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Understanding firn densification is essential for interpreting ice core records, predicting ice sheet mass balance, elevation changes and future sea-level rise. Current models of firn densification on the Antarctic ice sheet (AIS), such as the Herron and Langway (1980) model are either simple semi-empirical models that rely on sparse climatic data and surface density observations or complex physics-based models that rely on poorly understood physics. In this work, we introduce a deep learning technique to study firn densification on the AIS. Our model, FirnLearn, evaluated on 225 cores, shows an average root-mean-square error of 31 kg m−3 and explained variance of 91%. We use the model to generate surface density and the depths to the $550\\,\\mathrm{kg\\,m}^{-3}$ and $830\\,\\mathrm{kg\\,m}^{-3}$ density horizons across the AIS to assess spatial variability. Comparisons with the Herron and Langway (1980) model at ten locations with different climate conditions demonstrate that FirnLearn more accurately predicts density profiles in the second stage of densification and complete density profiles without direct surface density observations. This work establishes deep learning as a promising tool for understanding firn processes and advancing towards a universally applicable firn model.

The firn temperature is a crucial parameter for understanding firn densification processes of the Antarctic Ice Sheet (AIS). Simulations with firn densification models (FDM) can be conceptualized as a function that relies on forcing data, comprising temperature and surface mass balance, together with tuning parameters determined based on measured depth-density profiles from different locations. The simulated firn temperature is obtained in the firn densification models by solving the one-dimensional heat conduction equation. Microwave satellite data on brightness temperature at different frequencies can also provide remote sensing monitoring of firn temperature variations across the AIS (i.e., the L-band up to 1500 meters). The firn temperature can be estimated by the microwave emission model and the regression method, but these two methods need more observations of temperature profiles for correction and validation. Therefore, we compiled a dataset with temperature profiles and temperature observations with depth around 10 meters. In this work, two methods were used to simulate/retrieve firn temperature across the Antarctic ice sheet. One method estimated the temperature profiles by solving the one-dimensional heat conduction equation driven by reanalyses and regional climate models, which are used in the simulation of FDMs. The other one established a relationship between the multi-frequency brightness temperature data from microwave remote sensing satellites and the firn temperature.

Earth system models account for seasonal snow cover, but many do not accommodate the deeper snowpack on ice sheets (aka firn) that slowly transforms to ice under accumulating snowfall. To accommodate and resolve firn depths of up to 60 m in the Energy Exascale Earth System Model's land surface model (ELM), we add 11 layers to its snowpack and evaluate three dry snow compaction equations in multi‐century simulations. After comparing results from ELM simulations (forced with atmospheric reanalysis) with empirical data, we find that implementing into ELM a two‐stage firn densification model produces more accurate dry firn densities at intermediate depths of 20–60 m. Compared to modeling firn using the equations in the (12 layer) Community Land Model (version 5), switching to the two‐stage firn densification model (with 16 layers) significantly decreases root‐mean‐square errors in upper 60 m dry firn densities by an average of 41 kg m−3 (31%). Simulations with three different firn density parameterizations show that the two‐stage firn densification model should be used for applications that prioritize accurate upper 60 m firn air content (FAC) in regions where the mean annual surface temperature is greater than roughly −31°C. Because snow metamorphism, firn density, and FAC are major components in modeling ice sheet surface albedo, melt water retention, and climatic mass balance, these developments advance broader efforts to simulate the response of land ice to atmospheric forcing in Earth system models. Plain Language Summary Massive ice sheets cover Earth's largest island (Greenland) and the Antarctic continent. A large fraction of their surfaces consists of multi‐year snow, known as firn, which goes through the process of densification after falling from the atmosphere. Until now this fundamental process in glaciology has yet to be accounted for in the U.S. Department of Energy's Earth System Model (E3SM). Here, we enhance E3SM's snowpack model to accommodate greater firn depths on ice sheets. Our results demonstrate a new capability in an Earth system model, that is, calculating firn density as deep as 60 m below the surface. Our developments in E3SM combine both seasonal snow and firn processes to advance broader efforts toward simulating ice sheet evolution and sea level rise in Earth system models. Key Points We intercompare three snow density parameterizations and their effects on firn simulated in Energy Exascale Earth System Model's land model (ELM) Incorporating a two‐stage firn densification model into ELM improves densities at depths of 20–60 m Applied to Greenland and Antarctica, improving 20–60 m depth dry firn density decreases firn air content by more than 20%

Quantifying the mass balance of the Antarctic Ice Sheet (AIS), and the resulting sea level rise, requires an understanding of inter-annual variability and associated causal mechanisms. Very few studies have been exploring the influence of climate anomalies on the AIS and only a vague estimate of its impact is available. Changes to the ice sheet are quantified using observations from space-borne altimetry and gravimetry missions. We use data from Envisat (2002 to 2010) and Gravity Recovery And Climate Experiment (GRACE) (2002 to 2016) missions to estimate monthly elevation changes and mass changes, respectively. Similar estimates of the changes are made using weather variables (surface mass balance (SMB) and temperature) from a regional climate model (RACMO2.3p2) as inputs to a firn compaction (FC) model. Elevation changes estimated from different techniques are in good agreement with each other across the AIS especially in West Antarctica, Antarctic Peninsula, and along the coasts of East Antarctica. Inter-annual height change patterns are then extracted using for the first time an empirical mode decomposition followed by a principal component analysis to investigate for influences of climate anomalies on the AIS. Investigating the inter-annual signals in these regions revealed a sub-4-year periodic signal in the height change patterns. El Niño Southern Oscillation (ENSO) is a climate anomaly that alters, among other parameters, moisture transport, sea surface temperature, precipitation, in and around the AIS at similar frequency by alternating between warm and cold conditions. This periodic behavior in the height change patterns is altered in the Antarctic Pacific (AP) sector, possibly by the influence of multiple climate drivers, like the Amundsen Sea Low (ASL) and the Southern Annular Mode (SAM). Height change anomaly also appears to traverse eastwards from Coats Land to Pine Island Glacier (PIG) regions passing through Dronning Maud Land (DML) and Wilkes Land (WL) in 6 to 8 years. This is indicative of climate anomaly traversal due to the Antarctic Circumpolar Wave (ACW). Altogether, inter-annual variability in the SMB of the AIS is found to be modulated by multiple competing climate anomalies.

There is ample evidence for ice layers and lenses within glacial firn. The standard model for ice layer formation localizes the refreezing by perching of meltwater on pre‐existing discontinuities. Here we argue that even extreme melting events provide insufficient flux for this mechanism. Using a thermomechanical model we demonstrate a different mechanism of ice layer formation. After a melting event when the drying front catches up with the wetting front and arrests melt percolation, conductive heat loss freezes the remaining melt in place to form an ice layer. This model reproduces the depth of a new ice layer at the Dye‐2 site in Greenland. It provides a deeper insight into the interpretation of firn stratigraphy and past climate variability. It also improves the simulation of firn densification processes, a key source of uncertainty in assessing and attributing ice sheet mass balance based on satellite altimetry and gravimetry data. Plain Language Summary Firn covers a significant portion of Earth's glaciers and ice sheets. It can store surface meltwater and prevent runoff into the ocean. The widespread presence of ice layers embedded in firn formed by meltwater refreezing may prevent meltwater storage and contribute to sea level rise. However, current models of ice layer formation, originally developed for snow, do not seem to work in firn. This work presents a different mechanism for ice layer formation without invoking pre‐existing ice layers within the firn. Our model shows that the sequencing of ice layers formed by subsequent melting events depends on the overall heat added to the firn. Deeper layers occur in warmer, more porous firn during intense melt events in a warming climate. This insight enhances our understanding of firn layering and can help deduce past climate variations. Our model aids in understanding the density evolution of firn to reduce uncertainties in remote sensing data that determines the ice sheet mass loss and its contribution to global sea‐level rise. Key Points A new ice layer forms without meltwater perching when freezing localizes after a melt event as heat conduction dominates over advection Deeper ice layers form in warming climatic conditions whereas denser ice layers form near surface in net‐zero climatic conditions Results indicate the possibility of deducing past variability in climate from firn stratigraphy and vice versa

Current sea-level rise partly stems from increased surface melting and meltwater runoff from the Greenland ice sheet. Multi-year snow, also known as firn, covers about 80% of the ice sheet and retains part of the surface meltwater. Since the firn cold content integrates its physical and thermal characteristics, it is a valuable tool for determining the meltwater-retention potential of firn. We use gap-filled climatological data from nine automatic weather stations in the ice-sheet accumulation area to drive a surface-energy-budget and firn model, validated against firn density and temperature observations, over the 1998–2017 period. Our results show a stable top 20 m firn cold content (CC20) at most sites. Only at the lower-elevation Dye-2 site did CC20 decrease, by 24% in 2012, before recovering to its original value by 2017. Heat conduction towards the surface is the main process feeding CC20 at all nine sites, while CC20 reduction occurs through low-cold-content fresh-snow addition at the surface during snowfall and latent-heat release when meltwater refreezes. Our simulations suggest that firn densification, while reducing pore space for meltwater retention, increases the firn cold content, enhances near-surface meltwater refreezing and potentially sets favourable conditions for ice-slab formation.

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.

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.

Firn simulations are essential for understanding Antarctic ice sheet mass change, as they enable us to convert satellite altimetry observed volume changes to mass changes and column thickness to ice thickness and to quantify the meltwater buffering capacity of firn. Here, we present and evaluate a simulation of the contemporary Antarctic firn layer using the updated semi-empirical IMAU Firn Densification Model (IMAU-FDM) for the period 1979–2020. We have improved previous fresh-snow density and firn compaction parameterizations and used updated atmospheric forcing. In addition, the model has been calibrated and evaluated using 112 firn core density observations across the ice sheet. We found that 62 % of the seasonal and 67 % of the decadal surface height variability are due to variations in firn air content rather than firn mass. Comparison of simulated surface elevation change with a previously published multi-mission altimetry product for the period 2003–2015 shows that performance of the updated model has improved, notably in Dronning Maud Land and Wilkes Land. However, a substantial trend difference (>10 cm yr−1) remains in the Antarctic Peninsula and Ellsworth Land, mainly caused by uncertainties in the spin-up forcing. By estimating previous climatic conditions from ice core data, these trend differences can be reduced by 38 %.

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.