined) underwater with no visible air bubbles, inverted, and stored at room temperature until delivery to the University of Utah Dissolved and Noble Gas Lab the next day. The samples were analyzed to a precision of ±5%, and a detection limit of 1 pg/kg for CFC-113 and 0.5 pg/kg for CFC-11 and CFC-12.

Geochemical modeling

Reaction paths for water-chemistry evolution were created with the PHREEQC geochemical model using the llnl database (Parkhurst and Appelo 2013; after Langmuir 1971). The enthalpies of reaction for dissolution of stoichiometric calcite and stoichiometric dolomite were obtained from the PHREEQC llnl database. The enthalpy of reaction for dissolution of magnesian calcite was selected from Bischoff (1998). The enthalpy of reaction for dissolution of calcian dolomite was set to a default value of zero, which is standard in the absence of a thermodynamic estimate.

These models simulate simple end-member conditions for equilibrium water–rock–CO2 interactions in open- or closed-systems. Equilibrium speciation, mineral saturation indices and pCO2 were calculated for equilibration with dolomite or calcite to assess similarity of the models to field data. Carbon mass-balance modeling after Frondini et al. (2014) was performed using δ13C as a response variable to distinguish more readily open- and closed-system dissolution.

Lumped parameter modeling

Tracers such as 3H and CFCs are used to estimate groundwater ages by lumped-parameter modeling (Solder et al. 2016). The standard suite of lumped-parameter models, TracerLPM, is maintained by the US Geological Survey (USGS). Choosing the best model requires an understanding of the input functions for atmospheric concentrations of each tracer.

Tritium atmospheric concentrations were monitored at the IAEA Ottawa, Canada station until 2012 (IAEA 2014), after which records were extended with the known decay rate. It is the most complete atmospheric record in North America, and is commonly correlated with incomplete records at other locations to estimate the local atmospheric history (Michel 1989). The 3H record for Ottawa was correlated with the incomplete record from Salt Lake City (1963–1984) to produce a local estimate of atmospheric concentrations of 3H. Chlorofluorocarbon atmospheric concentrations are documented historically, and currently monitored at the Niwot Ridge facility in Colorado (Niwot Ridge LTER 2018).

Results

Field chemical parameters

Water with the lowest temperatures emerged from Dewitt and Spring Hollow springs (6.4 °C) in May and March, respectively, and the warmest water emerged from Benchmark Spring (11.0 °C) in May. All springs are near neutral, with pH values ranging from 7.1 to 7.8. Electrical conductivities ranged from 193 μS/cm at Woodcamp Hollow Spring in March to 446 μS/cm at China Row Spring in November. Dissolved-oxygen concentrations are relatively invariant across space and time, although concentrations in large springs (10.3–11.6 mg/L) exceeded concentrations in Benchmark and China Row Springs (5.4–8.8 mg/L). Alkalinity via laboratory colorimetric titration ranged from 208 and 305 mg/L (Table 1).

Table 1 Major ions in springs from all chemical sampling excursions (all units in mg/L)
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Major ion concentrations

Major-ion concentrations are summarized in Table 1. Major ions are dominated by Ca2+, Mg2+ and HCO3− across seasons. Anomalously high levels of Na+ and Cl− are present in China Row Spring in March and May, but were similar to other springs when resampled in November. Concentrations in the original two samples likely reflect contamination by road salt used during the winter months. These anomalous Na+ and Cl− results do not adversely impact interpretations presented in this paper.

Mineral saturation index and pCO2 calculations in PHREEQC

Mineral saturate states were determined using PHREEQC and are reported as the saturation index (SI):

$$ \mathrm{SI}=\left[\mathrm{ion}\ \mathrm{activity}\ \mathrm{product}\right]\div {K}_{\mathrm{sp}} $$
(1)

where Ksp is the solubility product (Table 2). Langmuir (1971) estimated equilibrium with respect to calcite and dolomite to be ±0.1 SI units (SI = 0 indicates equilibrium saturation), but propagation of error in this study (pH = ±0.1, Ca2+ and Mg2+ = ±1 mg/L) indicates that a value of ±0.3 is more appropriate. Saturation indices with respect to stoichiometric calcite and stoichiometric dolomite range from undersaturated to saturated and saturated to supersaturated, respectively. However, Spring Hollow Spring was undersaturated with respect to both calcite and dolomite in March. Carbon dioxide log partial pressures are shown in Table 2. Logan Cave and China Row Springs exhibit the highest partial pressures (log pCO2 = −2.1 atm). Benchmark and Woodcamp Hollow Springs exhibit the lowest (−2.5 atm).

Table 2 Calculated log pCO2 and saturation indices (SI) for stoichiometric calcite and dolomite, and calcian dolomite
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Stable isotope ratios

The δ18O, δ2H and δ13C (DIC) values for spring waters are reported in Table 3. The δ18O values for springs in 2017 range from −18.2 to −16.5‰ during high- and low-flow conditions, respectively. Corresponding spring δ2H values range from −135‰ during high-flow conditions up to −124‰ during low-flow conditions. The δ18O and δ2H values of snow core samples collected in March 2017 (Table 4) range from −18.9 and −145‰ to −16.0 and −125‰, respectively. During low-flow conditions spring water DIC δ13C values ranged from −11.8‰ (China Row Spring) to −9.9‰ (Ricks Spring). The range increased during high-flow conditions, from −12.3‰ (Ricks Spring) to −8.5‰ (Spring Hollow Spring).

Table 3 Oxygen and hydrogen (‰ versus VSMOW) and carbon (‰ versus VPDB) stable isotope values in springs
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Table 4 Locations and stable isotope values (‰ versus VSMOW) of snow cores collected at different elevations in the Bear River Range
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High-flow compositions in the springs represent a mixture of new seasonal snowmelt transported in surface water, shallow groundwater or both with preexisting groundwater. Thus, the high-flow isotope values for the snowmelt addition (Table 3) have been corrected using a simple volume-balance equation (after Kendall and Doctor 2003) that shift the high-flow δ18O values to −18.3‰ to −17.4‰. The δ2H and δ13C value adjustments are within analytical error (<2‰ and <0.1‰, respectively).

Tritium and CFCs

Tritium concentrations reported in tritium units (TU) and chlorofluorocarbon-11, -12, and - 113 concentrations in picomoles per kilogram (pmol/kg) are summarized in Table 5. In order to estimate the probable equivalent atmospheric concentration of CFCs at the time of recharge in parts-per-thousand by volume (pptv), a correction factor using estimates of recharge temperature and elevation was applied (Plummer et al. 2006). Air temperature in a thick unsaturated zone is typically close to the mean annual temperature (Busenberg and Plummer 1992). In Logan Canyon, the mean annual air temperature at SNOTEL sites from multiple elevations is approximately 4.5 °C (USDA 2018). Recharge elevations were estimated from highest-elevation dye-traced source locations (Spangler 2001) for Benchmark and Dewitt Springs. China Row and Spring Hollow springs were not dye traced. Their recharge elevations were estimated from the δ18O-elevation gradient determined in this study, and are presented in the following section.

Table 5 Chlorofluorocarbon (±5%) and tritium (±1 TU) concentrations in select springs
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A local record of 3H atmospheric concentrations was estimated by correlation of existing records from the Salt Lake City, Utah, station (1963–1984) with records from the Ottawa, Canada, station (1953–2012) following the linear regression procedure after Michel (1989):

$$ \mathrm{SL}=1.2\times \mathrm{OT}-9.0 $$
(2)

where SL is the atmospheric 3H concentration (in TU) at the Salt Lake City station, and OT is the concentration (in TU) at the Ottawa station. The reconstructed tritium curve for Salt Lake City is shown in Fig. 4. All spring concentrations lie within the range of estimated atmospheric values for Salt Lake City (Table 5), and hence may be assessed via lumped-parameter models (Solder et al. 2016).

Fig. 4
figure 4

Estimated time-series of atmospheric tritium concentrations (USGS GDL 2017) based on correlation with the Ottawa, Ontario IAEA station

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The CFC-12 concentration in China Row Spring is high enough to indicate some form of contamination (W. Mace, University of Utah Noble Gas Lab, written communication, 2018). The CFC-11 concentration in China Row Spring, if taken alone, is high enough to confound whether the recharge is contemporary or stems from the 1980s. However, the CFC-113 concentration is low enough to unambiguously attribute a pre-1990 recharge age. Values for all other springs are low enough to reasonably infer recharge ages.

Discussion

Water–rock interactions

PHREEQC water–rock reaction-path models

PHREEQC simulations of open and closed reaction paths of water with stoichiometric dolomite and calcite are explored for pCO2 conditions from 10–3.4 to 10–1.5 (Fig. 5). Measured spring values of pH and total dissolved inorganic carbon (TDIC) and calculated SI fall on open system simulations for pCO2 conditions between 10–2.5 and 10–2.0, consistent with the pCO2 for the spring waters (Table 2). Note that closed system reaction at a pCO2 of approximately 10–1.5 also matches the water compositions for the dolomite and calcite scenarios; however, this pCO2 is significantly higher than observed. Thus, these reaction-path models indicate that open-system water–rock reaction with calcite and dolomite are most likely.

Fig. 5
figure 5

a Reaction paths for groundwater interaction with stoichiometric dolomite along flowpaths with different fixed pCO2 values. b Reaction paths for groundwater interaction with calcite along flowpaths with different fixed pCO2 values

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Carbon stable isotope evolution models

Mass-balance calculations after Wigley (1972) were applied to test whether water–rock interactions likely occur in an open or closed system. For these calculations, the δ13C values of CO2 for precipitation in equilibrium with atmospheric CO2 was set to the current regional average (−7.3‰; Vogel et al. 1970), the δ13C for soil CO2 was set to the average value in the proximal Wasatch Mountains (−23.3‰; Cerling et al. 1991), and the mean δ13C value for the Garden City Limestone (−0.95‰; Davis 2017) was used to represent the carbonate bedrock.

Open- and closed-system water–rock reaction paths are explored in Fig. 6. The measured δ13C values and TDIC concentrations best match open-system evolution at pCO2 between 10–2.5 and 10–2.0 to equilibrium with calcite and dolomite. Closed-system paths at these pCO2 conditions can produce δ13C values similar to those observed, but at far lower TDIC concentrations. These simulations support evolution in an open system, implying that dissolution occurs mostly in conduit-dominated flowpaths that quickly transmit water. As this is the case across seasons for all observed springs, irrespective of discharge, it is likely that karst development is relatively uniform across the Bear River Range, and that flowpaths to each spring have similar hydrogeologic properties.

Fig. 6
figure 6

a Conceptual δ13C-evolution reaction-path model. b δ13C-evolution reaction-paths for groundwater dissolution of stoichiometric calcite in open- (O) or closed-system (C) conditions. c δ13C-evolution reaction-paths for groundwater dissolution of dolomite in open- (O) or closed-system (C) conditions

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Congruent versus incongruent dissolution along flowpaths

The geochemical modeling presented above assumes that the aquifer materials dissolve congruently, with no coincident mineral precipitation. If so, Ca:Mg molar ratios for stoichiometric dolomite (1.0), calcian dolomite (1.1–1.3), and calcite (44–89) in the Bear River Range (Kaliser 1972) should be reflected in spring compositions from flowpaths within different geologic units. Ratios cluster around one in all springs during low-flow conditions (Table 6).

Table 6 Ca:Mg molar ratios for springs in Logan Canyon
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Lower water temperatures during low-flow conditions (interpreted as baseflow) indicate the possibility for incongruent dissolution, driven by increased solubility of dolomite over calcite in colder water (Williams et al. 2007). Langmuir (1971) and Wigley (1972) document the incongruent dissolution of dolomite in low-temperature water; hence, winter baseflow conditions may drive water–rock interactions to achieve Ca:Mg molar ratios of less than one.

To test if low Ca:Mg molar ratios reflect incongruent dissolution, PHREEQC was used to simulate dissolution of stoichiometric or calcian dolomite (Fig. 7). Thermodynamic data from Wigley (1972) were used to represent calcian dolomite in the model (Ca:Mg molar ratio = 1.17:1). The results show that dissolution will proceed incongruently after water reaches supersaturation or saturation, respectively, with stoichiometric or calcian dolomite. Reaction paths for congruent dissolution of calcian dolomite, fixed at pCO2 values of 10–3.0 and 10–2.0 atm, respectively, explain the observed concentrations only for Spring Hollow and Ricks Springs. Similarly, reaction paths for congruent dissolution of stoichiometric dolomite at the same fixed pCO2 values explain the observed concentrations for Benchmark, Dewitt and Logan Cave springs, and possibly China Row Spring. However, reaction paths for incongruent dissolution of calcian dolomite at these fixed pCO2 values explain the observed concentrations for all seven springs, including Woodcamp Hollow Spring. This supports the notion that at least some incongruent dissolution occurs in the Bear River Range karst aquifer system. Hence, it is unlikely that Ca:Mg molar ratios are a reliable metric for fingerprinting particular hydrogeologic units in alpine karst.

Fig. 7
figure 7

Calcium and magnesium mass evolution via incongruent dissolution of stoichiometric or calcian dolomite and measured values in Bear River Range springs

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As with the Ca:Mg molar ratios, the saturation indices may yield insight into the type of dissolution. Saturation indices for calcian or stoichiometric dolomite and magnesian calcite of the March 2017 samples are positively correlated and adhere to a linear trend (Fig. 8a). Indices from subsequent sampling excursions cluster near slight dolomite supersaturation and calcite undersaturation. Calcite saturation is never exceeded, even though dolomite saturation indices exceed a value of one. This is a hallmark of incongruence (Langmuir 1971).

Fig. 8
figure 8

a Modeled saturation indices for dissolution of stoichiometric or calcian dolomite and magnesian calcite, along with calculated values for Bear River Range springs, shown in terms of saturation with respect to calcite and dolomite. b Modeled saturation indices for dissolution of stoichiometric or calcian dolomite and magnesian calcite, along with calculated values for Bear River Range springs, shown in terms of saturation with respect to calcite and calcian dolomite

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All springs except Spring Hollow Spring discharge groundwater supersaturated with respect to stoichiometric dolomite (Fig. 8a), but groundwater never exceeds saturation with respect to calcian dolomite (Fig. 8b). Undersaturation with respect to stoichiometric dolomite in Spring Hollow Spring waters may stem from mixing of groundwater from two different flowpaths. This likely is the case, as Spring Hollow Spring bears a δ13C value and a TDIC concentration of water supersaturated with respect to dolomite (Fig. 6).

Dissolution of calcian dolomite inherently produces one degree of supersaturation with respect to stoichiometric dolomite, removing the need for additional mechanisms. All springs adhere closely to the simulated reaction path of dissolving calcian dolomite, and never reach supersaturation with respect to it or calcite (Fig. 8b). Hence, it is likely that incongruent dissolution of calcian dolomite, where present, exerts a strong control on water–rock interactions.

Oxygen and hydrogen stable isotopes

Meteoric water isotopic characteristics

The δ18O and δ2H values for spring waters are similar to those for precipitation in Utah (Fig. 9; Bowen 2017). Most spring samples collected in March appear to fall below (to the right of) the global and local meteoric water lines (Craig 1961; Kendall and Coplen 2001). Snow samples lie along a significant linear trend (shown in blue on Fig. 9) with a slope similar to the Utah meteoric water line (Kendall and Coplen 2001) and given by the formula:

Fig. 9
figure 9

Oxygen and hydrogen isotopes for springs, streams, and snow in the Bear River Range in comparison to the global (Craig 1961) and Utah (Kendall and Coplen 2001) meteoric water lines (MWL)

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$$ {\updelta}^2\mathrm{H}=6.6\times {\updelta}^{18}\mathrm{O}+13.3 $$
(3)

On average, the spring isotope values measured in May are lower than those during March. This may reflect a seasonal difference where May conditions include winter precipitation in the form of snowmelt recharge and March reflects the isotopic value of late-fall recharge or a longer-term mean groundwater value. However, it seems unlikely that this represents an evaporative trend because all of the values lie within the range of observed values for precipitation in Utah (Bowen 2017). The range of snow isotope values encompasses the values measured in spring water, but also include much lower values. The lower values recorded by the snow is consistent with winter precipitation (Earman et al. 2006; Sharp 2007).

Stable-isotope elevation gradients

Oxygen stable isotope ratios for snow at different elevations are reported in Table 4. The δ18O values were assessed by analysis-of-variance (ANOVA) to correlate statistically the dominant geographic controls on fractionation. This tests the hypothesis proposed by Bright (2009) that progressive rainout (or precipitation as snow) of air masses traversing the Bear River Range is more significant than elevation on the δ18O values of precipitation. ANOVA ranks the significance of possible controlling factors (e.g., longitude and elevation), and informs the choice of variables for subsequent linear regression (Berthoux and Brown 2002).

The results (Table 7) suggest that elevation is the primary influence on fractionation in the Bear River Range. Although the F-statistic indicates a possible effect of longitude on δ18O values, iterative adjustment shows that it is not significant in conjunction with elevation, and decreases in significance when assessed separately. Elevation increases in significance to greater than 99.9% when used as the only predictor, which is evidence for a better empirical link. Hence, elevation (m asl) was chosen as the sole predictor variable for δ18O values in linear regression:

Table 7 Significance of longitude and elevation to δ18O in the analysis of variance
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$$ {\updelta}^{18}\mathrm{O}=-0.0028\times \mathrm{Elevation}-12.2 $$
(4)

The elevation isotope gradient (line slope) is −0.28‰ per 100 m. This gradient is similar to others for rain in the United States, but contradicts other interpretations that such gradients do not exist in snow or away from coasts (Abbott et al. 2000; James et al. 2000; Blasch and Bryson 2007; Brooks et al. 2012).

Groundwater recharge elevations often are estimated from elevation-gradient regression of δ18O snow values (James et al. 2000; Poage and Chamberlain 2001). Mean recharge elevations estimated from the linear relationship with δ18O values are summarized in Table 8. The δ18O-predicted mean recharge elevations qualitatively align with dye-trace estimates, except for Ricks and Benchmark springs. The mean δ18O-predicted recharge elevation for Ricks Spring is lower than the two far higher dye-traced sources (Fig. 2), Tony Grove (640 m) and Bunchgrass Hollow (805 m). The δ18O value for Ricks Spring (−17.4‰; Table 8) likely represents mixing of high-elevation recharge with a significant amount of Logan River water (δ18O = −17.6‰; Spangler 2001). In contrast, the δ18O-predicted mean recharge elevation for Benchmark Spring is higher than the dye-trace estimate (Table 8). Because Benchmark Spring’s stable-isotope signature is consistently more negative than Logan Cave Spring’s (Table 3), it is likely that the former’s recharge area is higher than the latter’s dye-traced source, despite dye traces that link both springs to a shared surface catchment (Fig. 2).

Table 8 Mean elevations and 95% confidence intervals for the snowpack contributing recharge to springs in Logan Canyon, estimated from the elevation gradient
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Groundwater residence times

Groundwater age estimates from lumped-parameter models (LPMs) of 3H and CFC data are presented in this section. Chlorofluorocarbon concentrations in pmol/kg were corrected for temperature and recharge elevation, then converted to atmospheric units of pptv after Busenberg et al. (2006). The corrected values are less than contemporary atmospheric concentrations except for CFC-12 in China Row Spring, which is likely contaminated (W. Mace, University of Utah Noble Gas Lab, written communication, 2018). Accordingly, China Row Spring was excluded from LPMs that involved CFC-12.

Binary-mixing model

Dye traces document the ability of some baseflow to move through Bear River Range karst with subannual transit times (Spangler 2002). This suggests that a binary-mixing model fixed at modern concentrations may be more accurate than a simple piston-flow model of older water.

The applicable age range for a binary-mixing model is limited to the date that each tracer was first detected in the atmosphere. The earliest detection at Niwot Ridge occurred in 1940 for CFC-11 and CFC-12, and in 1943 for CFC-113 (Jurgens et al. 2012). Earliest detection of tritium above background levels occurred in 1945 at the Ottawa, Ontario station. Hence, age estimates by this method are only possible if groundwater is younger than 75–80 years.

Binary mixing models of 3H and each CFC support the notion that groundwater is a mixture of subannual and decadal recharge, in this case 60–65 years old (Fig. 10; Table 9). The estimated percentages of decadal recharge present in baseflow using 3H (0–80% decadal) vary more than those predicted using CFCs (40–85% decadal).

Fig. 10
figure 10

Tritium and chlorofluorocarbon binary-mixing models of groundwater age in the Bear River Range alpine-karst aquifer system: a CFC-12, b CFC-113, c CFC-11. Dashed lines connect subannual recharge ages with decadal ages ranging from 60 to 65 years

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Table 9 Groundwater age in the Bear River Range alpine-karst aquifer system according to a binary-mixing model of chlorofluorocarbon and tritium concentrations
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It is likely that zones of lesser karstification exist in each spring’s groundwater basin, yet only inhibit flow by several decades; however, the results of the binary-mixing model do not rule out the possibility that a small percentage of much older (centennial to millennial) recharge may be mixing with subannual and decadal recharge.

Residence time of this magnitude was documented using 3H concentrations in dripwater recharge to a cave system in Israel (Even et al. 1986). The spread for the decadal-age component is similar to that of probability-density functions (PDFs) of age simulated for a karst aquifer in South Dakota (Long and Putnam 2009). If this is the case, extended droughts could significantly affect the baseflow of critical water resources decades later. Furthermore, the possible absence of matrix-dominated flow in alpine karst indicates that groundwater resources would be highly responsive to long-term climate shifts.

Conclusions

Observed spring δ13C DIC values range from −11.8 to −9.9‰, which are intermediate between carbonate bedrock (~ −1‰) and local soil CO2 (~ −23‰). Modeled reaction paths for dissolution in an open system align well with data presented in this study. Saturation indices and low Ca:Mg molar ratios indicate that incongruent dissolution exerts a strong control on water–rock interactions. Reaction path modeling indicates that dissolution of calcian dolomite (Ca:Mg molar ratio = 1.17:1), a primary aquifer material in the Bear River Range, exerts strong control on water geochemistry. These results support Bright’s (2009) conclusion that incongruent dissolution of calcian dolomite controls groundwater chemistry in the Bear River Range, and contrast with previous inferences of a less solution-enhanced, matrix-dominated flowpath that would be more resilient to climate change (Kolesar et al. 2005; Neilson et al. 2018).

Spring water δ18O and δ2H values are similar to Utah meteoric water. The δ18O values in the alpine snowpack display a significant statistical relationship with elevation (−0.28‰ per 100 m), suggesting that it may be a useful tracer for groundwater recharge elevation. Predicted recharge elevations from the δ18O gradient qualitatively align with dye-trace estimates. However, Ricks and Benchmark Springs have δ18O values that do not align well with dye-traced recharge elevations. It is likely that Ricks Spring represents a mix of alpine snowmelt and Logan River water. If Benchmark Spring, like Logan Cave Spring nearby, draws recharge from higher elevations, both should have similar isotopic values from snowmelt runoff during high-flow conditions. Benchmark Spring’s stable-isotope signature is clearly more negative across seasons (Table 3); hence, it is likely that a higher recharge zone supplies water to Benchmark Spring.

Tritium and chlorofluorocarbon concentrations in representative springs are likely best described by binary mixing of subannual recharge with 60- to 65-year-old groundwater. This suggests that the alpine karst aquifer system in the Bear River Range is best represented by a double-porosity, rather than a triple-porosity, model (Fig. 3b). The subannual recharge documented by dye traces implies that caverns are the primary flowpath to each spring, but the possible presence of decadal-age water may indicate that a slightly lower permeability flowpath dominates during baseflow. Nonetheless, the binary-mixing model results do not rule out the possibility that a relatively small proportion of matrix flow occurs, and that a triple-porosity system exists.

Neilson et al. (2018) concluded that matrix-dominated flow plays a role in the karst hydrology of the Bear River Range; however, the results of the present investigation suggest that such a role is negligible. The documented subannual recharge indicates the importance of conduit flow. This combined with the strong likelihood that open-system conditions dominate supports the conclusion that the alpine karst aquifer system can be described best by a double-porosity model. If this is indeed the case, the aquifer system may not provide drought resilience for water resources linked to it. Further study of this aquifer system, as well as other alpine karst systems in arid to semiarid settings, with an enhanced suite of geochemical tracers, including carbon-14 and helium-3, will help refine the understanding of potential matrix-dominated flow, and improve management of alpine-karst water resources in light of climate change.