“We could be up to a month behind where we should be at this time of year”
Last October, when Juuta Sarpinak of Igloolik set off on a seal hunt, he took his snowmobile. For the same trip exactly a year later, he’d need a boat.
Across Nunavut and the rest of the Arctic, the same scenario is playing out.
“It’s the latest I’ve ever seen it freeze up in my lifetime,” said Willie Aglukkaq, who’s lived in Gjoa Haven for nearly 40 years.
As of Oct. 15, sea ice levels hit 5.118 million square kilometres, making them the lowest on record, which began in 1968.
“Depending on the area, we could be up to a month behind where we should be at this time of year,” said Gilles Langis, senior ice forecaster with the meteorological service of Canada.
But it’s not the first time this year ice levels have been at record lows.
In August, the ice loss slowed.
“We were tied for the second-lowest [amount of ice] with 2007 and 2016, but quite a bit above 2012,” said Walt Meier, a senior research scientist at the National Snow and Ice Data Center.
“But now we’re actually below 2012 levels for this time of year because it’s a slow freeze-up—2012 recovered pretty quickly, but we’ve been very sluggish in growing ice this year.”
With sea ice growth, the big driver is air temperature.
“If you have an area of open water and the temperatures above it are cooler than the water temperature, it’ll lose heat into the atmosphere and the water will start cooling off to the point where it reaches freezing,” said Langis.
But Arctic air temperatures through October have been unseasonably warm, much like the previous six months.
“It was a pretty extreme summer,” said Meier.
From April onward, every month has ranked in the top three warmest—in terms of Arctic air temperature—on record, with May and August now holding top spots.
According to Meier, because of this, there was an abundance of ice-free water throughout the summer that absorbed a lot of solar energy and warmed up quite a bit.
“That heat is just taking a while to dissipate into the atmosphere and for the ocean to cool enough to grow ice.”
What’s going on this year is representative of something larger.
“Under the influence of global heating caused by human-induced greenhouse gases emissions, we have seen a sharp decrease in the extent of Arctic sea [ice] since 1979,” says Pascal Peduzzi, Director of GRID-Geneva, in a press release published by the UN Environment Programme (UNEP).
Much like the scenario currently playing out across the Arctic this year, declining sea ice has amplified Arctic warming over the last several decades.
According to the press release, “Temperatures increased by around 0.5°C per decade between 1982 and 2017, primarily due to increased absorbed solar radiation accompanying sea ice loss since 1979. This is twice as fast as the global average.”
This season isn’t an exception.
But while the year-to-year trend continues on, ice coverage this year is on the rebound.
“It’s just finally starting to freeze,” said Aglukkaq.
Over the last 10 days, since Oct. 20, sea ice coverage has increased by almost 1.5 million square kilometres, including the water near Gjoa Haven.
If the current pace of ice growth continues, 2019 may soon once again be above 2012 levels.
The Amery Ice Shelf in Antarctica has just produced its biggest iceberg in more than 50 years.
The calved block covers 1,636 sq km in area – a little smaller than Scotland’s Isle of Skye – and is called D28.
The scale of the berg means it will have to be monitored and tracked because it could in future pose a hazard to shipping.
Not since the early 1960s has Amery calved a bigger iceberg. That was a whopping 9,000 sq km in area.
Amery is the third largest ice shelf in Antarctica, and is a key drainage channel for the east of the continent.
The shelf is essentially the floating extension of a number of glaciers that flow off the land into the sea. Losing bergs to the ocean is how these ice streams maintain equilibrium, balancing the input of snow upstream.
So, scientists knew this calving event was coming. What’s interesting is that much attention in the area had actually been focussed just to the east of the section that’s now broken away.
This is a segment of Amery that has affectionately become known as “Loose Tooth” because of its resemblance in satellite images to the dentition of a small child. Both ice areas had shared the same rift system.
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But although wobbly, Loose tooth is still attached. It’s D28 that’s been extracted.
“It is the molar compared to a baby tooth,” Prof Helen Fricker from the Scripps Institution of Oceanography told BBC News.
Prof Fricker had predicted back in 2002 that Loose Tooth would come off sometime between 2010 and 2015.
“I am excited to see this calving event after all these years. We knew it would happen eventually, but just to keep us all on our toes, it is not exactly where we expected it to be,” she said.
The Scripps researcher stressed that there was no link between this event and climate change. Satellite data since the 1990s has shown that Amery is roughly in balance with its surroundings, despite experiencing strong surface melt in summer.
“While there is much to be concerned about in Antarctica, there is no cause for alarm yet for this particular ice shelf,” Prof Fricker added.
The Australian Antarctic Division will however be watching Amery closely to see if it reacts at all. The division’s scientists have instrumentation in the region.
It’s possible the loss of such a big berg will change the stress geometry across the front of the ice shelf. This could influence the behaviour of cracks, and even the stability of Loose Tooth.
D28 is calculated to be about 210m thick and contains some 315 billion tonnes of ice.
The name comes from a classification system run by the US National Ice Center, which divides the Antarctic into quadrants.
The D quadrant covers the longitudes 90 degrees East to zero degrees, the Prime Meridian. This is roughly Amery to the Eastern Weddell Sea.
D28 is dwarfed by the mighty A68 berg, which broke away from the Larsen C Ice Shelf in 2017. It currently covers an area more than three times as big.
Nearshore currents and winds will carry D28 westwards. It’s likely to take several years for it to break apart and melt completely.
Imagine, if you will, the engineers of the king’s court after Humpty Dumpty’s disastrous fall. As panicked men apparently competed with horses for access to the site of the accident, perhaps the engineers were scoping out scenarios, looking for a better method of reassembling the poor fellow. But presumably none of those plans worked out, given the dark ending to that fairy tale.
A recent study published in Science Advances might be relatable for those fairy tale engineers. Published by Johannes Feldmann, Anders Levermann, and Matthias Mengel at the Potsdam Institute for Climate Impact Research, the study tackles a remarkable question: could we save vulnerable Antarctic glaciers with artificial snow?
Keeping our cool
Antarctica’s ice is divided into two separate ice sheets by a mountain range, with the smaller but much more vulnerable West Antarctic Ice Sheet representing one of the biggest wildcards for future sea level rise. In 2014, a study showed that two of the largest glaciers within that ice sheet—known as the Pine Island Glacier and Thwaites Glacier—had likely crossed a tipping point, guaranteeing a large amount of future ice loss that would continue even if global warming were halted today.
Much of the bedrock beneath the West Antarctic Ice Sheet is actually below sea level, though it’s buried below kilometers of solid ice. This makes for situations where the bed beneath the ice slopes down as you go inland from the coast. That’s inherently unstable, and once a glacier starts retreating downslope, the invading water provides an increasing floating force that reduces the sliding friction that slows the seaward flow of ice.
In the case of the Pine Island and Thwaites Glaciers, it seems that this is exactly what’s happening. Although this process can take centuries to fully play out, this portion of the ice sheet contains enough ice to raise global sea level by more than a meter.
Is there some extraordinary measure that could prevent that loss and preserve these glaciers? It’s the kind of question people will often ask, and scientists (who know the scale of these things) generally ignore as implausible.
But in this case, the researchers decided to go wild. Using a computer model of the ice sheet, they simulated the effects of adding huge amounts of ice near the front of these two glaciers. The idea works like this: Where a glacier meets the sea, it transitions from grounded to floating. Behind this “grounding line,” the glacier sits on the bedrock and sediment beneath; in front it gets thinner and floats as an ice shelf. To preserve the glacier, you need to keep that grounding line from retreating downhill. Thicken the ice on the inland side of the grounding line, and the thickness of ice flowing over the line and into the ice shelf increases—its weight keeps the grounding line pinned in place.
The researchers played around with different amounts of ice added to the glaciers for different periods of time, ranging from 10 year treatments to 50 years. Spreading it out over a longer period could mean a less preposterous addition of ice each year, but they found that the total amount has to increase if you do it that way. So in the end, the scenario they selected was 7,400 billion tons of ice added over 10 years. That was enough to restabilize these glaciers, preventing their inexorable decline.
Two for one special
To put that into context, removing that much seawater from the ocean would lower global sea level by about 2 millimeters per year. Current total sea level rise is a little over 3 millimeters per year, so it would be like nearly halting sea level rise… by bailing water out of the ocean. We can call that a bonus positive.
This analysis is more about what it would take than what such a scheme would look like, but the basic options are to pump water up and hose it around—hoping it freezes quickly—or to freeze it into snow like the world’s most awkwardly located ski resort.
Here, the researchers transition to listing all the reasons this is impractical and all the negative impacts it could have. For starters, the seawater would have to be desalinated since salt would probably affect the physics and behavior of the ice. Simply pumping that much water up the 640 meters and spreading it over an area nearly the size of West Virginia would require the power of something like 12,000 wind turbines—and that’s without the very substantial energy requirements for desalination and snow-making.
“The practical realization of elevating and distributing the ocean water would mean an unprecedented effort for humankind in one of the harshest environments of the planet,” the researchers write.
The impacts on Antarctic ecosystems could also be huge. Pumping that water out of the sea near the coast would significantly alter the circulation of water, which might even become somewhat self-defeating, as it could bring more warm water up against the ice shelf, increasing melt.
In the Potsdam Institute’s press release, Levermann puts it this way: “The apparent absurdity of the endeavour to let it snow in Antarctica to stop an ice instability reflects the breath-taking dimension of the sea-level problem. Yet as scientists we feel it is our duty to inform society about each and every potential option to counter the problems ahead.”
And to be clear, this is in addition to halting climate change—the scenario the numbers are based on assumes the temperatures don’t keep rising. But as the alternative is eventual inundation of parts of the world’s coastal cities, an argument can be made that the cost could be worth paying. It least it gives us an idea just how hard it would be to put Humpty Dumpty back together again.
A model that simulates magnets can also reproduce pools of water on Arctic sea ice from just one real-world measurement. Researchers in the US and UK adapted the Ising statistical model of phase transitions in ferromagnets to recreate melt-pond patterns. Characterizing the distribution of meltwater at small scales could improve climate models and predict ice loss better.
As climate changes, warming is expected to be especially rapid at high latitudes. In the Arctic, a lengthening melt season over the last few decades has already reduced the volume and extent of sea ice, with year-on-year ice-loss rates generally exceeding predictions.
One reason for the failure of models to predict this loss accurately might lie in how they account for melt ponds. The formation and growth of these ponds, which occurs at the transition between sea ice and open ocean, includes a positive feedback loop that makes the system especially sensitive.
“Pond evolution largely controls sea-ice albedo, a key parameter in climate modelling and one of the most important — and least understood — processes in determining the role of sea ice in the climate system,” says Kenneth Golden of the University of Utah, US.
As melt ponds form on the sea-ice surface, highly-reflective ice and snow are replaced by darker pools of water. The meltwater absorbs more solar radiation and warms up more than the ice that it replaces; the extra energy can trigger additional melting in its surroundings. When the melt pond penetrates the full thickness of the ice, warmer ocean water floods in from below, accelerating the process.
Existing descriptions of pond formation in global climate models consider the overall volume of meltwater but not its surface distribution. Yet, because the albedo change caused by melt ponds is a surface process, and because the rate at which ponds conduct heat to their surroundings depends on their perimeter, understanding the rules governing melt pond sizes is crucial for climate modelling.
The standard Ising model comprises a lattice of interacting particles, each of which is assigned a spin value that is either up or down. To capture the detailed geometry of melt ponds, Golden, with colleagues at Northumbria University, UK, the University of Dayton, US, and the University of Utah, US, created a version where the lattice represents the sea-ice surface, and each node a pixel of either ice or liquid water.
Starting with a random input configuration that does not resemble the real-world, each node interacts with its neighbours until the system settles on a local low-energy state. With a lattice spacing of 1 metre – the length scale over which Arctic ice exhibits significant topographic differences – the pattern that emerges from the energy-minimization process closely matches the melt-pond distribution seen in real life. For example, both real and modelled ponds scale in size according to the same power law, and both form more complex, fractal shapes when they grow larger than 100 sq. m.
Advertisement“The approach could ultimately lead to a framework for representing pattern formation occurring at spatial scales smaller than the grid spacing used in global climate models, which currently track meltwater volume without representing its spatial distribution,” says Golden.
Other parameters that describe ferromagnetic behaviour in the original Ising model also have real-world analogues in the version adapted for sea-ice. The global magnetic field, for example, which conventionally governs how likely particle spins are to align as up or down, now corresponds to solar energy input, making each lattice point more or less likely to be water or ice. The strength of coupling between neighbouring particle spins, meanwhile, now describes heat flow between water and ice in adjacent pixels.
Although Golden and colleagues ran their model with zero global field and an infinite coupling strength, changing these parameters after the initial process could perturb a realistic pond arrangement from its metastable state into an alternative low-energy configuration. In this way, the researchers might simulate how sea ice evolves as melt ponds respond to changing environmental conditions.
Golden and colleagues reported their findings in New Journal of Physics.
Edited by Isabel J. Nias, Goddard Space Flight Center, Greenbelt, MD, and accepted by Editorial Board Member Jean Jouzel June 11, 2019 (received for review March 20, 2019)
The potential for collapse of the Antarctic ice sheet remains the largest single source of uncertainty in projections of future sea-level rise. This uncertainty comes from an imperfect understanding of ice sheet processes and the internal variability of climate forcing of ice sheets. Using a mathematical technique from statistical physics and large ensembles of state-of-the-art ice sheet simulations, we show that collapse of ice sheets widens the range of possible scenarios for future sea-level rise. We also find that the collapse of marine ice sheets makes worst-case scenarios of rapid sea-level rise more likely in future projections.
Sea-level rise may accelerate significantly if marine ice sheets become unstable. If such instability occurs, there would be considerable uncertainty in future sea-level rise projections due to imperfectly modeled ice sheet processes and unpredictable climate variability. In this study, we use mathematical and computational approaches to identify the ice sheet processes that drive uncertainty in sea-level projections. Using stochastic perturbation theory from statistical physics as a tool, we show mathematically that the marine ice sheet instability greatly amplifies and skews uncertainty in sea-level projections with worst-case scenarios of rapid sea-level rise being more likely than best-case scenarios of slower sea-level rise. We also perform large ensemble simulations with a state-of-the-art ice sheet model of Thwaites Glacier, a marine-terminating glacier in West Antarctica that is thought to be unstable. These ensemble simulations indicate that the uncertainty solely related to internal climate variability can be a large fraction of the total ice loss expected from Thwaites Glacier. We conclude that internal climate variability alone can be responsible for significant uncertainty in projections of sea-level rise and that large ensembles are a necessary tool for quantifying the upper bounds of this uncertainty.
In marine ice sheets, the grounding line is a critical boundary where ice flowing from the ice sheet interior becomes thin enough to float in ocean water. The grounding line location and ice flux are sensitive functions of the depth of the surrounding ocean (1⇓–3). When the bedrock beneath the grounding line is reverse sloping (i.e., deepens toward the ice sheet interior), a small retreat of the grounding line onto deeper bed leads to greater ice flux and therefore more retreat. This positive flux feedback leads to the potential for rapid and irreversible retreat wherever the bed is reverse sloping, which has been termed the “marine ice sheet instability” (4). Rapid ice loss from the Antarctic ice sheet through this instability will likely drive sea-level rise beyond the next century (5, 6). However, projections of future sea-level rise are uncertain due to imperfect representation of ice sheet processes in models, unknown future anthropogenic emissions, and the internal variability of future climate forcing of ice sheets. Even with improvements in ice sheet models and climate projections, there will always remain a component of sea-level projection uncertainty that cannot be reduced due to the fundamentally unpredictable internal variability of the climate system which causes ice sheet change. This fundamental lower bound in the uncertainty of projections due to internal climate variability (for ice sheets and other elements of the climate system) has been termed “irreducible uncertainty” (7). The inevitability of uncertainty remaining in sea-level projections necessitates robust modeling of the ice sheet dynamical factors which produce uncertainty in future ice sheet projections, for which there is no existing theoretical framework. In particular, it is critically important to constrain the upper bounds of uncertainty in sea-level rise projections, which have a disproportionate influence on planning for coastal adaptation measures (8).
Ice sheets evolve in response to changes in climate variables (i.e., climate “forcing”), such as snowfall and ocean temperature. The amount and structure of uncertainty in projections of the future ice sheet contribution to sea-level rise can thus be determined through large ensembles of ice sheet model simulations, which are plausible realizations of the future evolution of an ice sheet in response to climate forcing (see Fig. 1, Upper for a conceptual illustration of an ensemble). Each ensemble member is distinguished by selecting either a unique set of model parameters or one realization of future variable climate forcing from a distribution of possibilities. At a particular point in time, the statistical properties of the full ensemble represent the probability distribution of ice sheet state, represented by a variable such as extent or volume (conditioned on the probability of the model parameters or climate variability having particular values). The spread (or standard deviation [SD]) of the probability distribution quantifies the amount of uncertainty in the projection. In a probability distribution that is symmetric, the skewness is 0, and the projected change in ice sheet volume is equally likely to fall above or below the mostly likely projection (Fig. 1, Lower Left). A negative skewness of the probability distribution indicates that the probability of ice sheet volume turning out to be below the most likely projection is greater than that of ice sheet volume turning out to be above the most likely projection (and vice versa for positive skewness). Put another way, a negative skewness indicates that the probability of worst-case scenarios (i.e., more ice sheet mass loss and corresponding sea-level rise than is expected from the highest-likelihood projection) is greater than the probability of best-case scenarios (of less sea-level rise than the highest-likelihood projection).
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In this study, we develop a framework for determining how marine ice sheet processes produce uncertainty in projections of future sea level. We do so using 2 complementary approaches: 1) Stochastic perturbation analysis of a simple model of marine ice sheet evolution with one evolving quantity and 2) statistical analysis of a large number of simulations of the future evolution of a West Antarctic glacier using a state-of-the-art numerical ice sheet model with many thousands of evolving quantities. These 2 approaches represent end members of the hierarchy of modern ice sheet models. They provide both a theoretical framework for understanding the sources of uncertainty in projections of the future ice sheet contribution to sea level and an application of this framework to an actual glacier that is thought to be undergoing the marine ice sheet instability.
Stochastic Perturbation Theory
Over the past several decades, much of the observed increase in Antarctic ice loss has been caused by ocean-driven ice sheet melting (9). Our goal in this study is thus to quantify the uncertainty in projected ice sheet state that is caused by uncertainty in ocean-induced ice sheet melt, although the principles involved are extendable to uncertainty in other climate forcing (or uncertainty in glaciological parameters). We start by mathematically and numerically analyzing the uncertainty in ice sheet state simulated by a minimal model of grounding-line migration for a glacier under climate forcing (10, 11)
where L is the distance of the grounding line from the glacier onset, and is the thickness of ice at the grounding line, which depends on the ratio of seawater () and ice () densities and the local bedrock depth (). This model, which is derived and discussed in more detail in Robel et al. (11), tracks the total mass balance of the glacier, captured in 3 processes. The first term captures ice entering as snowfall over the glacier surface at accumulation rate P (averaged through glacier geometry: L and ). The second term captures ice leaving the glacier due to ice flow through the grounding line (). The third term captures ocean-induced melt at the grounding line (η). The parameters β and γ are related to the balance of glaciological processes which contribute to setting the velocity of ice at the grounding line (e.g., gravitational driving stress, basal sliding, and ice shelf buttressing). Observations (12), mathematical analyses (1⇓–3, 13), and numerical simulations (11, 14, 15) have all shown that grounding-line velocity is generally a nonlinear function of grounding-line ice thickness (as we assume in Eq. 1), even during periods of transient grounding-line migration, although there is perhaps some variation in the exact value of β that applies in such a situation. Still, this minimal model is meant as a tool to understand the processes which drive uncertainty in simulations of marine ice sheet instability, not a means for making actual predictions of ice sheet change. As we show later on, the conclusions drawn from this minimal model are reproduced in a state-of-the-art ice sheet model which does not make the same simplifying assumptions.
In Eq. 1, the rate at which the grounding line migrates in response to ocean-induced melting (or freezing) is , consisting of a time-averaged component () and a time-variable component (). The time-averaged ocean forcing may be uncertain and so is drawn from a Gaussian distribution with SD . The time-variable ocean forcing is a first-order autoregressive Gaussian noise process with interannual SD , and decorrelation timescale . Other studies have shown using a complex spatially resolved model that ocean-induced grounding-line variability is filtered through the frequency-dependent response of the ice shelf to ocean forcing (16). In this minimal model, we assume a simpler form for η in which all ocean-induced grounding-line migration is the result of melting directly at the grounding line and neglects effects from sub-ice shelf melt and buttressing. While this assumption will likely produce some quantitative difference than that of a model which includes sub-ice shelf melt beyond the grounding line, the more complicated ice-shelf–resolving simulations in the next section show that the qualitative aspects of our mathematical analysis do not appear to be changed by such detailed considerations.
Fig. 2 shows ensembles (with 10,000 simulations each) of simulated grounding-line migration over a bed of constant slope, calculated using Eq. 1 (details in Materials and Methods). The only forcing during the simulation period shown is ocean-induced grounding-line migration (η). The ensemble spread (represented in Fig. 2 by the interquartile range) captures the uncertainty in projected grounding-line position due to uncertainty in ocean forcing. On a forward-sloping bed (green shading/lines), small interannual forcing in the grounding-line position ( m/y, ) produces an ensemble spread that remains small, bounded, and symmetric. For the same stochastic forcing on a reverse-sloping bed (orange shading/lines), all ensemble members retreat, as the ensemble spread grows rapidly without bound and becomes skewed (negatively) toward more retreat.
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The growth in ensemble spread (i.e., uncertainty) occurs because the marine ice sheet instability amplifies (rather than damps) small perturbations from stochastic ocean forcing. These growing perturbations accumulate over time, leading to a divergence between ensemble members, which each experience a different series of perturbations from ocean forcing. The skewness of the ensemble can be understood physically and from an analysis of Eq. 1. For a retreating ice sheet, the rate of retreat is set by the difference between two fluxes: The accumulation flux and the grounding-line flux. If the grounding-line flux is more sensitive to the position of the grounding line than the accumulation (which it is for sufficiently nonlinear grounding-line flux), the net effect will be that the rate of retreat of more-retreated ensemble members will be greater than the rate of retreat of the less-retreated ensemble members. The result is that the retreat of the ensemble becomes progressively more negatively skewed with time. In ensembles where all simulations are advancing, the most advanced ensemble members accelerate faster, producing a positive skew.
Observations indicate that climate forcing of glaciers in Antarctica (and elsewhere) exhibits strong variability on decadal timescales (17, 18). In our minimal model, when stochastic forcing has decadal persistence, the ensemble spread and skewness grow considerably faster (blue shading/lines in Fig. 2). Such an amplified glacier response to temporal persistence in forcing agrees with previous model studies of mountain glaciers (19) and periodically forced ice streams (16, 20, 21).
For temporal ocean variability, stochastic perturbation theory (22) (SI Appendix) provides a theoretical framework for determining the physical processes which control the amplification and skewing of uncertainty in ice sheet projections. Analytic approximations for the spread and skewness of ensembles derived from stochastic perturbation theory (circles in Fig. 2 B and C) match well with numerically calculated ensemble statistics. This theoretical framework shows that ensemble spread grows exponentially with a rate that is proportional to the bed slope and the nonlinearity in grounding-line ice flux (β in Eq. 1). Thus, when the bed is forward sloping (negative), the ensemble spread remains bounded. When the bed is reverse sloping (positive), the marine ice sheet instability causes the ensemble spread to grow exponentially without bound. The ensemble variance is also proportional to the decorrelation timescale of the forcing, implying greater uncertainty in projections when climate forcing is persistent on longer timescales.
As alluded to above, the skewness of the ensemble is caused by the changing rate of grounding-line migration over a reverse-sloping bed. It can be shown analytically (see SI Appendix for details) that when the grounding-line ice flux is sufficiently nonlinear with respect to ice thickness ( in Eq. 1), then ensembles of a retreating grounding line will tend to be skewed toward more retreat. Conversely, when grounding-line ice flux is linear or weakly nonlinear (), then ensembles will tend to be skewed toward less retreat. In a wide range of realistic settings, we expect ensembles to skew toward more retreat during the retreating phase of the marine ice sheet instability because of the high-degree nonlinearity of grounding-line ice flux ( in ref. 1, in ref. 2, in ref. 3). In other words, the fact that the probability distribution is skewed in the direction of more sea-level rise is a fundamental consequence of the strong nonlinearity inherent in grounding-line dynamics.
Uncertainty in the time-averaged ocean forcing (; pink shading/lines in Fig. 2) produces even more ensemble spread (for relatively less uncertainty, m/y) and further indicates the importance of the marine ice sheet instability for amplifying and skewing uncertainty in ice sheet projections. Uncertainty in the time-averaged climate forcing can be thought of as a limiting case of the response to an initial impulse with an infinite decorrelation time (). However, for such a nonstochastic case, there is no formal limit from stochastic perturbation theory in which the ensemble spread can be predicted.
Large Ensembles of Thwaites Glacier Instability.
To demonstrate that the intuition gained from the theoretical framework developed in the previous section applies to realistic glacier models, we simulate ensembles of the future retreat of Thwaites Glacier in West Antarctica using the Ice Sheet System Model (ISSM), a state-of-the-art finite-element model of ice sheet flow (23). Thwaites Glacier rests on a reverse-sloping bed and is currently retreating rapidly, which is argued to be the result of the marine ice sheet instability (24, 25). In ISSM, as in other models, ocean-induced ice sheet melting is parameterized with a depth-dependent melt rate, with maximum melt rate, , prescribed at some depth (25). We treat as a first-order autoregressive noise process that varies monthly with a prescribed decorrelation timescale (), a mean of 80 m/y, no long-term trend, and no variation in space. Many observations and models indicate that subice shelf melt rates at glaciers in the Amundsen Sea, and elsewhere in Antarctica, exhibit strong variability on decadal (and longer) timescales (17, 26, 27). A short run of a regional ocean model simulation for the Amundsen Sea region (SI Appendix) produces variability in with interannual SD of 1.4 m/y. This estimate of variability is likely an underestimate since the ocean simulation was run for only 15 y (the time period over which reanalysis forcing is available) and did not include coupled ocean–atmosphere feedbacks. Thus, for our baseline ensemble of Thwaites Glacier, our conservative estimate for the statistics of ocean-induced melt variability is y and m/y. In reality, we also expect that varies in space, due to (for example) the Coriolis effect on ocean circulation in the subshelf cavity, which would quantitatively (but not necessarily qualitatively) affect our results.
Fig. 3A shows the evolution of the probability distribution of a 500-member ensemble of ISSM-simulated ice volume at Thwaites Glacier in response to decadal variability in subice shelf melt rate. All ensemble members initialized with the modern state of Thwaites Glacier eventually reach complete deglaciation (Fig. 3B), in agreement with previous studies (24, 25). The rate of grounding-line migration (Fig. 3C) experiences significant variability over the course of the retreat due to the stochastic ocean forcing and the presence of forward-sloping “speed bumps” in the bed topography, both of which can slow the rate of retreat or even cause advance for short durations (28). Even with the relatively conservative assumption that there is no variability in surface mass balance and a small amplitude of subshelf melt variability (representing of the time-averaged subshelf melt), the spread in the ensemble spans ∼20 cm of uncertainty in projected sea-level rise during periods of fast retreat (i.e., the green probability distribution functions [PDFs] in Fig. 3A), with a probability distribution skewed in the direction of lower ice volume (greater contribution to sea level). This uncertainty is over 25% of the entire sea-level rise due to deglaciation of Thwaites Glacier and 50% of the median sea-level rise achieved during those periods of fast retreat. This spread between simulations amounts to instantaneous differences of hundreds of kilometers in the grounding-line position (Fig. 3D). Following this growth of uncertainty during the centuries of most rapid retreat, the ensemble then contracts and skews in the opposite direction as individual ensemble members achieve complete deglaciation of Thwaites Glacier, due to the limited model domain used in our simulations. In simulations of the entire Antarctic Ice Sheet in which the marine ice sheet instability spreads to other glaciers (5, 6), we would expect even faster amplification of uncertainty as multiple glaciers become involved in deglaciation.
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In Fig. 4, we compare Thwaites Glacier ensemble statistics, given a comparable amplitude ( m/y) of variability in , but differing degrees of temporal persistence. As predicted by theory, ensemble spread (Fig. 4A) increases with longer persistence in forcing variability (proportional to ; SI Appendix). During the century of fastest retreat, multidecadal ocean variability (yellow line; y) produces skewed uncertainty that is nearly 50% of the total ice loss from Thwaites glacier or ∼40 cm of uncertainty in projected sea-level rise. Some studies have suggested that Antarctic glaciers may be subject to such multidecadal variability in forcing through low-frequency coupled modes of the ocean–atmosphere system (26) or sporadic detachment of very large tabular icebergs (29).
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Poorly constrained subice shelf properties [such as roughness (30)] and the small scale of the turbulent ice–ocean boundary layer make it difficult to accurately simulate even the time-averaged subice shelf melt rate given some change in global climate. Consequently, we also consider uncertainty in the time-averaged subshelf basal melt rate (which may also result from uncertainties in future anthropogenic emissions) by keeping constant in time, but varying it between ensemble members (drawing from a Gaussian distribution with SD of 5 m/y). As in the minimal model, this ensemble (purple line in Fig. 4) has a very strong amplification of skewed uncertainty due to the accumulation of differences in subshelf basal melt rate among ensemble members over the course of the instability. For several centuries, the spread in this ensemble amounts to nearly the entire signal of ice loss from Thwaites Glacier (i.e., some ensemble members have retreated completely while others have lost almost no ice at all), skewed in the direction of more ice loss throughout most of the early period of the simulation.
Discussion and Conclusions
Studies of the future evolution of the Antarctic Ice Sheet have estimated the uncertainty in future sea-level rise due to poorly constrained model parameters (5, 6, 31⇓⇓–34). Other studies (35) have investigated the role of internal climate variability in the Greenland Ice Sheet contribution to sea-level rise, but with simulations that were too short to capture much of the marine ice sheet instability that may occur in the future. No study has provided a theoretical framework explaining the role of ice sheet dynamics in setting the amount and structure of uncertainty in sea-level rise projections. We provide such a theoretical framework in this study and find that ice sheet instabilities are amplifiers of uncertainty, which is a common mathematical property of unstable nonlinear systems (22). Although there are processes not considered here that might stabilize (36) or further destabilize (6) an ice sheet, our analysis shows that we should expect more rapid instability (of any kind) to cause more rapid uncertainty growth. Indeed, the theoretical framework developed in this study applies to a sufficiently broad set of assumptions regarding ice sheet dynamics, such that we expect that any type of ice sheet instability, regardless of the processes involved, will experience rapid growth in the ice sheet projection uncertainty during periods of most rapid instability. Integrating the contribution of marine ice sheet instability over many glaciers also integrates the uncertainty of each glacier’s future evolution, potentially leading to considerable uncertainty in sea-level projections, as has been seen in ensemble studies of total ice sheet contribution to future sea-level rise (5, 6, 32, 34, 35). We have shown that model ensembles can be used to quantify a range of possible scenarios for future sea-level rise, including potentially catastrophic scenarios of rapid sea-level rise. However, large model ensembles can be prohibitively expensive when extended to the entire Antarctic Ice Sheet. To fully capture the complete range of possible Antarctic futures, we will need efficient methods for uncertainty quantification (32, 37) and model order reduction that captures the complexities of ice sheet dynamics (31, 34). Such sophisticated methods will ensure that we can make the most useful sea-level projections beyond 2100 for those stakeholders who depend on them.