Circulation and thermodynamics in a subglacial geothermal lake under the Western Skaftá cauldron of the Vatnajökull ice cap, Iceland

Authors


Abstract

[1] The subglacial, geothermal lake beneath the Western Skaftá cauldron (depression) in the Vatnajökull ice cap, Iceland, was accessed by hot water drilling through the overlying 300 m-thick ice shelf. Most of the ca. 100-m water column was near 4.7°C, but was underlain by a distinct ∼10 m-deep water mass at 3.5°C. The sensible heat content of the lake water is approximately twice the potential energy dissipated in outburst floods, and the temperature of the lake may be an important factor in the development of subglacial water courses of jökulhlaups from the lake. The lake temperature is higher than the temperature of maximum density, implying that convective heat transfer can take place in the lake. The vertical temperature structure suggests a large-scale recirculating flow in the lake, the rate of which was estimated from the lake temperatures and the chemical composition of a water sample.

1. Introduction

[2] Subglacial and marginal lakes exist in most glaciated areas on Earth and some are sources of damaging outburst floods (jökulhlaups) [Björnsson, 2002, 2004; Post and Mayo, 1971]. Research of subglacial lakes, in particular lakes below the Antarctic ice sheet, has received increased interest in recent years due to the potential for unusual life forms in the subglacial environment and because of climate records that may have accumulated over millions of years in sediments on the lake floors [Siegert, 2005]. The temperature of the lake water is thought to affect the development of jökulhlaups by contributing energy to melt basal ice and enlarge subglacial conduits. For example, the potential energy of water descending 1000 m corresponds to a temperature rise of 2.3°C, and thus source water temperatures of only a few degrees will contribute a comparable amount of energy. The hydrographs of many Icelandic jökulhlaups are difficult to explain with the theory of Nye [1976] unless the lake temperature is well above freezing [Björnsson, 1992; Clarke, 2003].

[3] However, very few direct or indirect measurements of the temperature of subglacial lakes are available. The vertical temperature profile in the Grímsvötn subglacial lake in Vatnajökull, southeastern Iceland, was measured in 1991 through a borehole near the center of the ∼250 m thick ice shelf [Ágústsdóttir and Brantley, 1994]. The lake was then ∼140 m deep at this location. The temperature was within a few tenths of a degree of the freezing point throughout the water column, except in a ∼10 m thick layer at the lake bottom where the temperature rose to 1–6°C. The temperature of the lake was again measured at a nearby location in 2002 when the ice shelf was at a comparatively low level so that the lake was only ∼20 m deep. The temperature was again found to be close to the pressure melting point, but higher temperatures near the lake bottom were not found [Gaidos et al., 2004]. On the other hand, the temperature of Lake Grímsvötn at the time of the large jökulhlaup due to the Gjálp eruption in 1996 [Guðmundsson et al., 1997] was inferred to be about 8°C [Björnsson, 2002]. These observations suggest that the temperature of the lake water in Grímsvötn can change significantly, a factor that may help explain the substantial variation in the observed shape of flood hydrographs from Grímsvötn.

[4] The vertical temperature profile in subglacial, geothermal lakes should reflect transport of geothermal heat from the lake bed to the bottom of the floating ice shelf. Time-averaged over the episodic drainage of the lake, melting at the bottom of the ice shelf should balance the inflow of ice from the surrounding ice cap. The geothermal heat flow, with an areal average on the order of 100 W m−2 for Grímsvötn and the Skaftá cauldrons [Björnsson and Guðmundsson, 1993; Jarosch and Guðmundsson, 2007] is much higher than can occur by conduction through the water column and must therefore take place by turbulent convection. Heat flow by convection can only occur if the temperature is above the maximum density point of water, Tmax, in at least some part of the lake. Tmax is in the range 3–4°C for pure water at pressures below 5 MPa (corresponding to water depth or head less than 500 m). If T < Tmax, heating of water will make it denser and convection is initially not possible. Continued heating from below will, however, raise the temperature above Tmax and large-scale overturning will eventually occur. Björnsson [1988] suggested that convection in the Grímsvötn lake would bring the temperature at the bottom of the lake to approximately 4°C, but assumed that the depth-averaged temperature of the lake would be close to the melting point of ice, in agreement with the measurements in 1991 reported by Ágústsdóttir and Brantley [1994]. The temperatures measured in Grímsvötn in 1991 and 2002 as mentioned above are not consistent with vertical transport of heat by convection in the lake or at least not at the locations of the boreholes, and those measurements may indicate that the geothermal melting is concentrated around the margin of the lake where ice is in contact with the bed.

[5] Jökulhlaups in the river Skaftá from western Vatnajökull occur at 1–2 year intervals with volumes of 0.05–0.4 km3 and a maximum discharge of 50–2000 m3 s−1 [Björnsson, 1977; Zóphóníasson, 2002]. The floods originate from two subglacial lakes below 50–150 m-deep and 1–2 km-wide depressions (cauldrons) in the ∼450 m-thick surrounding ice. In combination, the lakes drain approximately 50 km2 of the ice cap [Pálsson et al., 2006]. The rapid initial increase of the hydrograph of most jökulhlaups in Skaftá is difficult to explain without invoking an above-freezing temperature for the lake water [Björnsson, 1992].

[6] In June 2006, we used a hot water drill to penetrate the 300 meters of ice overlying the lake under the Western Skaftá cauldron. Calculations of melting rates indicate that a borehole with a diameter in the range 10–15 cm was produced in the lowest part of the ice shelf (T. Thorsteinsson et al., A hot water drill with built-in sterilization: Design, testing and performance, submitted to Jökull, 2007). We logged two independent temperature profiles through the lake water beneath the borehole and obtained a water sample at a level 3 m above the bed. One goal of these measurements was to quantitatively investigate the circulation, mixing, and heat transfer in the lake. We report here on the temperature measurements and present an analysis of vertical stratification and circulation in the lake based on the temperature profile and the composition of the lake water.

2. Methods

[7] Temperature profiles were obtained by manually lowering two Starmon mini temperature recorders and a DST milli combined pressure/temperature recorders (Star-Oddi Ltd.) slowly to the bottom of the lake and back, providing two profiles from the water level in the hole to the bottom of the lake from each sensor. The pressure sensor has an absolute accuracy of ±2 m and detects changes in depth to approximately 0.15 m. The accuracy of the Starmon mini temperature measurements was estimated to be ±0.02°C after zero-offset adjustment and correction for the approximately 12-second lag of the sensors using an exponential deconvolution procedure. The deconvolution procedure did not handle well the very rapid temperature changes that took place when the sensors crossed a thermocline near the bottom of the ice shelf separating cold borehole water from the considerably warmer lake water. Measurements from the next three minutes after each crossing, both on the way down and up, were therefore deleted from the records.

[8] A single 400 ml water sample was collected from a level about 3 m above the lake bottom using a gas- and water-tight sampler designed to operate in narrow boreholes in ice [Gaidos et al., 2007]. The water sample smelled strongly of hydrogen sulfide. For comparison, samples of snow were collected at the surface of the drill site and melted. The water sample, as well as snow samples for comparison with geochemical analyses, were filtered on site through a 0.2 μm Teflon filter into polypropylene bottles. Samples for determination of cations were acidified (Teflon distilled Suprapur®, Merck) whereas samples for anion constituents were not treated. Special gas-tight bottles were used to collect samples for determination of pH and total dissolved CO2. The concentrations of major cations and anions were analyzed using ICP-AES and RF-IC, respectively.

3. Results

[9] Figure 1 shows the temperature profile (as a function of depth below the upper surface of the ice shelf) in the entire water column (Figure 1, left) and in the upper, warmer water body with an expanded temperature scale (Figure 1, right). The temperature of the uppermost 90 m of the lake was 4.7 ± 0.1°C. This uniform water body was underlain by a ∼10 m-thick water mass with temperature close to 3.5°C and a ∼10 m-thick transition layer between the two water masses. The temperature rose 1–2°C within 1–2 m of the lake bed at 416 m depth. Figure 1 shows that the temperature of the lake water is at all depths above the temperature of maximum density of pure water, allowing for efficient transfer of heat by thermal convection. The total concentration of dissolved elements in the lake water was measured to be approximately 1500 mg kg−1 (Table 1), and mainly CO2, which is largely HCO3 at the pH of the lake). The dissolved elements lead to a slight lowering, on the order of a tenth of a degree or a few tenths of a degree, of the temperature of maximum density compared with that of pure water [Cawley et al., 2006], which is too small to concern us here. Figure 1 (right) with the expanded scale shows that the nearly constant temperature profile in the upper part of the water column contains fluctuations on a scale of 5–10 m and with an amplitude on the order of 0.05°C. These differ in the downward and upward profiles. Temperature variations with time were larger and more rapid in a 1–2 m thick layer next to the bed. The major elemental concentrations of the lake water and the snow samples are given in Table 1.

Figure 1.

The vertical temperature profile in the subglacial lake. (left) The temperature range of the whole lake. (right) An expanded temperature scale corresponding to the upper part of the lake above the cool water mass near the bottom. The profiles measured by the instruments on the way down and up are shown with separate curves. The bottom of the ice shelf (BS) and the bottom of the lake (BL) are indicated on the right hand axes. The dash-dotted line in Figure 1 (left) shows the temperature of maximum density, Tmax, for pure water at the pressure corresponding to the water depth [Caldwell, 1978].

Table 1. Major Chemical Composition of Lake Water, Snow, and Modeled Composition of the Aquifer Geothermal Fluid and Glacial Lake Watera
 06-SKJ04 Lake Water06-SKJ05 SnowGeothermal Water Modeledb14% Geothermal Water 86% Melted Ice
  • a

    Major chemical composition unit of measure, mg kg−1.

  • b

    According to mineral buffer vs. temperature equations given by Arnórsson et al. [1983].

  • c

    Stefánsson and Arnórsson [2002].

  • d

    Cl is a mobile component and can not be calculated; it depends on rock leaching in the geothermal system.

T (°C)4.50310 
pH/T (°C)5.22/16.15.71/21.56.8/310c 
CO21300 100301300
H2S36.90 23029.9
F4.220.030.130.04
SO415.790.05729.4
Cl1.950.26NAdNAd
Ca31.200.10.013
K1.590.038324.2
Mg1.5700.0010.0001
Na16.20.29614519
SiO260.49064884

4. Interpretation

[10] The temperature profile in Figure 1 implies that the water column is stably stratified at this location and thus not convecting except in the thin warm layer by the bed. Instead, we propose that heat transport into the lake occurs by buoyant geothermal plumes at discrete locations elsewhere in the lake and that large-scale circulation of the lake occurs when a denser fluid is formed by mixing of the upper, main water mass and meltwater, feeding the colder, lower water mass. Mixing of geothermal water with the lower water mass supplies the return flow to the upper, warmer water mass (Figure 2). The time-dependent fluctuations observed in the upper water mass might be caused by internal gravity waves. Disregarding possible vertical gradients in the concentration of dissolved elements, the period of internal gravity waves that might be excited in the lake can be estimated from the magnitude of the vertical temperature gradient and is approximately 3 hours in the uniform upper layer and about 20 minutes in the transition layer between the cold tongue and the warmer water above. This is short enough to produce the observed temperature fluctuations with time between the two measured vertical sections. According to this interpretation, the vertical temperature profile shows the internal thermal structure of a recirculating cell driven by nearby upwelling hot water and downwelling cold water. A peculiar feature of the convection in the lake arises because it takes place near the temperature of maximum density of water. The meltwater formed at the top of the lake has lower density than the main water body, but forms a higher density water mass when mixed with water from the main water mass.

Figure 2.

The recirculating flow in the lake below the cauldron. The dash-dotted rectangular region in the inset shows the location of the main drawing. The components in the flow of water into and out of the lake and between the two water masses in the lake are indicated in the figure (see text for explanations). (inset) Schematic drawing of the Western Skaftá cauldron.

[11] The chemical composition of the lake sample was dominated by high CO2 and H2S concentrations, the two weak acids (H2CO3/HCO3 and H2S/HS) buffering the water pH = ∼5. Other constituents were also very much enriched relative to the snow samples. The geochemical characteristics of Western Skaftá cauldron lake water are similar to Grímsvötn lake water, as inferred by Björnsson and Kristmannsdóttir [1984] from jökulhlaup samples and by Ágústsdóttir and Brantley [1994] from lake water samples, in that the water may be considered to be a mixture of two water bodies, geothermal fluid and melted ice. This mixture has reacted with volcanic rocks and sediments at low temperatures within the subglacial lake. The clearest indication of the geothermal fluid input are the very high CO2 and H2S concentrations. However, the lake water also had much greater concentrations of many components such as Mg and Ca than found in geothermal waters and glacial ice. These components are preferentially leached out of basaltic rocks during initial dissolution at low temperatures [White and Brantley, 1995] and we consider this to indicate leaching of volcanic rocks in the lake. This is supported by the fact that the silica concentration in the lake is close to equilibrium with amorphous silica, also a common observation at the initial stage of basalt leaching.

[12] The thermodynamics of the lake and the large-scale recirculating flow between the upper and lower water masses can be constrained by the temperature measurements together with the accumulated volume of flood water discharged in jökulhlaups from the lake and the chemical composition of the sample taken near the bottom. We assume that the lake is composed of two well-mixed water masses with uniform temperature, that the geothermal heat flow is continuously balanced by melting of ice and that the accumulation of water in the lake takes place by increasing the volume of upper water mass, while the colder tongue by the bed and fresh meltwater under the ice shelf maintain their volume. The assumption that the accumulation of water is confined to the much larger upper water mass is a simplification which does not affect our results much compared with assuming that the volume of the upper and lower water masses increases in the same proportion. Figure 2 shows a schematic diagram of the assumed exchange of water between the water masses and defines the notation used for the discharge components. Conservation of mass in the accumulation of water in the lake implies

equation image

where qjw is the average accumulation of water in the lake [m3 s−1], which is equal to the average discharge of water in jökulhlaups over time, qice is melting of ice in terms of the volume of melted water due to geothermal heat, qgw is the inflow of geothermal water into the lake, and qbw is the inflow of basal water due to precipitation falling as rain and melting of snow over the watershed of the cauldron. Conservation of mass in the internal circulation within the lake implies

equation image

where qlw is the outflow from the upper, main water mass in the lake, which is mixed with the meltwater and basal water to form the lower, colder water mass near the bed, and qtw is the outflow from the cold tongue near the bed, which is mixed with the geothermal water to form the upper, warmer water mass. Conservation of energy for the upper water mass implies

equation image

where h [kJ kg−1] denotes the specific enthalpy of the component indicated with superscript. The density of the flux components does not need to be specified in the individual terms of this equation because density differences between the components are so small that they may be ignored. The right hand side of this equation expresses the total inflow of heat into the upper water mass. This must balance the heat used to melt ice together with the outflow of heat corresponding to the flux component qlw and the accumulation of heat in the water mass corresponding to qjw. Conservation of energy in the mixing that generates the lower water mass implies

equation image

hice and hbw are equal and are both denoted by hmw because these components are both at the pressure melting point of ice. The enthalpies are known from the temperature of the respective water mass at the pressure encountered in the lake, here assumed to be 3.6 MPa, hmw = 2.77 kJ kg−1, hlw = 23.34 kJ kg−1, and htw = 18.31 kJ kg−1 [International Association for the Properties of Water and Steam (IAPWS), 1997]. Lice = 334 kJ kg−1 is the latent heat of fusion of ice. The accumulation of water in the cauldron, qjw ≈ 2.54 m3 s−1, and the inflow of basal water qbw ≈ 0.25 m3 s−1, are estimated from the history of jökulhlaups in the Skaftá river in the period 1994–2002 [Zóphóníasson, 2002] and assuming an average ablation and rainfall of 0.4 mw.e a−1 over a watershed of 20 km2 [Pálsson et al., 2006]. We assume that ground water recharge into the geothermal system is from source areas outside of the watershed of the cauldron so that the component qgw constitutes inflow into the lake in addition to qice and qbw. Equations (1) to (4) are four equations relating the four unknowns qice, qgw, qlw and qtw for a given value of the enthalpy of the geothermal water, hgw, entering the lake.

[13] The enthalpy of the geothermal water cannot be determined from the conservation equations for mass and energy alone. However, it can be inferred from the composition of the subglacial lake water, assuming closed system boiling (i.e., conservation of initial enthalpy of the geothermal fluid at depth). The chemistry of geothermal fluids is controlled by equilibrium with secondary minerals and the water for all major components except Cl [Giggenbach, 1980; Arnórsson et al., 1983; Stefánsson and Arnórsson, 2000]. The concentrations of chemical constituents that are not altered by further low-temperature water-rock interactions in the lake may then be found from the flux components determined from equations (1) to (4) for a given value of the temperature (and enthalpy) of the deep geothermal fluid. Lake water was clearly altered by low-temperature water-rock interactions as indicated by the comparatively high concentrations of Ca and Mg compared with the simulated concentrations in Table 1. However, dissolved major gases like CO2 and H2S are not affected by this process and can therefore be used as references.

[14] Equations (1) to (4) were solved using an empirical expression for the equilibrium concentration of CO2 for geothermal fluids as a function of temperature from Stefánsson and Arnórsson [2002]. This yielded the estimates Tgw = 310°C and hgw = 1401 kJ kg−1 for the temperature at depth and the enthalpy of the geothermal fluid. We find that the lower water mass in the subglacial lake is a mixture of 14% geothermal fluid and 86% melted ice. The corresponding fractions in the upper water mass are estimated as 19% and 81%, respectively, and the discharge components are qice = 1.8, qgw = 0.47, qlw = 6.4 and qtw = 8.4 m3 s−1. Uncertainty in the equilibrium CO2 concentration as a function of the temperature of the geothermal fluid at depth is a source of error in these estimates. If corresponding relations from Arnórsson and Gunnlaugsson [1985] are used, the inferred values for the temperature and enthalpy at depth become Tgw = 318°C and hgw = 1449 kJ kg−1. This only changes the fluxes by <0.1 m3 s−1. Another source of uncertainty is the assumption that ground water recharge into the geothermal system is from source areas outside of the watershed of the cauldron. If the geothermal system is assumed to be recharged from the lake itself, a slightly different system of equations needs to be solved, resulting in changes of 0.1–0.5 m3 s−1 in the estimated flux components. Similar calculations were carried out for open system boiling where the steam is separated from the water upon depressurization boiling and the enthalpy of pure steam at the boiling temperature (hsteam) is substituted for geothermal water enthalpy (hgw) in equation (3). However, for plausible temperatures for the deep geothermal system down to separation temperatures between 300 and 245°C, single-stage open system boiling produces a very CO2- and H2S-rich steam and lake concentrations of CO2 and H2S ten times greater than measured, indicating that the system is chemically closed rather than open.

[15] Our model and these thermodynamic and chemical constraints lead to predictions for the flow of heat, water and chemical constituents into the lake and mixing between the two water masses. The results indicate that geothermal melting of ice is the largest (71%) inflow into the lake, followed by geothermal fluid (19%) and basal water (10%). The continuous exchange of water between the water masses is approximately four times larger than the meltwater inflow. qice is found to be approximately 0.5 m3 s−1 larger and about 90% of the inflow to the lake if the geothermal system is assumed to be recharged from the lake.

5. Discussion

[16] Our model includes several simplifying assumptions: The assumption of well-mixed water bodies is justified by the comparatively uniform temperature of 4.7°C, indicating that the upper part of the lake is well-mixed, although heat is presumably added to it at one or more distinct locations. This assumption will of course not hold at downwelling locations and some nonuniformities must also be expected above the locations where geothermal fluid enters the lake. The use of a single water mass to describe the lower, more complex temperature profile is also crude. Our simple calculations also ignore seasonal variations in the inflow of surface meltwater and rain to the lake. This could reach ∼1 m3 s−1 during summer, but is much lower at other times of the year.

[17] Our model also implies but does not describe several important processes for which we have no direct information. Glacial meltwater is more buoyant than lake water and will therefore accumulate together with the meltwater from the ice shelf bottom at the highest locations within the lake. In our model, the meltwater mixes with warmer lake water to produce the lower water mass, but it is not clear where or how this mixing takes place. It is apparently not sampled in our temperature data, which includes an unresolved transition of a few cm across the ice-lake interface. It is likely to be localized in distinct downwelling areas within the lake and it could be episodic rather than steady. Our model also implies that the concentration of dissolved elements should be greater in the upper than in the lower water mass since the comparatively fresh meltwater is mixed with water from the upper water body to form the lower water mass. This should lead to density contrasts due to concentration gradients, which are likely to be important for the vertical stratification in the lake, in addition to the density contrasts due to temperature gradients, which usually drive thermal convection in water bodies. Our analysis does not explain what determines the temperature of the water masses. The density contrast between the upper water mass and the downwelling water drives the large-scale circulation. This density contrast, and therefore the intensity of the circulation and associated convective heat transfer, increases with increasing temperature of the upper water mass. Presumably, the temperature in the lake is set by a feedback between heat input and the intensity of the convection in the lake, but further analysis is needed to obtain a quantitative explanation of the lake temperature.

Acknowledgments

[18] Jón Örn Bjarnason at Iceland GeoSurvey provided thermodynamic tables of the enthalpy of water based on IAPWS [1997]. He also made valuable comments on an earlier version of the paper. Sigurður I. Gunnlaugsson at Star-Oddi Ltd. provided detailed information about the calibration and accuracy of the temperature and pressure recorders and assisted in the calibration and recalibration of the instruments. The Icelandic Research Fund, the Icelandic National Power Company, the Icelandic Road Administration and the Iceland Glaciological Society provided financial and field support which made this study possible. This material is based upon work supported in part by the National Aeronautics and Space Administration through the NASA Astrobiology Institute under Cooperative Agreement NNA04CC08A issued through the Office of Space Science. We thank the many people who worked with us in the field during the drilling through the ice shelf, in particular the drill “foreman” Vilhjálmur S. Kjartansson, and the designer of the drill, Sverrir Ó. Elefsen. We also thank Magnús Tumi Guðmundsson and an anonymous reviewer for helpful comments.

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