Why does the glacier keep shrinking after I cut emissions to zero?

Because it was never in balance with the climate it already had. The Jóhannesson response time — ice thickness at the terminus divided by the melt rate there — is decades to a century for a valley glacier. Stopping the warming stops the *change* in the target; the glacier still has to walk all the way to it.

What is the equilibrium line altitude?

The elevation where a year of snowfall exactly equals a year of melt. Above it the glacier gains mass, below it it loses. Warming lifts the ELA by roughly 100–150 m per degree, and a glacier whose whole surface ends up below the ELA has no accumulation area left and is simply finished.

Why is the sea-level band so wide after 2100?

Because the ice sheets are the dominant uncertainty and they are not well constrained. The band here is three parameter draws — a deliberately crude stand-in for a real ensemble, and it is narrower than the genuine uncertainty.

Ice & Coast — Four centuries in one sitting: a glacier, and the coast it drowns.

You are the glaciologist / coastal planner. Drag an emissions pathway and watch what it does at two very different speeds: a valley glacier that answers within decades, and a sea level that keeps rising for centuries after the forcing stops. Then defend a coastal city with a budget, a seawall and a discount rate, and find out what "committed" means.

Timescale: 1900–2300. Model: Two-box energy balance + shallow-ice flowline glacier + component sea-level budget + extreme-value coastal flooding

What you will learn

Why a glacier keeps retreating for decades after the climate stops changing — its response time.
Why a tidewater glacier on a bed that deepens inland cannot stop once it starts.
Why sea level keeps rising for centuries after emissions reach zero.
Why a seawall built for the sea level of its own decade is a seawall built too low.

Scenarios

Sandbox — 1900 to 2300, every control unlocked.
Alpine 2100 — Can this glacier be saved? Keep a fifth of its 1900 ice to 2100.
Tidewater Collapse — A glacier grounded below sea level on a bed that deepens inland.
The Delta City — Defend a city to 2150 on a $9 billion budget.
Stop Now — Emissions go to zero in 2040. Watch what does not stop.

What you control

Carbon emissions (GtC/yr) — The one control that matters most. Negative values are net removal — and the curve is drawn through your points, so the pathway is smooth.
Climate sensitivity (K per doubling) — Equilibrium warming for a doubling of CO₂. The single largest source of spread between climate models.
Ocean heat uptake (W/m²/K) — How fast the deep ocean takes up heat. High uptake delays the warming and lengthens the commitment.
Aerosol forcing (W/m²) — Present-day cooling from sulphate pollution. It disappears within a decade of cleaning up the air.
Glacier setting — The shape of the bed decides how the glacier can fail.
Equilibrium line, 1900 (m) — Where snowfall balanced melt at the start. Everything below it loses ice every year — and it has to match the setting you chose.
ELA sensitivity (m/K) — How far the equilibrium line climbs per degree of warming. Roughly the lapse rate, 6.5 °C/km, inverted.
Mass-balance gradient (m/yr per 100 m) — How quickly melt increases with depth below the equilibrium line. Maritime glaciers are steep, continental ones gentle.
Precipitation change (%/K) — Warmer air holds more water. More snow high up partly offsets a rising equilibrium line — partly.
Bed wetness — Meltwater at the bed lets the glacier slide instead of deform. Sliding moves ice to low elevations faster, where it melts.

Questions

Why does the glacier keep shrinking after I cut emissions to zero?: Because it was never in balance with the climate it already had. The Jóhannesson response time — ice thickness at the terminus divided by the melt rate there — is decades to a century for a valley glacier. Stopping the warming stops the *change* in the target; the glacier still has to walk all the way to it.
What is the equilibrium line altitude?: The elevation where a year of snowfall exactly equals a year of melt. Above it the glacier gains mass, below it it loses. Warming lifts the ELA by roughly 100–150 m per degree, and a glacier whose whole surface ends up below the ELA has no accumulation area left and is simply finished.
Why is the sea-level band so wide after 2100?: Because the ice sheets are the dominant uncertainty and they are not well constrained. The band here is three parameter draws — a deliberately crude stand-in for a real ensemble, and it is narrower than the genuine uncertainty.

What this model cannot do

A flowline, not a glacier. Real ice flows in three dimensions, and valley-wall drag alone changes the answer by tens of percent.
The mass balance is a function of altitude only: no debris cover, no avalanche input, no shading, no separate summer and winter balance.
Sea-level components are fitted curves, not ice-sheet models. The Antarctic term in particular stands in for a process — marine ice-sheet instability — whose real timing nobody can currently predict.
The uncertainty band is three parameter draws, not an ensemble. It is much narrower than the real uncertainty, especially after 2100.
The carbon cycle is one reservoir with a saturating sink. It has no permafrost feedback, no vegetation, and no ocean chemistry.
The coastal city is a one-dimensional elevation profile. Real flooding depends on drainage, defences failing in the wrong place, and where people actually are.
None of this is a projection for any real glacier, coastline or city.

Sources

Cuffey, K. M. & Paterson, W. S. B. (2010), The Physics of Glaciers — the flowline model and Glen’s law
Jóhannesson, T., Raymond, C. & Waddington, E. (1989), Time-scale for adjustment of glaciers to changes in mass balance — the response time reported on the panel
Oerlemans, J. (2001), Glaciers and Climate Change
Geoffroy, O. et al. (2013), Transient climate response in a two-layer energy-balance model — the two-box model and its parameters
Schoof, C. (2007), Ice sheet grounding line dynamics — why a retrograde bed has no stable grounding line
IPCC AR6 WGI Chapter 9 (2021), Ocean, cryosphere and sea level change — the component budget this is a caricature of
Vialov, S. S. (1958), Regularities of glacial shields movement — the analytic profile the tests check against