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Perennial snow, or firn, covers 80 % of the Greenland ice sheet and has the capacity to retain surface meltwater, influencing the ice sheet mass balance and contribution to sea-level rise. Multilayer firn models are traditionally used to simulate firn processes and estimate meltwater retention. We present, intercompare and evaluate outputs from nine firn models at four sites that represent the ice sheet's dry snow, percolation, ice slab and firn aquifer areas. The models are forced by mass and energy fluxes derived from automatic weather stations and compared to firn density, temperature and meltwater percolation depth observations. Models agree relatively well at the dry-snow site while elsewhere their meltwater infiltration schemes lead to marked differences in simulated firn characteristics. Models accounting for deep meltwater percolation overestimate percolation depth and firn temperature at the percolation and ice slab sites but accurately simulate recharge of the firn aquifer. Models using Darcy's law and bucket schemes compare favorably to observed firn temperature and meltwater percolation depth at the percolation site, but only the Darcy models accurately simulate firn temperature and percolation at the ice slab site. Despite good performance at certain locations, no single model currently simulates meltwater infiltration adequately at all sites. The model spread in estimated meltwater retention and runoff increases with increasing meltwater input. The highest runoff was calculated at the KAN_U site in 2012, when average total runoff across models (±2σ) was 353±610 mm w.e. (water equivalent), about 27±48 % of the surface meltwater input. We identify potential causes for the model spread and the mismatch with observations and provide recommendations for future model development and firn investigation.

Models that simulate the evolution of polar firn are important for several applications in glaciology, including converting ice-sheet elevation change measurements to mass change and interpreting climate records in ice cores. We have developed the Community Firn Model (CFM), an open-source, modular model framework designed to simulate numerous physical processes in firn. The modules include firn densification, heat transport, meltwater percolation and refreezing, water isotope diffusion, and firn-air diffusion. The CFM is designed so that new modules can be added with ease. In this paper, we first describe the CFM and its modules. We then demonstrate the CFM's usefulness in two model applications that utilize two of its novel aspects. The CFM currently has the ability to run any of 13 previously published firn densification models, and in the first application we compare those models' results when they are forced with regional climate model outputs for Summit, Greenland. The results show that the models do not agree well (spread greater than 10 %) when predicting depth-integrated porosity, firn age, or the trend in surface elevation change. In the second application, we show that the CFM's coupled firn-air and firn densification models can simulate noble gas records from an ice core better than a firn-air model alone.

As surface melt is increasing on the Greenland Ice Sheet (GrIS), quantifying the retention capacity of the firn layer is critical to linking meltwater production to meltwater runoff. Firn-densification models have so far relied on empirical approaches to account for the percolation–refreezing process, and more physically based representations of liquid water flow might bring improvements to model performance. Here we implement three types of water percolation schemes into the Community Firn Model: the bucket approach, the Richards equation in a single domain and the Richards equation in a dual domain, which accounts for partitioning between matrix and fast preferential flow. We investigate their impact on firn densification at four locations on the GrIS and compare model results with observations. We find that for all of the flow schemes, significant discrepancies remain with respect to observed firn density, particularly the density variability in depth, and that inter-model differences are large (porosity of the upper 15 m firn varies by up to 47 %). The simple bucket scheme is as efficient in replicating observed density profiles as the single-domain Richards equation, and the most physically detailed dual-domain scheme does not necessarily reach best agreement with observed data. However, we find that the implementation of preferential flow simulates ice-layer formation more reliably and allows for deeper percolation. We also find that the firn model is more sensitive to the choice of densification scheme than to the choice of water percolation scheme. The disagreements with observations and the spread in model results demonstrate that progress towards an accurate description of water flow in firn is necessary. The numerous uncertainties about firn structure (e.g. grain size and shape, presence of ice layers) and about its hydraulic properties, as well as the one-dimensionality of firn models, render the implementation of physically based percolation schemes difficult. Additionally, the performance of firn models is still affected by the various effects affecting the densification process such as microstructural effects, wet snow metamorphism and temperature sensitivity when meltwater is present.

Knowledge of snow and firn-density change is needed to use elevation-change measurements to estimate glacier mass change. Additionally, firn-density evolution on glaciers is closely connected to meltwater percolation, refreezing and runoff, which are key processes for glacier mass balance and hydrology. Since 2016, the U.S. Geological Survey Benchmark Glacier Project has recovered firn cores from a site on Wolverine Glacier in Alaska's Kenai Mountains. We use annual horizons in repeat cores to track firn densification and meltwater retention over seasonal and interannual timescales, and we use density measurements to quantify how the firn air content (FAC) changes through time. The results suggest the firn is densifying due primarily to compaction rather than refreezing. Liquid-water retention in the firn is transient, likely due to gravity-fed drainage and irreducible-water-content decreases that accompany decreasing porosity. We show that the uncertainty (±60 kg m−3) in the commonly used volume-to-mass conversion factor of 850 kg m−3 is an underestimation when glacier-wide FAC variability exceeds 12% of the glacier-averaged height change. Our results demonstrate how direct measurements of firn properties on mountain glaciers can be used to better quantify the uncertainty in geodetic volume-to-mass conversions.

A porous layer of multi-year snow known as firn covers the Greenland-ice-sheet interior. The firn layer buffers the ice-sheet contribution to sea-level rise by retaining a fraction of summer melt as liquid water and refrozen ice. In this study we quantify the Greenland ice-sheet firn air content (FAC), an indicator of meltwater retention capacity, based on 360 point observations. We quantify FAC in both the uppermost 10 m and the entire firn column before interpolating FAC over the entire ice-sheet firn area as an empirical function of long-term mean air temperature (Ta‾) and net snow accumulation (c˙‾). We estimate a total ice-sheet-wide FAC of 26 800±1840 km3, of which 6500±450 km3 resides within the uppermost 10 m of firn, for the 2010–2017 period. In the dry snow area (Ta‾≤-19 ∘C), FAC has not changed significantly since 1953. In the low-accumulation percolation area (Ta‾>-19 ∘C and c˙‾≤600 mm w.e. yr−1), FAC has decreased by 23±16 % between 1998–2008 and 2010–2017. This reflects a loss of firn retention capacity of between 150±100 Gt and 540±440 Gt, respectively, from the top 10 m and entire firn column. The top 10 m FACs simulated by three regional climate models (HIRHAM5, RACMO2.3p2, and MARv3.9) agree within 12 % with observations. However, model biases in the total FAC and marked regional differences highlight the need for caution when using models to quantify the current and future FAC and firn retention capacity.

Ice-sheet mass-balance estimates derived from repeat satellite-altimetry observations require accurate calculation of spatiotemporal variability in firn-air content (FAC). However, firn-compaction models remain a large source of uncertainty within mass-balance estimates. In this study, we investigate one process that is neglected in FAC estimates derived from firn-compaction models: enhanced layer thinning due to horizontal divergence. We incorporate a layer-thinning scheme into the Community Firn Model. At every time step, firn layers first densify according to a firn-compaction model and then thin further due to an imposed horizontal divergence rate without additional density changes. We find that horizontal divergence on Thwaites (THW) and Pine Island Glaciers can reduce local FAC by up to 41% and 18%, respectively. We also assess the impact of temporal variability of horizontal divergence on FAC. We find a 15% decrease in FAC between 2007 and 2016 due to horizontal divergence at a location that is characteristic of lower THW. This decrease accounts for 16% of the observed surface lowering, whereas climate variability alone causes negligible changes in FAC at this location. Omitting transient horizontal divergence in estimates of FAC leads to an overestimation of ice loss via satellite-altimetry methods in regions of dynamic ice flow.

Converting measurements of ice-sheet surface elevation change to mass change requires measurements of accumulation and knowledge of the evolution of the density profile in the firn. Most firn-densification models are tuned using measured depth–density profiles, a method which is based on an assumption that the density profile in the firn is invariant through time. Here we present continuous measurements of firn-compaction rates in 12 boreholes near the South Pole over a 2 year period. To our knowledge, these are the first continuous measurements of firn compaction on the Antarctic plateau. We use the data to derive a new firn-densification algorithm framed as a constitutive relationship. We also compare our measurements to compaction rates predicted by several existing firn-densification models. Results indicate that an activation energy of 60 kJ mol−1, a value within the range used by current models, best predicts the seasonal cycle in compaction rates on the Antarctic plateau. Our results suggest models can predict firn-compaction rates with at best 7% uncertainty and cumulative firn compaction on a 2 year timescale with at best 8% uncertainty.

Evolution of cold dry snow and firn plays important roles in glaciology; however, the physical formulation of a densification law is still an active research topic. We forced eight firn-densification models and one seasonal-snow model in six different experiments by imposing step changes in temperature and accumulation-rate boundary conditions; all of the boundary conditions were chosen to simulate firn densification in cold, dry environments. While the intended application of the participating models varies, they are describing the same physical system and should in principle yield the same solutions. The firn models all produce plausible depth-density profiles, but the model outputs in both steady state and transient modes differ for quantities that are of interest in ice core and altimetry research. These differences demonstrate that firn-densification models are incorrectly or incompletely representing physical processes. We quantitatively characterize the differences among the results from the various models. For example, we find depth-integrated porosity is unlikely to be inferred with confidence from a firn model to better than 2 m in steady state at a specific site with known accumulation rate and temperature. Firn Model Intercomparison Experiment can provide a benchmark of results for future models, provide a basis to quantify model uncertainties and guide future directions of firn-densification modeling.

An ice core drilled on the Renland ice cap in east-central Greenland contains a continuous climate record dating through the last glacial period. The Renland record is valuable because the coastal environment is more likely to reflect regional sea surface conditions compared to inland Greenland ice cores that capture synoptic variability. Here we present the δ18O water isotope record for the Holocene, in which decadal-scale climate information is retained for the last 8 kyr, while the annual water isotope signal is preserved throughout the last 2.6 kyr. To investigate regional climate information preserved in the water isotope record, we apply spectral analysis techniques to a 300-year moving window to determine the mean strength of varying frequency bands through time. We find that the strength of 15–20-year δ18O variability exhibits a millennial-scale signal in line with the well-known Bond events. Comparison to other North Atlantic proxy records suggests that the 15–20-year variability may reflect fluctuating sea surface conditions throughout the Holocene, driven by changes in the strength of the Atlantic Meridional Overturning Circulation. Additional analysis of the seasonal signal over the last 2.6 kyr reveals that the winter δ18O signal has experienced a decreasing trend, while the summer signal has predominantly remained stable. The winter trend may correspond to an increase in Arctic sea ice cover, which is driven by a decrease in total annual insolation, and is also likely influenced by regional climate variables such as atmospheric and oceanic circulation. In the context of anthropogenic climate change, the winter trend may have important implications for feedback processes as sea ice retreats in the Arctic.

Advances in analytical methods have made it possible to obtain high-resolution water isotopic data from ice cores. Their spectral signature contains information on the diffusion process that attenuated the isotopic signal during the firn densification process. Here, we provide a tool for estimating firn-diffusion rates that builds on the Community Firn Model. Our model requires two main inputs, temperature and accumulation, and it calculates the diffusion lengths for δ17O, δ18O and δD. Prior information on the isotopic signal of the precipitation is not a requirement. In combination with deconvolution techniques, diffusion lengths can be used in order reconstruct the pre-diffusion isotopic signal. Furthermore, the temperature dependence of the isotope diffusion and firn densification makes the diffusion length an interesting candidate as a temperature proxy. We test the model under steady state and transient scenarios and compare four densification models. Comparisons with ice core data provide an evaluation of the four models and indicate that there are differences in their performance. Combining data-based diffusion length estimates with information on past accumulation rates and ice flow thinning, we reconstruct absolute temperatures from three Antarctic ice core sites.