Combining the data sets from ice samples retrieved in different years allows for a complete coverage of the profile of the ice sheet on WSS by measured ages. However, as the cores taken in 2023 and 2024 were not drilled to bedrock and no common horizon was visible in the ice, the depth scale has to be established from the annual surface offsets. For this, the annual SMB, listed in Table 1, is considered. As indicated by Fischer et al. (2022) and Hartl et al. (2025a), the ablation can vary strongly across the summit region where differences between ablation stakes of up to 75 cm were seen. Furthermore, despite using a precise GPS to find the drilling location from former years, spatial deviations of up to 10 m are possible. Figure 1b shows that this can lead to depth topography changes of up to about 2 m. However, the effect is probably significantly smoothed out by the snow and ice build-up and effects like wind erosion. A well-visible dust layer that melted out quite homogeneously across the summit region in 2022 (see Fig. S2), rather points towards spatial layer height variations around 10–20 cm. In consequence, depth values of years other than 2019 are shifted according to the values in Table 1 and a conservative error of 1 m is estimated. GNSS measurements at the ablation stake positions show that the horizontal movement is almost zero, as can be expected for the ice divide setting with the remaining relatively thin ice cover. All (repeated) point measurements of the stake positions are located within a few meters to each other and are randomly distributed within the measurement accuracy (compare Fig. 2 in Hartl et al., 2025a). Horizontal movement, therefore, did not further affect the alignment of the drilling position.

Furthermore, as depth always refers to a reference surface, which in this setting is changing over time, everything is discussed in terms of height over bedrock in the following, instead of depth below some annual surface. The conversion was done with the 2019 thickness of the ice sheet of 10.2 m (from the logging data of the 2019 sampling campaign, length of core 1) and the surface mass balance listed in Table 1. With this measure, a more general metric is established, which can more easily be applied to potential future ice cores that are drilled to bedrock. Nonetheless, because the wording is otherwise uncommon, the profile of ages throughout the ice column is still referred to as age-depth profile.

All the models which are used in the following to fit the data describe glaciers in a steady state. This means that the conditions at the last steady state (LSS) at WSS have to be estimated and the models have to be fitted accordingly. The basic Sorge's law of glaciology states that the age-depth profile of an ice sheet remains constant under steady-state conditions. From Fischer et al. (2022), WSS is estimated to have experienced its LSS around the year 1914 ± 50 at an ice thickness of 47 ± 10 m. The timing of the LSS was chosen as the last time interval which showed no significant ice loss. However, accounting for the low accuracy of the early data stemming mostly from old maps and aerial photos, a conservative error of 50 a is chosen. This way, the LSS is estimated to lie between the Little Ice Age (LIA) maximum around 1864 and the beginning of in situ SMB measurements in 1969. With these estimates, the measured ages can be shifted to the time of the last steady state to fit the models before translating the age profiles back to 2019.

In March 2019, two parallel ice cores were drilled at the ice divide with nearly flat bed conditions. Analysis for micro-radiocarbon ice dating was performed on discrete samples from one of the cores at the Paul Scherrer Institute (PSI), and ³H was measured on three additional shallow cores from the same location at Seibersdorf Laboratories (Bohleber et al., 2020). The ³H analysis showed no sign of the elevated levels from after the 1960s, indicating surface ages beyond 60 a. The radiocarbon analysis, conducted for samples from the lowest 6 m above bedrock, revealed an age profile that increases with depth reaching a maximum calibrated ¹⁴C age of approximately 6000 a at the bottom and decreasing to below 1000 a at approximately 5 m above bedrock. A comprehensive account of the data set and the sample processing can be found in Bohleber et al. (2020).

To better constrain the ages at the top of the ice column, several sampling campaigns have been conducted in recent years to obtain ice for ³⁹Ar dating. In June 2023, a first attempt to retrieve a new core at the summit of WSS was conducted, however retrieving only 2.16 m with a thermal 3^′′ drill due to equipment failure.

A second attempt was conducted in May 2024, which again experienced a failure of the drilling equipment. Still, four surface samples and several cores (both, thermally and mechanically drilled) were taken. An overview of the sampling of the different years is given in Fig. 2.

For the 2023 and 2024 campaigns, the ice was packed into insulation boxes on site and transported to the cold-room facilities (-20 °C) at the Institute of Environmental Physics, Heidelberg. Here, the ice was decontaminated by cutting off the outer 2 mm and the gas in the air bubbles extracted and purified following the procedure described by Feng et al. (2019) and Arck et al. (2025). The combined ice pieces were transferred into a 12.6 L stainless steel container and after evacuating the container, the ice was melted and the released gas captured on liquid nitrogen cooled activated charcoal traps. To purify the contained argon, all reactive gases were removed using two getters at 900 °C and room temperature in series (Arck et al., 2025). The remaining > 98 % pure argon gas was collected on an activated charcoal trap. Using this method, between 0.4 to 1 mL of pure argon was extracted from 2.5 to 4.6 kg of sample ice.

³⁹Ar measurements were conducted in the ATTA laboratory at the Kirchhoff-Institute for Physics, Heidelberg. The atom-optical ATTA method enables the cooling and trapping of individual atoms in order to count them (for details see Ebser et al., 2018 and Lu et al., 2014). ³⁹Ar is measured as an isotopic abundance (³⁹Ar/Ar) and reported in percent modern argon (pmAr), which is the sample abundance normalized to the modern atmospheric abundance (RA). By comparing the obtained count rate to reference measurements with known isotopic abundance, the ³⁹Ar abundance in the sample can be inferred. With usual count rates of around 6 ³⁹Ar atoms h⁻¹ for modern concentrations, sample measurements were conducted in a gas recycling mode over 20 h to ensure high enough statistics (Ebser et al., 2018; Feng et al., 2019). Reference measurements were done with an enriched reference gas (10 RA), which was measured for 2 h to obtain similar statistics to the samples. Furthermore, to account for background counts in the apparatus, blank measurements are conducted on a weekly basis and incorporated into the data analysis.

The newly developed data analysis applied in this work incorporates all reference and blank measurements over a measurement period with an unchanged, stably operating apparatus, typically spanning one to several weeks. The data analysis employs the underlying Poissonian statistics of atom counting to fit the time between atom detection events with the exponential distribution 1pΔt;r=e-rΔt, where r1s denotes a rate parameter which is a function of the abundance in the sample, the performance of the apparatus (determined by the reference measurements), and of Δt itself due to contamination build-up in the system. The rate of the latter is determined by blank measurements. The contamination build-up originates from the recirculation of the sample gas in the apparatus allowing for an accumulation of degassing ³⁹Ar from the vacuum parts. Furthermore, the data evaluation routine performs a quality check of the measurement by testing for statistical outliers in the atom detection frequency, rejecting irregular measurements due to potential instabilities in the measurement. The details of the data analysis routine will be published elsewhere.

The measurements were carried out as part of a measurement period of several months in 2024 during which the measurement operation was continuously working under very stable conditions regarding count rates and blank measurements. Reference, sample and blank measurements were carried out under strictly equal conditions.

The resulting ³⁹Ar abundance is translated to an age using the ³⁹Ar half-life of 268 ± 3 a and a reconstructed atmospheric input curve similar to Gu et al. (2021).

Table 2 gives an overview of all measured samples. The ³⁹Ar samples are from the 2023 and 2024 sampling campaigns. All ages are already corrected for the varying atmospheric input function. Two samples, indicated with an asterisk, did not provide enough gas for a measurement and had to be diluted with ³⁹Ar-free Ar. The presented abundances and ages are already corrected for this mixing.

The ¹⁴C samples were measured on an ice core from 2019 and all except one are presented in the publication by Bohleber et al. (2020). The additional data point of the same core, WSS_Run15, was also measured at PSI in 2024 and added to the dataset.

Figure 3 shows a depth profile of all ³⁹Ar and ¹⁴C ages. The colors indicate the different years of sampling. Furthermore, data points not considered in the following are indicated in red. This selection was due to several quality checks. The samples WSS24_SurfaceA and WSS24_SurfaceB were discarded due to atmospheric contamination originating from incomplete cleaning of the ice prior to the gas extraction. Sample WSS24_Core3_Sample3 consisted of very brittle ice and was therefore likely to incorporate modern atmospheric air. Finally, sample WSS24_SurfaceC did not pass the final data analysis due to unstable measurement conditions.

Three models were fitted by least squares (Python Scipy curve_fit, Virtanen et al., 2020) to the combined ³⁹Ar and ¹⁴C data to test their applicability to the setting. In the following, all models are stated in terms of the age t in dependance of the height above bedrock h. The relation of h to the otherwise employed depth coordinate z is given by h=H-z, with H being the ice thickness in the steady state.

The first applied model is given by the Nye timescale (Nye, 1957, 1963), described by 2t(h)=Hbln⁡hH, where the model parameter b denotes the accumulation rate.

The second applied model was proposed by Raymond (1983) and is conceptualized for an ice-divide type setting: 3t(h)=-Hb1-Hh.

The third model fitted to the data is the 2-parameter (2p) model by Bolzan (1985) and Thompson et al. (1990), which was successfully applied to an Alpine ice core from Colle Gnifetti by Jenk et al. (2009) and is given by: 4t(h)=-Hbp1-Hhp.

Effectively, the 2p model adds a thinning parameter p to the Raymond model that was originally added to account for a non-isothermal polar ice sheet (Bolzan, 1985). For p = 1, the 2p model equals the Raymond model.

To obtain sensible age error estimates for the models, a Monte Carlo (MC) sampling based approach was developed. Both the ³⁹Ar and the ¹⁴C age data are given by non-symmetric probability distributions. Their non-Gaussian shape stems from the non-linear relationship between isotope abundance and age due to the exponential radioactive decay law as well as the varying atmospheric input functions of both tracers, and, in the case of ³⁹Ar, the underlying counting statistics of the ³⁹Ar measurement. To consider the full information of the distributions, an approach via MC sampling from the age distributions was taken. For each realization the distribution of each sample age was sampled and the obtained ensemble fitted with the model. The fitting of each realization was done by least squares fitting. While the best fit was obtained from fitting the measured values, the age uncertainties of the models at each depth were taken as the respective quantile of the MC fit realizations at each depth. Thus, the full complexity of the distributions for each data point can be accounted for in the fitting procedure. This was done for the data at hand with a sampling number of nMC = 10⁵.

Additional to the sampling from the age distributions of each measurement, the depth uncertainty of the ³⁹Ar measurements derived from the depth scale alignment (see Sect. 2.1 Surface Mass Balance and depth-scale alignment) with an error of 1 m as well as the timing and thickness uncertainties for the LSS (1914 ± 50, 47 ± 10 m, see Sect. 2.2 Last steady state) of the glacier were MC sampled as Gaussian distributed values with the indicated values as 3 standard deviations. The following analysis is conducted for height in meters ice equivalent (m i.e.), however no assumptions have been made regarding the firn thickness at the LSS, which would introduce a small thickness reduction in units of m i.e. due to the low firn density. Exemplary model fits showed no mentionable difference (few permille) in the age-depth relation for firn layers around 20 m.

With this approach, the non-linear interplay of the different parameters and their uncertainties are considered in the final age uncertainties by fitting statistically distributed data ensembles which contain all uncertainties in their distributions.

There is a distinct difference between the two employed tracers. While ¹⁴C dates the microscopic carbon deposits in the ice and thus the actual ice matrix, ³⁹Ar dates the gas trapped in the ice. The time interval between snowfall and the pore close-off further down in the firn column causes an age difference between dating tracers in the ice matrix and the gas, referred to as Δage. To correct for this difference, 30 a of Δage were added to the ³⁹Ar ages in the fitting process, an estimate based on the findings at nearby glaciers by Festi et al. (2021) and Gabrielli et al. (2016).

Table 3 lists the fitting results for the three models. From its last column, displaying the reduced chi-squared χred2 value, it is apparent that the Nye model is not able to capture the age profile of this ice cap. The model does not capture the thinning of the annual layers in the deeper parts as is also apparent from the visualization in Fig. 4. The two other models, conceptualized for an ice divide setting, are better suited to describe the age-depth relationship at WSS because of the dome shaped summit glacier. Due to its flat bed and therefore low flow conditions, it resembles the setting of an ice divide. The χred2 for the Raymond and 2p model are below 1 and thus demonstrate the good applicability of the models. As the 2p model shows the better fit quality it will be discussed in more detail in the following.

In the case of a glacier which is losing significant amounts of ice on its surface every year, each surface age needs an indication of the year it refers to. For the years 2023 and 2024, the uppermost ³⁹Ar measurements show ages of 300–400 a (compare Table 2). However, the samples consist of more than 60 cm long core pieces, so that a precise surface age cannot be given. Unfortunately, all three measurements from more shallow surface blocks had to be discarded (compare section “Radiometric age dating”).

From the 2p model, the surface age for 2019, at 10.2 m above bedrock, is 371-60+97 a, for 2023 434-72+115 a, and for 2024 441-73+116 a. The surface loss between 2019 and 2023 amounted to 1.67 m, while between 2023 and 2024 only 16 cm were lost.

These ages are clearly pre-industrial and show how far the prolonged mass loss is diminishing ice core records in Alpine regions and that ³⁹Ar was the only tracer to accurately constrain the surface age of this glacier. While tracers like ³H or ²¹⁰Pb can determine young surface ages and thus complement ¹⁴C ages from lower layers, this is often not possible anymore with the progressing melting of glaciers in the Alps. Without reliable surface ages, however, even if e.g. layer counting is possible, it can only provide a floating age-depth relationship with limited informative value.

The presented data set shows an example of the reconstruction of the age-depth relationship from a glacier of which only the lower ∼ 20 % are remaining, a setting which will become more frequent in the coming years. The combination of ³⁹Ar and ¹⁴C data allows to fully cover of the important age ranges.

Also depicted in Fig. 4 is the 2025 spring glacier surface after the 2024 summer melt, leaving the ice cap at a thickness of less than 6 m and emphasizing the rapid decline of the glacier.

One of the parameters fitted by the 2p model is the accumulation rate. However, the interpretation of the result is not trivial, as data from 6000 a is fitted to obtain this value. Due to the changing climatic history of the region and probably also changing weather patterns it cannot be expected that this parameter remained constant over time. Therefore, the result should be understood as a net accumulation rate parameter that gives a rough estimate of the long-term net accumulation rate average over the last six millennia. It should be noted that this does not trivially translate into a precipitation rate or other climatic factors. The 2p model results in a best fit value of b = 0.53 m w.e. a⁻¹, with 68.3 % of the MC realizations resulting in values between 0.38 and 0.63 m w.e. a⁻¹ (1σ interval). Within the 1σ interval this agrees with the value of 0.59 m w.e. which Fischer et al. (2022) gives for the total precipitation in months of snow accumulation for the years 1800 to 2014 (based on the HISTALP data from Auer et al., 2007).

The other fitted parameter, the thinning parameter p, results in a value of p = 0.92, with 68.3 % of the MC realizations resulting in values between 0.81 and 0.97. This parameter was introduced by Bolzan (1985) to account for non-isothermal conditions in the ice sheet, with p = 1 being the result for isothermal conditions (Raymond model). It is therefore not surprising to obtain a value close to 1 for a thin Alpine glacier, as was also found in the study of Jenk et al. (2009) for Colle Gnifetti (p = 0.867 ± 0.048).

With the ³⁹Ar data points completing the coverage of the whole ice column with measured ages and a suitable model to fit the data, the age-depth profile of the WSS summit glacier is well constrained. In Fig. 5 the resulting best fit of the 2p model and its uncertainties are displayed in an overview plot as well as a residual plot. The uncertainty ranges of the model (for 1σ, 2σ, and 3σ shaded in different shades of blue) are computed as the respective quantiles from the distribution of the MC model fit realizations at each depth and therefore incorporate all measurement and LSS uncertainties. Figures S3 and S4 give an overview of the distribution of the fit parameters for all fit realizations with indicated best fit parameters.

Considering the large amount of ice loss observed at WSS over the past decades, the question arises if the WSS summit has experienced similar periods of strong mass loss during the ∼ 6000 a recorded in the glacier ice. At least for the past 2000 a, a hiatus in the order of 400 annual layers seems to be unlikely given the good fit of the model to the data with errors of measurements and fit well below 400 a. For deeper layers, this is harder to constrain as the absolute errors of the ¹⁴C ages increase. Overall, melt events erasing several hundred years cannot be excluded for times > 2000 a BP, however indications for such events are absent in the dataset.

The models employed in this work are certainly simplifications. However, in order to draw conclusions from the limited data set, the complexity has to be reduced by a model. By the successful application of the 2p model in this work, we show that we can generate a good fit that is consistent with the hypothesis of no hiatus based on a simplifying assumption. This simplifying assumption is that of a constant net accumulation rate and thinning parameter over the whole profile of the ice column. In order to assess if this assumption is tenable, we performed a model fit with only the lower six sample ages, which represent all ¹⁴C samples and compare them to the full fit. It results in an accumulation rate parameter of blower = 0.42 (1σ interval: 0.30 to 0.56) [m w.e. a⁻¹]. Comparing this to the original value of b = 0.53 (1σ interval: 0.38 to 0.63) [m w.e. a⁻¹] ascertains that they only deviate within their 1σ intervals and therefore the difference is not significant. The same applies to the thinning parameter (plower = 0.84; 1σ interval: 0.72 to 0.93). This result gives confidence that the net accumulation rate did not significantly change between the older and younger parts of the ice profile, at least to the degree to which we can resolve it. Thus, the 2p model, despite its simplifying assumptions, does not lead to a problematic oversimplification and is able to capture the important aspects of the setting at the WSS summit glacier. The interpretation of this seemingly stable net accumulation rate in terms of climatic factors at this location is not trivial and can hardly be done in a non-speculative way with the data at hand. It will have to be done elsewhere in conjunction with more data.

A second conclusion can be drawn from comparing the purely ¹⁴C data based model analysis with the one containing all ¹⁴C and ³⁹Ar sample ages. The consistency between the fit results ascertains the compatibility of the dating techniques and shows how ³⁹Ar data helps to determine the younger parts of an age-depth model based on data and not only as a pure extrapolation of the older part.

In summary, this study shows the great value that ³⁹Ar dating has for alpine ice core dating. On the one hand, it provides surface ages where they become increasingly old thereby surpassing the range of traditional dating tracers. It can, on the other hand, also complete age-depth profiles where surface ages might still be acquired, but an obvious age data gap is present between the young age tracer results and the old ones as seen for example in the work of Jenk et al. (2009) and Gabrielli et al. (2016). Legrand et al. (2025) for the first time demonstrated the smooth closure of such a gap with ³⁹Ar in a long ice core from the high elevation summit glacier at Dôme du Goûter. More recently, also Hou et al. (2025) presented a similar combination of ²¹⁰Pb, ³⁹Ar, and ¹⁴C to cover the full dating range of a Tibetan ice core. For the study at hand, the ³⁹Ar tracer was the only way to obtain precise age constraints for the upper half of the ice core and in combination with ¹⁴C ages results in a well-covered age-depth profile.

In a recent (not yet peer-reviewed) publication by the DEAP Collaboration (2025), the ³⁹Ar half-life was redetermined by the direct observation of the decay curve. The proposed value for the half-life is 302 ± 8_stat ± 6_sys a. This is a significant relative increase of 13 % from the former value by Golovko (2023) and would affect all ³⁹Ar ages. To estimate the effect of this change, the 2p model was fitted to the updated ³⁹Ar ages together with the original ¹⁴C ages. The updated ³⁹Ar ages were calculated also considering an atmospheric input curve corrected for the new half-life. The new ages are systematically older but lie within the uncertainties of the original age values stated above.

The resulting fit parameter values are: b = 0.48 (1σ interval: 0.35 to 0.57) [m w.e. a⁻¹] and p = 0.88 (1σ interval: 0.77 to 0.93) and thus do not change significantly with the new proposed half-life. The χred2 of the 2p model fit reduces to 0.26 due to the slight increase of all ³⁹Ar age values (by 60–70 a for the ages around 400 a), which causes the ³⁹Ar ages to agree better with the trend of the upper ¹⁴C ages (see Figs. S5 and S6).

During the 2023 and 2024 sampling campaigns, different sampling techniques were employed to retrieve the ice. Surface samples were taken by chain saw and ice cores were drilled mechanically and thermally (compare Table 2). Unfortunately, all surface samples had to be discarded from the data set due to different quality checks (see above). However, both mechanically and thermally drilled samples were successfully dated. The agreement of the measured abundances between both methods is a strong indication that thermally drilled samples do not suffer from systematic modern air contamination. This was an open question because of the meltwater that fills the borehole during thermal drilling and the potential post-coring refreezing that could enclose modern air in previously open cracks in the ice. As thermal drilling offers the opportunity for more seasonally independent ice core retrieval, this outcome supports the robustness and the more versatile application of the ³⁹Ar dating tracer.

By establishing a reliable age-depth scale for the WSS summit glacier, depth resolved data can now be evaluated with its corresponding age information, making the interpretation of the data set as well as the comparison with other data sets and archives feasible. Spagnesi et al. (2023) published profiles of major ions, stable water isotopes and other tracers for the WSS summit glacier, showing a distinct peak in all major ion concentrations as well as levoglucosan at a depth of 6.4 m. The detailed investigation of the WSS isotope and impurity time series warrants a separate investigation. For a first comparison with other Alpine ice core data, we selected the Ca²⁺ profile, since a connection between high Ca²⁺ peaks and the occurrence of Saharan dust transport to the Alps is well established (e.g. Wagenbach et al., 1996). Considering that a meaningful comparison with WSS requires Alpine ice core data comprising an age span starting 400 a ago at reasonable time resolution, the immediate target is Colle Gnifetti (CG) – a well-characterized site with millennial time series (e.g. Wagenbach et al., 2012). The comparison is done as an example of how the derived age-depth relation can be applied to the interpretation of e.g. chemical profiles, despite the proneness of high elevation summit glacier sites to losing parts of the annual precipitation to wind erosion and therefore not preserving the complete record. It should therefore be noted that the presented records might suffer from such seasonal or long-term biases, the detailed analysis of which however is beyond the scope of this example.

We compared the WSS Ca²⁺ profile to a Ca²⁺ record from Colle Gnifetti (Bohleber et al., 2018). Interestingly, both Ca²⁺ records feature an outstanding anomaly around 1175. Applying the here derived age-depth scale to the WSS Ca²⁺ data and plotting it together with the CG data in Fig. 6, shows the good temporal alignment of the two anomalies within the uncertainties of the WSS time scale and not regarding the uncertainties of the CG time scale. Identifying the Ca²⁺ peak with a Saharan dust event, the agreement within these two Ca²⁺ records suggests that this dust event reached into both, the Western and the Eastern Alps. This implies a large Saharan dust event may have impacted large parts of central Europe at that time. On a tentative note, aligning the major peak in both data sets would require an offset of the WSS timescale of approximately 50 a. Such a shift results also in the temporal alignment of several smaller peaks between 1550 and 1700, possibly indicating further regional-scale dust signals recorded across the Alps. The dashed line in Fig. 6 shows the WSS Ca²⁺ record with a 50 a offset on the WSS timescale to visualize the alignment of the peaks.