Water composition

The single most important mechanism by which rock minerals are weathered is acid hydrolysis, the general principles of which can be demonstrated by reference to just three types of minerals; carbonates, silicates, and aluminosilicates.

In each of these reactions a metal cation is released to solution by a fixed amount of hydrogen ions and the anionic component of the mineral is completely solubilized (calcite, forsterite) or partially solubilized (albite) to give dissolved carbonate or silica species. Because of the partial solubilization of alumino-silicates (incongruent dissolution), a number of different chemical reactions can be written to produce different residual solid phases (gibbsite, kaolinite, montmorillonite) depending on the degree of solubilization. However, the same relationship between hydrogen ions consumed and cations released still applies.

It follows from this that the chemical weathering of rock minerals is controlled to a great extent by the supply of hydrogen ions by acids (Reference Curtis and DerbyshireCurtis, [^c1976]). The main sources of acids in natural systems arise from CO₂ (dissolved from the atmosphere and from biogenic respiratory sources), sulphide oxidation and pollutant acid gases such as SO₂. The present paper is restricted to modelling weathering reactions in melt waters prior to their emergence at the glacier portal (where biogenic contributions should be negligible) in glacial systems unperturbed by anthropogenic inputs. Hence the main sources of acids are considered to be from the equilibration of melt waters with atmospheric CO₂ and from the weathering of sulphide minerals in bedrock.

An aqueous solution of carbon dioxide contains simple dissolved CO₂ molecules (CO₂(aq)) as well as the hydrated species H₂CO₃, although the former is greatly predominant. Since the hydration equilibrium is established rapidly (less than a few minutes) the species CO₂(aq) and H₂CO₃ may be considered together and are so designated as H₂CO₃⋆, following the approach of Reference Stumm and MorganStumm and Morgan (1981). The H₂CO₃ may be dissociated in two steps to produce the hydrogen ions required for acid hydrolysis.

The final dissociation to CO₃ ²⁻ occurs only at high pH and does not make a significant contribution to hydrogen ions in most melt waters (see later). Thus, the weathering of forsterite can be re-written as;

An important general principle is indicated; the anionic components of melt waters demonstrate the acid source used in the dissolution and weathering of rock minerals. Similarly where acids are supplied by the oxidation of sulphides (commonly pyrite), sulphate is the dominant anion.

This brief summary of the role of hydrogen ions in weathering emphasizes that attention must be directed towards the anionic composition of melt waters, as indicators of the hydrogen-ion sources which determined the nature and extent of chemical weathering.

water flow rate

The influence of water flow rate can be assessed by considering the example of albite weathering (see above). The equilibrium constant for this reaction can be written as below and its value derived from thermodynamic data.

Many silicate and aluminosilicate weathering reactions have equilibrium constants of a similar magnitude, indicating that only small increases in the concentrations of the aqueous products (and decreases in [H⁺]) are needed to approach equilibrium and stabilize the solid phases. In these circumstances water flow rate can exert a critical control on the rate and extent of dissolution, since high flow rates have the effect of supplying a fresh source of H⁺ and flushing away the dissolved products of weathering, A close approach to equilibrium is therefore prevented and hence it is generally assumed that increased flushing rates cause an increased rate of mineral dissolution. Strictly this is only true when the waters are sufficiently close to saturation for the reactivity of the minerals to be neglected (Reference BernerBerner, 1978).

Rock mineralogy

Minerals weather at different rates and may additionally weather in a variety of ways to produce different solid-phase products (see earlier). Glacial bedrock mostly contains silicates, aluminosilicates, and carbonates with accessory sulphide minerals. Sulphides break down exceedingly rapidly in oxygenated surface environments and carbonate minerals generally weather more rapidly than silicates and aluminosilicates, although considerable variations result from grain-size and crystallinity effects. Despite these variations in the rate and directions of weathering, chemical evolution of the water phase always proceeds in the same direction and produces fixed quantitative relationships between the gain in cations and bicarbonate and the consumption of hydrogen ions.

Compositional variations in melt waters

Existing chemical data permit some useful limits to be placed on the range of compositional variation in glacial melt waters. Although these data have been obtained by many different sampling, storage and analytical methods, they are used uncritically with the limited objective of defining realistic constraints for chemical models. Nine studies of melt-water composition (Reference Rainwater and GuyRainwater and Guy, 1961; Reference Keller and ReesmanKeller and Reesman, 1963; Reference Reynolds and JohnsonReynolds and Johnson, 1972; Reference SlattSlatt, 1972; Reference ChurchChurch, 1974; Reference Zeman and SlaymakerZeman and Slaymaker, 1975; Reference Hallet, Hallet, Lorrain and SouchezHallet and others, 1978; Reference Lemmens and RogerLemmens and Roger, 1978, Reference ThomasThomas, unpublished) have been used, covering nearly 40 melt-water systems. Some systems are represented by only one analysis, others have been analysed several or more times by different workers. Any data set with two or more analyses is represented by two points which give the compositional extremes for pH, Σ⁺ (the sum of the cation equivalents), cation composition, and anion composition.

Hydrogen-ion concentration

Variations in pH (Fig. 1) range from 4–9.5, with most values between 6.5 and 8. Most samples were measured under field conditions and only four samples are specified as laboratory measurements under ambient conditions.

Fig.1. Range of pH variations in glacial melt waters.

Cation equivalents

Most data sets record only cation concentrations and the best measure of solute load is ∑ ⁺ . Glacial melt waters (Fig. 2) are dilute (∑⁺ ⩽ 3 X 10⁻³ eq. l ⁻¹ ).

Fig. 2. Range of solute load variations (expressed as Σ⁺) in glacial melt waters.

Cation composition

Calcium is the dominant cation in approximately 88% of the melt waters (Fig. 3) and often comprises more than 70% of the total cation equivalents.

Fig. 3. Variations in the cation composition of glacial melt waters.

Anion composition. Data are sparse. Only 23 data sets give HCO₃ ⁻ (strictly alkalinity), SO₄ ²⁻ _, and Cl⁻ and in eight of these sets Cl⁻ is below detection limit (< 10⁻⁶ mol l ⁻¹). In the remaining melt waters HCO₃ and SO₄ ²⁻ are each dominant in approximately half the analyses and Cl⁻ is almost invariably low.

The anion observations suggest that a simple and reasonably valid model of melt-water chemistry may be constructed by reference to systems where the hydrogen ions used in weathering are supplied through carbonate equilibria. Such models may have their usefulness extended by correcting for a limited supply of H⁺ from pyrite oxidation, but melt waters with high sulphate concentrations require a more complex treatment.

The above data suggest a maximum of pH of c. 9.5 and, since

then

For any pH 9.62 the [CO₃ ²⁻] is less than 10% of the [HCO₃ ⁻] and treatment of the carbonate equilibria is simplified by ignoring the presence of [CO₃ ²⁻]. For many melt waters the errors so introduced will be negligible.

A further useful simplication is to assume that activity and concentration are equal. In an ideal solution it is assumed that there are no interactions between dissolved ions, in fact in real solutions electrostatic interactions may give rise to both non-specific and specific (i.e. ion-pair) interactions. It can be shown that both of these effects can be safely neglected in most melt waters, which are sufficiently dilute to approximate to ideal solutions. Dealing first with non-specific interactions for a Ca²⁺ and HCO₃ ⁻ melt water, with ∑⁺ = 10⁻³ eq.l⁻¹; the ionic strength I is given by I = ∑ _cizi ²/2 where ci is the concentration of ion i and z_i its charge. This results in the numerical value

The non-specific interactions between dissolved species cause them to exhibit an activity which is less than their total concentration, thus the activity is γ times the concentration where γ is the activity coeefficient. Values of γ depend on ionic strength and can be estimated by Debye-Hückel theory (Reference Garrels and ChristGarrels and Christ, 1965)

The parameters A B depend only on temperature and solvent and a_o is constant for a specified ion. For Ca²⁺ in water at 0° C their values are respectively 0.4883, 0, 3241 × 10⁻⁸ and 6 × 10^−8. The Debye-Hückel expression then gives Y(Ca²⁺) = 0.85. Thus, for Ca²⁺, assuming an equality between activity and concentration will introduce a comparatively small error. Univalent ions exhibit smaller electrostatic interactions and Y(HCO₃ ⁻) = 0.96 for the same solution.

In addition to these non-specific interactions, various dissolved species may form complexes or ion pairs in solution. Again using the simple Ca²⁺ and HCO₃ ⁻ melt water as a model,_oion pairs of the form Ca(OH)⁺, Ca(HCO₃) and CaCo₃ may be expected. The dissociation constant for the reaction

has the value (Reference Garrels and ChristGarrels and Christ, 1965)

In the pH range of melt waters the highest [OH⁻]is approximately 10^−4.5. Thus

Clearly, the ion pair Ca(OH)⁺ is less than 0.1% of the free Ca²⁺ ion and ion pair formation can be neglected for these species, A similar conclusion can be reached for Ca(HCO₃)⁺ and CaCO₃ (Reference Garrels and ChristGarrels and Christ, 1965). It is concluded that both specific and non-specific interactions are negligible in dilute melt waters (Σ⁺< 10⁻³ eq.l⁻¹).

Finally, the following carbonate equilibria models are constructed using thermodynamic data for one atmosphere pressure and 0°C. Reduced pressures at high altitudes cause a small effect (equivalent to a reduction in p(CO₂) ≈ 10% at 2000 m a.s.l.). Changes in temperature produce a similarly small effect, as the dissociation constants for H₂CO₃ change by only 15% between 0 and 5° C. Most melt waters are in the range 0 – 2° C on emergence.

Chemical models: rationale

It has been demonstrated that chemical weathering in melt waters results in quantititave relationships between gains in cations and HCO₃ ⁻ and losses of H⁺ for any carbonate, silicate, or aluminosilicate bed-rock. Weathering thus always progresses in a similar direction although the extent of progression is determined by time-dependent (i.e. kinetic) factors, e.g. rates of H⁺ supply, rates of mineral reaction, and melt-water-rock contact times. Although the reaction stoichiometry of mineral dissolution suggests that simple numerical relationships exist between gains in cations and HCO₃ ⁻ and losses of H⁺, the situation is complicated because H⁺ and HCO₃ ⁻ are linked through the carbonate equilibria.

As hydrogen ions are consumed by weathering, so these equilibria are perturbed to the right, with H₂₋CO₃ ^⋆ being progressively dissociated to H⁺ and HCO₃. Where waters are in contact with the atmosphere (p(CO₂) = 10^−3.5 bar) the continued dissolution of CO₂ gas will occur to replace the H₂CO₃ ^⋆ used in weathering. Continued weathering causes the solution to accumulate HCO₃ ⁻, in the absence of removal mechanisms, hence pH is constrained by the increasing [HCO₃ ⁻] and constant [H₂CO₃⋆] values (see Equation (1) and (2). Clearly, the continued availability of H⁺ depends on the dissolution of CO₂(g) to form H₂CO₃⋆. However, the rate of CO₂ solution and transfer across the gas-liquid interface is slow, often slower than reactions (such as weathering and dissolution) which consume H₂CO₃⋆ (Reference Raiswell and ThomasStumm and Morgan, 1981).

The simplest example to consider is that in which it is assumed that no depletion of H₂CO₃⋆ occurs, indicating continued equilibrium or near-equilibrium with atmospheric CO₂. This constrains the variations in HCO₃ ⁻ and H⁺, through the first dissociation constant of H₂CO₃⋆, such that their product must remain constant. However with continued weathering the increases in HCO₃ ⁻ greatly exceed the depletions in H⁺ and thus the rate of H⁺ supply by CO₂ dissolution must approach the rate of H⁺ consumption (and HCO₃ ⁻ formation) by weathering. This case occurs with poorly reactive minerals where the rate of weathering is slow and the system behaves as though there were free and rapid CO₂ dissolution to maintain Η₂CO₃⋆ concentrations. This system can be designated as open (i.e. to CO₂ dissolution) and may therefore show large increases in total dissolved carbonate species during weathering. However the H⁺ used in weathering may also be derived from a flow of fresh, unreacted solution and in general H₂CO₃⋆ concentrations remain constant if the rates of H⁺ supply by flow and re-equilibration are sufficient to approach the rates of H⁺ consumption by weathering.

A closed system model can now be defined conversely by the requirement that there is no dissolution of CO₂(g) to replace the H₂CO₃⋆ used in weathering, hence the total concentrations of dissolved carbonate species remains constant. In this case the supply of H⁺ by the dissociation of H₂CO₃ reduces the concentration of undissociated H₂CO₃⋆ in the water. Since p(CO₂) is directly proportional to H₂CO₃⋆, the consequence of rapid H⁺ removal is to reduce the calculated equilibrium carbon dioxide content of the gas phase in contact with the water. Waters with these characteristics are so recognized and defined as closed system. This need not imply a physical constraint on access to atmospheric CO₂ but can be simply a kinetic effect which is maintained as long as rates of CO₂ removal exceed rates of supply. Clearly, closed-system weathering is limited in extent because the initial concentration of H₂CO₃⋆ can only supply an equivalent concentration of H⁺. Once this H⁺ has been consumed further weathering by acid hydrolysis is impossible. The closed-system model is recognized by H₂CO₃⋆concentrations which correspond to p(CO₂₎ below atmospheric (<10^−3.5 bar) and the extent of weathering is constrained by the original concentrations of H₂CO₃⋆, which determine H+ availability. Re-equi1ibration with the atmosphere does not occur instantaneously because of the small concentration gradient between gas and aqueous phases, hence waters with closed-system characteristics can retain a significant memory of their closed-system history for a period of 20–30 min after contact with atmospheric CO₂ (Reference ThomasThomas, unpublished).

Basic equations

The approach which follows has been modified from the more thorough treatments by Reference Garrels and ChristGarrels and Christ (1965), Reference Stumm and MorganStumm and Morgan (1981), and Reference ButlerButler (1982), When CO₂(g) dissolves in water the following equilibriurm is establistied:

Concentrations of CO₂(g) are usually expressed as atmospheric partial pressures, so that Henry’s Law for the solution of CO₂ in water is written as below. Activities are denoted by a followed by the chemical formula in parentheses and all equilibrium constants are for 0°C and dilute solutions with zero ionic strength, as in Reference Garrels and ChristGarrels and Christ (1965).

The dissociation of H₂CO₃⋆ proceeds by

A mass-balance equation can also be written for the total dissolved carbonate C_T , where

This mass-balance equation must be written in concentrations (as denoted by square brackets). Solutions must also preserve electroneutrality, so that;

For most melt waters this expression simplifies to

because both [H⁺] and [OH⁻] become insignificant provided [HCO₃ ⁻] ≥ 10⁻⁴ mol l⁻¹ and the pH lies between 5 and 9.

Equations (1) – (4) are sufficient for a complete description of the carbonate equilibria in melt waters, together with the following relationship between a(H⁺) and a(OH⁻):

Equations (1), (2), and (5) are written in terms of activities, whereas Equation (3) and (4) are expressed in concentrations. Since it is assumed that activity and concentration are equal all the terms in the following equations are expressed as concentrations, except for H⁺.

Relationships between pH and p(CO₂) for silicate weathering

Melt waters with a previous open-system weathering history must satisfy Equation (6) and (7) on their removal to a closed system, and must also be in equilibrium with atmospheric p(CO₂). Hence [H₂CO₃* ] is fixed but [HCO₃ ⁻] may vary. On initiation of closed- system conditions there can be no further addition of dissolved carbonate species (C_T constant) and weathering only proceeds to the extent that H₂CO₃⋆ can dissociate to form H⁺.

From Equation (1) and (2),

Hence,

This equation defines the relationship between pH and p(CO₂) for any fixed amount of prior open-system weathering (as defined by c_T) of silicate or aluminosilicate minerals. The minimum value of C_T is fixed by the total dissolved carbonate in pure water in equilibrium with atmospheric p(CO₂), which is mainly H₂CO₃* and therefore only fractionally larger than the term p(CO₂) 10^−1.12. In actual melt-water systems, minimum values of C_T seem to be approximately 10⁻⁴, sufficiently large that the term (c_T – p(CO₂)10^−1.12) remains essentially constant and graphs of pH and -log p(CO₂) plot as straight lines for different chosen C_T values (Fig. 4).

Fig. 4. Theoretical relationships between pH and p(CO₂), for different degrees of initial open-system weathering.

Relationships between pH and p(CO₂) for carbonate weathering

This example is more complex because variations in C_T occur which may become significant when the extent of open-system weathering is small. The initial [H₂CO₃*] is fixed by equilibrium with the atmosphere, so the maximum amount of weathering that can occur corresponds to complete dissociation of H₂CO₃* to HCO₃ ⁻ (giving a maximum of 2.4 × 10⁻⁵ equivalents of H⁺). Since silicate weathering may generate this amount of HCO_3‾ eq.. carbonate dissolution may generate up to 4.8 × 10⁻⁵ eq. of HCO₃ ⁻ and C_T may increase during carbonate dissolution by 2.4 × 10⁻⁵. However this increase may often be disregarded, either because it is small compared to c_T, or because carbonate dissolution may not be occurring to any significant extent. Raiswell and Reference Thomas and RaiswellThomas (1984) found c_T to be 2–3 × 10⁻⁴ mol l⁻1 at Fjallsjökull, rendering the p(CO₂) 10⁻⁷.7 term negligible in comparison to c_T for all p(CO₂) ⩽ 10^−3.5 bar With this proviso,

and Figure 4 is also valid for carbonate weathering.

Relationship between Σ⁺ and pH, for silicate weathering

The expressions used in the previous section can be also rearranged to define the relationship between solute load (i.e. ∑⁺) and pH. From Equations (1), (2) and (3),

Using Equation (4) and expressing each term in terms of H⁺

Inspection of this expression suggests that the first term dominates in the pH range of most melt waters, for any CT > 10⁻⁵ mol l-1. This approximation is valid for any pH from 6.6 – 9.6, the upper limit being fixed by the requirement that [HCO³ ‾] >> [CO32‾ ]. Hence

and plots of this expression (Fig. 5) show an asymptotic tendency, due to the existence of a maximum solute load which is fixed by complete dissociation of H²CO^3⋆.

Fig. 5. Theoretical relationships between Σ⁺ and pH during the closed-system weathering of silicate minerals, for different degrees of prior open-system weathering which produce concentrations of total dissolved carbonate of 1–5 × 10⁻⁴ mol l⁻¹.

Relationship between Σ⁺ and pH for carbonate weathering

This example is relevant to the acquisition of solutes by groundwaters in karstic terrain and has been treated theoretically by Reference LangmuirLangmuir (1971), who derived the following expression.

where C _i is a constant for any particular water and is determined by the extent of its prior open-system weathering history, as shown below.

But in an open system in equilibrium with the atmosphere:

Substituting in Equation (10),

Figure 6 shows the numerical variation of C_i with [HCO_3‾ ]. For any [HCO₃ ⁻ ] < 10 ⁻⁵ mol l^{− 1} values of c_i asymptotically approach a minimum of 1.3 × 10⁻¹¹. Using the electroneutrality relationship

Inspection of this expression reveals that the first term is smallest when C_i is a minimum, yet even then this term still dominates for any pH in the approximate range 6 to 9.6. Hence the above expression can be simplified for most melt waters to

Fig. 6. variations in C_i with HCO₃ − concentration during open-system weathering, P(CO₂)≈ 10^−3.5 bar.

Note that Equation (9) and (11) (Figs. 5 and 7) indicate that ∑⁺ values are asymptotic for increasing pH, since additional cations (over and above those acquired in the prior open-system weathering) can only be derived to the extent represented by complete dissociation of H₂CO₃⋆ to HCO3⁻.

Fig. 7. Theoretical relationships between ∑⁺ and pH during the closed-system weathering of carbonate minerals, following different degrees of open-system weathering which produce concentrations of total dissolved carbonate of 1–5 × 10⁻⁴ mol l⁻¹.

The supraglacial environment

The dissolved and suspended loads of supraglacial melt waters are low (Reference CollinsCollins,1978; Reference Collins1979[a], Reference Collins[b]) and the extent of mineral-water reactions must generally be limited by:

• (i) Time. The model residence time of water on the glacier surface is relatively small, probably of less than 24 h duration (Reference EllistonElliston, 1973; Reference CollinsCollins 1979[b]).

• (ii) Surface Area. the low suspended-sediment loads suggest that fine-grained, readily reactive material is not abundant in the supraglacial environment.

• (iii) Reactivity. Rock debris may have a long residence time on the glacier surface with little opportunity for surface abrasion. High flushing rates ensure that surfaces will experience some weathering and hence may become partially protected by residual, low-reactivity weathering products.

Under these circumstances the rates of H⁺ consumption by weathering will be low, or even negligible, and supraglacial melt should maintain open- system weathering characteristics. Samples of precipitation may be compared to supraglacial melt to ascertain the extent of solute acquisition in the latter, as revealed by higher pH and Σ⁺ (Equation (7)). Reference Raiswell and ThomasRaiswell and Thomas (1984) show that supraglacial melt at Fjallsjökull exhibits open-system characteristics and that little weathering occurs in the supraglacial environment.

The englacial environment

The time, surface area, and reactivity constraints of the supraglacial environment are likely to be similar, or more limiting, in the englacial environment. Thus, although the englacial system may be isolated from physical contact with atmospheric CO₂, the limited capacity for mineral-water reactions should ensure that H₂CO₃⋆ concentrations are undepleted and that these waters display open-system behaviour. No observations of englacial melt are, at present, available.

The subglacial environment

The subglacial environment is in many respects the antithesis of the supraglacial and englacial systems. The residence time of subglacial melt is likely to be at least several days, since subglacial recession flows can be maintained in the absence of ablation and after the drainage of englacial reservoirs (Reference EllistonElliston, 1973; Reference CollinsCollins, 1978, Reference Collins1979[b]). Furthermore, the suspended sediment load of the bulk melt water is almost exclusively contributed by the subglacial component (Reference CollinsCollins, 1979[a]) and may contain a significant fraction of fine-grained material. The < 2μm fraction of suspended sediment typically ranged from 10–20% (by weight) in the Argentière and Fjallsjökull melt waters (Reference ThomasThomas, unpublished). The suspended load also contains abundant sub-micrometre sized particles of enhanced solubility (paper on microparticle production, preservation, and adhesion in laboratory and glacial systems in preparation by R. Raiswell and M. Tranter). The reactivity of mineral grains is also maintained at an optimal level by abrasion, crushing, and fracture processes which continuously generate fresh surfaces.

These factors indicate that rapid weathering and dissolution are likely to be initiated in the subglacial environment, with the consequence that this component should exhibit closed-system characteristics. The depletion of H₂CO₃⋆ and resulting p(CO₂) values less than 10^−3.5 bar reflect the superiority of mineral dissolution kinetics over rates of CO₂ dissolution and hydration, and/or physical constraints on the access of atmospheric CO₂ to the subglacial environment. Observations of subglacial melt at Argentière (Reference Thomas and RaiswellThomas and Raiswell, 1984) confirm that subglacial melt displays closed-system characteristics.

Post-mixing behaviour

Fig. 8. Schematic representation of the possibilities for the chemical evolution of glacial melt waters. Melt waters dominated by englacial (originally supraglacial) melt are identified by open arrows, subglacially dominated melts by filled arrows. Open- and closed- system characteristics are controlled initially by the extent of contact with the reactive rock debris, then modified successively by the mixing ratio between englacial and subglacial melt, the extent of renewed reaction with rock debris, and lastly by the possibility of reequilibration with the atmosphere or mixing with open-system ground waters.

The englacial and subglacial components probably mix over a region of several kilometres near the glacier portal. Previous studies have assumed that mixing is conservative, i.e. that there is no change in the mass of solutes although concentration changes occur by dilution. However, the proposed and observed characteristics of the englacial and subglacial components suggest otherwise. A subglacial water with closed-system characteristics has a limited capacity for mineral dissolution determined initially by its undissociated H₂CO₃⋆ concentrations. There is no a priori reason to believe that this must be more than sufficient to react with all the available, freshly abraded solid phases. Solute acquisition in the subglacial component may instead be limited by the availability of hydrogen ions. Thus, subglacial melt at Argentiere (Reference Thomas and RaiswellThomas and Raiswell, 1984) has a high pH (9.4 to 9.7), is close to equilibrium with carbonate phases, and has little further capacity for dissolution. However, the accompanying suspended sediment may still contain reactive material. Under these circumstances an englacial water with open-system characteristics (i.e. with undissociated H₂CO₃⋆ available for dissolution reactions) may initiate further solute acquisition after mixing.

The various complex possibilities for post-mixing behaviour can be evaluated by reference to Fig. 8. The initial factor which determines the characteristics of the bulk melt water is the mixing ratio between the englacial and subglacial components. During recession flows the subglacial component predominates and the bulk melt water may be expected to retain subglacial characteristics. However, during sustained ablation and typical diurnal discharge variations the bulk melt water may be 60–80% englacial (Reference CollinsCollins, 1979[b]) and mixing will initially result in a bulk melt water which has essentially open-system characteristics, provided no H₂CO₃⋆ is consumed by sediment-melt-water weathering reactions. The behaviour of the carbonate equilibria during mixing depends on many factors and does not exhibit a simple linear variation with the mixing ratio (Reference Wigley and PlummerWigley and Plummer, 1976). However depending on the magnitude of the mixing ratio, the bulk melt water may range through various degrees of closed-system behaviour to essentially open-system behaviour. However, there is also the possibility for further solute acquisition if reactive solid phases are available (either from suspended sediment originally supplied by the subglacial component or by contact with moraine debris). The time scale for further dissolution is short (possibly only hours), but the presence of abundant reactive solid phases may still cause the bulk melt waters to exhibit more closed-system behaviour. Thus, the bulk melt will lie on the appropriate pH/p(CO₂) and pH/Σ⁺ contour as fixed by the dissolved carbonate content of the supraglacial component (Figs 4 and 5 or 7), and the proposed chemical models may be tested by matching supraglacial melt composition with bulk meltwater composition. Data obtained at Fjallsjökull (Reference Raiswell and ThomasRaiswell and Thomas, 1984) are consistent with the proposed models. The pΗ/Σ⁺ relationships (Equation (11)) also suggest that solute sources (carbonates or silicates) can be recognized, but the distinctions are not large and it is likely that only predominantly carbonate or silicate systems will be recognized with any confidence. Accurate analytical data will be required even for this purpose.

Lastly, closed-system bulk melt waters may evolve towards open-system conditions either by reequilibration with atmospheric CO₂ or by mixing with another open-system water (either ground water or surface water).

The proposed models depend on the assumption that the hydrogen ions consumed in weathering are generated through carbonate equilibria. The presence of high sulphate concentrations suggests that hydrogen ions are supplied by pyrite oxidation. Assuming these H⁺ ions are completely utilized in dissolution, the models may still be used if values of Σ⁺ are reduced by their equivalent sulphate concentrations.

This correction is valid where:

• 1. Carbonate equilibria are the dominant H⁺ source, as demonstrated by [HCO₃ ⁻] >>[SO₄ ²⁻ ].

• 2. Atmospheric inputs of sulphate are negligible, as shown by the chemistry of precipitation samples.

• 3. We have open systems, where the Σ⁺/p(CO₂) and Σ⁺/pH relationships are essentially independent of mineralogy.

In closed systems the correction to be applied must be either equal to the equivalent sulphate concentrations (for silicate weathering) as above, or must be twice the equivalent sulphate concentrations (for carbonate weathering). Independent evidence of the relative contributions of carbonate and silicate phases will generally be absent and the best procedure is to apply the minimum correction initially and interpret the data accordingly (see Reference Raiswell and ThomasRaiswell and Thomas, 1984). Melt waters with low sulphate contents will show little ambiguity.

Finally, it should be emphasized that the different pathways of open- and closed-system evolution could also be distinguished by other variables than pH and Σ⁺. The use of these variables in the models considered here was determined by the literature survey of melt-water analysis, which indicated that these are probably the variables most readily measured. Combinations of other variables, for example Σ⁺ and [HCO₃‾] could be derived from the equations presented here.