Surface ablation

Surface ablation is the removal of surface snow or ice from a site. It occurs through sublimation, melting and, on a local scale, wind-scouring. Surface melting is the dominant ablation mechanism for all global ice masses with the exception of the Antarctic Ice Sheet, where temperatures are too low to produce large-scale melting. Summertime surface melting occurs on all major Arctic and alpine icefields. Melting is limited in interior and northern regions of the Greenland Ice Sheet, but a narrow ablation zone is present around the entire ice-sheet periphery (Abdalati & Steffen, 2001; Plate 32.1). Surface melting in ablation zones of southern and southwestern Greenland is extensive, up to a few metres per year. Melt rates as high as 10myr-1 occur in maritime icefields in Iceland, Svalbard, and western North America (e.g. Bjornsson, 1979). Similar annual melt rates are found in the ablation zones of mid-latitude alpine ice masses (e.g. in the Andes, the Alps and the Rockies).

The case study by Bintanja (this volume, Chapter 33) discusses the importance of sublimation in Antarctica, where mass is lost to the atmosphere through both direct surface sublimation and, under sufficiently windy conditions, sublimation of windblown snow. The latter case can be a very effective ablation mechanism where loose surface snow is available, as winds can move the snow above the near-surface boundary layer, which quickly becomes saturated by surface sublimation. Simulations of Greenland Ice Sheet mass balance suggest that surface- and blowing-snow sublimation may contribute up to 15% of the total ablation from the ice sheet (Box et al., 2004), suggesting that these processes are also important to glacier mass balance in Arctic regions. One outstanding question is whether the net effect of sublimation is similar to wind scour, serving to redistribute snow rather than remove it from the system.

The physics of snow and ice melt are well understood; melt rates m are governed by local surface energy balance ps/ILm = Qv (1 - a) + Qml - QjrT + Qh + Ql - Qc + Qp - Qr (4)

where pS/I is the snow or ice density, L is the latent heat of fusion for water, a is the surface albedo, Qv is incoming solar radiation, Qir^ and Qirt are incoming and outgoing infrared radiation, Qh and Ql are the sensible and latent heat fluxes, QC is the flux of energy conducted into the snow or ice, QP is the advective energy delivered by precipitation, and QR is the advective energy associated with meltwater runoff from the snow or ice surface. All fluxes have units Wm-2, and fluxes are defined to be positive for heat transfer from the atmosphere to the snow/ice. Hence QIRT, QC and QR are energy losses from the surface-atmosphere interface. Latent heat exchange occurs through sublimation, deposition and evaporation of surface water during the melt season. The

2s 2

dtdT

precipitation source term, QP, accounts for heat transferred to the snowpack or ice surface as rainwater of temperature TP cools to 0°C

QP Pwcw PTP

where pw and cw are the density and specific heat capacity of water. Rainfall temperature TP is measured in °C.

Further elaborations of the terms in the energy balance can be found in Arnold et al. (1996), Cline (1997a, b), and Marks et al. (1999). Klok & Oerlemans (2002) discuss the spatial variability of energy balance terms on Morteratschgletscher in the Swiss Alps, and Denby et al. (2002) introduce a boundary layer model for simulation of energy balance at ice-sheet scales. Case studies and chapters in this volume from Braithwaite, Klok and Bintanja provide further insight into the energy balance terms and their relative importance for snow and ice ablation.

Equations (4) and (5) assume that the snow/ice surface is at the melting point, such that all available energy at the snow/ice surface is dedicated to meltwater production. In most glacier environments, however, overnight radiative cooling leads to refreezing and cooling of the snow/ice surface during the ablation season, leading to refreezing of both ponded surface water and near-surface snowpack porewater. This delays the onset of 'new' melt until the surface warms to the melting point and refrozen water thaws the next day. If significant refrozen water is present this delay can be significant, delaying melting until several hours after local sunrise on both snow and ice surfaces. This effect can be incorporated through the QL term above, but it is not generally accounted for as it requires a separate parameterization for the amount of free surface water.

In the most cold glacial environments (polar regions and extremely high altitudes), the snowpack remains below the melting point throughout the ablation season, and surface meltwater percolates into the snowpack, where it will refreeze and release latent heat. This also occurs in alpine snowpacks in springtime, limiting the amount of net mass loss via runoff, m, and having an impact on the snowpack energy balance. This refreez-ing is difficult to quantify, as a proper treatment of the process requires two- or three-dimensional modelling of surface runoff, meltwater percolation in the snowpack, and the detailed vertical thermodynamic evolution of the snow and firn. The customary approach in ice-sheet modelling is to crudely estimate a fraction of the total melt that refreezes, of the order of 60% in the icesheet accumulation area. Total refreezing quantities are much less in ablation zones or in alpine settings, of the order of 2-5% (Jóhannesson et al., 1995).

A study by Janssens & Huybrechts (2000) explored explicit modelling of the refreezing process in Greenland, concluding that differences from the assumption of 60% refreezing had only minor impacts on the modelled mass balance. The extent of refreezing, however, will vary in different climatic and topographic settings, as well as temporally during the melt season, so physically based models of the process are clearly preferable for application in different environments (e.g. ice-sheet ablation versus accumulation zones; polar versus mid-latitudes; steep, confined glacier outlets versus gently sloping lobes). Internal snow-pack thermodynamical models are well-developed in avalanche, sea-ice and snow-hydrology research and can be expected to become standard in glacier-climate modelling. In addition to improving the representation of meltwater refreezing, internal snowpack thermodynamics and hydrological modelling will allow consideration of important energy balance feed-backs on Equation (4), including thermodynamically explicit modelling of internal heat conduction, QC, advective heat transport via precipitation, QP, and meltwater heat transport, QR. All three of these terms are better-quantified as volume rather than surface processes.

The controls of surface melt are amenable to field measurement, making them reasonably well understood, but they are difficult to quantify in a spatially distributed model owing to their dependence on local meteorological conditions. The turbulent heat fluxes, QH and QL, for instance, are governed by local wind, humidity, and surface roughness properties, which exhibit substantial spatial and temporal variability. Other processes such as albedo evolution and snowpack hydrology are spatially complex and difficult to quantify in large-scale models.

The meteorological data demands and the spatial variability of governing processes make it difficult to apply a rigorous energy balance model to surface-melt modelling in ice-sheet models. As a gross but tractable simplification, temperature-index models are widely used for estimation of surface melt (e.g. Huybrechts et al., 1991; Johannesson et al., 1995). These models make use of observations that air temperature is a strong indicator of radiative and sensible heat energy available for melting, and parameterize meltwater generation over time interval t, m(t), as a function of positive degree days, PDD(t), m(T ) = dS/I PDD(t )

where dS/I is the degree-day melt factor for snow or ice, an empirically determined coefficient that differs for snow and ice to reflect the higher albedo of snow. Degree-day factors have units of metres water-equivalent melt production per °C per day. The PDD is a measure of the integrated heat energy in excess of the melting point over the time interval of interest. Surface melt estimation from Equation (6) is convenient because temperature (hence, PDD) is the only governing meteorological variable and is relatively amenable to spatial interpolation/extrapolation. Temperature fields from climate models or point measurements at automatic weather stations can be distributed over the landscape through application of atmospheric temperature lapse rates (e.g. Giorgi et al., 2003).

In glacier and ice-sheet modelling, where decadal to millennial time-scales are of interest, either monthly or mean annual temperatures are applied to estimate net annual melt via temperature-index models. Where monthly temperature fields are available, monthly mean temperatures are used to calculate PDDm (Braithwaite & Olesen, 1989; Braithwaite, 1995),

J T exp

2s 2

where t is the length of the month in days and sm is the standard deviation in monthly temperature, as in Equation (1). The primary objective of the statistical distribution of temperatures is to capture the critical influence of daily temperature maxima on meltwater production.

If annual mean climatology is applied, using the Reeh (1991) sinusoidal function as in Equations (2) and (3), net annual PDD are calculated from

2a,2

dtdT

Monthly or annual PDD go first towards melting of this year's snow accumulation, where available. Once there is no remaining snow from the annual accumulation, it is assumed that melting has penetrated to the previous year's firn or ice surface, and any remaining melt energy is directed to ice melt (cf. Marshall & Clarke, 1999). Degree-day factors dS/I most commonly used in icesheet modelling are taken from Greenland Ice Sheet studies (e.g. Braithwaite & Zhang, 2000), although it is recognized that these values may not be appropriate for the extremely different radiation regime of mid-latitude and tropical glaciers. Even within Greenland, different sets of degree-day factors appear preferable in different geographical sectors of the ice sheet (B0ggild et al., 1996; Lefebre et al., 2002), possibly related to local meteorological conditions and snow/ice surface properties (albedo, roughness).

The technical step of improving snow-hydrology and melt-rate calculations in ice-sheet models is within reach, and more physically based process models are likely to become the glaciological modelling standard over the next few years. This advance will be driven in part by the current effort to improve coupling between sophisticated atmospheric and ice-sheet models. It should be possible to move towards a more physical energy balance approach, including snow hydrology, following similar developments in atmospheric general circulation model (AGCM) simulation of present-day seasonal snowpack evolution (e.g. Marshall & Oglesby, 1994; Yang et al., 1999).

An intermediate step towards the goal of more physically based melt models that do not have prohibitive data demands is to include the effects of solar radiation in heat-index modelling (e.g. Cazorzi & Dalla Fontana, 1996; Hock, 1999). This can be done through a parameterization of the form m = dS/I PDD + fS/I (l, 9, t )Q

where QV is incoming solar radiation and fS/I(1, 9, t) is a radiation index for snow/ice melt. It is spatially and temporally variable to allow the effects of changing surface albedo to be parameterized (e.g. Shea et al., in press).

This relationship can be calibrated empirically through field observations, and it has important advantages over pure temperature-index modelling. In particular, incorporation of incoming solar radiation allows the effects of latitude and time of year (length of day, solar zenith effects), as well as terrain effects (shading, aspect) to be explicitly and objectively built into the melt model. For distributed modelling, where spatial estimation of variables is required over a much larger area than is amenable to monitoring, Hock (1999) used potential direct solar radiation for QV, with a univariate regression equation of the form in Equation (9b). Potential direct radiation can be calculated for any place and time, with shading effects incorporated through digital elevation models (DEMs); the relationship is purely geometric and straightforward to implement.

As it is surface radiation (rather than potential direct radiation) that matters for snow and ice melt, additional data are required to apply radiation-temperature melt models to a broad region, including parameterizations of diffuse versus direct radiation and atmospheric transmissivity, which includes the important influence of varying cloud cover. Given sufficient insights about actual meteorological conditions or statistical cloud distributions in a region, the radiation index fS/I(1, 9, t) could be made more complex to parameterize the effects of cloud cover as well as changing albedo. This has not yet been attempted in glacier-climate modelling, but it is a promising avenue to pursue until a full energy balance becomes practical. Statistically based insights into regional and seasonal cloud conditions can be derived from regional-scale climate modelling, or they can be based more crudely on local/regional precipitation rates.

32.2.3 Marine ablation

In present-day Antarctica, the dominant ice-sheet ablation mechanisms are iceberg calving and basal melting beneath floating ice shelves, as air temperatures are too cold to produce surface melting on most of the continent. The controls of ice-shelf wastage through both calving and subshelf melting are complex and are not well quantified. Calving involves fracture generation and propagation processes and is known to be dependent on ice thickness and tensile strength (hence temperature), water depth, tidal forcing, coastal/embayment geometry, and the flux of ice across the grounding line. There also appears to be a close relationship with spring/summer air temperatures, via the extent of the summer melt season (Doake & Vaughan, 1991; Vaughan & Doake, 1996). Scambos et al. (2000) demonstrate the role of water-filled crevasses in weakening overall ice-shelf competence, through forcing of vertical crack propagation.

Melting beneath ice shelves is also difficult to quantify and is known to be spatially variable, ranging from centimetres per year to several metres per year. Basal accretion occurs beneath some Antarctic ice shelves. Melt (or accretion) rates are controlled by ocean water temperature, density and subshelf bathymetry, with much of the spatial variability associated with convection cells in subshelf waters (Jacobs et al., 1992, 1996; Jenkins et al., 1997).

Ice shelves that drain the Greenland Ice Sheet and Arctic icefields in Canada and Russia are modest in scale relative to their Antarctic counterparts, but behave in similar fashion, calving large tabular icebergs. Other marine-based outlets of the Greenland Ice Sheet and the high Arctic islands are more akin to tidewater valley glaciers, calving blocky icebergs from floating glacier tongues or at the marine grounding line. Fracture propagation is still the primary control on the calving process in this case, but the flux of inland ice across the grounding line is the main determinant of or calving rates. Approximately 50% of Greenland's total ablation is believed to occur through iceberg calving (Paterson, 1994). Recent interferometric studies in northern Greenland ice shelves indicate that basal melting beneath ice shelves is an important ablation mechanism in northern Greenland (Rignot et al., 1997, 2000), with inferred melt rates as high as 20myr-1.

Current continental-scale ice-sheet models do not have the technical capacity for explicit representation of the processes of iceberg calving, ice-shelf breakup and subshelf melting. The governing mechanisms in each case have a finer scale than present model resolution (ca. 20km), and the governing physics for calving and ice-shelf breakup are not fully understood and may not be deterministic. Explicit modelling of ice-shelf basal melting requires coupling with a regional-scale ocean model (e.g. Hellmer & Olbers, 1989; Beckmann et al., 1999). This is technically feasible but has not yet been attempted in the ice-sheet modelling community.

From the perspective of modelling ice-sheet mass balance, it may be sufficient for many studies to neglect the details of marine-based ablation and accept that all ice to cross the grounding line ablates—the mechanism is unimportant. This is probably acceptable for first-order ice-sheet reconstructions, and it is essentially valid if one is not interested in the detailed timing of ice loss in coastal regions, as the marine ablation mechanisms discussed above will effectively dispose of ice to cross the grounding line within a time frame of years to centuries. However, the details of marine ablation processes become very important for questions of marine-triggered ice-sheet instability (e.g. tidewater glacier or ice-shelf collapse). This is therefore an important area of uncertainty for decade- and century-scale forecasts of West Antarctic ice-sheet response to climate change, ocean warming and sea-level change.

Zweck & Huybrechts (2003) give a summary of current methods of portraying marine ablation mechanisms in continental ice-sheet models. In the simplest treatments, all ice to cross the grounding line or a predefined bathymetric contour (e.g. 400 m water depth) is simply removed. Zweck and Huybrechts introduce a slight variation on modern bathymetric controls, allowing time-varying water depth controls on calving rates. This builds in both the bathymetric and sea-level influences on marine ice extent. Other studies parameterize calving losses, mC, as a function of water depth, ice thickness and ice temperature, proxy for ice strength/stiffness (e.g. Marshall et al., 2000):

to the truth; effects of oceanic circulation, air temperature (crevasse-forced fracture propagation) and the geometry of marine embayments are not captured. Pfeffer et al. (1997) explored a calving parameterization similar to that above, but including an explicit treatment of fracture propagation. Highresolution ice-shelf models that include the physics of ice-shelf deformation (longitudinal stress/strain and horizontal shear stress) are better able to simulate these processes and controls (MacAyeal et al., 1995). These models are difficult to couple with inland ice models, and fully articulated ice-shelf models have not yet been coupled with continental-scale ice-sheet models. This technical step is imminent, however, with considerable recent progress focused on the West Antarctic Ice Sheet (Payne, 1998; Hulbe & MacAyeal, 1999).

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