Introduction
Alpine glacial meltwaters exhibit diurnal, inverse relationships between discharge and total dissolved solids (or conductivity) during the ablation season (Reference CollinsCollins, 1978). Each day, maximum concentrations of solute are found in meltwaters at low discharge, and, conversely, minimum concentrations are found at maximum discharge (see Fig. 1). The simplest model of melt-water hydrochemistry considers that the meltwaters issuing from the portal, the bulk meltwaters, consist of two components (Reference CollinsCollins, 1978), although more complex models exist (e.g. Reference Oerter, Behrens, Hibsch, Rauert and StichlerOerter and others, 1980). Here, we consider hydrograph separation based on the two-component mixing model, and begin by describing the components. The first, the englacial component, has a significant contribution of waters generated near the snout, which have a rapid transit through the hydroglacial system, largely in ice-walled channels. A proportion of englacial meltwaters is generated farther from the snout, and can be considered to be present in, or passing through, a longer-term, ice-walled reservoir. However, englacial waters are relatively dilute, because the suspended load is small and rock-water contact times are relatively short. Hence, the potential for solute acquisition is limited to rapid reactions such as surface exchange (Reference LermanLerman, 1979). By contrast, the second, or subglacial component, is composed of waters, which have had a relatively slow transit through the hydrological system, are subglacially routed and have had at least some contact with till and/or the glacier bed or with debris-rich basal ice (Reference CollinsCollins, 1978). Subglacial waters are relatively concentrated because rock-water contact times are long, allowing solute acquisition both by surface exchange and slower dissolution of glacial flour. Bulk meltwaters are believed to form by the mixing of these two components in conduits in the near-snout region.
Fig. 1. Discharge and conductivity variations for the Gornera, the main stream draining Gornergletscher, (a) 16 September 1980; (b) 18ߝ20 September 1980.
Hydrograph separation has been performed by assigning conductivity values to each of the components (Reference CollinsCollins, 1978,1979a). The conductivity of the englacial component is set at the minimum recorded conductivity of the bulk meltwaters or that of supraglacial streams, while that of the subglacial component is set at the maximum recorded conductivity. This pragmatic method has two main weaknesses. It is assumed that neither component exhibits any temporal variation in chemical composition and that no post-mixing chemical evolution of meltwaters occurs. However, it is likely that each component will demonstrate some temporal variation during the course of the ablation season (e.g. due to the development of different hydrological routings) and that post-mixing chemical evolution will occur when relatively reactive sediment is transported into and through the mixing environment (Reference Raiswell and ThomasRaiswell and Thomas, 1984; Reference Tranter, Raiswell, Mills and MilesTranter and others, 1989).
Here, we examine the characteristics of bulk melt-water chemistry with the aim of achieving a unique hydrograph separation over a short time-scale. Information is presented from the late ablation season, where the seasonal maximum and minimum conductivity values may not be representative of the true composition of the components.
Methodology
Study area
The catchment of the Gornergletscher is located in canton Wallis, Switzerland. It has been the subject of several studies of the composition of glacial meltwater (Reference CollinsCollins, 1978,1979a,b,c). Approximately 80% of the 82km2 catchment is glacierized. The lithology of the catchment is diverse, and consists of gneiss, mica-schist, gabbro and serpentine. Calcareous mica-schist and dolomite comprise 5% of the bedrock (Reference CollinsCollins, 1979b).
Discharge
Discharge was obtained directly from the Grande Dixence gauging station, located approximately 1 km downstream from the snout. The accuracy of the discharge measurements is ±10% (personal communication from D.N. Collins).
Conductivity measurement
All bulk meltwater samples of approximately 1 litre were collected near to the gauging station from a mid-channel location. Conductivity was determined on a 50 ml aliquot of unfiltered sample by use of a portable Hach Model 17250 mini-conductivity meter with a probe-type sensor. The instrument was calibrated with 0.005 M KCl (conductivity 780µS cm−1 at 25°C). Automatic temperature compensation was employed.
Alkalinity
The alkalinity of a rapidly filtered 50 ml aliquot was performed by titration with 4.0 mM HCl to an end point of pH 4.5, as determined by a mixed BDH indicator. The titration precision was ±0.03 cm3 over a range of titres from 1.50 to 3.00 cm3.
Cations and other anions
A 100 ml aliquot of filtered solution was stored in pre-cleaned plastic bottles and acidified with 1.0 cm3 ofconc. HCl. A similar volume of acidified solution was stored and used for anion analysis.
Fig. 2. Variation in meltwater chemistry, (a) 16 September (A samples); (b) 18–20 September (Β samples). Note that sulphate concentrations for the Β samples are estimated from the charge-balance deficit (see Appendix).
Base cations were determined by atomic adsorption spectrophotometry on a Pye-Unicam SP9. Detection limits were: Ca2+, 1µeq.l−1; Mg2+, 0.3µeq.l−1; K+, 0.3 µeq.l−1; and Na+, 0.4 µeq.l−1. Precision was ±4% (±10% for Na+). Sulphate and chloride were determined by ion chromatography on a Dionex Model 12 Ion Chromatograph, or were estimated from charge-balance errors (see Appendix). Detection limits were 2µeq.l−1 for SO4 2- and NO3 −, and 0.3 µeq. l−1 for Cl−. Precision was ±5%.
Results
Two suites of samples, hereafter referred to as the A and Β samples, were collected on 16 September and 18–20 September 1980, respectively. Sulphate analyses are only available for the A samples. Discharge and conductivity curves from the two sampling periods are shown in Figure 1. Discharge varies from 5.4 to 9.2 m3 s−1, and conductivity from 10 to 48µScm−1.
The temporal variation of the chemical compositon of the meltwaters is shown in Figure 2. The cations are dominated by calcium and magnesium. The anions are dominated by bicarbonate and sulphate. The molar ratio of SO4 2- : HCO3 − in the more dilute meltwaters is 1: 3.3, while the ratio in more concentrated meltwaters approaches 1.9: 1. Nitrate and chloride were detected, but only in small concentrations ( < 2 µeq. l−1).
All major ion concentrations (Ca2+, Mg2+, HCO3 − and SO4 >2-) are well correlated (Table 1).
The Composition of the Englacial and Sub-Glacial Components and Hydro-Graph Separation of the Bulk Meltwaters
Bulk meltwaters can be considered to be derived from the mixing of at least two components (Reference Collins and YoungCollins and Young, 1981). Here, we assume that there arc only two components, the englacial and subglacial components, whose conservative mixing requires that
where Q represents the water discharge and C is the concentration of species i. Subscripts b, e and s denote the bulk, englacial and subglacial components, respectively. Continuity of flow requires that
Combining Equations (1) and (2) gives the following expression:
Equation (3) illustrates that four parameters must be determined to perform a hydrograph separation. Of these, only two, Q b and C b i are.routinely measured. Hence, the other two parameters, C e i and C s i , need to be evaluated by independent means. The usual method is to equate C e i and C s i with the minimum and maximum conductivity values recorded during the sampling season (Collins, Reference Collins1978, Reference Collins1979b). As noted earlier, this pragmatic approach has a major weakness because the composition of either or both components may vary throughout the season.
The chemistry of the Gornergletscher bulk meltwaters allows the determination of C e i by a more rigorous method, which depends on the sulphate concentration of englacial waters being essentially zero during the late ablation season. There are two lines of evidence to support this view.
First, the sulphate concentration of supraglacial meltwaters collected during the sampling period is zero (see Table 3). This is consistent with sulphate being largely removed from snow and ice early in the ablation season. Data on sulphate concentrations in Alpine snow and ice are only sparsely available in the literature, but values are typically <20µeq./l (Reference Psenner and NickusPsenner and Nickus, 1987; Reference DelmasDclmas, 1989). Successive diurnal melting of snow and ice rapidly leaches most of the sulphate from the snow and ice crystals (Reference Davies, Jones and Orville–ThomasDavies and others, 1987). Hence, later on in the season, the leached snow and ice gives rise to sulphate-depleted supraglacial meltwaters. Since supra-glacial meltwaters evolve to form waters of the englacial component, the sulphate concentration of the englacial component is likely to be negligible during all except the early melt season.
Secondly, Figure 2a shows that the sulphate concentration of the A samples approaches zero at maximum discharge (note that maximum discharge is not shown). This is also the case for the estimated sulphate concentrations of the Β samples (see Fig. 2b). The data clearly indicate that the bulk sulphate concentration is close to zero at maximum discharge. Since the englacial component dominates at maximum discharge, it follows that the sulphate concentration of the englacial component must also be negligible. We will assume that the sulphate concentration of the englacial component is zero. Hence, sulphate is only found in the subglacial component, where it is formed by the oxidation of pyrite (Reference LermanLerman, 1979). Pyrite is a ubiquitous mineral, being found in many sedimentary, metamorphic and igneous rocks. We therefore assume that sulphate is formed from the oxidation of pyrite throughout the subglacial hydrological system where freshly comminuted rock flour comes into contact with oxygenated meltwaters.
The regression equations of Table 2 now enable us to determine the composition of the englacial component. The concentration of any ion in the englacial component (C e i ) is given by the regression constant, i.e. the value when sulphate concentrations are zero. It can be seen that the composition of the englacial component (Table 2) is that of a dilute bicarbonate solution, as would from the weathering of aluminosilicate, silicate and carbonate minerals by relatively pure water. The estimated cation concentration of the englacial component is somewhat larger than that measured in supraglacial meltwaters (see Table 3), probably because of post-mixing chemical evolution of bulk meltwaters (Reference Raiswell and ThomasRaiswell and Thomas, 1984; Reference Tranter, Raiswell, Mills and MilesTranter and others, 1989).
Since sulphate is not found in significant concentrations in the englacial component at this stage of the ablation season, it acts as a marker for the subglacial component. Figure 3 shows a plot of bulk sulphate (A samples) and estimated sulphate concentrations (B samples, see Appendix) against discharge. It is apparent that the bulk sulphate concentration is linearly related to discharge, both for ascending and descending limbs of the hydrograph. The precise relationship may change between successive ascending and descending limbs of the hydrograph, since a number of straight-line relationships may be defined (see Fig. 3a and b). We note that for the A samples, there is some scatter of points around the minimum discharge. This phenomenon has been attributed to the flushing of subglacial waters by englacial waters at the onset of rising discharge (Reference CollinsCollins, 1979a; Reference Gurnell and FennGurnell and Fenn, 1984).
Similar linear relationships between bulk sulphate and discharge have been observed in other Alpine glaciers, Les Bossons (see Fig. 4; from Reference TranterTranter, 1982) and Upper Arolla (Reference Brown and TranterBrown and Tranter, 1990). Hence, on occasion, the linear relationship between sulphate and discharge may also be common to other Alpine glaciers.
Two component-mixing relationships are normally plotted with the independent variable representing the mass fraction of one of the components. The composition of each component or end member is defined when the mass fraction is 0 and 1, respectively. The interpretation of
Table 2. Regression equations for the relationship between bulk meltwater sulphate concentrations and other ions (units: µeq. l−1)
The englacial component is defined by the regression constants (see text for details).
Table 3. The range in composition of supraglacial meltwaters (units: µ.eq. l−1
The number of samples is eight, but only the most concentrated sample was analysed for sulphate. Charge-balance calculations imply that sulphate concentrations in the other samples should be near zero.
Figure 3 is obscured because the independent variable, Q b, is not obviously related to the mass fraction of the englacial component, defined as Q e/Q b. It will be demonstrated that this is the case if there is a linear relationship between bulk sulphate and discharge.
For sulphate, assuming C e s = 0; Equation (3) can be rewritten as follows:
where the superscript s denotes sulphate. There is a linear relationship between bulk sulphate and discharge. Hence,
where m and c are constants.
Fig. 3. (a) A samples. Measured sulphate concentration versus discharge. The ascending limb of the hydrograph follows the linear relationship: SO4 2- = −190Qb + 1700 (R = −0.998; n = 4). We are not confident of the trend defined by the four points on the descending limb of the hydrograph. (b) Β samples. Sulphate concentrations estimated from the charge-balancedeficit (see Appendix), versus discharge.
Two distinct linear trends are evident. The first is defined by four consecutive points on the ascending limb of the hydrograph on the morning of 17 September: SO4 2- = −28Qb + 370 (R = −0.982; n = 4) The remainder of the data defines the following relationship: SO4 2- = −32Qb + 300 (R = −0.872; n = 34). Both correlation coefficients are significant at 0.1%.
Hence, combining Equations (4) and (5) gives
On the righthand side of Equation (6), only Q b is a variable. Hence, the bulk discharge, Qb, is a simple measure of the mass fraction of the englacial component in the bulk discharge.
The subglacial component is defined when the mass fraction of the englacial component is zero, that is, when the lefthand side of Equation (6) is zero. Examination of Equation (6) reveals that the maximum concentration of sulphate in the subglacial component is c, the regression constant from the linear bulk sulphate versus bulk discharge relationship, since by setting the mass fraction of the englacial component to zero, C s s is a maximum when Q b is zero (Q b cannot be a negative number).
Fig. 4. The relationship between sulphate and discharge (ascending limb of the hydrograph) in the main stream draining Les Bossons, (a) 24 September 1981. The four points on the ascending limb of the hydrograph define the following expression: SO4 2- = −140Qb + 110 (R = −0.986; n = 4).(b) 25 September 1981. The five points on the ascending limb of the hydrograph define the following expression: SO4 2- = −290Qb + 170 (R = −0.995; n = 5). Both correlation coefficients are significant at 0.1%.
The following calculations and discussion are based on the assumption that the composition of the subglacial component is set at the maximum permissible value, c. Calculated discharge of the subglacial component will therefore be a minimum estimate.
Table 4 gives the composition of the subglacial component. The sulphate concentrations were derived from the linear bulk discharge-sulphate relationships defined in Figure 3. Given these sulphate concentrations, the regression equations in Table 2 were used to determine the cation and bicarbonate concentrations. Because the major ions are well correlated, apportionment of the other ions between the two components based on sulphate concentrations in the subglacial component leads to observed and calculated masses of ions in the bulk meltwaters being nearly identical. Figure 5 shows the hydrograph separation derived from Equations (3) and (4), based on the sulphate concentrations in Table 4.
Table 4. Composition of the subglacial component (units: µeq. l−1)
*Correlation coefficients are such that these concentrations cannot be determined with certitude.
Discussion
The above method of hydrograph separation produces results which are similar to the conductivity-based separation of Reference CollinsCollins (1979b). The proportion of the subglacial component decreases from 30 to 50% at minimum discharge to near zero at maximum discharge. A refinement of the present method is that the assumption of constant composition throughout the ablation season can be partially tested. On different days, a new mixing line may be defined (see Fig. 3b). If the same method is applied to Les Bossons bulk meltwaters, the subglacial sulphate concentration changes from 110 to 170 µeq./l on consecutive days (see Fig. 4). Apart from the poorly defined mixing line for the ascending limb, shown in Figure 3a, the other mixing lines do not intercept at low bulk discharge. Hence, even though we calculate maximum compositions, the composition of the subglacial component must have changed.
Fig. 5. Hydrograph separation of bulk meltwaters draining Gornergletscher, (a) 16 September 1980 (A samples); (b) 18–20 September 1980 (B samples).
For the Gornergletscher, the composition of the subglacial component may remain constant during successive descending and ascending limbs of the hydro-graph (see the main mixing line defined in Figure 3b). However, Figures 3b and 4 show that significant changes in the concentration of the subglacial component may occur between consecutive ascending and descending limbs of the hydrograph, and between consecutive ascending limbs.
This rather stepwise variability in the composition of the subglacial component, alternating between periods of relatively constant composition and times of relatively large change, has important implications. Methods of hydrograph separation which rely on the composition of the subglacial component remaining constant throughout the melt season will clearly be in error on occasions. The stepwise variability suggests that the composition of subglacial waters is controlled by physical, rather than chemical, processes, since the latter impart chemical inertia to the system as concentration increases. Rather like the composition of bulk meltwaters is determined by the mixing of concentrated and dilute components, the composition of the subglacial component may be controlled by similar mixing processes. This hypothesis requires the transfer of concentrated and dilute meltwaters between subglacial reservoirs at specific times during the diurnal discharge cycle. However, it seems premature to speculate further on the dynamic controls on the composition of the subglacial component given the limited data set presented here.
Conclusions
A new method of separating the hydrograph of the Gornergletscher into englacial and subglacial components has been presented. The englacial component is found to be dilute, but more concentrated than supraglacial meltwaters. This suggests that post-mixing chemical weathering reactions lead to the acquisition of cations and bicarbonate. The subglacial component is concentrated and may remain essentially constant over much of the ascending and descending limb of the diurnal hydrograph. The proportion of the subglacial component approaches zero at maximum discharge, and approximately 50% at minimum discharge. However, the composition of the subglacial component may vary between consecutive ascending limbs, and between consecutive ascending and descending limbs. This step-wise change in composition suggests that the subglacial component could itself be a mixture of concentrated and dilute waters, and that extension of the simple two-component mixing model is necessary (e.g. Reference Oerter, Behrens, Hibsch, Rauert and StichlerOerter and others, 1980).
Acknowledgements
We wish to thank Dr D. Ν. Collins for allowing us access to his field-work facilities at the Gornera, and to Dr A. G. Thomas for performing the discharge measurements at Les Bossons. The manuscript was improved following discussion with Dr A. M. Gurnell and Mr G. S. Brown.
Appendix
The following expression was used to define (SO4 2-)*:
Concentration is expressed in units of equivalents. The calculation of (SO4 2-)* can be checked by comparing estimated against real values for the A samples. The best-fit regression equation is (SO4 2-)* = 0.79(SO4 2-) − 41; R = 0.997; n = 7. This implies that the method of estimation is accurate, but that cation concentrations are underestimated. The underestimation of cations in glacial meltwater samples is likely to be a common problem because matrices of samples and standards are often not matched, and is addressed in detail by Brown and Tranter (paper in preparation). The fact that the cations are underestimated does not detract from the conclusions reached in this paper, although the precise concentration of cations in each component is likely to be underestimated by up to 20%.
