Hidden Time Step Bias in Firn Models Could Skew Ice Loss Estimates

Beneath the vast white surfaces of Greenland and Antarctica lies a layer of old snow called firn, a porous, slowly compacting medium that acts as the ice sheets’ first line of defense against a warming climate. When surface snow melts, much of that water trickles into the firn’s air-filled pores, where it refreezes or is stored as liquid rather than running off into the ocean. Roughly 39 percent of surface meltwater on the Greenland Ice Sheet and about 94 percent on the Antarctic Ice Sheet is retained this way. Because the firn layer buffers meltwater, it also keeps water away from crevasses and ice shelves where it could otherwise drive fracturing. A new study published in The Cryosphere by Tesse van den Aker of Utrecht University and colleagues reveals that a seemingly mundane technical choice, the time step at which climate data feed firn models, can substantially change how much pore space these models predict, with consequences for how we measure ice loss from space.

Firn models are numerical tools that simulate how snow densifies into glacial ice, how heat moves through the column, and how meltwater percolates and refreezes. They are used to interpret satellite observations, to understand firn physics, and to project future surface mass balance of the ice sheets. Every such model integrates coupled differential equations in time, and the boundary conditions at the surface, such as snowfall, melt, temperature, and wind speed, must be supplied at some discrete interval. In the published literature, that climate forcing time step varies enormously, from one hour to days, months, and even years. The reasons for these choices are usually practical rather than physical: forcing data may not exist at finer resolution, files become unwieldy, or computational budgets run out. Until now, the implications of this choice had barely been evaluated.

The research team tested the sensitivity of the IMAU firn densification model, or IMAU-FDM, by forcing it with output from the regional climate model RACMO2.3p2, itself downscaled from the ERA5 reanalysis. They ran simulations for the Antarctic Peninsula Ice Sheet and the southern Greenland Ice Sheet, two regions spanning a wide range of accumulation and melt conditions, using four different forcing time steps: 3 hours, 6 hours, 1 day, and 1 month. The model itself integrates at a 15-minute step, but the climate inputs were averaged to the coarser intervals and held constant between updates. The team focused on firn air content, the vertically integrated pore space of the firn column, a key quantity that determines how much meltwater the firn can absorb before runoff begins.

The results were striking. Across both regions, larger forcing time steps systematically produced more firn air in the final simulated firn layer, and the size of the discrepancy grew with the time step. On the Antarctic Peninsula, the effect was largest on the low-lying ice shelves, where firn air content is naturally small: switching from 3-hourly to daily forcing inflated firn air content by about 15 percent, and monthly forcing by up to 44 percent. In the southern Greenland Ice Sheet, the largest differences appeared in a band at intermediate elevations, where melt is substantial but the firn is not yet fully depleted. There, daily forcing added on average 2.1 meters of firn air compared to 3-hourly forcing, and monthly forcing added 4.0 meters, differences that are far from trivial for meltwater retention studies.

The root cause, the authors show, is the presence or absence of a diurnal cycle in the input data. With 3-hourly or 6-hourly forcing, surface temperatures swing through the daily cycle, reaching the melting point during melt events and dropping below freezing at night. Melt and refreezing therefore alternate in time. With daily or monthly averages, however, temperature and melt become decoupled: the model can simultaneously apply a melt flux and hold the surface below zero degrees, a physically impossible combination. In that unphysical state, any meltwater that the pore space can retain refreezes immediately near the surface, forming a dense, ice-like crust. Subsequent melt events then strip away this dense refrozen material rather than the porous firn beneath it, so the model loses less firn air than it should. The result is an overestimate of the firn’s water-buffering capacity, an artifact born purely of the forcing resolution.

Deeper in the column, a second mechanism amplifies the differences. With 3-hourly forcing, meltwater percolates farther down before refreezing, releasing its latent heat at depth. Because firn conducts heat poorly, that trapped warmth makes the deeper firn warmer, which accelerates densification. Simulations with coarse forcing, by contrast, refreeze water near the surface and keep the deeper column colder, slowing compaction. The team also uncovered a subtler artifact tied to the fresh snow density parameterization used for Antarctica, which depends on instantaneous surface temperature and 10-meter wind speed. Averaging the wind speed over longer intervals changes the snowfall-weighted wind speed, altering the modeled density of newly fallen snow. In nearly melt-free zones this effect can even reverse the sign of the bias, producing slightly less firn air at fine resolution, on the order of half a meter.

The stakes become clearest in Greenland, where melt rates above roughly 500 kilograms per square meter per year can sustain firn aquifers, perennial reservoirs of liquid water buried in the firn. In the team’s simulations, aquifers formed during the spin-up period under 3-hourly forcing but never developed under daily forcing, because the deeper refreezing associated with fine resolution leaves the firn column warmer and less able to freeze all incoming water. Where aquifers did form under both resolutions, the timing and evolution diverged: under fine forcing the aquifer existed from the start of the historical simulation, while under daily forcing it emerged only around 2005. Because liquid water pins the firn temperature to the freezing point, the densification equations respond differently in each case, and the simulated firn air content trends can even acquire opposite signs. The modeled runoff limit, the elevation above which meltwater no longer escapes to the sea, shifted more than 10 kilometers inland between 3-hourly and daily forcing, and up to 35 kilometers compared to monthly forcing.

These discrepancies ripple directly into satellite altimetry, one of the primary tools for tracking ice sheet mass balance. Altimeters measure changes in surface height, but part of that signal reflects firn compaction rather than genuine ice loss, so firn models supply the correction. The study found that surface height changes differed by 0.2 to 0.4 meters on the Antarctic Peninsula depending on forcing resolution, and by 8 to 30 percent of the firn air content at a Greenland aquifer site. Corrections based on coarsely forced simulations would overestimate surface height gains, which means that during periods of thinning, ice loss would be underestimated, and during thickening, ice gain would be underestimated. In a warming Arctic where Greenland’s contribution to sea level rise is closely watched, a bias of this kind matters for projections and for the satellite records that policymakers rely on.

The authors distill two lessons for the modeling community. First, firn models that are prescribed melt fluxes and surface temperatures, as IMAU-FDM is, need a forcing time step fine enough to resolve at least the diurnal cycle; otherwise melt and subfreezing temperatures coexist and the physics breaks down. Models that compute melt internally from a surface energy balance may be less vulnerable to this specific artifact, though they face their own accuracy challenges. Second, parameterizations should be applied only under the conditions and resolutions for which they were developed. The Antarctic fresh snow density formula was tuned for 3-hourly forcing, and the densification equation assumes dry, steady-state snow, yet both are routinely stretched beyond those limits. As climate change accelerates melt across the polar regions, the study argues, the humble choice of a time step deserves the same scrutiny as the equations themselves, because it quietly shapes how much water the firn can hold, where runoff begins, and how vulnerable ice shelves are to collapse.

Subject of Research: Effect of climate forcing time step resolution on firn air content simulated by an ice-sheet firn densification model

Article Title: Impact of climate forcing time step in an ice-sheet firn model

Article References: Impact of climate forcing time step in an ice-sheet firn model. (n.d.). https://doi.org/10.5194/tc-20-5475-2026

Image Credits: AI Generated

DOI: 10.5194/tc-20-5475-2026

Keywords: firn, ice sheet, Greenland, Antarctic Peninsula, firn air content, firn model, climate forcing, time step, meltwater retention, firn aquifer, satellite altimetry, The Cryosphere