Discharge variations

Temporal variations in discharge are plotted in Figure 2. The characteristic diurnal variation in discharge recognized elsewhere (e.g. Reference Rainwater and GuyRainwater and Guy, 1961; Reference CollinsCollins, [1978]) is also apparent at Fjallsjökull, despite scatter in the data. Such diurnal variations generally reflect changes in the amounts of supraglacial melt water produced in response to daily variations in radiation input.

Fig. 2. Temporal Variations in discharge at Fjallsjökull, showing best fit curve (r = 0.52) of form y = a + b sinx + c cosx.

Water may be derived from a number of sources in predominantly glacierized catchments namely subglacial melting, precipitation, ground-water, surface melting, and internal melting (Reference CollinsCollins, [1978]). Subglacial and internal melting produce only trivial quantities of water (Reference ShreveShreve, 1972) and both chemical (Reference CollinsCollins, 1979[b]) and isotopic (Reference Behrens, Behrens, Bergmann, Moser, Rauert, Stichler, Ambach, Eisner and PesslBehrens and others, 1971) measurements indicate that surface melt waters are the major source of water from Alpine glaciers during the summer ablation period. A further significant source of water from Alpine glaciers may arise from subglacial ground-water systems (Reference Ambach, von, Ambach, Behrens, Bergmann and MoserAmbach and others, 1972) but this situation may not be common. At Fjallsjökull precipitation was absent both during, and for 10 d preceding, the measurements. Assuming that the ground-water contribution is negligible, the major source of water at Fjallsjökull is likely to arise from surface melt.

Various heat sources can contribute to surface ablation, but only radiation, convection, and heat of condensation can vary diurnally and hence initiate the observed discharge variations. There are no data on the relative magnitudes of these different heat fluxes at Fjallsjökull, but Reference PatersonPaterson (1969) has estimated that the dominant heat input is convection, with a minor contribution from radiation, at the Hoffelsjökul (another outlet glacier from Vatnajökull, 50 km north of Fjallsjökull).

Using air temperature as a crude measure of convectional energy input, the links between discharge and convectional energy input can be explored in a series of scatter diagrams (Fig. 3). A direct plot of air temperature against discharge gives a correlation coefficient r = 0.48 (significant at the 5% level). However it seems unlikely that there could be an instantaneous relationship between the two variables, because of the finite time taken to induce melting and transmit water from the glacier surface to the snout, through the internal hydrological system. An estimate of the delay time can be made by interpolating from the air temperature/time graph the values for air temperature at times 0.5, 1.0, and 2.0 h before the corresponding discharge value. Thus scatter diagrams can be plotted for discharge against air temperature for each of these lag times. The best correlations between discharge and temperature are achieved at lag times of 0.5–1.0 h (r = 0.7, significant at < 0.1% level). This period of time can be envisaged as the most common or modal time taken for the melting and transit of supraglacial waters. The mean time is likely to be considerably longer as some supraglacial melt may be delayed by up to 24 h (Reference EllistonElliston, 1973; Reference CollinsCollins, 1979[b]). Similar modal transit times have been identified by Reference Meier and TangbornMeier and Tangborn (1961) for South Cascade Glacier (4 h) and by Reference LangLang (1968) for Grosser Aletschergletscher (1 h). These times are broadly consistent with the picture of glacial hydrology developed by Reference CollinsCollins ([1978], Reference Collins1979[b]) in which the bulk of the melt water (supraglacial in origin) is envisaged to flow rapidly through the glacier from the surface to the snout.

Fig. 3. Scatter diagrams of instantaneous discharge and air temperature readings, with discharge values lagging air temperature by 0, 0.5, 1 and 2 h respectively. Best correlation of discharge and air temperature is achieved if values of the former are taken at 0.5 to 1 h later than the corresponding air temperature reading.

Variations in total dissolved load

Hydrological investigations of non-glacierized catchments suggest that there is often an inverse relationship between conductivity (as a measure of dissolved load) and discharge. Solute-rich base flows are produced from water percolating slowly through sediments and are diluted during precipitation events by rapid surface and sub-surface run-off, giving the following relationship between discharge and dissolved load (Reference HemHem, 1970):

where C is the conductivity, Q the discharge, and a and k are constants. This relationship is usually plotted as the straight line

Dilution relationships of this type have been identified in glacial melt waters by Reference Rainwater and GuyRainwater and Guy (1961) and Reference Lemmens and RogerLemmens and Roger (1978). However Reference CollinsCollins (1979[a]) has argued that simple mixing models of this type are inappropriate for melt waters draining from the Gornergletscher, because a range of dissolved loads may be associated with a given discharge. Whilst this is demonstrably true on time scales which encompass more than one diurnal cycle, the mixing model may still prove to be useful over a single cycle, where it can assist in the recognition of chemical evolution in the melt waters on relatively short time scales.

Figure 4 shows the relationships between the logarithm of discharge and that of dissolved load, the latter expressed as ∑⁺(meq. l⁻¹), the sum of the cation equivalents. Twelve points define a good straight line (r = 0.88, significant at the < 0.1% level) but pronounced deviations exist at both high discharge (where solute contents are high) and low discharge (where solute contents are low). A combination of the errors involved in discharge measurement and analysis (10–15%) is insufficient to explain these deviations.

Fig. 4. Relationship between logarithm of discharge and ∑⁺. Twelve points define the plotted regression line (r = 0.88) and represent simple mixing behaviour. The three highest and lowest discharge samples lying on the vertical dashed lines represent deviations from simple mixing behaviour and are shown with their p(C0₂) and (SI) _calcite values respectively. Horizontal dashed line represents the approximate position of melt waters with (SI)_calcite = 0.

Variations in ionic composition

Relationships between the different dissolved species in the bulk melt waters are expressed in a correlation matrix (Table II), which provides an indication of the sources of each element. Calcium, potassium and magnesium are at least fairly well correlated with bicarbonate (significant at the 4% level or better) as a result of weathering reactions which involve the concomitant production of bicarbonate ions from dissolved carbon dioxide and release of cations from rock minerals (see later). Calcium is however poorly correlated with magnesium (significant at the 10% level) and not at all related to potassium and sodium. These relationships are consistent with a dominant carbonate source (for most Ca²⁺ and some Mg²⁺) together with various silicate minerals as the main sources of Na⁺, K⁺, and the remaining Mg²⁺. The contributions of dissolved salts originally in precipitation cannot be reliably estimated in view of contamination effects (see later).

TABLE II. Correlation Matrix for the Diurnal Samples

The different melt waters show relatively little variation in cation composition. The main variations are in Ca²⁺ (53–77% of the total cation equivalents) and K⁺ + Na⁺ (12–32%), with Mg²⁺ relatively constant (9–15%). Variations in cation composition show no consistent relationship with discharge.

Carbonate equilibria

In general the hydrogen ions required for weathering and dissolution reactions in melt waters are derived from the solution of atmospheric carbon dioxide and the oxidative breakdown of sulphide minerals (Reference RaiswellRaiswell, 1984). The relative impact of both contributions can be evaluated if melt waters are fully analysed for anionic species. The analyses of total alkalinity and pH reported here allow a full description of the dissolved carbonate speciation, by solution of the carbonate equilibria using the computer programme WATSPEC (Reference WigleyWigley, 1977).

WATSPEC uses input data of temperature, density, pH, and alkalinity together with the measured concentrations of the individual cationic and anionic species. Its output relevant to the present discussion is the partial pressure of carbon dioxide p(CO₂) in equilibrium with the water and the extent of the saturation of the water by various minerals, as estimated by the logarithm of the ratio of ion activity product to solubility product, known as the saturation index (SI). Waters with (SI)<0 indicate their thermodynamic potential for dissolution (undersaturation) and (SI)>0 indicates potential for precipitation (oversaturation). Table III summarizes the measured and computed variables relevant to carbonate equilibria in the bulk melt water, supraglacial run-off, and precipitation at Fjallsjökull. The bulk melt waters generally have lowerp(CO₂) values and higher (SI)_calcite (the saturation index of calcite) values than precipitation or supraglacial melt.

TABLE III. Carbonate Equilibria Data

(i) p(CO₂) values. Surface waters in equilibrium with the atmosphere should have p(CO₂) ≈ 10^−3.5 bar. Such waters apparently undergo chemical weathering in an open system where there is unrestricted transport of CO₂ between gas and water phases. However the rate of CO₂ transfer across the gas-liquid interface is frequently slower than reactions (such as weathering and dissolution) which consume CO₂ in the aqueous phase (Reference Stumm and MorganStumrn and Morgan, 1981). In these circumstances the supply of hydrogen ions by the dissociation of H₂CO₃* reduces the concentration of undissociated H₂CO₃* detected in the water,

where (g), (l), (aq), and (s) denote gaseous, liquid, aqueous and solid phases respectively. The apparent CO₂ content of the gas phase in contact with the water (as calculated from water analyses) is thus reduced, and waters with these characteristics are held to have evolved in a closed system. This need not imply a physical constraint on access to atmospheric CO₂ but can simply be a kinetic effect which is maintained only as long as rates of CO₂ removal exceed rates of supply. Clearly waters in contact with the atmosphere may exhibit different characteristics depending on the rates at which hydrogen ions are consumed by weathering. Slow rates of weathering, comparable with rates of CO₂ transfer, allow waters to maintain equilibrium with atmospheric CO₂, (p(CO₂) = 10^−3.5 bar). Conversely with typical, rapid weathering waters become depleted in H₂CO₃* and are no longer in equilibrium with the atmosphere (p(CO₂) < 10^−3.5 bar). Re-equilibration with the atmosphere takes place relatively slowly, since the low levels of p(CO₂) in the atmosphere result at best in only a small concentration gradient between gas and aqueous phases. Hence waters with closed-system characteristics will retain a memory of their closed-system history for a subsequent period of approximately 20–30 min.

The samples of precipitation and supraglacial melt have p(CO₂) values close to those expected for open-system conditions, where equilibration with atmospheric CO₂ occurs. However the p(CO₂) values of the bulk melt waters have values considerably below 10^−3.5 bar and are characteristic of closed-system evolution. The open-system p(CO₂) values for supraglacial melt and precipitation are to be expected in view of their continued access to the atmosphere and the limited extent of their solute acquisition by weathering, but the detection of closed-system conditions for the evolution of the bulk melt waters is of considerable significance. Where p(CO₂) values are low, the depletion of hydrogen ions is likely to control the extent and nature of solute acquisition by mineral-water reactions.

(ii)(SI)_calcite values. The (SI)_calcite value for precipitation (−5. 7, −4.9) and supraglacial melt (−3.5, −2.6) indicate that these samples are several orders of magnitude undersaturated with respect to calcite. These values of (SI)_calcite are much lower than for the bulk melt waters (−1.3 to −0.14), where lower (SI)_calcite values are clearly correlated with lower dissolved loads (as indicated by ∑⁺ values). The maximum value recorded (–0.14) in the sample taken at 3.00 h indicates near saturation with calcite and the higher (SI)_calcite values are linked to high pH and total alkalinity and low p(CO)₂. Some of the bulk melt waters have (SI)_calcite values which are sufficiently high to indicate that the subglacial waters may be saturated with calcite, prior to mixing and dilution with englacial water. Although subglacial precipitates have not been recorded at Fjallsjökull, the concentration of solutes by freezing subglacial water would certainly create the necessary oversaturation with respect to calcite.

Chemical evolution in the supraglacial environment

Precipitation must clearly be the source material for supraglacial melt and, although the number of samples is too small to account for temporal and spatial variations, some useful comparisons between precipitation and supraglacial melt can be made. Thus both precipitation and supraglacial melt clearly have lower solute contents, pH, and total alkalinity than the bulk melt waters (Table I). The values of p(CO₂) and (SI)_calcite should be regarded as no more than indicative in the case of precipitation because there are considerable difficulties in the determination of pH in poorly buffered samples and also because the total alkalinity values are close to the detection limit. Despite these errors, both groups of samples have p(CO₂) values which are generally much closer to equilibrium with atmospheric levels (Table III), suggesting that solutes have been acquired in open-system weathering conditions. The (SI)_calcite values steadily increase in passing from precipitation to supraglacial melt and thence to the bulk melt waters. The precipitation samples have rather low solute levels (cf. ∑⁺ = 0.121 meq. l⁻¹ in average rainwater; Reference Garrels and MackenzieGarrels and Mackenzie, 1971) but show considerable variability, possibly due to the dissolution of wind-blown dust found in all the samples There are however significantly higher solute levels in the supraglacial samples than in the precipitation and it is clear that some chemical reaction has occurred in the supraglacial environment. Under open-system weathering conditions it can be shown that solutes are acquired according to the relationship (Reference RaiswellRaiswell, 1984)

where [∑⁺] the concentration of cation equivalents. Figure 5 shows both the precipitation and supraglacial samples plotted on a graph of log [∑⁺] against pH. Considering the errors in the determination of pH in dilute solutions (Reference BatesBates, 1973), both sample groups lie close to the straight line representing open-system weathering. The separation of precipitation samples from supraglacial melt occurs along the straight line in the direction expected, in view of the more extensive weathering history of the latter. These solute/pH relationships indicate the occurrence of chemical weathering in the supraglacial environment, since concentration or modification by firnification or regelation (Reference CollinsCollins, 1979[b]) could not produce measurable changes in pH. Note that the points for the bulk melt waters plot in the shaded area lying above the open-system weathering line. Clearly, supraglacial melt can chemically evolve from precipitation by open-system weathering, but different reaction conditions or source materials are required to produce the bulk melt waters.

Fig. 5. Relationship between log (∑⁺ ) and pH. Theoretical open-system relationship shown by straight line, positions of precipitation (▴) and supraglacial melt (0) as shown

Chemical evolution in the englacial and subglacial environments

All the bulk melt waters are characterized by p(CO₂)< 10^−3.5 bar (Table III), indicating that hydrogen-ion removal by weathering exceeded supply by CO₂ transfer. Hence continued weathering depended on hydrogen ions supplied by the dissociation of H₂CO₃* inherited from the preceding phases of open-system evolution. The only other glacial melt waters for which reliable analytical data are available are from the Chamberlain, South Cascade, Argentière, Mer de Glace, and des Bosson glaciers, all of which exhibit open-system characteristics (Reference Thomas and RaiswellThomas and Raiswell,1984). In the case of Argentière, the mixing of closed-system, subglacial waters with open-system, englacial waters still gives bulk melt waters with open-system characteristics, which suggests that the nature of the bulk melt waters is mainly determined by the relatively large englacial component. Since the modal transit time of the englacial component is approximately 0.5–1.0 h, rapid solute acquisition must occur to give closed-system characteristics. The development of closed-system characteristics thus refiects:

• (i) Availability of easily weathered minerals (such as CaCO₃) to the englacial component. Solute acquisition by the englacial component prior to mixing seems unlikely, but post-mixing reactions may occur with the sediment supplied by the subglacial component. The comparatively long transit times and high sediment loads of the subglacial component suggest a near equilibrium between solids and solution (see later), allowing the possible survival of reactive minerals. Mixing with the englacial component could then initiate the continuation of further weathering and solute acquisition.

• (ii) Hydrological variables which constrain rates of CO₂ transfer to the melt waters, either directly by limiting access to atmospheric CO₂ or indirectly by affecting rates of CO₂ transfer from gas to liquid (e.g. by reduced turbulence).

The relative influence of these factors cannot yet be distinguished. Figure 6 shows the changes in pH and p(C0₂) (Reference RaiswellRaiswell, 1984) expected for closed-system evolution of supraglacial melt waters with different initial dissolved carbonate contents. With one exception all the bulk melt waters plot within the pH and p(CO₂) values expected for the closed-system weathering of supraglacial melts with 2–3 x 10⁻⁴mol l⁻¹ dissolved carbonate (close to the observed range of 1.8–2.9 x 10⁻⁴ mol l⁻¹). Thus the compositional trends from supraglacial melt to the bulk melt waters are entirely those expected where solutes are acquired under closed-system conditions. The pH/p(CO₂) relationships represent trends in the mean chemical weathering history of the bulk meltwaters, as determined by variations in the mixing ratio of englacial and subglacial components (the latter with a more extensive weathering history) and post-mixing evolution.

Fig. 6. Relationships between pH and p(CO₂,) for the closed-system evolution of supraglacial melt waters with different initial dissolved carbonate contents. The shaded area shows the observed range of dissolved carbonate contents in supraglacial melt at Fjallsjökull (o). Bulk melt waters (•) emerging from the glacier portal fall within the shaded area, as expected for closed-system evolution from the observed composition of supraglacial melt.

The relationships between pH and ∑⁺ are plotted in Figure 7 for the closed-system evolution of waters with different initial dissolved carbonate contents, but with cations derived by either silicate weathering or carbonate dissolution. Under closed system conditions the dissolution of CaCO₃ requires only one mole of H₂CO₃* to produce a mole of Ca²⁺. By contrast one mole of H₂CO₃* is required for each mole of a univalent ion derived from silicate weathering (Reference RaiswellRaiswell, 1984). This important distinction indicates that solution of CaCO₃ can supply a larger dissolved load (expressed as ∑⁺) than can result from the dissolution of silicates, for any fixed H⁺ concentration. In closed-system weathering, where the availability of H⁺ is limited by the initial dissolved CO₂, this distinction produces different curves for the pH/∑⁺ relationships.

Fig. 7. Relationship between pH and ∑⁺ for the closed system evolution of bulk melt waters with different initial dissolved carbonate contents (obtained in the supraglacial environment). Upper diagram refers to subsequent closed-system evolution by reaction with silicates, lower diagram to reaction with carbonates. Bulk melt waters are connected for the influence of solute aquisition by sulphide oxidation.

Curves of pH against cation load (Fig.7) are shown for solute acquisition by carbonate dissolution and silicate weathering, at each of the two initial dissolved carbonate contents (2 and 3 x 10⁻⁴ mol l⁻¹) corresponding to the range observed in the supraglacial melts. Both sets of curves show that supraglacial melt composition exerts an important influence on the extent of subsequent closed-system evolution. In the present data, supraglacial melt composition is characterized by only two samples and errors may arise if these are unrepresentative. Agreement between observed and predicted pH/p(CO₂) relationships suggests that this error is relatively small in comparison with that arising from the assumption that hydrogen ions are only supplied by dissociation of dissolved CO₂. Sulphate concentrations in the bulk melt waters are too large to originate solely from atmospheric precipitation, since Cl⁻/SO₄ ²⁻ < 0.08 in melt waters compared with c. 5.4 in average rain-water (Reference Garrels and MackenzieGarrels and Mackenzie, 1971). Oxidative weathering of sulphides (commonly pyrite) is the main alternative source of sulphate, augmented by acidic sulphur gases in areas of atmospheric pollution.

Oxidative weathering produces a 2:1 molar ratio of hydrogen ions to sulphate and so, assuming these hydrogen ions generate an equivalent amount of cations, the sulphate analyses can be used to correct for the extra cations resulting from sulphide breakdown. The melt waters with corrected cation contents (Fig.7) plot close to the curves showing pH/cation values for closed system CaCO₃ dissolution (starting from supraglacial melts with 2–3 x 10⁻⁴ mol l⁻¹ dissolved carbonate), but lie outside the curves for closed-system silicate dissolution. Using the larger ∑⁺ corrections appropriate for closed-system carbonate dissolution (Reference RaiswellRaiswell, 1984), either with or without further corrections for the sulphate content of supraglacial melt or precipitation, does not significantly modify the distribution of the data. These plots suggest that the major source of solutes was from CaCO₃ dissolution, and that oxidative weathering of sulphides accounted for perhaps 15% of the cation load. The conclusion that CaCO₃ dissolution was the major source of solutes agrees with the inter-element correlations (see earlier). Calcite, however, only constitutes 1–3% of the bedrock and its disproportionately large solute contribution arises because the modal residence time of water in the glacial hydrological system is short and because calcite is dissolved more readily than silicates. These features are common to many other glacial systems and, provided CaCO₃ is available even in small quantities, its dissolution may often be the major source of solutes.

Solute/discharge relationships

A linear, inverse relationship between solute levels and discharge implies that bulk melt-water composition is determined by a variable mixing ratio between englacial and subglacial components of constant composition. However preceding sections indicate that post-mixing evolution exerted an important influence on bulk melt-water chemistry. Thus the solute/discharge relationships (Fig.4) show that a simple mixing model is only valid over intermediate discharge and that large deviations occur at high and low discharge. However, the clearly defined mixing behaviour (r = 0.88) provides a useful starting point to consider solute/discharge behaviour. The mixing line spans a range of dissolved load from ∑⁺ = 0.34–0.45 meq. l⁻¹ approximately, representing the range where variations in the composition of either the englacial or subglacial components are relatively small and bulk melt water composition is mainly controlled by changes in the ratio of englacial to subglacial water. Reference CollinsCollins (1979[b]) assumes that the englacial component undergoes little or no chemical evolution and hence is similar in composition to supraglacial melts (observed range in ∑⁺ of 0.14–0.22 meq. l⁻¹). In the case of the subglacial component, Reference CollinsCollins ( 1979[bJ) assumes that the composition is that of the repeatedly observed value for maximum dissolved load, as measured during periods of recession flows induced by snow-fall. In the absence of such data at Fjallsjökull a theoretical, rather than an observational, approach must be adopted. Consider the samples taken at 3.00 and 4.30 h which contain the highest dissolved loads on the mixing line and which are close to saturation with calcite ((SI)_calcite = −0.14 and −0.29 respectively). It is unlikely that these two low-discharge samples consist entirely of subglacial water. During stable diurnal cycles, Reference CollinsCollins (1979[b]) estimated that minimum observed flows consisted of 30–70% subglacial water. Thus these two low-discharge samples at the solute-rich end of the mixing line have almost certainly experienced some dilution by englacial waters and must have lower dissolved loads than subglacial water. In the case of Fjallsjökull, where calcite dissolution is the main source of solutes (see above), there must also be a maximum possible dissolved load which corresponds to saturation or near-saturation with calcite (marked by the horizontal dashed line in Fig.4). Thus the composition of subglacial waters must lie close to, or within, the limits of dissolved load represented by calcite saturation levels (∑⁺ = 0.5 meq. l⁻¹), and the samples taken at 3.00 and 4.30 h (∑⁺ = 0.44 meq. l⁻¹). Assuming that the minimum composition of the englacial waters is ∑⁺ = 0.14–0.22 meq. l⁻¹ and that the subglacial waters are saturated with calcite, then samples 3.00 and 4.30 h would have a maximum subglacial contribution of approximately 80%. The existence of repeatedly observed maximum dissolved loads is entirely to be expected if the composition of subglacial waters is limited by saturation with respect to a solid phase such as calcite, as was the case in subglacial streams from Argentiēre (Reference Thomas and RaiswellThomas and Raiswell, 1984).

The deviations from mixing behaviour are represented by two groups of samples occurring at the highest and lowest discharges. Each group of samples shows a significant range in dissolved load ( ∑⁺ = 0.37–0.41 and 0.27–0.41 meq. l^−l respectively) with little variation in discharge. It is considered that these samples are particularly influenced by hydrological events which affect the degree of post-mixing evolution and which are masked at intermediate discharges by larger variations in the mixing ratio. Rates of mineral dissolution (Reference BernerBerner, 1978) decline markedly close to saturation, thus closed-system, solute-rich subglacial melt at Fjallsjökull (inferred to be close to saturation with calcite) and at Argentiēre (close to saturation with calcite and aluminosilicates; Reference Thomas and RaiswellThomas and Raiswell, 1984) are capable of only slow rates of solute acquisition. By contrast the englacial waters are dilute and are capable of undergoing rapid weathering and dissolution on contact with reactive rock minerals. However the negligible sediment loads of supraglacial melt (Reference CollinsCollins, [1978]) which constitutes most of the englacial component, implies that the opportunity for further reaction in the englacial system is minimal. The chemical situation changes dramatically on mixing with sediment-rich subglacial water and further solute acquisition by the englacial component (more strictly the bulk melt waters) is possible.

Clearly mixing-line behaviour will occur as long as the extent of post-mixing evolution remains constant. However short-term hydrological events which significantly modify the transit time of a portion of the melt waters (before or after mixing) will cause deviations from mixing behaviour. Reference CollinsCollins (1979[b]) also recognized the importance of time-dependent chemical evolution in suggesting that stored and chemically enriched water can be returned to the main flow system at high discharge, following the ablation peak. An explanation of this type may apply to the high-discharge deviations from mixing behaviour at Fjallsjökull. In general terms, the hydrological environment beneath glaciers is complex and dissolved loads in bulk melt waters will be sensitive to a variety of factors which influence the kinetics of solute acquisition, principally water composition (extent of saturation with respect to rock minerals and aluminosilicate weathering products), reactivity of rock debris (grain-size, abundance, and composition), and duration of access to rock debris (mean flow rates and storage times).