The firn layer that covers 90 % of the Greenland ice sheet (GrIS) plays an important role in determining the response of the ice sheet to climate change. Meltwater can percolate into the firn layer and refreeze at greater depths, thereby temporarily preventing mass loss. However, as global warming leads to increasing surface melt, more surface melt may refreeze in the firn layer, thereby reducing the capacity to buffer subsequent episodes of melt. This can lead to a tipping point in meltwater runoff. It is therefore important to study the evolution of the Greenland firn layer in the past, present and future. In this study, we present the latest version of our firn model, IMAU-FDM (Firn Densification Model) v1.2G, with an application to the GrIS. We improved the density of freshly fallen snow, the dry-snow densification rate and the firn's thermal conductivity using recently published parametrizations and by calibration to an extended set of observations of firn density, temperature and liquid water content at the GrIS. Overall, the updated model settings lead to higher firn air content and higher 10 m firn temperatures, owing to a lower density near the surface. The effect of the new model settings on the surface elevation change is investigated through three case studies located at Summit, KAN-U and FA-13. Most notably, the updated model shows greater inter- and intra-annual variability in elevation and an increased sensitivity to climate forcing.
Firn, the transitional stage between seasonal snow and ice in the accumulation zone of glaciers, strongly influences the climate response of mountain glaciers, ice caps and ice sheets. Pore space between snow grains that make up the firn layer enables meltwater to percolate into the firn layer and refreeze – if the firn temperature is below freezing. This prevents runoff, which means that firn acts as an efficient buffer against ice sheet mass loss. Diagnosing the current state of the Greenland ice sheet (GrIS) firn layer, and predicting its future, is therefore important in order to understand current and future changes in the mass balance of the GrIS.
A common method to assess the GrIS mass balance is altimetry.
With altimetry, elevation changes are monitored by repeated scanning of the ice sheet surface with an active laser or radar instruments on board aeroplanes or satellites.
A crucial step in translating the observed volume change to a mass change is to determine the density of the firn associated with the elevation change.
To account for variability and changes in the surface mass balance and firn processes like compaction, percolation and refreezing, a firn model is often employed for this step
Firn models can also be used to assess the evolution of the aforementioned buffer capacity of the firn layer and how it is impacted by refreezing.
It has been demonstrated that refreezing is a critical process for many ice caps to survive, for example, in the Canadian Arctic.
On these ice caps, summer melt consistently exceeds annual snowfall, and refreezing is required to maintain a near-zero mass balance
Refreezing also plays an important role in the Greenland ice sheet (GrIS), but it has not yet reached this saturation tipping point
Surface melt is also increasing in the GrIS accumulation zone, with the extreme melt summers of 2012 and 2019 as vivid examples
Lastly, firn models can be used to interpolate between observations such as density, temperature and age of the firn
Some (regional) climate models, such as RACMO and MAR, are coupled interactively to a snow/firn module, but these often use simplified initialization, parametrizations and/or reduced vertical resolution for computational efficiency.
The main advantage of using a dedicated, offline firn densification model is the lower computational cost, which enables the use of higher vertical resolution, a proper initialization of the firn layer and extensive sensitivity testing
In this study we present an updated version of the firn densification model of the Institute for Marine and Atmospheric research Utrecht (IMAU-FDM v1.2G, henceforth IMAU-FDM) applied to the GrIS, forced at the upper boundary by the latest 3-hourly output of the polar version of the Regional Atmospheric Climate Model (RACMO2;
We use recently published parametrizations and previously existing and newly obtained observations of firn density, temperature and liquid water content from the GrIS to calibrate model parametrizations for surface (fresh snow) density, dry-snow densification rate, thermal conductivity and meltwater percolation. The updated model is subsequently used to perform case studies of contemporary firn depth variability in three climatologically distinct locations of the GrIS accumulation zone: (1) the dry and cold interior, (2) the relatively low-accumulation western percolation zone and (3) the high-accumulation southeastern percolation zone.
This paper is organized as follows: in Sect.
For this work we use the offline IMAU-FDM, a semi-empirical firn densification model that simulates the time evolution of firn density, temperature, liquid water content and changes in surface elevation owing to variability of firn depth.
The model has been compared extensively to, and calibrated with, observations of firn density and temperature from the ice sheets of Greenland and Antarctica
An important boundary condition for the model is the density of freshly fallen snow,
In the updated model, a new parameterization for fresh-snow density
Firstly, the parameterization is derived by fitting the measured snow densities to mean annual temperatures, not the temperature at the time of the accumulation event. Thus the equation itself links snow density to annual temperatures, not instantaneous temperatures. Therefore, using the instantaneous temperatures would introduce an additional uncertainty.
Secondly, in deriving their parameterization,
Thirdly, using a climatological mean value suppresses the year-to-year variability in snow density.
This is undesirable, especially because the model will also be used for future scenarios in which long-term trends in temperature may have an effect.
On the other hand, using instantaneous temperature values may introduce an excessive variability, which, in reality, is smoothened by the effects of the snow being subjected to settling by wind and metamorphosis through numerous daily warming and cooling cycles.
Calculating
Figure
Daily averages of Das 2 (southeast Greenland; see Fig.
IMAU-FDM is a 1D vertical Lagrangian model.
When new snow accumulates at the surface (model top), the model layers are buried deeper and tracked during their downward motion.
At every time step, each layer is compacted under the influence of the pressure exerted by the mass of snow/firn above it.
However, in IMAU-FDM the densification rate
Equation (
Compared to observations of the depth of the
Ratio between modelled and observed depth at which the density reaches
In the model update, we recalibrated the dry densification correction factor MO as a function of mean annual accumulation, using an updated, high-resolution GrIS accumulation field
Figure
Values of the old and new linear regression of Eq. (
In IMAU-FDM, the vertical temperature distribution and its evolution are obtained by solving the one-dimensional heat transfer equation
The heat equation is solved numerically using the so-called “splitting method”.
In the first half of a time step, we solve for water transport using the bucket scheme (described in more detail in Sect.
The thermal conductivity is assumed to depend on firn density and temperature and in previous versions of IMAU-FDM followed the expression for seasonal snow due to
Comparison of the thermal conductivity parametrization by
IMAU-FDM employs a tipping bucket method to treat the percolation, irreducible (capillary) retention and (re)freezing of water, by filling up subsequent deeper layers to maximum capacity in a single model time step (i.e. quasi-instantaneously).
The latest IMAU-FDM model runs span the period 10 November 1957–31 December 2020.
The initial model density, temperature and liquid water content in the firn column are obtained by repeatedly applying the spin-up period 1960–1979 during which the forcing (i.e. surface accumulation, liquid water flux and temperature) is assumed to have remained reasonably constant (i.e. no significant long-term trends;
At the upper boundary of IMAU-FDM, mass accumulation (solid precipitation minus sublimation minus drifting snow erosion), liquid water fluxes (melt plus rainfall minus evaporation) and surface temperature are prescribed from the regional atmospheric climate model RACMO2.3p2, which has been used to simulate the climate and surface mass balance of the GrIS and its immediate surroundings for the period 1958–2020 at a horizontal resolution of
IMAU-FDM tracks the total firn thickness and changes in it. The resulting vertical velocity of the ice sheet surface due to changes in the firn layer (
IMAU-FDM output is evaluated using previously available and newly obtained profiles of firn density, temperature and liquid water content from the GrIS accumulation zone.
In total there are 124 observations, which cover a wide area to ensure that the various ice facies and climate zones of the GrIS are well represented (Fig.
Temperature observations include profiles ranging in depth between
For observations of liquid water in firn, we use observations from Dye-2
Locations of observed density (upward triangle), 10
Modelled vs. observed firn air content in metres. Dry locations are indicated with circles, whereas wet locations are indicated with triangles. A location is labelled as dry if it experiences 5 % less melt than accumulation during the spin-up period. The blue lines indicate the uncertainty in the v1.2G results.
The vertical density profiles of 92 GrIS firn cores are used to assess the performance of the updated model.
For each available firn core, IMAU-FDM has been run at the grid point closest to that location.
The evaluation is not completely independent of the calibration, as the 29 cores used for fitting the MO values are also included.
As an integrated measure of porosity, we compare modelled and observed vertically integrated firn air content (FAC), i.e. the vertical distance over which the firn layer can be compressed until the density of glacier ice is reached across the entire firn column.
FAC is an indicator of the meltwater retention capacity of the firn layer and therewith an important parameter to simulate correctly.
With the newly adopted parametrizations, the simulation of FAC in dry locations has significantly improved (Fig.
As mentioned in Sect.
Density profiles for v1.2G
Figure
For FA-13, the lower surface density also matches the upper
Modelled and measured
Modelled vs. observed temperature at 10 m depth (in
Figure
The summer profile of Dye-2 clearly shows a temperature maximum in v1.2G.
Such a maximum was not present in v1.1G and is also not present at Summit.
It is found that refreezing occurs at a greater depth than before (see Sect.
Comparison between observed temperature profiles vs. modelled profiles by v1.1G and v1.2G in summer (dashed lines) and winter (solid lines) at Summit in winter (9 March 2002) and summer (6 August 2002) and Dye-2 in the summer (10 August 2007) and winter (13 March 2007). The blue lines indicate the uncertainty in the v1.2G results.
The liquid water percolation and retention schemes have not been updated, but the changes made to the parameterizations that impact density and temperature do influence water percolation and therewith liquid water content (LWC), and these changes are discussed here.
Very few in situ, vertically resolved observations of LWC are available.
Here we used data from a recent study that used upward-looking ground-penetrating radar (upGPR) at Dye-2 in the higher percolation zone of the southwestern GrIS (
Figure
Comparison between the observed penetration depth
In this section we compare time series (1958–2020) of firn-induced surface elevation (i.e. firn depth) changes at three key locations: Summit in the cold and dry ice sheet interior, KAN-U in the relatively warm and dry southwestern percolation zone, and FA-13 in the wet and relatively mild southeastern firn aquifer region (
Location and climate of the three case study sites. The annual mean accumulation is calculated over the whole simulation period (1957–2020).
Time series of the total annual accumulation
Summit is located at the centre of the GrIS at a high elevation, and therefore it experiences a low amount of snowfall and a negligible amount of rain and melt.
The evolution of its elevation is therefore closely linked to changes in the temperature (higher temperatures lead to a higher compaction rate) and accumulation (higher accumulation leads to a thicker firn layer).
Panels (a) and (c) in Fig.
At Summit, an
However, v1.2G does show larger seasonal and interannual oscillations in the firn depth.
This is because
Situated in the southwest and at a lower elevation, KAN-U is warmer than Summit, and melting occurs every year during the summer, which greatly affects the firn properties at its location (Fig.
When comparing the vertical surface velocities between v1.1G and v1.2G, we again see an increased accumulation velocity
FA-13, a site with a firn aquifer, experiences a warmer and wetter climate than KAN-U, which leads to a rapid densification in the upper part of the firn column (Fig.
For the vertical velocity components, a similar picture emerges at FA-13 as at KAN-U:
Both the variability and the magnitude of the melt are stronger in v1.2G.
In the period 1990–2020, 8.5
In order to quantify the model uncertainty, we performed sensitivity tests in which the model settings, spin-up settings and the RACMO forcing were varied.
The parametrizations for the snow density (Eq.
These error margins do not include the uncertainty caused by missing physical processes in the model.
For example, the lack of deep water percolation may cause additional errors at wet locations.
From these tests, it turns out that the uncertainty in the modelled FAC (Fig.
The sensitivity of the modelled
The blue shaded area in Fig.
List of sensitivity tests conducted for determining the model uncertainty.
Temporal and spatial variability in firn layer thickness is highly relevant for studying the mass balance of the Greenland ice sheet (GrIS) because it directly impacts its refreezing efficiency. Moreover, firn thickness change is an important component of surface elevation change, and improved knowledge is required to accurately convert remotely sensed GrIS volume to mass changes. In this paper, we presented improvements in the offline version of the IMAU firn densification model (IMAU-FDM v1.2G), forced by 3-hourly output of the regional climate model RACMO2.3p2. Taking advantage of improved climate forcing and newly available observations of surface and subsurface firn density and temperature, the improvements are systematically implemented in the parametrizations of surface density, dry-snow densification and thermal conductivity. The treatment of liquid water is not changed, owing to a lack of sufficient observations to justify changes in the current configuration.
The updated model predicts higher firn air content (FAC), which at three selected sites in the interior GrIS and in the southwestern and southeastern percolation zone results in a larger sensitivity of firn thickness to intra- and interannual variations in snowfall, melt and temperature. As an important consequence of a change in fresh-snow density parameterization, the inter- and intra-annual variations in elevation have increased, owing to an increased sensitivity to changes in its forcing. In a warmer climate, firn thinning owing to increased surface melt becomes increasingly important at the marginal sites, both in the mean and as a component of interannual variability. Future applications of the improved model include a full GrIS assessment of contemporary and future firn mass and thickness changes, as well as explanation of areas where firn aquifers and ice slabs currently occur, and their future changes.
The code of IMAU-FDM v1.2G used in this project is available on GitHub at
Jason E. Box, Ellen Mosley-Thompson, Joseph R. Mc-Connell, Konrad Steffen,
Joel T. Harper and Sarah B. Das provided us with some of the firn core data that have been used to calibrate and validate IMAU-FDM.
The rest of the firn cores were obtained from the SUMup dataset
The supplement related to this article is available online at:
MB, PKM, WJvdB and MvdB started this project, decided on its scope and which parts of the model required further development, and interpreted the results. MB performed the model simulations, implemented the changes to the model and comparisons, and led the writing of the manuscript. All authors contributed to discussions on the manuscript.
The contact author has declared that none of the authors has any competing interests.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This work was carried out under the programme of the Netherlands Earth System Science Centre (NESSC), financially supported by the Ministry of Education, Culture and Science (OCW grant no. 024.002.001). We acknowledge ECMWF for computational time on their supercomputers.
This research has been supported by the Netherlands Earth System Science Centre (grant no. 024.002.001).
This paper was edited by Philippe Huybrechts and reviewed by Baptiste Vandecrux, Xavier Fettweis, and C. Max Stevens.