BLOG

We have a new study in the current issue of The Cryosphere that looks at the surface energy budget at a site on the Greenland Ice Sheet, and particularly the energy available for meltwater production, over a five-year period spanning the 2010 and 2012 exceptional melt years¹. While both the summers of 2010 and 2012 were exceptionally warm, only 2012 resulted in a negative mass balance. In fact, 2012 was the first year since records began that there was more meltwater runoff than snowfall at the site (KAN_U at 1840 m elevation in Southwest Greenland).

In the study we describe how the 2010 exceptional melt year appears to have preconditioned the near-surface layers of the ice sheet to dramatically strengthen the melt-albedo feedback in the subsequent 2012 exceptional melt year. Essentially, we suggest that near-surface ice lenses created by refreezing meltwater in the 2010 melt season made the ice sheet surface transition more readily from relatively high albedo light snow to relatively low albedo dark ice in the 2012 melt season. The substantially darker 2012 ice sheet surface absorbed more solar energy, and therefore caused more melt per ray of sunshine, than in 2010. We estimate that this melt-albedo feedback resulted in approximately 58 % more solar energy absorbed, and available for melt, in 2012 than in 2010.

While 2010 and 2012 were exceptional melt seasons in the context of the past thirty years, they are likely to have foreshadowed the upcoming thirty years. As Greenland climate is now rapidly warming, summer melt intensity no longer oscillates around its long term mean, and instead previously exceptional events are becoming normal. We therefore speculate that under persistent climate change, the firn at the KAN_U site will likely become saturated with refrozen ice lenses, which will enhance the melt-albedo feedback and perhaps even inhibit the downward percolation of meltwater. Ultimately, this will accelerate the transition of the contemporary lower accumulation area underlain by firn into an ablation area underlain by superimposed ice.

Maintaining the relatively sensitive automatic weather station needed to accurately measure surface energy fluxes in the relatively harsh ice sheet environment was no easy task. It took a number of scientists and funding agencies, which are listed in the acknowledgement section of the paper, to make this study possible. The KAN_U weather station continues to report real-time climate data via the Programme for Monitoring of the Greenland Ice Sheet (PROMICE) data portal: www.promice.dk.

Figure 1 – Monthly mean energy fluxes observed at KAN_U: shortwave (E_S), longwave (E_L), sensible heat (E_H), evaporative (E_E), geothermal (E_G), precipitation (E_P) and melt (E_M). The melt flux was calculated as a residual.

Figure 2 – A: Location of Kangerlussuaq Upper Station (KAN_U) on the Greenland Ice Sheet. B: The PROMICE climate station deployed to measure surface energy budget.

¹Charalampidis, C., D. van As, J. Box, M. van den Broeke, W. Colgan, S. Doyle, A. Hubbard, M. MacFerrin, H. Machguth and C. Smeets. 2015. Changing surface–atmosphere energy exchange and refreezing capacity of the lower accumulation area, West Greenland. The Cryosphere. 9: 2163-2181.

Quick intro to our study on the #Greenland ice sheet melt-albedo #climate #feedback: https://t.co/ecE2N3DbCZ pic.twitter.com/zFA32tTuJj

— William Colgan (@GlacierBytes) December 1, 2015

We have a new study in the AGU open access journal Earth’s Future this month, which introduces the notion of thermal-viscous collapse of the Greenland ice sheet¹. While people tend to think of ice as a solid, it is actually a non-Newtonian fluid, because it deforms and flows over longer time-scales. Of the many strange material properties of ice, the non-linear temperature dependence of its viscosity is especially notable; ice at 0 °C deforms almost ten times more than ice at -10 °C at the same stress. This temperature-dependent viscosity makes ice flow very sensitive to ice temperature. We know that the extra meltwater now being produced at the surface of the Greenland ice sheet, relative to 50 or 100 years ago, contains tremendous latent heat energy. So, in the study, we set out to see if the latent heat in future extra meltwater might have a significant impact on future ice sheet form and flow.

We first developed a conceptual model of what we called “thermal-viscous collapse”, which we define as the enhanced ice flow resulting from warming ice temperatures and subsequently softer ice viscosities. We decided there were three key processes necessary for initiating a thermal-viscous collapse: (1) sufficient energy available in future meltwater runoff, (2) routing of that extra meltwater to the ice-bed interface, and (3) efficient transfer of latent energy from meltwater to the ice. Drawing on previous model projections and observational process studies, and admittedly an injection of explicit speculation, we concluded that it is plausible to warm the deepest 15 % of the Greenland ice sheet, where the majority of deformation occurs, from characteristic Holocene temperatures to the melting-point in the next four centuries.

Figure 1 – Three key elements of thermal-viscous Greenland ice sheet collapse: (1) Sufficient energy available in projected Greenland meltwater runoff, (2) Routing of a fraction of meltwater to the interior ice-bed interface, and (3) Efficient energy transfer from meltwater to ice. This cross-sectional profile reflects mean observed Greenland ice surface and bedrock elevations between 74.1 and 76.4°N. Dashed lines illustrate stylized marine and land glacier termini.

We then used a simple (first-order Navier-Stokes) model of ice flow to simulate the effect of this warming and softening on the ice sheet over the next five centuries. We used a Monte Carlo approach, whereby we ran fifty simulations in which multiple key parameters were varied within their associated uncertainty. As may be expected, warming the deepest 15 % of the ice sheet by 8.8 °C, from characteristic Holocene temperatures to the melting-point, had a significant influence on ice sheet form and flow. Due to softer ice viscosities, the mean ice sheet surface velocity increased three fold, from 43 ± 4 m/yr to 126 ± 17 m/yr, resulting in an ice dynamic drawdown of the ice sheet, causing a 5 ± 2 % ice sheet volume reduction within 500 years. This is equivalent to a global mean sea-level rise contribution of 33 ± 18 cm (or just over one US foot). Of course, the vast majority of the sea level rise associated with thermal-viscous collapse would occur over subsequent millennia.

Figure 2 – Probability density time series of ensemble spread of 50 simulations in prescribed ice temperature (a), mean surface ice velocity (b), and ice volume (c), over a 200-year spin-up to transient equilibrium, and the subsequent 500-year combined transient forcing and spin-down period.

Perhaps a caveat or two: Just like simulating a marine instability induced collapse of the West Antarctic ice sheet, our simulation of a thermal-viscous collapse of the Greenland ice sheet is an entirely hypothetical end-member scenario. It is admittedly difficult to interpret end-member assessments when their probability of occurrence is unknown. In our case, we did not attempt to constrain the probability of a thermal-viscous collapse of the Greenland ice sheet, we merely demonstrated that initiating a thermal-viscous collapse appears plausible within four centuries, and assessed the associated sea-level rise contribution. Additionally, it may be debatable whether the combination of crevasses and reverse drainage can indeed route meltwater throughout the ice sheet interior, but I suppose that is a debate worth having!

Reference

¹Colgan, W., A. Sommers, H. Rajaram, W. Abdalati, and J. Frahm. 2015. Considering thermal-viscous collapse of the Greenland ice sheet. Earth’s Future. 3. doi:10.1002/2015EF000301.

Blog intro to our new paper on "thermal-viscous collapse" of the #Greenland #ice sheet: http://t.co/Qw1PUzviHr pic.twitter.com/8GCLmeRHdZ

— William Colgan (@GlacierBytes) July 19, 2015

We have a new study in this month’s Remote Sensing of Environment, which examines satellite-derived glacier mass balance in Greenland and the Canadian Arctic¹. Satellites are generally used to assess glacier mass balance through changes in volume (via satellite altimetry) or changes in mass (via satellite gravimetry). While satellite altimetry observes volume changes at relatively high spatial resolution, it necessitates the forward modeling of firn processes to convert volume changes into mass changes. Conversely, the cryosphere-attributed mass changes observed by satellite gravimetry, while very accurate in absolute terms, have relatively low spatial resolution. In this study, we sought to combine the complementary strengths of both approaches. Using an iterative inversion process that was essentially sequential guess-and-check with a supercomputer, we refined gravimetry-derived observations of cryosphere-attributed mass changes to the relatively high spatial resolution of altimetry-derived volume changes. This gave us a 26 km spatial resolution mass balance field across Greenland and the Canadian Arctic that was simultaneously consistent with: (1) glacier and ice-sheet extent derived from optical imagery, (2) cryospheric-attributed mass trends derived from gravimetry, and (3) ice surface elevation changes derived from altimetry. We have made digital versions of this product available in the supplementary material associated with the publication.

Figure 1 – Observational data inputs to our inversion algorithm. A: Cryosphere-attributed mass changes observed by gravimetry. B: Land ice extent observed by optical imagery. C: Ice surface elevation changes observed by altimetry.

To make sure our inferred mass balance field was reasonable, we evaluated it against all in situ point mass balance observations we could find. Statistically, the validation was great, yielding an RMSE of 15 cm/a between the inversion product and in situ measurements. Practically, however, this apparent agreement largely stems from the fact that we could only find forty in situ point mass balance observations against which to compare. Evaluating our area-aggregated sector-scale mass balance estimates against all previously published sector-scale estimates provides a more meaningful validation. This suggests the magnitude and spatial distribution of inferred mass balance is reasonable, but highlights that the community needs more in situ point observations of mass balance, especially from peripheral glaciers and regions of high dynamic drawdown in Greenland. (For the glaciology hardcores I will note that “mass balance” is distinct from “surface mass balance”, in that the former measurement also includes the ice dynamic portion of mass change.)

Figure 2 – A comparison of similar sector scale mass balance estimates and associated uncertainties across Greenland and the Canadian Arctic. Dashed lines denote estimates that pertain to the Greenland ice sheet proper (i.e. exclusive of peripheral glaciers). Jacob et al. (2012) estimates pertain to Canada, while Sasgen et al. (2012) estimates pertain to Greenland.

This new inversion mass balance product, which we are calling “HIGA” (Hybrid glacier Inventory, Gravimetry and Altimetry), suggests that between 2003 to 2009 Greenland lost 292 ± 78 Gt/yr of ice and the Canadian Arctic lost  42 ± 11 Gt/yr of ice. While the majority of Greenland’s ice loss was associated with the ice sheet proper (212 ± 67 Gt/yr), peripheral glaciers and ice caps, which comprise < 5 % of Greenland’s ice-covered area, produced ~ 15 % of Greenland mass loss (38 ± 11 Gt/yr). A good reminder that ice loss from “Greenland” is not synonymous with ice loss from the “Greenland ice sheet”. Differencing our tri-constrained mass balance product from a simulated surface mass balance field allowed us to assess the ice dynamic component of mass balance (technically termed the “horizontal divergence of ice flux”). This residual ice dynamic field infers flux divergence (or submergent ice flow) in the ice sheet accumulation area and at tidewater margins, and flux convergence (or emergent ice flow) in land-terminating ablation areas. This is consistent with continuum mechanics theory, and really highlights the difference in ice dynamics between the ice sheet’s east and west margins.

Figure 3 – Spatially partitioning the glacier continuity equation in surface and ice dynamic components. A: Transient glacier and ice sheet mass balance. B: Simulated surface mass balance. C: Residual ice dynamic (or horizontal divergence of ice flux) term. The ∇Q color scale is reversed to maintain blue shading for mass gain and red shading for mass loss in all subplots. Color scales saturate at minimum and maximum values. Black contours denote zero.

As with some scientific publications, this one has a bit of a backstory. In this case, we submitted a preliminary version of the study to The Cryosphere in December 2013. After undergoing three rounds of review at The Cryosphere, the first one of which is archived in perpetuity here, it was rejected, primarily for insufficient treatment of the uncertainty associated with firn compaction. Coincidentally, on the same day I received The Cryosphere rejection letter, I received a letter from the European Space Agency (ESA) granting funding for a follow-up study. A mixed day on email indeed! After substantial retooling, including a discussion section dedicated to firn compaction and the most conservative error bounds conceivable, we were happy to see this GRACE-ICESat study funded by NASA and the Danish Council for Independent Research appear in Remote Sensing of Environment. The editors at both journals, however, were very helpful in moving us forward. Our ESA-funded GRACE-CryoSat product development is now ongoing, but a sneak peek is below.

Figure 4 – Same as Figure 3, except using a 5 km resolution GRACE-CryoSat inversion product instead of a 26 km resolution GRACE-ICESat inversion product. Colorbars are different in shading, but identical in magnitude.

Reference

¹W. Colgan, W. Abdalati, M. Citterio, B. Csatho, X. Fettweis, S. Luthcke, G. Moholdt, S. Simonsen, M. Stober. 2015. Hybrid glacier Inventory, Gravimetry and Altimetry (HIGA) mass balance product for Greenland and the Canadian Arctic. Remote Sensing of Environment. 168: 24-39.

Our new #Greenland mass balance product assimilates satellite gravimetry and altimetry data: http://t.co/4FucwYzUGA pic.twitter.com/Kbekmq6uUU

— William Colgan (@GlacierBytes) July 7, 2015

As the 2015 Greenland expedition season gets underway, I want to comment on the insurance overlap between research and sport expeditions on the ice sheet.

Greenland can be a very windy place. The world’s fourth fastest observed wind speed, 333 km/h, was clocked at Thule, Northwest Greenland, in a March 1972 storm¹. The “piteraq” (or “ambush”) wind is an especially strong type of wind, unique to Greenland, which occurs when katabatic winds align with the regional geostrophic wind field. During piteraq events, relatively cold and dense air not only flows down from the top of the ice sheet under gravity, but is also sucked down by low atmospheric pressure at the coast². Piteraqs are strongest around the ice sheet periphery, especially in Southeast Greenland, adjacent to the Icelandic Low.

In April 2013, a few colleagues and I were doing fieldwork on the ice sheet at KAN_U in Southwest Greenland, when a piteraq struck Southeast Greenland. Our TAS_U weather station there recorded sustained winds of just over 150 km/hr during the piteraq³. Since 2007, TAS_U has recorded a number of piteraqs, some have even been strong enough to knock over or damage the station. The April 2013 event, which left the TAS_U station standing, would probably not have been noteworthy if it had not claimed the life of Philip Goodeve-Docker, who was just two days into a three-man sport expedition to cross the ice sheet from Isortoq to Kangerlussuaq⁴.

Mean hourly wind speeds at KAN_U and TAS_U weather stations during the April 2013 piteraq event. Inset: Locations of KAN and TAS transects, as well as other transects, in South Greenland. (source: van As et al., 2014)

The number of annually permitted Greenland sport expeditions is perhaps surprisingly high. An information request to Greenland Government by my colleague, Dirk van As, found that, during the 2010 to 2012 seasons, approximately 78 teams annually undertook sport expeditions in Greenland (including coastal kayaking), of which approximately 24 teams per year were dedicated ice sheet crossings⁵. Assuming a sport expedition team size of four people, that is approximately 100 individuals per year crossing the ice sheet, mostly along the 67th parallel (the “Isortoq-Kangerlussuaq highway”). All of these sport individuals are obliged to purchase search and rescue (SAR) insurance. While some nationally-funded research expeditions (basically just Danish and American) are permitted to “self-insure”, all other research expeditions have to buy into the same SAR insurance. Occasionally, and strictly speaking, even just specific members of a research expedition, such as persons not employed within the sponsoring nation, may be obliged to purchase their own SAR.

Map of permitted and non-permitted expedition areas in Greenland, as well as the approximate location of the Isortoq-Kangerlussuaq sport route. (source: Greenland Government)

In 2011, I received a SAR quote of 6200 DKK (900 USD) to cover a non-Danish member of a Danish expedition for just eight days. I shudder to think what some colleagues must pay to insure a six person research expedition for a month. At the time, the round-trip helicopter flight to our ice sheet site cost only about ten times our quote premium, meaning that in a zero profit world the underwriters would be recusing approximately 10 % of policyholders. Turns out, that is not far off the truth for sport expeditions. Of the 234 sport expeditions initiated in Greenland between 2010 and 2012, sixteen ended in emergency evacuation⁵. That is 7 % of all Greenland sport expeditions. The ice sheet teams were evidently better prepared with a lower, but still non-trivial, evacuation rate of 3 %.

As Greenland SAR insurance treats research and sport expeditions as functionally equivalent, both are technically required to bring more daily calories than even an Olympic swimmer might consume. The above 6.6a clause obliges a 21 day expedition to bring the equivalent of 30 kg of peanut butter per person. (source: Insurance for journeys and expeditions in Greenland policy drawn up in cooperation with the Danish Polar Center conditions no. 101B)

For insurance purposes, both sport and research expeditions are effectively regarded as having the same safety margin. In fact, research expeditions, often delivered by aircraft with >1000 kg of cargo per person, have an inherently higher safety margin than skiers pulling a <200 kg sled. I would love to have the comparable evacuation statistic for research expeditions. We have such an information request pending with Greenland Government, but I will go out on a limb and guess that the research expedition evacuation rate is not nil, but an order of magnitude lower than the sport expedition evacuation. This asymmetry in evacuation risk means that when predominately publicly-funded research expeditions buy SAR insurance, they are effectively subsidizing the SAR costs of predominately privately-funded sport expeditions. To make an analogy, auto insurance rates usually vary between motorcycles and mini-vans. In lieu of different insurance premiums for research and sport expeditions, perhaps the safety of sport expeditions could at least be further optimized by drawing on ice sheet research. (Not forgetting that reducing SAR calls is not just about cost, but also about the preservation of life!)

Vastly differing resource levels: Our 2013 research expedition being delivered by LC-130 with two of three pallets (left: Charalampos (Babis) Charalampidis) and a 2008 sport expedition arriving at our West Greenland campsite (right).

This brings us back to piteraqs, which should probably rank at the top of sport expedition hazards, above the more often cited trio of “cold, crevasses and polar bears”. For example, if research suggests that the ice sheet flank is windier in the Southeast than the Southwest, east to west crossings (Isortoq to Kangerlussuaq) would appear to provide sport teams more ample opportunity to wait for an appropriate weather window before setting upon the relatively piteraq prone Southeast flank. Right now, however, the majority of crossings (61 %) are in the opposite direction (west to east), with sport teams arriving in “piteraq alley” with no possibility for retreat⁵. Danish Meteorological Institute forecasts already include piteraq warnings for Greenland coastal towns. But while research has made piteraqs eminently predictable from 48 hours away, the Goodeve-Docker expedition was jeopardized within 48 hours of departing Isortoq. Evidently, more applied publications and outreach, to better communicate such research insight directly to teams, is needed.

So, those are some thoughts on how sport and research expeditions are linked by common SAR insurance, perhaps arguably to the detriment of research expeditions, and how the piteraq hazard might be mitigated for sport expeditions. Unfortunately, regional climate model simulations suggest that wind speeds around the ice sheet periphery will increase under climate change⁶, meaning that there will likely be more piteraqs in everyone’s future.

I should probably make explicitly clear that these are my own thoughts, and not those of my employing institution.

¹Stansfield, J. 1972. The severe Arctic storm of 8–9 March 1972 at Thule
Air Force Base, Greenland. Weatherwise. 25: 228–233.

²Oltmanns, M., et al. 2014. Strong Downslope Wind Events in Ammassalik, Southeast Greenland. Journal of Climate. 27: 977–993.

³van As, D., et al. 2014. Katabatic winds and piteraq storms: observations from the Greenland ice sheet. Geological Survey of Denmark and Greenland Bulletin. 31: 83-86.

⁴Edmonds, R. 1 May 2014. Explorer Philip Goodeve-Docker freezes to death on second day of trek across Greenland. London Evening Standard.

⁵Greenland Government. 2013. Statistik fra Administration af rejseaktivitet I Grønland. 6 pages.

⁶Gorter, W. et al. 2013. Present and future near-surface wind climate of Greenland from high resolution regional climate modeling. Climate Dynamics. 42: 1595-1611.

There are a variety of methods used to estimate the present rate of mass loss from the Greenland ice sheet, including satellite altimetry, satellite gravimetry and input-output assessments. All of these methods generally agree that since 2005 the ice sheet has been losing c. 250 Gt/yr of mass (equivalent to 8000 tonnes of ice per second). Partitioning this mass loss into climatic surface balance (i.e. snowfall minus runoff) and ice dynamic (i.e. iceberg calving) contributions is a little more challenging. Partitioning recent mass loss into surface balance or ice dynamic components requires us to look at the changes in each of these terms since a period during which the ice sheet was approximately in equilibrium. Conventionally, the ice sheet is assumed to have been in equilibrium during the 1961-1990 so-called “reference period”.¹

The three main methods of measuring present-day ice sheet mass balance: (1) snowfall input minus iceberg output, (2) changes in elevation using satellite altimetry, and (3) changes in gravity using satellite gravimetry (from Alison et al., 2014)⁵.

Our recently published study in the Annals of Glaciology takes a hard look at the mass balance of the high elevation interior of the Greenland ice sheet during the reference period². We difference the ice flowing out of a high elevation perimeter from the snow falling within it, and conclude that the ice sheet was likely gaining at least 20 Gt/yr of mass during the reference period. This implies that rather than ice sheet mass balance decreasing from c. 0 Gt/yr (or “equilibrium”) during reference period to c. -250 Gt/yr since 2005, it may have actually decreased from c. +20 Gt/yr of subtle mass gain during reference period to c. -250 Gt/yr since 2005. This interpretation would mean the “recent” (pre-1990 to post-2005) mass loss of the ice sheet is actually 7 % greater than might conventionally be assumed (270 vs. 250 Gt/yr). Seven percent more recent mass loss than conventionally assumed might not sound like much, but it becomes important when we try to partition mass loss in surface balance or ice dynamics components.

Illustration of how a subtle mass gain during reference period (1961-1990) , when the Greenland ice sheet is conventionally assumed to have been in approximate equilibrium, can influence the magnitude of “recent mass loss” used to partition surface balance and ice dynamics components of mass loss.

We also assessed whether surface balance or ice dynamics were responsible for subtle reference period mass gain. We concluded it was more likely long term ice dynamics, resulting from the downward advection through the ice sheet of the transition between relatively soft Wisconsin ice (deposited > 10.8 KaBP) and relatively hard Holocene ice (deposited < 10.8 KaBP). In 1985, Niels Reeh proposed that subtly increasing effective ice viscosity was resulting in cm-scale ice sheet thickening³. Increased iceberg calving, or enhanced ice dynamics, are conventionally assumed to be responsible for c. 100 Gt/yr of recent mass loss⁴. Since we conclude ice dynamics were likely responsible for subtle reference period mass gain, we are implying that mass loss due to ice dynamics may actually be c. 20 Gt/yr greater than conventionally assumed, or c. 120 Gt/yr rather than c. 100 Gt/yr since 2005. Without invoking any departures from the conventional view of changes in surface balance since reference period, this infers 20 % more mass loss due to ice dynamics since reference period. This becomes important if diagnostic ice sheet model simulations are calibrated to underestimated recent ice dynamic mass loss, which may subsequently bias prognostic model simulations to similarly underestimate future ice dynamic mass loss.

An ice sheet composed of relatively hard Holocene ice is theoretically c. 15 % thicker than one composed of relative soft Wisconsin ice. Today’s ongoing transition from Wisconsin to Holocene ice within the Greenland ice sheet should theoretically result in cm-scale transient thickening (after Reeh, 1985).

Pondering how a millennial-scale shift in ice dynamics may be responsible for subtle mass gain during the 1961-1990 period, and how that ultimately influences our understanding of present-day mass loss partition, is definitely a rather nuanced topic. I am guessing there are not many non-scientists still reading at this point. Spread over the high elevation ice sheet interior, a 20 Gt/yr mass gain is equivalent to a thickening rate of just 2 cm/yr, which is within the uncertainty of virtually all mass balance observation methods, including in situ point measurements. I suppose the thrust of our study is to be receptive to the idea that millennial scale ice dynamics may be contributing to a subtle ice sheet thickening that underlies both past and present ice sheet mass balance, and to appreciate the non-trivial uncertainty in partitioning recent mass loss into surface balance and ice dynamic components that stems from the particular reference period mass balance assumption that is invoked.

¹Van den Broeke, M., J. Bamber, J. Ettema, E. Rignot, E. Schrama, W. van de Berg, E. van Meijgaard, I. Velicogna and B. Wouters. 2009. Partitioning Recent Greenland Mass Loss. Science. 326: 984-986.

²Colgan, W., J. Box, M. Andersen, X. Fettweis, B. Csatho, R. Fausto, D. van As and J. Wahr. 2015. Greenland high-elevation mass balance: inference and implication of reference period (1961-90) imbalance. Annals of Glaciology. 56: doi:10.3189/2015AoG70A967.

³Reeh, N. 1985. Was the Greenland ice sheet thinner in the late Wisconsinan than now?
Nature. 317: 797-799.

⁴Enderlin, E., I. Howat, S. Jeong, M. Noh, J. van Angelen and M. van den Broeke. 2014. An improved mass budget for the Greenland ice sheet. Geophysical Research Letters. 41: doi:10.1002/2013GL059010.

⁵Alison, I., W. Colgan, M. King and F. Paul. 2014. Ice Sheets, Glaciers, and Sea Level Rise. Snow and Ice-Related Hazards, Risks and Disasters. W. Haeberli and C. Whiteman. Elsevier. 713-747.