Climate Change: The Exponential Curve of Sea Level Rise


Climate change is all about water. Water plays a key role from microscopic to local to global perspectives. Hydrogen bonding. Freezing point. Heat of vaporization. Surface tension. Viscosity. Cohesion … Atmospheric rivers. Hurricanes and cyclones. Ocean currents. The hydrological cycle. Monsoons. Storms. Floods. Deluge. Drought…

Water is either there; or ostensibly not there. Either way, it is a key player.

Greenland meltwater burrow-moulin

surface melt of Greenland ice sheet

One of the key effects that water plays in climate change and global warming is in the melting of the ice caps and the expansion of warming oceans; both of which are raising sea levels. This is unarguably already happening. What remains arguable is how fast. According to imminent climatologists and glaciologists, this is because, while most agree that it is, in fact, accelerating; the slope of the predictive curve is difficult to pin down because “the current rate of carbon emissions is unprecedented … the most extreme global warming event of the past 66 million years” according to geologist Peter Stassen at the University of Leuven in Belgium.

Most of us can understand linear change; change based on a steady, logical path easily visualized through a constant ratio. We also understand abrupt changes, calamities and storms that hit with sudden intensity: the 100-year flood calculated by hydrologists, for instance. However, we seem unable to comprehend change that occurs exponentially: starting out with a low slope (called a lag period) that steepens over time. “People want to believe that the flat part of the curve in the early phase of change is really linear, not the start of an exponential curve,” write landscape architects Kristina Hill and Jonathan Barnett in Harvard Design Magazine. “And when the big changes occur later on, we often treat them as “sudden” disasters when, in reality, they were quite predictable.”

logistic curve

Logistic (s-shaped) Curve

Many phenomena in Nature, such as populations, experience an exponential phase (J-shaped curve) in growth; but the growth is usually limited by resources and morphs into logistic growth (S-shaped curve) that tapers as the carrying capacity of the resource is reached. Climate doesn’t behave in this way. The process itself may have self-limiting aspects through various negative feedbacks; however, the negative feedbacks may themselves pose violent environmental reaction (e.g. storms). They may even trigger positive feedbacks.

SLR exponential curve“No matter what happens in the world of politics, sea levels are going to rise faster in our lifetimes than they have since before the first cities were built,” write Hill and Barnett.

Most scientists agree with NASA researcher and climatologist James Hansen who proposed that the ice sheet disintegration follows an exponential trajectory and massive acceleration of losses will cause sea levels to rise by at least 1 meter and likely 5 metres (or more) in the next 100 years. This is supported by the World Bank in a recent report that predicts, along with most scientists, that if no significant policy changes are undertaken, the planet will warm by 4-degrees Celcius by the end of the century with the following consequences:

  • inundation of coastal cities
  • increasing risk for food production, leading to malnutrition (dry areas becoming dryer and wet regions wetter)
  • unprecedented heat waves (leading to heat-related mortality, forest fires, harvest losses and biodiversity loss and extinction)
  • increased water scarcity
  • increased frequency and intensity of tropical cyclones
  • irreversible loss of biodiversity, including coral reef systems (with acidification of oceans)

In his article in Fairfax Climate Watch (2013) Matt Owens explained that negative feedbacks would be a mixed bag of “on the one hand slowing sea level rise (at least for a while), and on the other hand, leading to larger, more violent storms, and other climate problems like extreme drought.” This is the very rollercoaster unpredictability of the complex system dynamic that climate modelers and system ecologists must grapple with.


melting ice in the Arctic

Hansen’s most recent paper, published in Atmospheric Chemistry and Physics, references past climatic conditions, recent observations and future models to warn that the melting of the Antarctic and Greenland ice sheets will contribute to a far worse sea level increase than previously thought, writes Oliver Milman in the Guardian. Large scale and disruptive changes–tipping points–are generally not included in models. One example is the collapse of an ice sheet. Without a sharp reduction in greenhouse gas emissions, the global sea level is likely to increase “several meters over a timescale of 50 to 150 years”, warns Hansen.

Hansen’s paper demonstrated that the Earth’s oceans were six to nine meters higher during the Eemian period – an interglacial phase about 120,000 years ago that was less than 1C warmer than it is today.

According to Owens, ocean circulation patterns are big unknowns and could be the largest component of how fast any ice flows melt. “It is even conceivable,” says Owens, “that circulation patterns could shift in such a way to bring warmer water to the Antarctic ice sheets than before. In such a case, positive feedbacks could overwhelm the negative ones on longer timescales,” and trigger tipping points of large scale disruption.

Mixing is a form of mostly vertical circulation in the oceans, and it could become severe, with sudden large-scale upwelling (pulling up of deeper ocean waters). In fact, there is evidence of massive upwellings during some Heinrich events (widespread rafting of ice fragments that migrate as far as the equator; Julian Sachs, 2005). This enhanced mixing could bring warmer waters to the surface and melt more ice, and/or bring warmer waters to the bottom of the ocean, and trigger methane releases from clathrates.

Methane & The Clathrate Gun Hypothesis 

Because methane is present in much smaller concentrations it is not currently deemed as important as carbon dioxide in the climate change equation; however, it poses hidden danger. Methane is twenty times more efficient in trapping heat than carbon dioxide. Permafrost—which is currently melting rapidly in the north—contains almost twice as much carbon as is currently in the atmosphere. In the rapidly warming Arctic (warming twice as fast as the globe as a whole), the upper layers of this frozen soil are thawing, allowing deposited organic material to decompose and release methane.

ice bubbles in lake

frozen bubbles of methane gas in a northern Canadian lake

The clathrate gun hypothesis is the notion that sea temperature rises (and/or drops in sea levels) may trigger a catastrophic positive feedback on climate:  warming would cause a sudden release of methane from methane clathrate (hydrate) compounds buried in seabeds, in the permafrost, and under ice sheets.

Creation of gas hydrates requires high pressure; water; gas—mainly methane—and low temperatures. Three environments considered suitable for this process to occur include: sub-seabed along the world’s continental margins; permafrost areas on land and off shore; and now a third process for storing methane hydrates: ice sheets. As long as the climate is cold and the ice sheet stable, the gas hydrate zone remains stable. As the ice sheets melt, the pressure on the ground decreases; hydrates would destabilize and release methane into rising seawater and finally into the atmosphere.

clathrate methane

A recent study in Science revealed that hundreds of massive, kilometer-wide craters on the ocean floor in the Arctic were formed by substantial methane expulsions. Because methane is a powerful greenhouse gas, temperatures would rise exponentially. Once started, this runaway process could be as irreversible as the firing of a gun—and on a time scale less than a human lifetime.

The sudden release of large amounts of natural warming gas from methane clathrate deposits in runaway climate change could be a cause of past, future, and present climate changes.

Latest research on the Greenland ice sheet and elsewhere throughout the Arctic has revealed major methane discharges in Arctic lakes in areas of permafrost thaw. Scientists are exploring areas where methane is bubbling to the surface and releasing to the atmosphere.

Melting permafrost is a quiet sleeper in the climate change procession. The effects that the thaw exerts is masked to the casual observer by the pristine natural setting that hides the perturbations roiling beneath. At the microscopic level, in the chemistry of the water and in the change in the atmosphere, a time bomb is ticking.


If human emissions continue at their current rate, rapidly changing ocean currents and retreating ice sheets may uncork methane from under ice caps, ocean sediments and Arctic permafrost, causing a jump in radiative forcing. Even if rapid ice sheet disintegration were to scatter large amounts of ice into the oceans, the net cooling effect would be strongly countered and likely overwhelmed. The areas that did cool would likely trigger severe weather outbreaks.

As I write, we are pumping out CO2 into the atmosphere at a rate 10 times faster than at any point in the past 66 m years, with the resulting sea level rises, extreme weather events, heat waves, droughts, unseasonal storms, and stress on biodiversity around the globe.  Research published in the journal Nature Geoscience demonstrates that “the world has entered ‘uncharted territory’ and that the consequences for life on land and in the oceans may be more severe than at any time since the extinction of the dinosaurs,” writes Damian Carrington of The Guardian.

In an interview with Guardian reporter John Abraham, Woods Hole expert Robert Max Holmes, exhorted:

It’s essential that policymakers begin to seriously consider the possibility of a substantial permafrost carbon feedback to global warming. If they don’t, I suspect that down the road we’ll all be looking at the 2°C threshold in our rear-view mirror.


Coast of Nova Scotia near Kingsburg (photo by Nina Munteanu)



Hansen, James and Sato, Makiko; Update of Greenland ice sheet mass loss: Exponential?; (26 December 2012).

Sachs, Julian and Anderson, Robert; Increased productivity in the subantarctic ocean during Heinrich events; Nature 434, 1118-1121;(28 April 2005).

Adams, J., M.A. Maslin and E. Thomas Sudden climate transitions during the Quaternary; Progress in Physical Geography, 23, 1, 1-36 (1999)

Sojtaric, Maja. Ice Sheets May be Hiding Vast Reservoirs of Powerful Greenhouse Gas. CAGE, (2016)

Portnov et al. Ice-sheet-driven methane storage and release in the Arctic. Nature Communications 7 (2016)

Andreassen el al., “Massive blow-out craters formed by hydrate-controlled methane expulsion from the Arctic seafloor,”Science(2017). … 1126/science.aal4500
Carrington, Damian. 2016. “Carbon emission release rate ‘unprecedented’ in past 66 m years.” The Guardian, March 21, 2016.


nina-2014aaaNina Munteanu is an ecologist, limnologist and internationally published author of award-nominated speculative novels, short stories and non-fiction. She is co-editor of Europa SF and currently teaches writing courses at George Brown College and the University of Toronto. Visit for the latest on her books. 

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