Introduction

Isotope concentration in polar snow and ice is considered to be a good indicator of temperature, and many workers have reconstructed past temperature records at various places in Greenland and Antarctica by looking at the concentration change along ice cores (e.g. Reference Dansgaard, Johnsen, Clausen and GundestrupDansgaard and others, 1973; Reference LoriusLorius and others, 1985). This method has been extended to ice cores taken at rather warm sites where snow particles in surface layers are subjected to wet-snow metamorphism for a significant period of time.

In wet snow metamorphism, the rate of grain coarsening is much faster than in dry metamorphism (e.g.Reference Wakahama akahama, 1968). This is mainly due to melting of small particles and freezing of surrounding liquid water on to large particles, and the major portion of their volume has been slowly frozen from the liquid phase at an advanced stage (Reference Raymond and TusimaRaymond and Tusima, 1979). Isotope concentration of snow particles as well as surrounding water evolves considerably during wet-snow metamorphism, since isotopie fractionation takes place with the phase changes. Reference asonBúason (1972) examined the isotopie fractionation in a melting snow column by assuming an exponential decay of fractionation with time. It is important to know how isotopie fractionation takes place during grain coarsening in wet snow.

This paper aims at investigating quantitatively the isotopic fractionation in wet-snow metamorphism, and at providing basic knowledge for interpretation of isotope data collected from ice cores from relatively warm areas.

Notation

αfractionation factor

αD fractionation factor for deuterium, 1.0206

(Reference Suzuoki and KimuraSuzuoki and Kimura, 1973)

Q¹⁸O fractionation factor for ¹⁸O, 1.0028

(Reference Suzuoki and KimuraSuzuoki and Kimura, 1973)

δ isotopie composition denoted with a reference of

Standard Mean Ocean Water (SMOW):

δ = (a_sample−a_SMOW)/a_SMOW , where a is the

isotopie ratio, D/H or ¹⁸O/¹⁶O

δDδvalue for deuterium

δ¹⁸Oδ value for ¹⁸O

δ_i δ value for freezing ice

δ_iz δ value for total ice portion (snow particles)

δ_W δ value for water

δ_io δ value for original snow particles

δ_wo δ value for original water

f fraction of freezing (or melting)

Experiment

Sieved snow kept in a 0°C chamber (a container surrounded by snow-water mixture) was mixed with an equal amount of water also stored in the chamber. The wet snow of 50% water content thus prepared was bottled in 100 cc plastic containers; these were submerged in a large container of snow jam (water-rich wet snow), which was placed in the 0°C chamber. The whole system was kept in a cold room at a temperature of 0° ± 2°C.

The samples were analyzed in a series of experiments. First a subsample from a bottle was photographed under a microscope for analyzing particle size distribution. The rest of the sample was then centrifuged to separate liquid and solid portions.

Pre-experiments were conducted to determine how long the centrifuge should be operated to achieve complete separation. Wet-Snow samples prepared as above were subjected to separation for certain time periods, and the water content of the resultant solid portion of each sample was measured with a calorimetrie method having an accuracy of ±1% (Reference AkitayaAkitaya, 1978). The water content decreased as the time period increased, as shown in Figure 1. The scatter in water content before separation began indicates that 60–80% of the liquid water between the snow particles drained off naturally when the sample was placed in a container. By rotating the separator, most of the rest of the water was extracted from the sample. The water content of the sample stabilized at ∼3% after several minutes’ rotation.

Fig.1 . Water content change of wet-snow sample by centrifugal separation.

In each experimental run the liquid and the solid portions were subjected to the isotope analyses after ten minutes of separation. Their δ¹⁸O values were measured using the CO₂ equilibration method (Reference Yoshida and MizutaniYoshida and Mizutani, 1986). Some portion of each sample was converted to hydrogen gas by hot uranium, and its deuterium concentration δD was measured with a mass spectrometer, Micro Mass 602E. The δ¹⁸O and δD values of the solid ice portion (δ¹⁸O_iz and δD_iz respectively) were calibrated with the values for the liquid portion (δ¹⁸O_w and δD_W) assuming the 3% liquid-water content established in the pre-experiments.

Four experimental runs were carried out, as shown in Table 1. In runs Β and C, isotopically heavier snow from Sapporo, Japan, was mixed with lighter water prepared by melting Antarctic snow. The electrical conductivity of the snow collected at Sapporo is 10–100 μS cm⁻¹ (Suzuki, 1987), and the Antarctic snow has conductivity of 1–10 μS cm⁻¹. In run A, Antarctic snow was mixed with distilled and de-ionized tap water with electrical conductivity of <(6 × 10⁻²) μS cm⁻¹. In run D, an NaCl solution of (8 × 10⁻⁴) mol kg⁻¹ was mixed with Antarctic snow. In runs A and D, therefore, the snow was isotopically lighter than the water prepared from tap water at Nagaoka, Japan.

Ion concentration of the initial snow or water samples was highest in the NaCl solution and second highest in Sapporo snow. Raymond and Tusima (1979) found, however, that the rate of grain coarsening was not affected by the presence of impurities when their concentration was <0.01 mol kg⁻¹. The present study also showed no discernible difference between the different runs in the temporal change of the particle size distribution, which will be discussed later.

Slope of δ;D – δ¹⁸O Diagram

Grain coarsening of wet snow has been explained in terms of heat-flow controlled melting and refreezing determined by the curvature of particle surfaces (Raymond and Tusima, 1979). Under an isothermal conditon at 0°C, the amount of melting of relatively small particles is identical with the amount of freezing of water on to large particles. The δ values for the total ice portion is hence given by

Because of the fractionation of heavy isotopes during freezing,

The mass conservation law gives

From Equations (1), (2) and (3)

and

Equations (5) and (6) hold for either deuterium or ¹⁸O, and

where

and

Equation (7) gives a slope in δD − δ¹⁸O diagram as shown in Figures 2 and 3, where experimental data are plotted. Straight lines in the figures are linear regressions for each run of the experiment, and their slopes are given in Table 2.

Fig. 2. δD−δ¹⁸O diagram for ice portion (snow particles). Straight lines are linear regressions.

Fig. 3. δD−δ¹⁸O diagram for liquid water. Straight lines are linear regressions.

The function g(f) is a monotonously decreasing function from 1 for f = 0 to 0.99 for f = 1, which, therefore, can be practically regarded as 1. The slope of δ change in δD − δ¹⁸O diagram is hence essentially dependent on K, a function of initial δ values. The Κ values for different runs are given in Table 2 in association with the values for K.g(f) , where g(f), is the average g(f) for f = 0 to 1. No significant difference can be seen between the values of Κ and K.g(f) , as mentioned above.

The calculation of the slope by Equation (7) compares favourably with those derived by regression analysis. This indicates that we would be able to estimate the change in isotopie composition through wet snow metamorphism, when we know δ values for both the initial snow and water components. The slope given by Equation (7) is different from those derived by Souchez and Reference Jouzel and SouchezJouzel (1984) for successive freezing of water in a closed system.

Fractionation With Time

Examples of temporal changes in δ_iz and δ_w are shown in Figure 4. In both runs C and D the δ values of ice and water changed, approaching each other with time. In run D, where ice was originally lighter than water, the δ values crossed and ice became heavier than water at an advanced stage. On the other hand, in run C where ice was heavier than water when the experiment started, the rate of δ change was more gentle and the δ values appeared stable after a certain period. This feature is considered reasonable, since ice should be heavier than water at the equilibrium state.

Fig. 4. Examples of temporal change of 6 values.

Raymond and Tusima (1979) examined in detail the evolution of the particle size distribution of water-saturated snow. They proposed the following equation to represent the normalized cumulative frequency curve for the size distribution during the grain coarsening of wet snow:

where v is the volume of a particle, v_m is the median volume, and a and b are constants to be 0.23 and 1.55, respectively. It predicts zero probability for particles larger than a maximum volume of u_mb/a. Equation (8) fits nicely to our data, as shown in Figure 5, except for small sizes, say v/v_m < 0.5 and for the relatively early stage. The frequency curve ϕ* is then given by differentiating Equation (8), hence

Raymond and Tusima (1979) derived also the freezing rate S(v, t) for a particle with the volume v:

where t is time. Taking V to be the total volume and N to be the the number of snow particles in the system under consideration, the rate of increase in freezing fraction for the total snow particles is given by

since the grain coarsening takes place only for particles larger than the average grain volume, which is expressed by bv_m /(1 + a) (Raymond and Tusima, 1979). Substitution of Equations (9) and (10) into Equation (11), and performing the integration gives the following equation, taking into account that N(t) is given by ((1 + a)V>)/(bV_a):

where

and v₀ is the initial median volume.

Substitution of Equation (12) into Equations (5) and (6) gives δ_iz or δ_w as a function of time. When δ_iz and δ_W are normalized,

Equation (13) is plotted in Figure 6 for deuterium and in Figure 7 for ¹⁸O. Solid lines in the figures were calculated with the average value of

for all the experiments. Dashed lines are for the extreme values of in the experiments. These curves are essentially the same in both figures, since the difference between αD and a ¹⁸O is very small.

Fig. 5. Example of particle size distribution plotted as function of v/v_m.

Experimental data on δ_iz and δ_w are also plotted in Figures 6 and 7. It is found that the δ change is more gentle in the experiment than predicted by Equation (13). This indicates that at an earlier stage, the rate is faster than the prediction, since the normalized δ should be zero when t is zero.

Fig.6 . Evolution of normalized δ values for deuterium. Solid and dashed curves are given by Equation (13) for different values of .

Fig.7. Evolution of normalized δ values for ¹⁸O. Solid and dashed curves are given by Equation (13) for different values of

Discussion

Snow particles at a certain grain-size grow in an early stage but they melt out in an advanced stage, when the average grain-size becomes larger. In the model calculation these particles are assumed, when they melt, to have the same isotopie concentration as the original snow, although they consist of the original snow portion plus the newly frozen portion with different δ values. This, however, cannot be a major cause of the discrepancy between the data and the theory found in Figures 6 and 7, since the different combinations with initially heavier ice than water and with lighter ice than water gave similar results, as can be seen in the figures.

In deriving Equation (13), the following assumptions were made implicitly.

1. Diffusion of the heavy isotopes can be neglected in the ice matrix.

2. Listitemquid portion of wet snow is isotopically homogeneous: heavy isotopes diffuse very rapidly in water.

3. Fractionation during grain coarsening is an equilibrium process and the fractionation factor has a constant value throughout the process.

The diffusion coefficient of the heavy isotopes is of the order of 10 ⁻¹⁴ m² s⁻¹ for ice at 0°C (Reference HobbsHobbs, 1974) and of 10⁻⁹ m² s⁻¹ for water near 0°C (Reference Eisenberg and KauzmannEisenberg and Kauzmann, 1969). The order of diffusion distance, for example, becomes 10⁻⁷ m in ice and 10⁻⁵ m in water, say in 1 s. The speed of displacement of the solid-liquid interface through melting or freezing of snow particles was considered, based on the experiments, as having an order of 10⁻⁴ m s⁻¹, which is much faster than the diffusion speed in the ice matrix. The first assumption, therefore, would be a reasonable one.

In liquid water, however, the diffusion speed is almost equivalent with or even smaller than the speed of interface movement owing to the grain coarsening. Isotope concentration of the water adjacent to growing grains, therefore, would become smaller because of the fractionation at the interface. After the initial stage of grain growth, this would lead to a slower rate in the temporal change of δ values for ice and water. The discrepancy between the data and the theory, therefore, could be due to the “diffusion layer” surrounding growing grains.

The δ values seem to change more rapidly than predicted by Equation (13) at an early stage of the process, as was mentioned in the previous section. A possible e3xplanation for the difference is that the fractionation factor may not be a constant and could be larger, at an early stage of the process, than the value used in the calculation. It might depend on curvature. The equilibrium temperature at an ice-water interface is lower than 0°C when the snow particles are small, because of the curvature effect. The depression of the equilibrium temperature would decrease as the grain-size increases with time. At an early stage the fractionation factor can possibly be larger than that at a later stage, since it generally becomes large with decreasing temperature. The amount of the temperature depression caused by the curvature effect, however, is rather small, and may not be able to explain the discrepancy between the theory and the data at an early stage of the grain coarsening. Detailed study would have to be carried out to answer this question.

The model calculation of the temporal change of δ values for both the ice portion and the liquid portion was not very successful. The estimate of the slopes for δD − δ¹⁸O diagram, however, was compatible with the experimental data, as mentioned above. This is attributed to the fact that the ratio of fractionation of deuterium to that of ¹⁸O would not be affected by the rate of fractionation which could be controlled by the formation of the “diffusion layer” surrounding growing snow particles. Since the slope of the δD − δ¹⁸O diagram can be estimated from the initial δ values of snow and water before mixing, the frozen fraction, the part of the liquid which refreezes to relatively large particles during grain coarsening, could possibly be estimated by measuring the isotopie composition, as was done by Jouzel and Reference Souchez and JouzelSouchez (1982) for regelation ice at a glacier bed, since the slope in wet snow metamorphism is different from 8, the value in evaporation-condensation process (Reference Craig, Gordon and HoribeCraig and others, 1963).