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 (
In response to higher air temperatures and increased surface melt, the Greenland ice sheet has been losing mass at an accelerating rate over recent decades and is responsible for about 20 % of observed global sea-level rise (Van den Broeke et al., 2016; IMBIE Team, 2020). Increasing temperatures have introduced melt at higher elevations where it was previously seldom observed (Nghiem et al., 2012). In these colder, elevated areas, snow builds up into a thick layer of firn. Increased surface melt in the firn area of the Greenland ice sheet affects the firn structure (Machguth et al., 2016; Mikkelsen et al., 2016), density (de la Peña et al., 2015; Vandecrux et al., 2018), air content (van Angelen et al., 2013; Vandecrux et al., 2019) and temperature (Polashenski et al., 2014; Van den Broeke et al., 2016). These changing characteristics impact the firn's meltwater storage capacity, through its ability to either refreeze meltwater (Pfeffer et al., 1991; Braithwaite et al., 1994; Harper et al., 2012) or retain liquid water in perennial firn aquifers (e.g., Forster et al., 2014; Miège et al., 2016). Meltwater refreezing can for instance form continuous ice layers that are several meters thick (MacFerrin et al., 2019). These ice slabs impede vertical meltwater percolation, enhance surface water runoff (Machguth et al., 2016; Mikkelsen et al., 2016; MacFerrin et al., 2019) and lower the surface albedo (Charalampidis et al., 2015), further amplifying Greenland's contribution to sea-level rise. The evolution of firn on the Greenland ice sheet is important for two additional reasons. First, knowledge about how firn air content evolves through time is necessary for the conversion of space-borne observations of ice sheet volume change into mass change (e.g., Sørensen et al., 2011; Zwally et al., 2011). Secondly, the depth of firn-to-ice transition as well as the mobility of gases through the firn before they are trapped in bubbles within glacial ice is necessary for the interpretation of ice cores and heavily depends on the fine coupling between the firn characteristics and surface conditions (e.g., Schwander et al., 1993).
Snow and firn models have been traditionally used to calculate the evolution of firn characteristics and meltwater retention at scales ranging from tens of meters to tens of kilometers. The performance of these models, when coupled to regional and global climate models, has a direct impact on the fidelity of ice sheet mass balance calculations (Fettweis et al., 2020) and sea-level change estimations (Nowicki et al., 2016). In previous work, Reijmer at al. (2012) suggested that, provided reasonable tuning, simple parameterizations of the subsurface processes calculate refreezing rates for the Greenland ice sheet in agreement with results from physically based, multilayer firn models. However, spatial patterns varied widely, and evaluation against field observations remained challenging. Steger et al. (2017) and more recently Verjans et al. (2019) investigated the impact of meltwater infiltration schemes on the simulated properties of the firn in Greenland. These studies highlighted the potential of deep-percolation schemes, for instance for the simulation of firn aquifers but also the sensitivity of simulated infiltration to the firn structure and hydraulic properties. In these previous studies, the surface conditions were prescribed by a regional climate model. Inaccuracies in this forcing could therefore explain some of the deviation between model outputs and firn observations and prevented a full assessment of different firn model designs.
The meltwater Retention Model Intercomparison Project (RetMIP) compares results from nine firn models currently used for the Greenland ice sheet. The models are forced with consistent surface inputs of mass and energy, and simulations are performed at four sites where surface conditions could be derived from automatic weather station (AWS) observations and where firn observations are available. These four sites were chosen to represent various climatic zones of the Greenland ice sheet firn area: the dry-snow area, where melt is rare, and temperatures are low, is represented by Summit; the percolation area, where melt occurs every summer at the surface, infiltrates in the snow and firn and refreezes there, is represented by Dye-2; ice slab regions, where a thick ice layer hinders deep meltwater percolation, is represented by KAN_U; and firn aquifer regions, where infiltrated meltwater remains liquid at depth, is represented by FA. At each site, we compare simulated temperatures, densities and the resulting meltwater infiltration patterns between models and to in situ measurements. We discuss model features that can be responsible for the model spread and deviations from observations. Lastly, we evaluate how differences in simulated firn characteristics result in various simulated refreezing and runoff values at Dye-2 and KAN_U and attempt to quantify uncertainties linked to firn models.
Models evaluated in this study.
The multilayer firn models investigated here are listed in Table 1. They all have density, temperature and liquid water content as prognostic variables and apply a framework whereby firn is divided into multiple layers for which these characteristics can be calculated. The number of layers varies in each model (Table 2), and we distinguish between two distinct types of layer management strategies: all models except DMIHH and MeyerHewitt follow a Lagrangian framework; i.e., they add new layers at the top of the model column during snowfall, and these layers are advected downward as new material accumulates at the surface. DMIHH and MeyerHewitt follow an Eulerian framework in which the layers have either fixed mass or fixed volumes. During snowfall, new material is added to the first layer, and an equivalent mass or volume is transferred by each layer to its underlying neighbor. At each time step, the models calculate firn density according to different densification formulations and update the layer temperature using different values of thermal conductivity (Table 2). The DMIHH, GEUS and DTU models have a fixed temperature at the bottom of their column (Dirichlet boundary condition), while other models have a fixed temperature gradient (Neuman boundary condition).
All models simulate meltwater percolation and transfer water vertically from one layer to the next according to the routines listed in Table 2. They also simulate meltwater refreezing and latent-heat release. All models simulate the retention of meltwater within a layer due to capillary suction, either explicitly (MeyerHewitt, CFM-Cr and CFM-KM) or, for all the other models, parameterized through the use of an irreducible water content (Coléou and Lesaffre, 1998; Schneider and Jansson, 2004). When meltwater cannot be transferred to the next layer or be retained within the layer by capillary suction, lateral runoff can occur according to model-specific rules (Table 2). The background and specifics of each model are described in greater detail in the following paragraphs.
The Community Firn Model (CFM) is an open-source, modular model framework designed to simulate a range of physical processes in firn (Stevens et al., 2020). The number of layers for a particular model run is fixed and determined by the accumulation rate and time step size. New snow accumulation at each time step is added as a new layer, and a layer is removed from the bottom of the model domain. A layer-merging routine prevents the number of layers from becoming too large. CFM-Cr and CFM-KM use the Crocus (Vionnet et al., 2012) and Kuipers Munneke et al. (2015) densification schemes, respectively (Table 2). Both use the same meltwater percolation scheme: a dual-domain approach that closely follows the implementation of the SNOWPACK snow model (Wever et al., 2016). It accounts for the duality of water flow in firn by simulating both slow matrix flow and fast, localized, preferential flow (Verjans et al., 2019). In the matrix flow domain, water percolation is prescribed by the Richards equation; ice layers are impermeable, and runoff is allowed. In contrast, water in the preferential-flow domain is allowed to bypass such barriers but not to run off. Water is exchanged between both domains as a function of the firn layer properties: density, temperature and grain size. As such, when water in the matrix flow domain accumulates above an ice layer, it is progressively depleted by runoff and by transfer of water into the preferential-flow domain. In the deepest firn layers, above the impermeable ice sheet, water accumulates, and no runoff is prescribed, which allows for the buildup of firn aquifers.
The DTU firn model was developed to derive the Greenland ice sheet mass balance from the satellite observations of ice sheet elevation change (Sørensen et al., 2011) and to describe the firn stratigraphy and annual layers in the dry-snow zone along the EGIG line in central Greenland (Simonsen et al., 2013). The DTU model uses the densification scheme from Arthern et al. (2010) and a bucket scheme for meltwater infiltration and retention. If meltwater is conveyed to a model layer, the water is refrozen if sufficient pore space and cold content are available in the layer. Additional liquid water can be retained in a layer by capillary forces calculated after Schneider and Jansson (2004). This formulation does not allow for the formation of firn aquifers. Percolation continues until the water encounters a layer at ice density or the bottom of the model, where, in both cases, it is assumed to run off. The model follows a Lagrangian scheme of advection of layers down into the firn, and the model layering is defined by the time-stepping of the model.
The DMIHH model was developed to provide firn subsurface details for the
HIRHAM regional climate model experiments (Langen et al., 2017). DMIHH
employs 32 layers, within which snow, ice and liquid water fractions can vary
and where each layer has a constant mass. Layer thicknesses increase with
depth to increase resolution near the surface and give a full model depth of
60 m water equivalent (w.e.). Mass added at the surface (e.g., snowfall) or
removed as runoff causes the scheme to advect mass downward or upward to
ensure the constant w.e. layer thicknesses. DMIHH uses Darcy's law to
describe meltwater infiltration. In addition to the saturated and
unsaturated hydraulic conductivities (Table 2), the water flow through
layers containing ice follows the model of Colbeck (1975) for a snowpack
with discontinuous ice layers. A parameter describing the ratio between the
characteristic distance between two adjacent ice lenses and the
characteristic width of an ice lens was set to 1, meaning that ice lenses
have a horizontal extent of half the unit area. A layer is considered
impermeable if its bulk dry density exceeds 810
The GEUS model is based on the DMIHH model (Langen et al., 2017) and is further developed in Vandecrux et al. (2018, 2020a). The main differences from DMIHH are the Lagrangian management of model layers and the increased vertical resolution with 200 layers. As in the DMIHH model, the layer's ice content decreases its hydraulic conductivity according to Colbeck (1975), but the ice layer geometry parameter was set to 0.1 as detailed in Vandecrux et al. (2018). Water exceeding the irreducible water content that could not percolate downward is available for runoff and is removed from the layer at a rate that depends on the firn characteristics and on surface slope, according to Darcy's law. More details about this runoff scheme are provided in the Supplement Text S1.
The IMAU-FDM model has been used in combination with the RACMO regional climate model in Greenland, Arctic Canadian ice caps and Antarctica. Firn compaction follows a semiempirical, temperature-based equation from Arthern (2010). The compaction rate is tuned to observations from Greenland firn cores using an accumulation-based correction factor (Kuipers Munneke et al., 2015). IMAU-FDM includes meltwater percolation following a bucket approach. Percolating meltwater is refrozen if there is space available in the layer and if the latent heat of refreezing can be released in the layer. As opposed to other models in this study, runoff is not allowed over ice layers but only when percolating meltwater has reached the pore close-off depth. Upon reaching that depth, runoff is instantaneous. The rationale for allowing percolation through thick ice slabs is that IMAU-FDM is mainly used to simulate firn at scales of tens to hundreds of square kilometers, and at these spatial scales, meltwater is assumed to always find a way through even the thickest of ice slabs.
Meyer and Hewitt (2017) present a continuum model for meltwater percolation in compacting snow and firn. The MeyerHewitt model includes heat conduction, meltwater percolation and refreezing as well as mechanical compaction using the empirical Herron and Langway (1980) model. In the MeyerHewitt model, water percolation is described using Darcy's law, allowing for both partially and fully saturated pore space. Water is allowed to run off from the surface if the snow is fully saturated. Using an enthalpy formulation for the problem, the MeyerHewitt model is discretized using an Eulerian, conservative finite-volume method that is fixed to the surface.
Model characteristics.
UppsalaUniBucket and UppsalaUniDeepPerc have been developed for the Norwegian Arctic (Van Pelt et al., 2012, 2019; Marchenko et al., 2017) and only differ in their representation of vertical water transport. UppsalaUniBucket simulates meltwater percolation according to a bucket scheme, while UppsalaUniDeepPerc uses a deep-percolation scheme which mimics the effect of fast vertical transport due to preferential flow (Marchenko et al., 2017). This deep-percolation scheme acts before the bucket scheme and instantaneously transfers the meltwater available at the surface to underlying layers using a linear distribution function of depth that reaches 0 at 6 m depth (Marchenko et al., 2017). The water transport model incorporates irreducible water storage and allows infiltration through ice-dominated layers. All water that reaches the base of the firn column is set to run off instantaneously. References for the parameterizations used for gravitational settling, thermal conductivity, irreducible water storage and water percolation are given in Table 2.
Differences between firn model outputs and observations depend on the model formulation but also on the forcing data that are given to the model: any bias in forcing data propagates into the model output. To make sure we compare and evaluate the models independently of biases that may exist in forcing datasets that come from regional climate models, we use meteorological fields derived from five AWSs at four sites.
These sites represent a broad range of climatic conditions on the Greenland ice sheet (Table 3, Fig. 1) that produce a wide variety of firn density and temperature profiles. For example, the cold and dry climate at the Summit station produces cold firn with low compaction rates representative of the “dry snow” area as defined by Benson (1962). Dye-2, located in an area with higher melt (Table 3), is representative of the “percolation area” (Benson, 1962), where meltwater generated at the surface percolates into the firn and releases latent heat when refreezing into ice lenses. At the KAN_U site, lower accumulation rates and increasing melt have led to the formation of thick ice slabs (Machguth et al., 2016; MacFerrin et al., 2019) that impede meltwater percolation below 5 m. The firn aquifer (FA) site in southeastern Greenland has both high surface melt and high accumulation rate, leading to the formation of a perennial body of liquid water at a depth of 12 m and below (Forster et al., 2014; Kuipers Munneke et al., 2014).
We use data from the Greenland Climate Network (GC-Net) AWS at Dye-2 and Summit (Steffen et al., 1996) and from the Programme for Monitoring of the Greenland Ice Sheet (PROMICE) station at KAN_U (Ahlstrøm et al., 2008; Charalampidis et al., 2015). For Dye-2 in 2016, we use an AWS installed by the University of Calgary and described in Samimi et al. (2020). Since this station was more recently installed than the GC-Net station, it ensures better meteorological observations (leveling, absence of frost or mist on radiometers) and therefore better forcing for the models over the 2016 melting season, during which an extensive observational dataset is available for model evaluation. This simulation is henceforth referred to as Dye-2_16, while the longer simulation using the GC-Net AWS is referred to as Dye-2_long. At FA, we use data from the S21 AWS maintained by Utrecht University. The S21 AWS measures air temperature, relative humidity (Vaisala HMP35AC), air pressure (Vaisala PTB101B), wind speed and direction (Young 05103), the shortwave and longwave radiative fluxes (Kipp and Zonen CNR1), station tilt, and instrument height. All quantities are sampled every 6 min, and hourly averages are recorded by a Campbell CR10X data logger.
Data from each AWS were quality-checked, and obvious sensor malfunctions were discarded. No data were discarded at FA and Dye-2_16. Gaps in the temperature, wind speed, humidity, air pressure, and incoming shortwave and longwave radiation were filled with adjusted values from either nearby stations or HIRHAM5, following Vandecrux et al. (2018). Gaps in upward shortwave radiation were filled using gap-filled downward shortwave radiation and the nearest daily albedo values from the Moderate Resolution Imaging Spectroradiometer (MODIS) satellite (Box et al., 2017). Downward longwave radiation is not monitored by the GC-Net stations (Dye-2_long and Summit) and is taken entirely from HIRHAM5 output.
The gap-filled meteorological fields are used to calculate the surface
energy balance based on the model developed by van As et al. (2005) and
applied in Vandecrux et al. (2018). We use surface height measurements and
available snow pit information to calculate snowfall rates as in Vandecrux
et al. (2018). This surface energy and mass balance provides, at
3-hourly resolution, the three surface forcing fields that were used by
all models: the surface skin temperature, the amount of meltwater generated
at the surface, and net snow accumulation (snowfall
Map of the four study sites. Elevation contours are in meters above sea level.
Information about the four sites and five model runs considered in
the comparison, including mean annual accumulation (
To allow fair comparison, all models shared as many boundary conditions as possible. A key
parameter in firn models is the density of fresh snow added at the top of
the model column. Here, all models used the value of 315
Participating models provided simulated firn density, temperature and liquid water content at 3-hourly time steps, interpolated to a common 10 cm grid from the surface to 20 m depth. Additionally, 3-hourly vertically integrated refreezing and runoff were calculated by each model.
Three types of datasets are available at our sites for model evaluation: (i) firn temperature observations from AWS as presented by Vandecrux et al. (2020a) at Summit and Dye-2_long, Heilig et al. (2018) at Dye-2_16 , Charalampidis et al. (2015) at KAN_U and Koenig et al. (2014) at FA; (ii) firn density profiles (Table 4); and (iii) observations of meltwater infiltration depth at Dye-2 from an upward-looking ground-penetrating radar (upGPR) during summer 2016 (Heilig et al., 2018).
Firn cores used for model evaluation.
Simulated firn density
For firn density, we calculate for each time step the average firn density
over the 0–1, 1–10 and 10–20 m depth ranges and discuss the standard
deviation of these values among models and their deviation from firn core
observations. We also compare the simulated density profiles to the firn
core data at each site. For firn temperature, we compare hourly observations
of firn temperature to interpolated temperature from the closest model
layers and use the mean error (ME), root mean square error (RMSE) and
coefficient of determination (
Modeled (colored lines) and observed (black diamonds with
In the following, we present comparisons of firn model outputs and model deviations from observations for firn temperature, density and liquid water content at sites representing different firn and meltwater regimes: dry firn (Summit), the percolation zone (Dye-2), ice slabs (KAN_U), and a firn aquifer (FA).
At Summit, density evolves in a similar manner across all models: low-density snow is deposited at the surface and is advected to greater depth
(Fig. 2a). All models except DMIHH and MeyerHewitt preserve and advect downward the initial density profile and generate layered firn at the surface. The temporal evolution of the average density
for the 0–1 m depth range follows similar seasonality and slight increasing
trend (Fig. 3a). Over the 1–10 and 10–20 m depth (Fig. 3b, c), most
models produce increasing firn density apart from IMAU-FDM, in which the firn
density slightly decreases. All models agree relatively well on the average
density independent of the depth range, with a maximum standard deviation
among models of 15
Regarding firn temperature, in most models, seasonal skin temperature
fluctuations drive firn temperature variability in the top few meters of the
column. However, seasonal temperature fluctuations propagate much deeper in
the DTU model, while it is almost not visible in the MeyerHewitt model (Fig. 2b). This results in much lower
Simulated firn density
Modeled (colored lines) and observed (black diamonds with 40
At Dye-2, surface melt occurs every summer. Consequently, refreezing of
percolating meltwater has a significant effect on simulated density and
temperature (Fig. 4). The investigated models span a large spectrum of
meltwater infiltration strategies (Table 2), leading to greater differences
between models in firn density, temperature and liquid water content (Fig. 4). Simulated meltwater percolation depth varies greatly among the models
(Fig. 4c). At one end of the spectrum, the DTU model only allows meltwater
in the top model layer: an ice layer is built right at the start of the
simulation, and water is not able to penetrate ice layers in this model. At
the other end, CFM-Cr and CFM-KM, which do allow meltwater to pass through
ice layers and explicitly account for fast preferential flow, simulate
percolation down to 10 m depth. In between these end-member models,
UppsalaUniDeepPerc simulates percolation down to
Simulated firn density
Comparison of the simulated (colored lines) and upGPR-derived (black line) meltwater percolation depth at Dye-2 over the 2016 melting season.
These differences in meltwater infiltration, when accumulated over a
17-year-long run, lead to large differences in firn density and temperature
evolution across models (Fig. 4). Models that include deep water
infiltration (CFM-Cr, CFM-KM and UppsalaUniDeepPerc) build up a thick
high-density layer at 3–10 m depth. In contrast, DTU, GEUS, IMAU-FDM and
UppsalaUniBucket simulate thinner, high-density layers that form each
summer at the surface and are buried in the following months and years.
These sharp contrasts between low- and high-density layers are smoothed in
the Eulerian DMIHH and MeyerHewitt models. For each model, the simulated
firn temperature at Dye-2 (Fig. 4b) and its deviation from observations
(Fig. 4d) respond closely to the simulated meltwater infiltration each
summer (Fig. 4c). Models that include explicitly deep percolation (CFM-Cr,
CFM-Kr, UppsalaUniDeep) also present the greatest firn warming at depth due
to refreezing and latent-heat release (Fig. 4b) and consequently have a
positive ME ranging from 3.6 to 6.2
The impact of these different infiltration patterns on the long-term
evolution of the average firn density and how simulated firn density
compares to observations are presented in Fig. 5. The standard deviation
(model spread) of density reaches 161
Simulated firn density
Modeled (colored lines) and observed (black diamonds with 40
Simulated firn density
The use of a more recent AWS to derive the climate forcing at
Dye-2_16 allows the assessment of the firn models and their
infiltration schemes in the best conditions. Over a single melt season, the
meltwater infiltration and refreezing do not produce drastic changes in
the simulated density profiles (Fig. 6a). Yet, the meltwater is
distributed at different depths and with different timing depending on the
model (Fig. 6c). The dual-domain approach of CFM-Cr and CFM-KM is visible
with higher liquid water content close to the surface, corresponding to the
matrix flow, and low water content infiltrating down to 10 m depth in the
heterogenous percolation domain. UppsalaUniDeep, which also includes deep
percolation, infiltrates water down to
UpGPR observations (Fig. 7) show that the meltwater did not reach below 2.5 m depth during the 2016 melt season. The melt was concentrated around three periods of increasing intensity, between May and June and a period when meltwater was continuously present in the firn, between 20 July and 25 September. Compared to the upGPR, the CFM-Cr and CFM-KM models substantially overestimate percolation depth (Fig. 7a, red and blue lines), suggesting that, in the current configuration, these models exaggerate the effects of preferential flow, at least at this location. The DTU model does not simulate any percolation, and the MeyerHewitt model simulates the presence of meltwater in short-lived, episodic pulses rather than the continuous presence of meltwater that the upGPR observed. The other models simulate a percolation depth and temporal behavior closer to the upGPR observations.
At KAN-U, surface melt is more intense than at Dye-2. As a result, refreezing of infiltrated meltwater forms ice slabs that can be tens of centimeters to several meters thick. This site is therefore an interesting test for the firn models to see how they handle the presence of an ice slab and the effects of ice slabs on the vertical profiles of temperature and liquid water. Note that the firn models are initialized in spring 2012 with a preexisting ice slab, which means that we do not assess the model capacity to form an ice slab; we only assess the effect of the ice slab on the evolution of the firn column.
The evolution of the density profile at KAN_U strongly
depends on whether the model allows percolation past the ice slab (Fig. 8a, c). The DMIHH, MeyerHewitt and DTU models do not allow such percolation
at all, and thus refreezing-related densification only occurs on top of the
ice slab. The absence of latent-heat release below the ice slab causes these
models to exhibit colder temperatures than observed (Fig. 8b, c). Another
group of models (CFM-Cr, CFM-KM, IMAU-FDM, UppsalaUniBucket and
UppsalaUniDeepPerc) does allow percolation of meltwater through the ice
slab, to depths of 10–15 m. As a result, the small amount of available pore
space within the ice slab is used for refreezing and is progressively filled
(Fig. 8a). Nevertheless, the sealing of the ice slab in these models does
not prevent the meltwater from percolating through, and meltwater refreezing
continues to occur at depth and to densify the firn there. These models
overestimate deep-firn temperatures compared to observations (Fig. 8d),
presumably as a result of excess refreezing. In the MeyerHewitt and DMIHH
models, the initial ice layers are gradually smoothed over time (Fig. 9d–g). We relate this behavior to their Eulerian framework that implies
frequent averaging of firn density and temperature when mass is added or
removed from the model column. Still, they keep higher density between 5 and
10 m depth, where the ice slab is. The model spread in the top 1 m average
density is minimal in the spring and increases in the summer (Fig. 9a).
The simulated average densities for 0–1, 1–10 and 10–20 m depth ranges
compare well with punctual observations (Fig. 9a–c), but deviations between
simulated and observed density profiles increase with time (Fig. 9d–g).
Comparison of the simulated firn temperature to hourly observations confirms
that models including deep percolation (CFM-Cr, CFM-KM and UppsalaUniDeep)
and bucket schemes (IMAU-FDM and UppsalaUniBucket) infiltrate too much water
at depth, resulting in a positive bias in temperature and an ME ranging from
1.8 to 4.7
At the firn aquifer site, both melting and snowfall are high, leading to
perennial storage of liquid water within the firn. In terms of firn
density, vertical gradients are similar among models, but both the
MeyerHewitt and DMIHH models simulate smoother profiles (Fig. 10a). This
is likely due to their use of an Eulerian framework, as also seen in the
results for KAN-U. Temporal evolution in density is also similar among
models given the short span of the simulation. The DTU model simulates
slightly denser firn in the top few meters of the column as a result of
refreezing (Fig. 10a). Models which account for preferential flow (both
CFM models and UppsalaUniDeep) simulate meltwater infiltration to the
aquifer, although with a slight difference in timing (Fig. 10b, c).
Unfortunately, the firn temperature observations do not allow us to
ascertain how much water was transferred to the aquifer but only that the
whole firn column was at 0
The variability in simulated firn density, temperature and water content among the models and the deviation between simulations and observations (Sect. 4) can be explained by the various ways physical processes are accounted for in the models. In this section we detail what can be learned from the comparison, and we explore current knowledge gaps and potential improvements for firn models.
At Summit, comparisons with observations suggest that with appropriate forcing, the various densification formulations perform similarly and within observational uncertainty. The ability of firn models in the dry-snow area to reproduce measured density profiles has been established from previous comparisons (Steger et al., 2017; Alexander et al., 2019) and can be attributed to the fact that most densification schemes are calibrated against firn density profiles from dry-snow areas. The simulated densities at Summit show that densification schemes provide similar outputs despite modeled temperatures being slightly different (Fig. 2a, b). Still, the ability of firn densification models to simulate firn changes in a transient climate is less certain (Lundin et al., 2017) and should remain a priority for future study. We also note that densification schemes developed for dry firn are applied to wet-firn zones, and further research is needed to determine the validity of this assumption.
At Summit, the top of the initial firn density profile is advected to 10 m depth by the end of the simulation (Fig. 2). Consequently, we assess here both the models' capacity to accommodate and transform new snow at shallow depth and how models densify the initial density profile as it is advected downward. The persistence of the initial conditions consequently influences the performance of the models but has the advantage of giving all models the same starting point. An alternative strategy would have been to allow models to equilibrate with the surface forcing during a spin-up period. But such an approach would initiate models with their own spin-up result and would make it more difficult to assign differences in model outputs to either model design or different initial conditions. Our observation-based initialization was therefore deemed more suitable to intercompare the meltwater retention in different models. In spite of measurement uncertainty and firn spatial heterogeneity, the firn density and temperature measurements used to initialize and evaluate the models represent the closest estimation of actual firn characteristics. Additionally, important biases in initial firn density and temperature would lead to a visible adjustment of the simulated firn characteristics in the first months or years as the model reacts to the surface forcing. No abrupt change can be seen in the simulations (Fig. 2), which gives confidence that the initial conditions were appropriate.
Models exhibit small but clearly discernible differences in firn temperature at Summit (Fig. 2b). In our model experiments, downward advection due to accumulation was identical for all models, suggesting that this spread must be caused by the parameterization of thermal conductivity and/or the models' differing numerical schemes. Also, a suite of models exhibit colder temperatures compared with observations at Summit (DTU, DMIHH, GEUS, IMAU-FDM, UppsalaUniBucket). We interpret this as an indication that heat transfer through the firn is still not accurately handled in most firn models. The heterogeneous nature of the firn, the presence of vertical ice features in the firn, the variability in surface snow density and thermal conductivity, and firn ventilation are processes that are oversimplified or absent in the models and should be the subject of future research. Errors due to inaccurate estimates of thermal conductivity affect firn temperature, densification rates and meltwater refreezing potential. We recommend that further work investigates potential improvements of the parameterization of thermal conductivity, either using recent studies (e.g., Calonne et al., 2019; Marchenko et al., 2019) or model calibration to observed firn temperature at dry-firn locations. Other causes of mismatch between models and observations could be that certain processes (e.g., radiation penetration or variable fresh-snow density) are not provided to the models or that uncertainty in the forcing data derived from AWS observations will propagate into the model simulations.
Many observational studies have demonstrated that there are two pathways for meltwater to infiltrate into the firn, namely by homogeneous wetting front, also called matrix flow, and by preferential flow through vertically extended channels (e.g., Marsh and Woo, 1984; Pfeffer and Humphrey, 1996). Some of the nine participating firn models do include both percolation regimes, and others do not. The lack of preferential-flow routines has recently been described as a limitation of firn models (e.g., van As et al., 2016). Yet, little is known about how often this phenomenon occurs in the firn, how deep meltwater is transported and which process triggers preferential flow. Here, the models that explicitly include deep percolation (CFM-Cr, CFM-KM and UppsalaDeepPerc) overestimate percolation depth and firn temperature at Dye-2, KAN_U and even Summit, where the surface meltwater production is minimal. In their current configurations, the deep-percolation schemes seem less adapted for areas with minor melt. Our results suggest that until the physics of preferential flow in firn are better understood, these more complex models do not necessarily provide better results than simple bucket schemes. We recommend targeted field campaigns and laboratory studies to better understand preferential flow and using those to constrain the firn conditions and meltwater input under which deep percolation occurs. These steps are necessary to develop accurate deep-percolation schemes in firn models.
On the other hand, models that keep meltwater close to the surface because they do not include any form of deep percolation do not always show better performance. At Dye-2_16, DTU, DMIHH, GEUS, IMAU-FDM and UppsalaUniBucket all exhibit temperatures that are too cold compared with the observations. The cold bias could be due partly to an underestimation of thermal conductivity (Sect. 5.1) or to insufficient meltwater percolation. The upGPR observations at Dye-2 in 2016 indicate a reasonable percolation depth for all these models except DTU. It is conceivable that these models do simulate a reasonable percolation depth but that the volume of percolating and refreezing meltwater is underestimated. Firn temperature observations and upGPR measurements can detect the presence of liquid water, but currently, no technique allows the vertically resolved measurement of water content. The models that use Darcy's law (CFM-Cr, CFM-KM, DMIHH, GEUS, MeyerHewitt) use different formulations for the firn permeability (Table 2), which also contribute to differences in meltwater percolation and refreezing results. Firn permeability can be related to grain size and firn density (Calonne et al., 2012). However, firn grain size and permeability observations are scarce, and these variables remain totally unconstrained in current models. Future model evaluation should include the existing data where available (e.g., Albert and Shultz, 2002), and more field observations of these grain-scale characteristics should be collected.
The formation of ice slabs is a complex interplay between accumulation,
densification, meltwater percolation and refreezing (Machguth et al.,
2016). Simulation of ice slabs by a firn model is therefore highly
challenging, and success or failure to reproduce ice slabs depends on a
number of processes that are closely linked and difficult to disentangle.
Models that include deep percolation (CFM-Cr, CFM-KM and UppsalaUniDeepPerc)
grow an ice layer of several meters thickness close to the surface at Dye-2,
where no such ice slabs are observed. This model behavior can be explained
by the simulation of water percolation bypassing ice layers and thus
refreezing in cold underlying firn. At KAN_U, where ice slabs
do exist, the DMIHH and GEUS models predict firn temperatures closest to the
observations (lowest RMSE and ME) when compared to observations (Fig. 8d). The performance of DMIHH at
KAN_U can be explained by the absence of meltwater
infiltration below the ice slab (Fig. 8c), which agrees with recent field
evidence of the ice slabs' impermeability (MacFerrin et al., 2019). In
DMIHH, the blocking of percolation originates from a simple permeability
criterion: a layer reaching 810
Two models with a bucket-type percolation scheme, IMAU-FDM and UppsalaUniBucket, use an irreducible water content formulation established by Coléou and Lesaffre (1998) from laboratory measurements. They consequently present similar and realistic percolation depths at Dye-2 (Figs. 4, 6 and 7). At KAN_U, however, in the presence of an ice slab, the two bucket scheme models overestimate percolation: this is evident from a warm bias there, relative to the firn temperature observations (Fig. 8d). We therefore conclude that bucket schemes perform relatively well in the absence of ice slabs and that they could benefit from an improved representation of flow-impeding ice layers.
Finally, we make a note on discretization strategies of firn models. In Lagrangian models, the numerical grid follows the firn as layers get buried under accumulating snow. In Eulerian models the firn is being transferred through a fixed numerical grid. The Eulerian models, DMIHH and MeyerHewitt, smooth the firn density profile, reducing and dissipating contrasts in firn density (Figs. 2, 4 and 8). This smoothing is not prevented by increased vertical resolution since MeyerHewitt has 18 times more layers than DMIHH. At KAN_U, these two models gradually lose the contrast between the layers that compose the ice slab and the firn below (Fig. 8). Therefore, Eulerian models tend to represent ice slabs in terms of a depth range with increased density rather than marked layers of ice. This limitation of Eulerian models does not prevent the DMIHH model from adequately simulating firn temperature at KAN_U (Fig. 8d) and water infiltration at Dye-2 (Fig. 6). Further testing of Eulerian models should investigate how this smoothing affects the modeled firn characteristics over longer runs and how ice slabs are represented in these models.
Like ice slabs, firn aquifers form in locations with a complex combination of accumulation, surface melt, percolation and refreezing (Forster et al., 2014; Kuipers Munneke et al., 2014). Both the thermodynamic and the hydrological components of a firn model play an important role in its capacity to simulate firn aquifers.
As a general observation, aquifers are poorly represented in the firn models considered in this intercomparison, which poses the question of the suitability of the models to simulate aquifers in Greenland. For example, horizontal water flow at depth plays a crucial role in the evolution of firn aquifers (Miller et al., 2018). However, the nine models investigated here and, to our knowledge, all firn models currently used to evaluate surface mass balance on the Greenland ice sheet are one-dimensional. As such, the water available for lateral movement in these models is sent to runoff, which is itself governed by poorly constrained parameterizations. Also, IMAU-FDM and UppsalaUniBucket do not allow for the presence of water beyond the irreducible water content: after the initialization of these models, all the excess water within the aquifer is run off instantaneously. As a result, these models are incapable of modeling actual aquifers (defined as saturated firn). Still, the regional climate model RACMO2, which includes IMAU-FDM, has been used previously to map aquifers over the entire ice sheet (Forster et al., 2014). Areas where the model showed residual subsurface water (within the irreducible water content) remaining in spring were assumed to represent areas where firn aquifers might be present. Although this approach succeeded at mapping the current firn aquifer areas, the difference between what is tracked in the model and what actually happens at a firn aquifer puts doubt on the current capacity of firn models to predict firn aquifer evolution in future climate. Other models show an intermediate type of behavior: the DMIHH model runs off excess water according to the parameterization by Zuo and Oerlemans (1996). This leads to the gradual decrease in water content within the aquifer. The GEUS model incorporates a Darcy-like parameterization of the subsurface runoff, which results in faster drainage of the aquifer than DMIHH. However, observations showed that excess water in the aquifer does not run off immediately but flows laterally and can remain in the aquifer for several decades (Miller et al., 2019).
Another challenging question for understanding and modeling firn aquifers is where and when the meltwater generated at the surface percolates down to the aquifer. Firn temperature observations show that the top 20 m of firn remained at melting point during the 2014 melt season. This indicates that meltwater from the surface reached the aquifer. The firn models do not conclusively answer how and when deep percolation to the firn aquifer takes place. Given the same surface forcing and initial firn conditions, only the models with explicit deep-percolation schemes (CFM-Cr, CFM-KM and UppsalaUniDeepPerc) infiltrate water down to the aquifer. This could indicate that the recharge of the firn aquifer has to be through heterogeneous percolation because it is the only way firn models can mimic observations. However, such a systematic infiltration through vertical channels should leave visible traces in the form of altered stratigraphy or ice columns (Marsh and Woo, 1984) or show repeatedly in firn temperature observations when meltwater infiltrates into cold firn in spring (Pfeffer and Humphrey, 1996; Charalampidis et al., 2016). Future field investigation should ascertain whether preferential flow is indeed the only process infiltrating water to the aquifer. Another interpretation could be that models using a bucket scheme (DTU, IMAU-FDM and UppsalaUniBucket) or Darcy's law (DMIHH, GEUS and MeyerHewitt) do not infiltrate water deep enough because of inappropriate irreducible water content or firn permeability for the firn aquifer site. Yet, few in situ datasets are available to constrain these firn characteristics in the models. One last possibility could be the misrepresentation of surface conditions: the melt calculated at the surface is subject to the biases and the uncertainties that apply to the so-called “bulk approach” used here in the energy budget calculation (Box and Steffen, 2001; Fausto et al., 2016). Although it was ensured that the calculated skin surface temperature agreed with observations available at KAN_U and FA, no direct observation of melt is available at our sites. Furthermore, the horizontal mobility of the meltwater, especially at high-melt sites such as FA, could lead to the injection of more meltwater at the surface than what is being melted. Therefore, more work is needed to quantify liquid water input at the top of the model in the firn aquifer region.
Given the complexity of the firn models, it is difficult to propagate uncertainty and account for model assumptions and parameterizations. As a consequence, firn model outputs have commonly been given without an uncertainty range, which prevents the assessment of the robustness of model-based inferences. Taking inspiration from previous ensemble-based modeling approaches (e.g., Nowicki et al., 2016), we provide a multimodel estimation of the uncertainty that applies to any simulated value of firn temperature and density and, more importantly, to the simulated values of meltwater retention (through refreezing) and runoff.
We see from Figs. 2 to 7 that the spread among models increases as we move
from the dry-snow area to the percolation area, peaking in areas with
high-melt features such as ice slabs and firn aquifers. We suggest that the
model spread presented here can provide a baseline for uncertainty whenever
a single model is used. At Summit, representative of the dry-snow area,
modeled average densities in the top meter of firn have a standard
deviation of 13
Simulated meltwater refreezing and runoff at Dye-2
The differences among simulated firn density, temperature and liquid water
distribution can cause them to retain and run off different amounts of
meltwater and therefore affect the surface mass balance. The models agree
that all meltwater is retained, meaning refrozen, at Summit and Dye-2_16. At
Dye-2_long and KAN_U, the intermodel average
and
At Dye-2, the DTU model produces unrealistic runoff values (Fig. 11c)
because of the impermeability of near-surface ice layers blocking downward
percolation and enhancing runoff. This highlights how a model designed for
the dry-snow area (Simonsen et al., 2013) can fail to capture meltwater
retention in the percolation area. We therefore do not consider this model
in our multimodel uncertainty estimation. All the other models agree that
runoff is minimal compared to refreezing at Dye-2 (Fig. 11a–c). CFM-KM and
CFM-Cr are the only models that calculate minor runoff some of the years
(Fig. 11b). This is likely linked to the buildup of denser firn layers
close to the surface (Fig. 4) through which water in the matrix flow
domain could not percolate. Even though the preferential-flow domain could
infiltrate some of the meltwater at depth (Fig. 4c), this was insufficient
to accommodate all the meltwater input. As a consequence, in 2012, the year with
the highest meltwater input, models on average calculate that
At KAN_U, the impact of the ice slab on the surface mass
balance is critical. The different simulated meltwater infiltration patterns
(Fig. 8c) lead to varying total amounts of meltwater either refrozen or
run off (Fig. 11d–f). The bucket schemes (IMAU-FDM, UppsalaUniBucket) and
UppsalaUniDeep percolate meltwater through the ice slab and refreeze all of
the input meltwater. In all the other models, the presence of ice layers
prevents or slows down meltwater infiltration as well as triggers ponding and lateral
runoff, including in the CFM models, where the preferential-flow domain is
unable to accommodate all the incoming water. The lowest-melt year, 2015,
has the lowest model spread, with
We do not evaluate meltwater retention and runoff at FA owing to the major limitations that we highlighted in the current handling of firn aquifers in firn models. Indeed, modeled runoff, traditionally defined as excess water entering an efficient drainage system and leaving the ice sheet, does not occur at FA (Miller et al., 2018). Instead, the excess water saturates the firn and slowly moves downstream within the aquifer, which none of the models can represent. In the percolation sites represented here by Dye-2 and KAN_U, the model spread generally increases with increasing surface melt and when more of that meltwater runs off (Fig. 11). This intermodel variability largely stems from the differences in meltwater infiltration and refreezing patterns, which themselves depend on meltwater input (see Sects. 4.2, 4.3, 5.2 and 5.3). We therefore highlight the disagreement of the firn models in their simulations of the meltwater retention, refreezing and runoff in the lower accumulation area of the ice sheet. High-melt accumulation areas should therefore be the subject of further field investigations to ascertain the actual meltwater retention there and better constrain firn models.
Nine state-of-the-art firn models were forced with mass and energy fluxes calculated from weather station data at four sites representative of various climatic zones of the Greenland ice sheet. From the intercomparison of their simulated firn temperature, density and water content and from evaluation against various firn observations, we identified specific routines within the models that are responsible for the models' behaviors. We later quantified uncertainties that apply to the firn model outputs and their evaluation of meltwater retention. We identified key topics for future development of models and for the investigation of firn processes.
We identified the following disagreements among models and discrepancies
between model outputs and observations. Runoff-enhancing ice slabs were
formed in certain models at the Dye-2 site, where they are not observed. At
the KAN_U site, where models were initialized with a
several-meter-thick ice slab according to observations, models do not agree
about whether such ice layers allow meltwater infiltration or not. Models that
explicitly include deep percolation allow water infiltration through the ice
slab, which is incompatible with the relatively cold firn observed at depth.
At the aquifer site, only deep-percolation models infiltrate meltwater to
the aquifer. Nevertheless, all models misrepresent the aquifer either
because of the inability of some models to simulate saturated conditions,
the different timescales at which the excess water is sent to runoff or
the absence of horizontal subsurface water movement. At all sites, Eulerian
models smooth the firn density profile and dissipate contrasts in firn
density, even in a model with high vertical resolution. Model spread and
deviation between simulated and observed firn density and temperature are
largest at the sites that experience more melt. Using twice the standard
deviation in model outputs as an indicator of the uncertainty envelope, we found
that firn models can estimate firn density within
Differences in simulated firn characteristics in the nine models led to
different amounts of meltwater being retained through refreezing or being
lost through runoff. Models that percolate meltwater deeper (shallower) calculate higher (lower) retention through refreezing and
therefore less (more) lateral runoff. The spread among models
regarding annual meltwater retention is positively correlated with surface
meltwater input and is maximal, on absolute values, at KAN_U
in 2012, the highest-melt year. Still, during that year, the intermodel
average runoff is only
These mixed results show that even the newest models need further
development to perform satisfactorily under the wide range of climate and
firn conditions of the Greenland ice sheet. We recommend the following
topics for future investigations:
More observations of firn permeability should be conducted at both the point and
regional scale. Measurements of grain size and other microstructural
properties would also help to evaluate the parameterizations currently used
by some of the firn models for permeability. These measurements should focus
on the lower percolation area, where meltwater infiltration and runoff play
an important role in the surface mass balance. Bucket schemes, which do not calculate firn permeability, would benefit from
a density-based impermeability criterion. This criterion needs to be drawn
from field evidence at the scale at which the models operate. Recent work on firn thermal conductivity (e.g., Calonne et al., 2019;
Marchenko et al., 2019) should also be used to improve the firn models.
Furthermore, the impact of vertical ice features and firn ventilation on
firn temperature is currently not included in any of the firn models. Firn
temperature observations are now available to assess model performance. Eulerian models should be used bearing in mind that they gradually smooth
firn characteristics. This issue does not prevent the use of such models as
long as the features that are being studied (e.g., ice slab, runoff, firn
aquifer etc.) are being defined in ways that are compatible with the Eulerian
framework. A major rethinking of firn models is necessary to better represent firn
aquifers. In these regions, models need to allow saturated conditions and
lateral subsurface water flow either explicitly with a multidimensional
model or through an adapted parameterization. More field observations are
also needed to ascertain the surface meltwater input at these sites; whether
near-surface drainage occurs; and, if it does, the size of such drainage
area. Recent efforts were made to explicitly describe heterogeneous meltwater
infiltration in firn models. While they allowed better performance at the
firn aquifer site, they infiltrate water too deeply and produce positive
biases in firn temperature at the dry-snow site and the two percolation
sites. Further work is needed to understand, under various surface and firn
conditions, when heterogeneous percolation occurs, how deep it should reach
and how much water it should transport. Only after these questions are
understood can a reliable preferential-flow scheme be developed. The fresh-snow density is known to have an impact on the firn model outputs
but was here set to a site-invariant value derived from observations. Fresh-snow density is known to vary considerably in space and time, although no
statistically robust parameterization exists up to date for the Greenland
ice sheet. Future measurement campaigns and modeling efforts could help to
prescribe surface snow density and to better capture its interactions with
the densification and heat transfer schemes.
Considering the number of firn characteristics that remain to be
investigated and the cost of field surveys, laboratory experiments could be
highly valuable if they can address the boundary effects and the scale of the
process being investigated as well as provide realistic surface and firn
conditions. Investigation of the points listed above will collectively
improve our understanding of firn and meltwater dynamics; improve the
representation of these processes in firn models; and eventually reduce the
uncertainty that applies to their output when assessing the surface mass
balance of the Greenland ice sheet in past, present and future times.
The scripts and datasets produced for this study are available at the following links.
Surface forcing data:
RetMIP protocol and metadata:
Model outputs:
Plotting scripts:
CFM model code:
GEUS model code: at
The supplement related to this article is available online at:
RM, PLL, RSF and JEB secured and administrated the funding as well as conceptualized and supervised the RetMIP project. PLL, CMS, VV, SL, PKM, SM, WvP, CM, SS and BV provided the model runs. AH, SS, SM, HM, MM and BV provided the observations against which the models could be evaluated. MO participated in the data visualization. BV, with input from the coauthors, designed the methods, conducted the intercomparison and wrote the original draft. All coauthors contributed to the review and the editing of the manuscript.
The authors declare that they have no conflict of interest.
We are grateful to Ian Hewitt for his insight on the MeyerHewitt model. We thank our scientific editor Xavier Fettweis as well as Samuel Morin, Kendall FitzGerald and an anonymous reviewer for comments and suggestions that significantly improved the study.
This research has been supported by the Danmarks Frie Froskningsfund (grant no. 4002-00234) and the Programme for Monitoring of the Greenland Ice Sheet. Achim Heilig was supported by the Deutsche Forschungsgemeinschaft (grant no. HE 7501/1-1); Horst Machguth was supported by the European Research Council (CoG Nr. 818994). The AWS used at Dye-2 during the 2016 melt season is supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada, ArcTrain and the Arctic Institute of North America (NSTP). Olivia Miller and Clifford I. Voss were supported by the US Geological Survey. C. Max Stevens and Michael MacFerrin were supported by the National Aeronautics and Space Administration (NASA; grant no. NNX15AC62G).
This paper was edited by Xavier Fettweis and reviewed by Samuel Morin and one anonymous referee.