Sea Level Rise: Thermal Expansion, Ice Melt and the Coastline of 2100

Two numbers add up to one curve

Global mean sea level is a budget, not a single mechanism. Since the 1970s roughly 40% of the observed rise comes from thermal expansion of seawater, and the remainder from melting land ice: mountain glaciers, the Greenland ice sheet and the Antarctic ice sheet, with a smaller and more variable contribution from changes in how much water is stored on land in reservoirs, aquifers and soil moisture. Every credible sea level projection is a sum of these terms tracked separately, because each one responds to warming on a different timescale.

Between 1901 and 2018 global mean sea level rose by around 20 centimetres, and the rate has roughly tripled since the early twentieth century, from about 1.4 millimetres a year to more than 4 millimetres a year today. That acceleration, not the absolute number, is the part that worries planners: the same emissions path produces a slow, almost linear rise this century and a much faster one next century as ice sheets catch up with the warming already committed.

Thermal expansion: warm water takes more room

Water, like almost everything else, expands when it warms. The effect is called steric sea level rise, and it is not a fixed percentage — the thermal expansion coefficient of seawater itself grows with temperature and pressure, so a degree of warming in the tropics raises sea level more than the same degree of warming near the poles. Because the ocean is enormous and a poor conductor of heat, most of this warming enters through the surface and diffuses downward over decades, which means the steric contribution keeps climbing for a long time after the atmosphere itself stops warming.

steric rise  =  integral over ocean depth of  alpha(T, S, p) * dT(z) * dz

  alpha(T, S, p)  thermal expansion coefficient (rises with T)
  dT(z)           temperature change at depth z
  ocean heat content change measured by Argo float network (2000-present)

Ice melt: glaciers now, ice sheets later

Mountain glaciers are small and thin, so they respond to warming within years to decades, and most of the world's roughly 200,000 glaciers are now losing mass every year. The two ice sheets behave very differently. Greenland loses mass mainly through surface melt running off into the ocean, a process that is fast and directly tied to summer temperature. Antarctica loses mass mostly through ice discharge at its edges, where floating ice shelves buttress the ice sheet behind them; when a shelf thins or collapses, the glaciers it was holding back can accelerate sharply. This is why Antarctica dominates the uncertainty range in long-term projections — its response depends on structural failure of ice, which is far harder to model than simple melting.

Why local sea level is not global sea level

A melting ice sheet does not raise sea level evenly around the planet. Ice has mass and therefore gravity, and a large ice sheet pulls the surrounding ocean toward itself; as it shrinks, that pull weakens and sea level actually falls within roughly 2,000 kilometres of the ice sheet while rising more than average everywhere else. Add land subsidence from groundwater extraction, ongoing glacial isostatic adjustment left over from the last ice age, and shifts in ocean currents that pile water against particular coastlines, and you get local sea level trends that can be double the global average in one city and near zero a thousand kilometres away.

Turning a number into a flood map

The simplest way to visualise impact is a bathtub model: take a digital elevation model of the coast, pick a target sea level, and flood every cell below that elevation that is hydraulically connected to the open ocean — a flood-fill, not just a threshold, because a low-lying valley cut off by a ridge should stay dry. More sophisticated coastal models replace the static flood-fill with the shallow-water equations, adding storm surge, tides and wave run-up so the map shows not just where water could reach but how fast and how often it actually will.

queue = [ every coastal cell touching open ocean ]
while queue is not empty:
    cell = queue.pop()
    for neighbour in cell.neighbours:
        if neighbour.elevation < targetSeaLevel and not neighbour.flooded:
            neighbour.flooded = true
            queue.push(neighbour)

Frequently asked questions

Try it live

Everything above runs in your browser — open Sea Level Rise Simulation and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.