Proceedings of the South Dakota Academy of Science, Vol. 97 (2018) 155

TRITIUM AND CARBON-14 IN THE MADISON LIMESTONE AQUIFER

Perry H. Rahn*Department of Geology and Geological Engineering

South Dakota School of Mines and TechnologyRapid City, SD 57701

*Corresponding author email: perry.rahn@sdsmt.edu

ABSTRACT

Back et al. (1983) dated groundwater in the Madison Limestone using car-bon-14. The groundwater ages range from recent values (“modern” at Rhoads Fork, Jones Spring, and Cleghorn Spring) to much older values (8,300 YBP at Upton, 17,300 YBP at Ellsworth AFB, 2,400 YBP at Evans Plunge, ~7,920 YBP at Cascade Springs, and 16,800 YBP at Philip). Assuming the 14C age is the time required for water to flow from the recharge area to the sampling point, Back et al. (1983) determined the hydraulic conductivity of the Madison Limestone.

Tritium concentration data were published by Naus et al. (2001). Tritium, a product of fallout from H-bomb testing, peaked in 1963. As a generality, the amount of tritium in water (tritium units, TU) is used by hydrogeologists to determine if recharge occurred before or after year 1963. The groundwater samples studied by Naus et al. (2001) showed that springs near recharge areas (including Rhoads Fork, Jones Spring, and Cleghorn Springs) have high tri-tium concentrations (62 TU, 276 TU, and 90 TU, respectively). Because these springs contain high tritium concentrations, the water includes precipitation recharged since 1963. The groundwater farther from recharge areas (wells such as Newcastle and Osage) have very low tritium concentrations (0.1 TU and 0.5 TU, respectively).

The 14C and tritium methods of dating groundwater help define a general model of groundwater velocity and flow direction. The radiometric data indicate short travel paths from recharge areas to “headwater springs”, and long ground-water–flow paths and long travel times for deep wells downdip from Madison Limestone outcrops. Most of the water from Cascade Springs and the spring at Evans Plunge (Hot Springs, SD) originates a great distance away because it takes thousands of years to get from the recharge area to the spring. Groundwater from deep wells in the Madison Limestone in the surrounding prairie region has taken tens of thousands of years to flow from its recharge area.

Keywords

Tritium, Carbon-14, Madison Limestone, Black Hills

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INTRODUCTION

The Madison Limestone, originally called the Pahasapa Limestone, is a dolomitic limestone ranging from approximately 600 ft (180 m) thick in the northern Black Hills to 400 ft (120 m) thick in the southern Black Hills. This Mississippian-aged unit crops out around the perimeter of the Black Hills. Where saturated, it is an enormous aquifer and serves as the water supply for Rapid City and other communities and private developments. All the large caves in the Black Hills are in the unsaturated parts of the Madison Limestone.

Large springs occur at the outer edge of the Madison Limestone outcrops. Rahn and Gries (1973) showed the location and discharge of the major springs as well as the location and recharge by streams that lose water to this unit (Figure 1). Rahn and Gries (1973) referred to the Madison Limestone and the overlying Minnelusa Formation as the “Paleozoic carbonate aquifer.” Generalized ground-water flow directions, estimated from discharge data of streams and springs in outcrop areas of the Madison Limestone and Minnelusa Formation are shown in Figure 1. Driscoll and Carter (2001) showed more recent U.S. Geological Survey gaging station discharge data for these Black Hills streams. Figure 2 is a regional map showing the potentiometric surface of the Madison Limestone for the south-western South Dakota area published by Back et al. (1983). Carter et al. (2002) showed more detailed potentiometric maps for major aquifers in the Black Hills including the Madison Limestone and Minnelusa Formation.

While these published reports give a general sense of groundwater flow direc-tions in the Madison Limestone, the intent of this paper is to examine tritium (3H) and carbon-14 (14C) data as a way to confirm flow directions and help deter-mine groundwater recharge areas. Specifically, the question of the origin of water that supplies several large springs is addressed.

TRITIUM

Tritium in groundwater is a result of fallout from hydrogen-bomb testing. Atmospheric nuclear bomb testing occurred in the 1950s and 1960s, and tritium concentration in rainfall over the Black Hills peaked in 1963 (Naus et al. 2001; Rahn et al. 2017). The amount of tritium in water can be used by hydrogeolo-gists to determine if recharge occurred before or after year 1963. The tritium concentration (tritium units, TU) in groundwater from a well or spring draining the Madison aquifer is related to mixing of this tritiated water with other ground-water in this aquifer and also to radioactive decay during the travel time from the recharge site to the sampling locale.

Naus et al. (2001) summarized the groundwater data collected from samples from the Madison and Minnelusa aquifers. Their data, summarized as “box plots” (Figure 3), includes the mean tritium units (TU) of numerous water samples.  They found that deep wells average ~2 TU and headwater springs average ~40 TU. The groundwater samples in that publication showed springs near recharge areas (including Rhoads Fork, Jones Spring, and Cleghorn Springs) have high

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tritium concentrations (62 TU, 276 TU, and 90 TU, respectively). Because these springs contain relatively high tritium concentrations, the water includes precipitation recharged since 1963. The groundwater farther from recharge areas, in wells such as Newcastle and Osage, have very low tritium concentrations (0.1 TU and 0.5 TU, respectively), and consists mostly of pre-bomb water.

Figure 1. Geologic map of the Black Hills showing interpreted groundwater-flow lines in the Paleozoic carbonate aquifer (from Rahn and Gries 1973, plate 3).

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Figure 2. Potentiometric map of western South Dakota area showing interpreted flow lines for groundwater in the Madison Limestone (from Back et al. 1983).

Figure 3. Tritium concentrations from four sites in the Black Hills (from Naus et al. 2001).

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Naus et al. (2001, Figure 30) described “Jones Spring” (site #277) as a “headwa-ter spring”. Jones Spring has a tritium concentration of 278.0 TU, much higher than the concentrations in any of the 166 other samples shown in their summary Table 7.  At first glance, it would seem that Jones Spring received an exceptionally high dose of radioactive fallout. However, the reason for the high TU at Jones Spring is most likely that it was sampled on 01-01-78, the date indicated in the footnote showing that this sample was reported by Busby et al. (1983). It was not sampled between 1993 and 1998, when most other samples were collected. With a half-life of 12.43 years for tritium, if the Jones Spring sample (278.0 TU) had been collected in 1993, it would have had a very high concentration when tritium rainout occurred in 1963. However, the main reason for the exceptionally high TU for Jones Spring is that the sample was taken in 1978, much earlier than other samples. A sample that measured 278 TU in 1978 would be expected to have about 120 TU in 1993, fifteen years later. Another reason for high 3H water in Jones Springs is that it is a perched spring (Rahn and Gries 1973). Precipitation would quickly recharge this spring that drains the limestone perched above a Tertiary laccolith intrusion. Since Jones Spring is a local perched hydrogeologic situation, it is not part of the overall groundwater flow map shown on Figure 1.

Back et al. (1983) supplied additional tritium concentration data for samples taken in 1978:

Rhoads Fork 62 ± 2 TUJones Spring 276 ± 10 TUSpearfish 90 ± 5 TUCleghorn Springs 182 ± 8 TUNewcastle 0.1 ± 0.2 TUOsage 0.5 ± 0.2 TUMcNenny 116 ± 5 TUBear Butte 0.3 ± 0.2 TUCascade Springs  4.7 ± 1.0 TU

Groundwater samples by Back et al. (1983) showed that springs near recharge areas, including Rhoads Fork, Jones Spring, and Cleghorn Springs, have high tri-tium concentrations: 62 TU, 276 TU, and 182 TU, respectively. The deep wells such as Newcastle, Osage, and Bear Butte have very low tritium concentrations: 0.1, TU, 0.5 TU, and 0.3 TU, respectively. Thus, the tritium data from Back et al. (1983) are consistent with the tritium data from Naus et al. (2001).

CARBON-14

Table 1 shows 14C age (years before present, YBP) for groundwater from the Madison Limestone groundwater. Plummer et al. (1990) adjusted these ages at some of the locations: Upton: 8,300 YBP; Evans Plunge: 2,400 YBP; Philip: 16,800 YBP; and Midland: 16,300 YBP. In general, the 14C ages range from young values (“modern” at Rhoads Fork, Jones Spring, and Cleghorn Spring) to

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older values (8,300 YBP at Upton; 17,300 YBP at Ellsworth AFB; 2,400 YBP at Evans Plunge; ~7,920 YBP at Cascade Springs; and 16,800 YBP at Philip). Assuming the 14C age is the time required for water to flow from the recharge area to a distant sampling point, Back et al. (1983) determined that the hydraulic conductivity of the Madison Limestone ranges from 0.5 X 10-6 m/s to ~24 X 10-6 m/s. Some of these hydraulic conductivity values were adjusted later for tempera-ture (Back et al. 1985), and by more refined 14C dating techniques (Plummer et al. 1990; Busby et al. 1991).

Table 1 (first column showing YBP dates) shows “unadjusted” 14C dates for Rhoads Fork: 610 YBP; Jones Spring: 0 YBP; and Cleghorn Springs: 730 YBP.   They also show much older 14C dates at Newcastle: 6,380 YBP; Osage: 4,990 YBP; and Cascade Springs: 13,560 YBP. The 14C dates are generally consistent with the 3H data. Deep wells downdip from outcrops of the Madison Limestone have low 3H and groundwater that consists almost completely of water recharged prior to hydrogen-bomb fallout. The 14C data indicate these waters were recharged thousands of years ago.

Table 1. 14C data for groundwater in the Madison Limestone (from Back et al. 1983, Table 4). The three columns showing ages (YBP) were calculated using different assump-tions and techniques. Some of these ages were slightly modified by Plummer et al. (1990) and Busby et al. (1991).

Location δ 14C 14C % mdn (lab) YBP* YBP† YBP§

1 Rhoads Fork -71 92 610 >mdn …

2 Jones Springs 0 100 0 >mdn …

3 Spearfish -257 74.3 2,460 >mdn >mdn

4 Cleghorn Springs -84 91.6 730 >mdn …

5 Newcastle -538 46.2 6,380 1,850 7006 Osage -453 54.7 4,990 130 >mdn7 McNenny -204 793.6 1,890 >mdn >mdn8 Upton -853 14.7 15,850 9,350 8,7009 Ellsworth AFB -942 5.8 23,540 17,900 17,300

10 Provo -927 7.3 21,640 16,270 ..**

11 Evans Plunge -715 28.5 10,380 5,270 1,90012 Philip -972 2.8 29,560 21,980 20,00013 Midland -976 2.4 30,830 22,020 20,100

14 Bear Butte -776 22.4 12,370 138 ..**

15 Cascade Springs -806 19.4 13,560 7,920 ..**

*Unadjusted ages: t = 5,730/loge 2 × loge (100/A) , where 5,730 is the half life (in years) of 14C †Adjusted age (See Back et al. 1983) §Additional adjustment age (See Back et al. 1983) 

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REGIONAL FLOW PATTERNS

Figure 1 shows groundwater-flow directions in the Madison Limestone and Minnelusa Formation within their outcrop area. This map was prepared using spring discharge data as well as the discharge of “disappearing” streams. The flow direction at the Boxelder Creek area was established by dye tests. The bulk of the flow directions are simply an interpretation using the geology and recharge/discharge values for the Madison/Minnelusa hydrologic unit.

A closer look is warranted to examine the flow directions shown in Figure 1 using both the 3H data from Naus et al. (2001) and 14C data from Back et al. (1983) as adjusted by Plummer et al. (1990). For example, the headwater springs (such as Rhoads Fork spring and Jones Spring) have high 3H as well as young 14C ages that both indicate limited travel distance as shown by the groundwater flow lines in Figure 1. On the other hand, the 14C data (second YBP column of Table 1) indicate that it took 7,920 years to travel from the recharge area for Cascade Springs to the spring outlet. The flow directions shown in Figure 1 indicate Cascade Springs water originates as far as 11 km north of Jewel Cave, about 62 km away. The 14C data confirm that a great distance such as this is required.

Naus et al. (2001), using stable isotopes of oxygen data, also indicated that the recharge area for Cascade Springs includes a large area in the western Black Hills. Additional confirmation of the immense catchment area for Cascade Springs is its total dissolved solids load (50 million kg/year), by far the highest of any spring or spring-fed drainage in the Black Hills (Rahn 2005).

Cascade Springs is the largest spring in the Black Hills, yet the USGS 1:24,000 scale topographic map shows that Cascade Springs has a very small topographic drainage basin. According to Driscoll and Carter (2001), the average discharge of Cascade Springs (from 1977 through 1995) was 0.55 m3/sec, yet the topo-graphic drainage area serving this spring is only 1.22 km2. After one year this spring would produce 0.55 m3/sec (3.1536 × 107 sec/yr) = 1.74 × 107 m3 of water. Therefore, theoretically, after one year this water volume would cover this 1.22 km2 to a depth = 1.74 × 107 m3 / 1.22 × 106 m2 = 14.3 m. This value is unrealistically large.  A much better recharge calculation would involve the entire groundwater drainage basin, which, from flow lines shown in Figure 1, is esti-mated to be 699 km2. A year’s worth of water from Cascade Springs would then cover this land to a depth = 1.74 × 107 m3 / 6.99 × 108 m2 = 0.0257 m. This is a much more reasonable value for the annual recharge (from precipitation) for this Madison Limestone aquifer.

An evaluation of the Madison Limestone’s permeability for the Cascade Springs groundwater catchment area can be made using 14C data and flowlines shown in Figure 1. The age (7,920 YBP) of the water discharging from Cascade Springs is a general value; the water molecules arriving at Cascade Springs are a compos-ite that come from all over the 699 km2 catchment area. Driscoll et al. (2002) showed that the northern part of the recharge area for Cascade Springs receives approximately twice the recharge as the southern part. Weighting these two areas shows the center of gravity of the recharge area to be approximately 48 km from the spring outlet. The 7,920 YBP travel time produces an average groundwater

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velocity reaching the spring of 6.06 m/yr. Although the porosity of the Madison Limestone is affected by karst conduits near sinking streams (Long et al. 2008), for simplicity it is assumed to have an effective porosity of 3% (Busby et al. 1991). Therefore, the specific discharge, also referred to as the Darcy velocity (Vd) = 0.182 m/yr. Inserting a hydraulic gradient (H/L) in this area of approximately 0.012 into Darcy’s Law can be used to calculate the hydraulic conductivity (K) = (Vd ) /H/L = (00.182 m/yr) /0.012 = 15.2 m/yr = 4.8 × 10-7 m/sec. This value is similar to the values calculated by Back et al. (1983) who determined Madison Limestone hydraulic conductivities ranging from 0.5 × 10-6 m/s to ~24 × 10-6 m/s in the area from the Black Hills to Philip and Midland.

Tritium and carbon-14 data can be used also to help evaluate recharge areas for the headwater springs on Spearfish, Rapid, and Castle creeks. Relatively short groundwater flow lines for these springs are shown on Figure 1. The 3H box plots (Figure 3) indicate recent recharge, and the 14C data (Figure 4, 2nd YBP column) show springs at Rhoads Fork and Spearfish Canyon as “modern.” Jones Spring, on the other hand, is unique in that it has a short travel time from precipitation recharge to the spring outflow due to a perched water table.

CONCLUSIONS

Tritium and carbon-14 age dates for groundwater in the Madison Limestone are generally consistent with groundwater-flow paths shown by Rahn and Gries (1973). The radiometric data indicate short flow paths from recharge areas to “headwater springs.” Jones Spring, for example, shows that the highest 3H and 14C data indicate recent recharge. The radiometric data indicate long groundwater-flow paths and long travel times for deep wells downdip from Madison Limestone outcrops. While the groundwater flow lines shown in Figure 1 give a general sense of flow paths and recharge areas, they are not completely accurate. For example, Putnam and Long (2007) show that dye tests, originating at the Spring Creek sinkhole area, indicate the direction of a conduit flow path is to the northeast.

The radiometric data help explain seemingly enigmatic hydrogeologic situ-ations such as Cascade Springs, an enormous spring discharging from a very small topographic basin. However, the surface watershed is not the same as the groundwater catchment basin. Geologic maps, potentiometric data, and dis-charge measurements, combined with radiometric data, show the large extent of the catchment area that serves to recharge Cascade Springs. This catchment area extends to the high limestone plateau north of Jewel Cave. It takes thousands of years for groundwater, initially recharged by precipitation, to reach the spring.

LITERATURE CITED

Back, W., B.B. Hanshaw, L.N. Plummer, P.H. Rahn, C.T. Rightmire, and M. Rubin. 1983. Process and rate of dedolomitization: mass transfer and 14 C dating in a regional carbonate aquifer. Bulletin, Geological Society of America 94:1415-1429.

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Back, W., B.B. Hanshaw, L.N. Plummer, P.H. Rahn, C.T. Rightmire, and M. Rubin. 1985. Process and rate of dedolomitization: mass transfer and 14 C dating in a regional carbonate aquifer. Reply. Bulletin, Geological Society of America 96:1098-1099.

Busby, J.J., R. Lee, and B.B. Hanshaw. 1983. Major geochemical processes related to the hydrology of the Madison aquifer system and associated rocks in parts of Montana, South Dakota, and Wyoming. U.S. Geological Survey. Water-Resources Investigations Report 83-4093, 180 p

Busby, J.F., L.N. Plummer, R.W. Lee, and B.B. Hanshaw. 1991. Geochemical evolution of water in the Madison aquifer in parts of Montana, South Dakota, and Wyoming. U.S. Geological Survey. Professional Paper 1273-F, 89 p.

Carter, J.M., D.G. Driscoll, J.E. Williamson, and V.A. Lindquist. 2002. Atlas of water resources in the Black Hills area, South Dakota. U.S. Geological Survey. Hydrologic Atlas HA-747, 117 p.

Driscoll, D.G., and J.M. Carter. 2001. Hydrologic conditions and budgets for the Black Hills of South Dakota, through water year 1998. U.S. Geological Survey. Water-Resources Investigations Report 01-4226, 143 p.

Driscoll, D.G., J.M. Carter, J.E. Williamson, and L.D. Putnam. 2002. Hydrology of the Black Hills Area, South Dakota. U.S. Geological Survey. Water-Resources Invest. Report 02-4094, 150 p.

Long, A.J., J.F. Sawyer, and L.D. Putnam. 2008. Environmental tracers as indica-tors of karst conduits in groundwater in South Dakota, USA. Hydrogeology Journal 16:263-280.

Naus, C.A.,  D.G. Driscoll, and J.M. Carter. 2001. Geochemistry of the Madison and Minnelusa aquifers in the Black Hills area, South Dakota. U.S. Geological Survey. Water-Resources Investigations Report 01-4129, 118 p. 

Plummer, L.N., J.F. Busby, R.W. Lee, and B.B. Hanshaw. 1990. Geochemical modeling of the Madison aquifer in parts of Montana, Wyoming, and South Dakota. Water Resources Research 26(9):1981-2014.

Putnam, L.D., and A.J. Long. 2007. Analysis of ground-water flow in the Madison aquifer using fluorescent dyes injected in Spring Creek and Rapid Creek near Rapid City, South Dakota, 2003-04. U.S. Geological Survey. Scientific Investigations Report 2007-5137, 27 p.

Rahn, P.H. 2005. Chemical weathering and land denudation of Paleozoic car-bonate rocks in the Black Hills, South Dakota and Wyoming. Proceedings of the South Dakota Academy of Science 84:55-69.

Rahn, P.H., and J.P. Gries. 1973. Large springs in the Black Hills, South Dakota and Wyoming. South Dakota Geological Survey. Report of Invest. No. 107, 46 p.

Rahn, P.H., A.G. Detwiler, and A.D. Davis. 2017. Tritium in groundwater in the Black Hills of South Dakota. Environmental Earth Sciences 76:762, 11 p.

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