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Numerical models predict that discharge from the polar ice sheets will become the largest contributor to sea-level rise over the coming centuries. However, the predicted amount of ice discharge and associated thinning depends on how well ice sheet models reproduce glaciological processes, such as ice flow in regions of large topographic relief, where ice flows around bedrock summits (i.e. nunataks) and through outlet glaciers. The ability of ice sheet models to capture long-term ice loss is best tested by comparing model simulations against geological data. A benchmark for such models is ice surface elevation change, which has been constrained empirically at nunataks and along margins of outlet glaciers using cosmogenic exposure dating. However, the usefulness of this approach in quantifying ice sheet thinning relies on how well such records represent changes in regional ice surface elevation. Here we examine how ice surface elevations respond to the presence of strong topographic relief that acts as an obstacle by modelling ice flow around and between idealised nunataks during periods of imposed ice sheet thinning. We find that, for realistic Antarctic conditions, a single nunatak can exert an impact on ice thickness over 20km away from its summit, with its most prominent effect being a local increase (decrease) of the ice surface elevation of hundreds of metres upstream (downstream) of the obstacle. A direct consequence of this differential surface response for cosmogenic exposure dating is a delay in the time of bedrock exposure upstream relative to downstream of a nunatak summit. A nunatak elongated transversely to ice flow is able to increase ice retention and therefore impose steeper ice surface gradients, while efficient ice drainage through outlet glaciers produces gentler gradients. Such differences, however, are not typically captured by continent-wide ice sheet models due to their coarse grid resolutions. Their inability to capture site-specific surface elevation changes appears to be a key reason for the observed mismatches between the timing of ice-free conditions from cosmogenic exposure dating and model simulations. We conclude that a model grid refinement over complex topography and information about sample position relative to ice flow near the nunatak are necessary to improve data-model comparisons of ice surface elevation and therefore the ability of models to simulate ice discharge in regions of large topographic relief.

The timing of past glaciation across the Tian Shan provides a proxy for past climate change in this critical area. Correlating glacial stages across the region is difficult but cosmogenic exposure ages have considerable potential. A drawback is the large observed scatter in Be-10 surface exposure data. To quantify the robustness of the dating, we compile, recalculate, and perform statistical analyses on sets of 10Be surface exposure ages from 25 moraines, consisting of 114 new and previously published ages. We assess boulder age scatter by dividing boulder groups into quality classes and rejecting boulder groups of poor quality. This allows us to distinguish and correlate robustly dated glacier limits, resulting in a more conservative chronology than advanced in previous publications. Our analysis shows that only one regional glacial stage can be reliably correlated across the Tian Shan, with glacier expansions occurring between 15 and 281 a during marine oxygen isotope stage (MIS) 2. However, there are examples of older more extensive indicators of glacial stages between MIS 3 and MIS 6. Paleoglacier extent during MIS 2 was mainly restricted to valley glaciation. Local deviations occur: in the central Kyrgyz Tian Shan paleoglaciers were more extensive and we propose that the topographic context explains this pattern. Correlation between glacial stages prior to late MIS 2 is less reliable, because of the low number of samples and/or the poor resolution of the dating. With the current resolution and spatial coverage of robustly-dated glacier limits we advise that paleoclimatic implications for the Tian Shan glacial chronology beyond MIS 2 are speculative and that continued work toward robust glacial chronologies is needed to resolve questions regarding drivers of past glaciation in the Tian Shan and Central Asia.

Over the last decades, cosmogenic exposure dating has permitted major advances in many fields of Earth surface sciences and particularly in paleoglaciology. Yet, exposure age calculation remains a complicated and dense procedure. It requires numerous choices of parameterization and the use of an accurate production rate. This study describes the CREp program and the ICE-D production rate online database. This system is designed so that the CREp calculator will automatically reflect the current state of this global calibration database production rate, ICE-D. ICE-D will be regularly updated in order to incorporate new calibration data and reflect the current state of the available literature. CREp is a Octave/Matlab© online code that computes Cosmic Ray Exposure (CRE) ages for 3He and 10Be, available at crep.crpg.cnrs-nancy.fr. A stand-alone version of the CREp code is also released with the present article. Note however that only the online version is connected to the online database ICE-D. The CREp program offers the possibility to calculate ages with two scaling models: i.e. the empirical Lal-Stone time-dependent model (Balco et al., 2008; Lal, 1991; Stone, 2000) with the muon parameters of Braucher et al. (2011), and the Lifton-Sato-Dunai (LSD) theoretical model (Lifton et al., 2014). The default atmosphere model is the ERA-40 database (Uppala et al., 2005), but one may also use the standard atmosphere for comparison (N.O.A.A, 1976) to apply the atmospheric correction. To perform the time-dependent correction, users may import their own geomagnetic database for paleomagnetic corrections or opt for one of the three proposed datasets (Lifton, 2016; Lifton et al., 2014; Muscheler et al., 2005). For the important choice of the production rate, CREp is linked to a database of production rate calibration data that is part of the ICE-D (Informal Cosmogenic-nuclide Exposure-age Database) project (http://calibration.ice-d.org). This database includes published empirical calibration rate studies that are publicly available at present, comprising those of the CRONUS-Earth and CRONUS-EU projects, as well as studies from other projects. In the present study, the efficacy of the different scaling models has also been evaluated looking at the statistical dispersion of the computed Sea Level High Latitude (SLHL) production rates. Lal/Stone and LSD models have comparable efficacies, and the impact of the tested atmospheric model and the geomagnetic database is also limited. Users however have several possibilities to select the production rate: 1) using a worldwide mean value, 2) a regionally averaged value (not available in regions with no data), 3) a local unique value, which can be chosen among the existing dataset or imported by the user, or 4) any combination of single or multiple calibration data. If a global mean is chosen, the 1σ uncertainty arising from the production rate is about 5% for 10Be and 10% for 3He. If a regional production rate is picked, these uncertainties are potentially lower. CREp is able to calculate a large number of ages in a reasonable time (typically < 30 s for 50 samples). The user may export a summary table of the computed ages and the density probability function associated with each age (in the form of a spreadsheet).