2.1. Ice-core drilling

In October 1994 an ice core 125 m long was recovered from upper Grenzgletscher (4200 m a.s.l.; 45°55′28′′ N, 7°52′3′′ E, Swiss coordinates 633 250/085 890) at a site presumably located on the flowline of Colle Gnifetti in the Monte Rosa massif (see Fig. 1). This drilling site was selected because wind erosion of the accumulated precipitation is much less than at the Colle Gnifetti saddle. Analyses of shallow firn cores from the area of upper Grenzgletscher (Reference DöscherDöscher, 1996; Reference Gäggeler, Stauffer, Döscher and BlunierGäggeler and others, 1997) indicated an annual accumulation rate of about 2 m w.e. at the drilling site.

During the campaign, ice-core sections (0.5–0.8 m long) with a diameter of 7.8 cm were electromechanically drilled (for details see Reference Gäggeler, Stauffer, Döscher and BlunierGäggeler and others, 1997), packed and sealed in polyethylene tubes in the field and kept frozen in a cold room at −25°C until sample preparation.

2.2. Radar soundings

Measurements of the glacier thickness by radar soundings were performed at the drill site in order to investigate the flow behaviour of the glacier and to predict the source area of the drilled firn and ice (Vonder Mühll and Funk, unpublished). The results of the radar soundings show an increase of the glacier thickness and a slope of the glacier bed down along the flowline of Grenzgletscher from east-northeast (ENE) to west-southwest (WSW) (Figs 2 and 3). The glacier thickness doubles from 100 to 200 m within a horizontal distance of 400 m. We assume that the glacier thickness at the drilling site is approximately 190 m. With a relatively flat glacier geometry (slope of about 10°; Fig. 3), upper Grenzgletscher is well suited to serve as an archive for atmospheric species.

Fig. 2. Glacier thickness (in meters) at the drilling site of upper Grenzgletscher interpolated from radar profiles (stars) (after Vonder Mühll and Funk, unpublished), along with the flowline used in Figure 3 (thick line). Swiss and international coordinates are given.

Fig. 3. Schematic cross-section of upper Grenzgletscher at the drilling site.

2.3. Measurement of borehole temperatures

For the preservation of ice-core records of water-soluble trace components, the absence of meltwater percolation and temperate firn is essential, since the inflow of meltwater could change the initial composition of firn and ice. Measurements of borehole temperatures at the drilling site were carried out using thermistor chains (personal communication from S. Suter, 1999). The measured continuous negative borehole temperatures (Fig. 4) indicate that Grenzgletscher consists of cold firn and ice down to at least 4000 m a.s.l.. A relatively high temperature of −0.4°C at 2.5 m w.e. depth shows that the upper firn layer was nearly temperate down to this depth: a result of the unusually high temperatures in summer 1994. We conclude that the drilling site belongs to the cold infiltration zone where meltwater may be present in the upper firn layer.

Fig. 4. Borehole temperatures along the drilling (personal communication from S. Suter, 1999). The ice-core depth of 104 m w.e. represents the total length of 125 m.

Conspicuous in the temperature profile is the local temperature maximum of about −1°C at 18 m w.e. depth. It has been suggested that this temperature anomaly is due to meltwater inflow at 11–12 m w.e. depth, most probably through a crevasse system in the glacier (Reference Eichler, Schwikowski and GäggelerEichler and others, in press). Additionally, draining of the meltwater at 20–24 m w.e. depth was supposed. Meltwater percolation led to a preferential leaching of various species. Concentrations of some ions (e.g. SO₄ ²⁻, Ca²⁺, Na⁺) were drastically reduced, whereas species discussed in this work (NH₄ ⁺, δ ¹⁸O and ²¹⁰Pb) were preserved (see also Fig. 5). The preferential leaching was attributed to fractionation between different species occurring during snow metamorphic processes (Reference Eichler, Schwikowski and GäggelerEichler and others, in press). Thus, the methods used in this study can be applied for dating glaciers even where partial percolation of meltwater has occurred. The borehole temperature decreased below 18 m w.e. down to −9°C in 80 m w.e. depth, indicating an inflow of colder ice, presumably from the area of Colle Gnifetti.

Fig. 5. Record of the ²¹⁰Pb activity along the ice core.

2.4. Sample preparation

In the cold room of the Paul Scherrer Institute, each core section with a length up to 55 cm was photographed for documentation of stratigraphic characteristics (e.g. ice lenses, dust layers). Sectioning and decontamination of the firn and ice were carried out using a modified band-saw setup (stainless-steel blades; tabletops and saw guides covered with Teflon) which was regularly cleaned with acetone (Merck). The ice-core sections were cut into 5 cm pieces. Outer parts, which might have been chemically contaminated by the drill and the plastic storage bag, were used to analyze the isotopes ²¹⁰Pb, ³H, ¹³⁷Cs, ³⁶Cl and the isotopic ratio δ ¹⁸O. From the inner parts the concentrations of the main ionic species, pH and conductivity were determined.

Due to the low concentrations of chemical species in ice and firn, materials in contact with the samples had to be very carefully cleaned. Thus, all storage bags, instruments and sample vials used were rinsed several times with ultra-pure water (18 MΩ cm quality).

2.5. Chemical and isotopic analyses

The quantitative analysis of the NH₄ ⁺ concentrations in the firn and ice samples (sample volume 1 mL) was performed by ion chromatography (IC) with conductivity detection (Reference Döscher, Schwikowski and GäggelerDöscher and others, 1995a; Eichler, unpublished).

The pH was determined using an 8103 Orion Electrode coupled to a Metrohm pH meter 605 (sample volume 1 mL, addition of 10 μL 1 M KC1) (Eichler, unpublished).

The analysis of the isotopic ratio δ ¹⁸O (defined as the relative deviation of the ¹⁸O/¹⁶O ratio of the sample from the Vienna standard mean ocean water) was carried out by equilibration of a 5 mL sample with CO₂ gas (0.8 bar) over 8 h (T = 19°C) (Reference Epstein and MayedaEpstein and Mayeda, 1953). The C¹⁸O¹⁶O/C¹⁶O₂ ratio of the gas was measured using an isotope-ratio mass spectrometer (delta-S, Finnigan MAT).

The ²¹⁰Pb activity (sample volume 200 mL) was indirectly determined over the activity of its granddaughter nuclide ²¹⁰Po electrolytically deposited on Ag plates. The ²¹⁰Po activity was determined by measuring its α decay at an energy of 5.3 MeV (Reference Gäggeler, von Gunten, Rössler, Oeschger and SchottererGäggeler and others, 1983; Eichler, unpublished).

For the determination of the ¹³⁷Cs activity, the sample (1 L) was passed through a cation exchange column. Then the exchange resin containing the ¹³⁷Cs⁺ was placed in an HPGeγ-borehole detector, and the ¹³⁷Cs activity was measured via its γ-decay energy of 662 keV.

The ³H content of the samples (sample volume 10–70 mL) was determined by direct β measurement in a liquid-scintillation spectrometer (Reference Schotterer, Schwarz and RajnerSchotterer and others, 1998).

The analysis of the isotope ³⁶Cl was performed by accelerator mass spectrometry (AMS). For this purpose a Cl carrier was added to the sample (about 1 L). The Cl⁻ of the sample was precipitated as AgCl, dried and pressed into a Cu (Ta) target. Afterwards, the ratio ³⁶Cl/Cl was determined by AMS at the Zürich facility (Reference Synal, Beer, Bonani, Lukasczyk and SuterSynal and others, 1994, Reference Synal1997).

3.1. Dating by radioactive decay of ²¹⁰Pb

The radioactive isotope ²¹⁰Pb can be used for dating glacier ice on a century time-scale. Reference Gäggeler, von Gunten, Rössler, Oeschger and SchottererGäggeler and others (1983) and Reference Gäggeler, von Gunten, Rössler, Oeschger and Schotterervon Gunten and others (1983) showed that the ²¹⁰Pb method can even be used for dating temperate glaciers and glacier sites with an irregular deposition of precipitation, where most of the conventional dating methods cannot be applied.

²¹⁰Pb with a half-life of 22.3 years is a decay product of which emanates continuously from the Earth’s crust into the atmosphere. Attached to aerosol particles, ²¹⁰Pb can reach the glacier surface by dry or wet deposition after a residence time in the atmosphere of a few days to a few weeks. In firn and ice the activity of ²¹⁰Pb decreases with increasing depth due to its radioactive decay. The exponential decay of the isotope can be used for dating under the following assumptions (Reference Gäggeler, von Gunten, Rössler, Oeschger and SchottererGäggeler and others, 1983):

1. (a) constant input of ²¹⁰Pb

2. (b) no transport of the initial deposited ²¹⁰Pb in firn and ice (e.g. by meltwater running through the glacier).

We used the ²¹⁰Pb method for a first estimation of the time period covered by the Grenzgletscher core. The record of the ²¹⁰Pb activities measured along the ice core is shown in Figure 5. We observed a decrease of the ²¹⁰Pb activity with depth superimposed on strong fluctuations. These fluctuations of the measured ²¹⁰Pb activities indicate that the input of ²¹⁰Pb at this high-Alpine site is not constant throughout the year, in contradiction of assumption (a) above. Reference Von Gunten and MoserVon Gunten and Moser (1993) illustrated that ²¹⁰Pb activities at low altitudes (Fribourg, Switzerland) do not exhibit a pronounced seasonal pattern, indicating that emissions of ²¹⁰Pb from rocks and soils are independent of the season. On the other hand, strong seasonal variations of the ²¹⁰Pb activity, with maximum values in August/September, have been observed at the high-Alpine research station Jungfraujoch, Switzerland (3450 m a.s.l.; Reference GäggelerGäggeler, 1995). These were attributed to seasonal variations in the transport of pollutants to the high-elevation sites. A higher frequency of convective weather types in summer yields a stronger vertical transport of aerosol-rich air from the atmospheric boundary layer to the high-Alpine sites. Therefore, higher concentrations of trace species are found in the summer snow, whereas, due to a suppression of the vertical motion by the great stability of the atmosphere, the concentrations in winter are low (Reference LugauerLugauer and others, 1998).

Dating of the Grenzgletscher ice core, based on the radioactive decay of ²¹⁰Pb, is shown in Figure 6. For this purpose we used mean values of the measured ²¹⁰Pb activity over sections of about 10 m w.e., thus averaging the described transport fluctuations. It is remarkable that a decrease of ²¹⁰Pb activity due to decay is not visible in the part from 15 to 55 m w.e. This indicates that the input of ²¹⁰Pb at the glacier site has not been constant over the last 60 years. We attribute this phenomenon to a stronger input of ²¹⁰Pb in the 1970s. Concurrent with the high ²¹⁰Pb activities, concentration records of the species sulphate, nitrate and ammonium showed maximum values at 50–55 m w.e. depth, due to enhanced emissions of SO₂, NOx and NH₃ from anthropogenic activities. We assume that during this period larger amounts of ²¹⁰Pb were transported to the high-Alpine sites because of increased concentrations of aerosol particles acting as transport vehicles.

Fig. 6. 10 m w.e. mean ²¹⁰Pb activity (triangles, lefthand logarithmic scale) together with a linear trend line (solid line) and a fitted function after Equation (1) (dashed line) vs depth of the ice core and the calculated age (righthand scale).

From the linear regression plot of the logarithmic ²¹⁰Pb activities against depth (solid line, Fig. 6) we derived an age for the deepest part of the ice core of 55 ± 7 years with respect to the drilling date. The value of the axis intercept (85 ± 10 mBq kg⁻¹) corresponds to the ²¹⁰Pb activity at the surface of Grenzgletscher. This result agrees well with the ²¹⁰Pb surface activity obtained from other Alpine sites: Colle Gnifetti (4450 m a.s.l.) 85 ± 27 mBq kg⁻¹ (Füeg, unpubished); Jungfraujoch (3545 m a.s.l.) 78 ± 5 mBq kg⁻¹ (Reference SchottererSchotterer and others, 1977); Vernagtferner (3150 m a.s.l.) 83 ± 17 mBq kg⁻¹ (Reference Gäggeler, von Gunten, Rössler, Oeschger and Schotterervon Gunten and others, 1983).

From the slope of the regression line, we derived a mean annual accumulation rate of 1.9 m w.e.. This value does not include a thinning of the annual-layer thickness with depth (see section 3.4). The estimated age–depth relation (Fig. 6, solid line, righthand scale) has uncertainties of ±7 years.

3.2. Dating by seasonally varying signals

NH₄ ⁺

As already pointed out in previous work on Alpine glaciers (e.g. Reference Maupetit, Wagenbach, Weddeking and DelmasMaupetit and others, 1995; Reference Schwikowski, Döscher, Gäggeler and SchottererSchwikowski and others, 1999a), NH₄ ⁺ concentrations in high-altitude glacier ice show the most pronounced seasonal pattern of any deposited major ion. This strong seasonal behaviour, with concentrations about one order of magnitude higher in summer precipitation than in winter precipitation, is due to two synergistic effects. First, the gaseous precursor NH₃ is mainly emitted into the atmosphere in the warmer months (Reference AsmanAsman, 1992) because a high proportion of it (up to 90%) originates from agricultural emissions of livestock excreta and of fertilizers. Second, a strong vertical transport of pollutants from the planetary boundary layer to high-Alpine sites occurs mainly in the summer months (see section 3.1).

The record of the NH₄ ⁺ concentration along the 125 m (104 m w.e.) ice core from Grenzgletscher is shown in Figure 7. Because of poor ice quality, the part between 58 and 60 m w.e. could not be analyzed. In order to highlight the seasonality, seven-point moving averages were used. The expected seasonal variations are indicated by up to 20 times higher summer than winter concentrations. Reported values were statistically different from the blank value (0.07 μeq L⁻¹). Dating was performed by annual-layer counting, revealing an age of the deepest part of the core of 57 years with respect to the drilling date. Dating uncertainty is 1–2 years for each 5 year period because of certain difficulties with the identification of annual layers. Such difficulties were encountered for periods with small precipitation amounts (e.g. winter 1980/81), with relatively high concentrations in winter (e.g. 1982/83) or with low concentrations in summer (e.g. 1980). High concentrations in winter can be related to cyclonic weather types, whereas summer minima are due to the advection of fresh maritime air from the Atlantic (Reference LugauerLugauer and others, 1998). A cumulative dating uncertainty of 12–24 years is finally observed from counting annual NH₄ ⁺ layers.

Fig. 7 Records of NH₄ ⁺ (seven-point moving average, solid line) and δ¹⁸O (dotted line) vs depth of the ice core in m w.e., together with 5 year segments (dashed lines) and six reference horizons (Saharan dust events 1990, 1977, 1947: arrows; Chernobyl accident 1986: star; nuclear weapon tests 1963, 1959: triangles).

δ ¹⁸O

Temperature- and vapour-pressure-dependent fractionation of the main isotopic components of water H₂ ¹⁶O and H₂ ¹⁸O during evaporation and condensation processes in the hydrological cycle causes lower δ ¹⁸O values in winter and higher values in summer precipitation (Reference Dansgaard, Johnsen, Clausen and GundestrupDansgaard and others, 1973). The correlation between monthly mean δ ¹⁸O values of precipitation and the atmospheric temperatures at high-Alpine sites was described by Reference SchottererSchotterer and others (1997), for instance. The δ ¹⁸O record of the ice core from Grenzgletscher is shown in Figure 7 against depth (dotted line). Strong seasonal patterns with maximum values of up to −10‰ and minimum values of −25‰ corresponding to deposited summer and winter precipitation, respectively, are observed. These are typical values for Alpine precipitation at these altitudes (Reference SchottererSchotterer and others, 1997). The dating performed by the annual-layer counting using the varying δ ¹⁸O signal has an uncertainty of ±1 year in the upper part of the ice core (<58 m w.e.). Due to the thinning of the annual layers and the smoothing of the signal with depth by diffusion processes (Reference JohnsenJohnsen, 1977), the dating error is about 1 year for each 5 year period between 60 and 90 m w.e. Thus, cumulative dating uncertainty is about 6 years for the upper 90 m w.e. Dating is hardly possible for the deepest part (>90 m w.e.).

However, a combined evaluation of the NH₄ ⁺ and δ ¹⁸O profiles improved the dating precision significantly. Generally, in time periods poorly resolved by NH₄ ⁺, δ ¹⁸O seasonal layers were well produced and vice versa (see, e.g., time periods 84–80 and 44–40). The resulting uncertainty is ±1 year for the period 1970–94 and ±3 years for the period 1937–69.

The strong seasonal variation of NH₄ ⁺ concentrations together with the δ ¹⁸O values indicate that precipitation at the drilling site is regularly distributed throughout the year. In order to examine if the measured amount of precipitation at Grenzgletscher is representative for this part of the Alps, we compared the net annual accumulation rate deduced from the ice core with annual precipitation data of the 50 km distant weather station at Col du Grand St Bernard (2469 m a.s.l.; see Fig. 1). This is the closest high-mountain weather station, with the longest precipitation series in the higher European Alps (Reference Wanner, Rickli, Salvisberg, Schmutz and SchüeppWanner and others, 1997). Reasonable agreement was found in the trend for the period 1977–93 (r = 0.7; Fig. 8). This time period was selected because the thinning of annual layers in this part of the glacier is negligible. A mean precipitation rate of 2.4 ± 0.3 m w.e. was registered at the Col du Grand St Bernard station, and 2.7 ±0.4 m w.e. at Grenzgletscher, suggesting that the accumulated precipitation at Grenzgletscher corresponds roughly to the actually fallen precipitation at this site. Thus, wind erosion or drift seems to be of much less importance than at more exposed saddle sites, such as Colle Gnifetti. Precipitation data from the weather station during the period 1935–94 show that precipitation in this area is nearly uniformly distributed throughout the year. Exceptions (e.g. seasons with extremely small or large amounts of precipitation) can sometimes be clearly identified from the measured δ ¹⁸O record. For instance, the pronounced δ ¹⁸O minimum of −27% at 86 m w.e. depth (see Fig. 7) is due to the well-known heavy snowfall in January and February 1951 causing a large number of avalanches (Reference PfisterPfister, 1999).

Fig. 8. Comparison of the annual accumulation rate calculated from ice-core data (columns) with the annual precipitation measured at the weather station Col du Grand St Bernard (line) 1977–93.

3.3. Dating by stratigraphic markers

Saharan dust falls

Mineral dust originating from the Sahara can be transported over a distance of several thousand kilometers towards the Alps. As already known from studies at high-Alpine sites (e.g. at Colle Gnifetti (Reference Wagenbach, Geis, Leinen and SarntheinWagenbach and Geis, 1989) and Mont Blanc, French Alps (Reference De Angelis and Gaudichetde Angelis and Gaudichet, 1991)), the portion of Saharan dust amounts to approximately two-thirds of the overall mineral dust content. Mineralogical composition of Saharan dust can vary with the source region in Africa. A pronounced abundance of carbonates (as calcite) (Reference Schütz and SebertSchütz and Sebert, 1987), as well as high contents of the minerals quartz, gypsum, muscovite, anorthite and montmorillonite (Reference Schwikowski, Seibert, Baltensperger and GäggelerSchwikowski and others, 1995), were detected. Because of the high amount of basic minerals in Saharan dust aerosols, Saharan dust-bearing snow layers are marked not only by the often occurring yellow-orange colouring, but also chemically by a high Ca²⁺ content and increased pH values. Ca²⁺/H⁺ concentration ratios along the ice core from Grenzgletscher are presented in Figure 9. Three maxima of the Ca²⁺/H⁺ concentration ratio are attributed to intense Saharan dust-fall events described in the literature: March 1990 (Reference Schwikowski, Seibert, Baltensperger and GäggelerSchwikowski and others, 1995), May 1977 (Reference Prodi and FeaProdi and Fea, 1978; Reference Wagenbach, Geis, Leinen and SarntheinWagenbach and Geis, 1989) and 1947 (Reference Wagenbach, Geis, Leinen and SarntheinWagenbach and Geis, 1989). No additional dust peak was observed in the deepest part of the core, which would have corresponded to the well-known Saharan dust fall in 1936/37 (Reference Wagenbach, Geis, Leinen and SarntheinWagenbach and Geis, 1989; Reference DöscherDöscher, 1996). Thus, the deepest part is not older than 58 years with respect to the drilling date.

Fig. 9. Identification of strong Saharan dust falls by high Ca²⁺/H⁺ concentration ratios.

³H and¹³⁷Cs

Tritium is naturally produced in the atmosphere by the ¹⁴N(n, ³H) ¹²C reaction of cosmic-ray-induced neutrons with atmospheric nitrogen. ³H is directly incorporated into the water molecule by its reaction with stratospheric oxygen. Natural background tritium levels in precipitation before 1951 are very low, approximately 0.1–1 Bq L⁻¹. With the detonation of the world’s first thermonuclear explosion by the U.S.A. in May 1951, a period of anthropogenic ³H production began, increasing stratospheric ³H concentrations by several orders of magnitude. The amount of tritium released into the atmosphere during the period 1951–62 was estimated to be about 2.4 × 10¹⁴ Bq (Reference Clark and FritzClark and Fritz, 1997). Until the Soviet–U.S. Test Ban Treaty in 1963, a stratospheric reservoir of ³H was built up, influencing the precipitation composition up to the present.

The radioactive isotope is, along with , one of the longer-lived nuclear fission products. During the atmospheric nuclear weapon tests in the 1950s and early 1960s (see above), large amounts of ¹³⁷Cs were ejected into the stratosphere with debris. The main portion of ¹³⁷Cs reaches the Earth’s surface adsorbed onto aerosol particles with a time delay of a few months to a few years because of the long stratospheric residence time (Reference Emeleus and SharpeEmeleus and Sharpe, 1961). Another event increasing the ¹³⁷Cs activity in the atmosphere was the nuclear reactor accident at Chernobyl on 26 April 1986. Huge amounts of radioactive material were spread over a large area of the Northern Hemisphere, being either transported as gaseous species (e.g. Kr and Xe) or adsorbed onto aerosol particles (e.g. ¹³⁷Cs). As a result, increased activity of ¹³⁷Cs was detected even in Alpine glaciers (Reference Haeberli, Gäggeler, Baltensperger, Jost and SchottererHaeberli and others, 1988).

The activities of the isotopes ¹³⁷Cs and ³H measured along the Grenzgletscher ice core are presented in Figure 10a and b. Both records reflect the atmospheric weapon tests in the 1950s and 1960s in a broad activity peak at 55–85 m w.e. depth. The maxima at approximately 76 and 69 m w.e. depth are related to the test maxima of the years 1958 and 1962. They appear in the ice core with a time delay of approximately 1 year because of the above-mentioned slow stratosphere–troposphere transfer (see, e.g., Reference Emeleus and SharpeEmeleus and Sharpe, 1961). For the same reason, activities appear in a broad peak. The maximum of the ¹³⁷Cs activity at 20 m w.e. depth can be attributed to the radioactive fallout from the nuclear reactor accident at Chernobyl. The tropospheric transport of the aerosol-bound fission products, and their fast removal by wet deposition in the first week of May 1986, yielded a sharp signal in the ¹³⁷Cs activity record.

Fig. 10. Records of the ¹³⁷Cs (a) and ³H (b) activities and ³⁶Cl concentration (c) vs depth of the ice core; the activities were calculated back to the date of drilling in October 1994.

The integrated ¹³⁷Cs activity from nuclear weapons fallout (3500 ± 800 Bq m⁻²) agrees well with estimated values (e.g. 5040 Bq m⁻² between 40° and 50° N (Reference KieferKiefer, 1986), or approximately 4500 Bq m⁻² at Jungfraujoch, Switzerland (von Gunten and Rössler, unpublished)). The calculated ¹³⁷Cs fallout from the Chernobyl accident (800 ± 200 Bq m⁻²) is at the lower limit of the values determined at Alpine sites (400–15 000 Bq m⁻²; Reference Haeberli, Gäggeler, Baltensperger, Jost and SchottererHaeberli and others, 1988). These differences in the deposited activities reflect the known regional heterogeneity of the Chernobyl fallout, which was strongly dependent on the precipitation pattern in the first days of May 1986.

3.4. Determination of the thinning effect

Figure 11 shows the age–depth relationship resulting from a combination of all methods described above (triangles). The included linear trend line (dashed line), which represents a constant annual-layer thickness λ of 2.7 m w.e., describes the data only in the upper 50 m w.e. With increasing depth the data differ more from this line and show a steeper slope. This means that the annual layer thickness (1/slope) decreases as a function of depth, due to an increasing vertical strain of the glacier ice with depth. The thinning in the deepest core parts amounts to about 60%, corresponding to an annual layer thickness λ_E of 1 m w.e. in comparison to the initial value λ₀ of 2.7 m w.e.

Fig. 11. Age–depth relationship established in this work (triangles), together with a line representing a constant annual-layer thickness of λ = 2.7 m w.e. (dashed line). In addition, the age–depth relationship after Nye’s model is given (solid line) with λ ₀ = 2.7 m w.e. and H = 170 m w.e., describing the thinning of the annual layers with depth from λ ₀ to λ_E = 1 m w.e.

For the description of the observed thinning effect, a simple kinematic ice-flow model developed by Nye (Reference HaefeliHaefeli 1961; Reference NyeNye, 1963; Reference Dansgaard and JohnsenDansgaard and Johnsen, 1969) was used. This model implies a uniform vertical strain rate and therefore a constant horizontal velocity along any vertical line in an ice cap. Melting at the bottom is assumed to be negligible. The age t of a layer y below the surface can be calculated from the absolute ice thickness H and from the initial annual layer thickness λ ₀:

(1)

This one-dimensional pure kinematic flow model does not take into account any dynamical ice-flow law. Nevertheless, Nye’s model was successfully applied to the estimation of time-scales covered by Greenland ice cores down to depths of about 2/3H (Reference Hammer, Clausen, Dansgaard, Gundestrup, Johnsen and ReehHammer and others, 1978). The calculated age–depth relationship for the Grenzgletscher core with λ₀ = 2.7 m w.e. and H = 170 m w.e. (see section 2.2) is shown in Figure 11 (solid line). The agreement with the established dating based on chemical records is remarkably good. Possible reasons for the applicability of Nye’s model are that the investigated ice core represents only about two-thirds of the total glacier thickness and that Grenzgletscher has a relatively simple topography with a proportionally large extent and a small slope in the drilling area.

In order to take into account the annual-layer thinning with depth, the ²¹⁰Pb data were re-analyzed. The simple linear regression of the logarithmic activities vs depth (see section 3.1; Fig. 6, solid line) yields an inaccurate average annual-layer thickness of 1.9 m w.e. In order to include thinning, the age–depth relationship derived from Equation (1) and shown in Figure 11 was added in Figure 6 (dashed line). This curve fits the experimental data better (χ ² = 1) than the linear regression (χ ² = 1.5).