What is GIA?

Glacial isostatic adjustment (GIA) is the response of the solid Earth — together with its gravity field, its oceans and even its rotation axis — to the redistribution of mass at its surface as ice, liquid water and sediments come and go. When an ice sheet grows, its weight pushes the ground down; when it melts, the ground slowly springs back up. The magnitude and, crucially, the time scale of this response depend both on the load that is applied and on the properties of the solid Earth: the mantle viscosity, the lithosphere thickness and their respective densities. These parameters vary with depth (radially) and, in many regions, also from place to place (laterally) (Wiens et al. (2022); Ivins et al. (2022)).

If you are new to the field and want a thorough but still accessible overview, the review by Whitehouse et al. (2019) is an excellent starting point; the sections below distil the ideas most relevant to using this package.

The load: what drives GIA

The "load" is simply the weight sitting on top of the solid Earth, and any change in it drives GIA. In a glacial context the dominant terms are:

Ice: kilometre-thick ice sheets impose enormous stresses on the ground. A 1 km column of ice weighs roughly as much as a 300 m column of rock.
Liquid water: as ice melts, meltwater is redistributed across the global ocean, loading the sea floor and unloading the formerly glaciated regions.
Sediments: erosion and deposition move mass around more slowly, and are usually a second-order effect.

Because ice and water exchange mass, GIA is intrinsically a coupled problem: you cannot solve for the deformation of the land without also keeping track of where the ocean water goes.

How the solid Earth responds

The key to GIA is that the solid Earth is viscoelastic: it behaves like a spring on short time scales and like an extremely viscous fluid on long ones. A useful mental picture is memory foam. Press a finger into it and it deforms instantly (the elastic response); keep pressing and it keeps sinking slowly towards a new equilibrium (the viscous response); lift your finger and it recovers, but only gradually.

The elastic part is essentially instantaneous and reversible. It is what lets the lithosphere flex like a stiff plate over a load.
The viscous part is delayed and controls the long tail of the adjustment. It reflects the slow flow of mantle rock over thousands of years.

The single most important control on the time scale is the mantle viscosity. Where the mantle is stiff (high viscosity, of order $10^{21}$–$10^{23}\, \mathrm{Pa\,s}$), the ground rebounds over many millennia: Scandinavia and the Hudson Bay region are still rising at roughly a centimetre per year in response to the disappearance of ice-age ice sheets that vanished over ten thousand years ago. Where the mantle is weak (low viscosity, down to $10^{18}$–$10^{19}\, \mathrm{Pa\,s}$, as beneath West Antarctica, Iceland or Patagonia), the response is much faster — decades to centuries — so the ground can react on the same time scale as the ice it supports (Whitehouse et al., 2019). This distinction is central: fast GIA can influence an evolving ice sheet within our lifetimes, not just over deglacial history.

The structure of the solid Earth

For GIA purposes the Earth is usually described as a layered body:

a relatively cold, rigid lithosphere that flexes elastically. Its thickness ranges from a few tens of kilometres in tectonically active regions (again, West Antarctica) to well over 200 km beneath old, stable cratons (such as much of East Antarctica);
a mantle beneath it that flows viscously, often subdivided into an upper and a lower mantle with different viscosities.

Radial profiles of density, viscosity and elastic moduli are commonly taken from seismically derived reference models such as PREM (Dziewonski and Anderson, 1981). Real Earth structure is not only radially layered but also laterally variable, and viscosity in particular can change by several orders of magnitude over relatively short distances. Whether, and how well, a GIA model captures this lateral variability is one of the main factors distinguishing different modelling approaches (see below).

More than deformation: gravity, sea level and rotation

GIA is often abbreviated GRD, for its gravitational, rotational and deformational components — a reminder that the ground moving up and down is only part of the story.

Deformation is the vertical (and horizontal) motion of the solid surface.
Gravity: mass redistribution changes Earth's gravity field, which reshapes the sea surface. A large ice sheet gravitationally attracts the surrounding ocean, piling water up against itself; when it melts, that pull weakens and the local sea surface drops, even as sea level rises far away. This gravitationally self-consistent pattern is the reason melting the West Antarctic Ice Sheet would raise sea level in the Northern Hemisphere by more than the global average.
Rotation: redistributing mass also nudges Earth's rotation axis, feeding back weakly onto sea level.

Solving for how meltwater redistributes itself while accounting for the deforming solid surface and the changing gravity field is the classic sea-level equation. FastIsostasy focuses on the deformational response, approximates the gravitational one and neglects rotation; see Swierczek-Jereczek et al. (2024) for exactly which components are modelled and how.

Why do we care?

GIA presents many feedbacks on ice-sheet evolution (Whitehouse et al., 2019), and their net effect is negative: GIA tends to inhibit both ice-sheet growth and retreat. Two mechanisms are especially important for marine ice sheets, whose beds lie below sea level:

Bedrock uplift near the grounding line. As a marine ice sheet thins and unloads its bed, the ground rebounds, making the water column shallower. Shallower water reduces the ice's tendency to float, which can slow or halt grounding-line retreat — a stabilising, negative feedback on the marine ice-sheet instability.
The gravitational fingerprint. A shrinking ice sheet pulls the nearby sea surface down, again lowering the water depth at the grounding line and reinforcing the same stabilising effect.

Because these feedbacks are strongest where the mantle is weak — precisely under the vulnerable West Antarctic Ice Sheet — they can act on the decade-to-century time scales that matter for future projections (Gomez et al. (2018); Coulon et al. (2021); Book et al. (2022); Van Calcar et al. (2023)). A faithful representation of GIA is therefore needed to obtain realistic paleoclimatic reconstructions of ice sheets, and reliable projections of future sea-level rise under anthropogenic warming — a question of direct concern given how much of humanity lives along coasts.

How is GIA modelled?

Three broad families of models have traditionally been used:

Regional GIA models focus on a limited domain that can be considered as flat with an appropriate projection. They are computationally cheap, but rely on strong simplifications of the physics and often don't represent the lateral variations in viscosity or lithosphere thickness.
Global 1D GIA models treat the Earth as spherically symmetric (1-D, radially layered) and are elegant and efficient, but by construction cannot represent lateral variations in viscosity or lithosphere thickness.
Gloabl 3D GIA models can resolve fully 3-D Earth structure, including lateral variability, but at a considerable computational cost that makes long or repeated simulations expensive — a real obstacle when GIA must be coupled to an evolving ice sheet.

FastIsostasy sits between these extremes. It captures the laterally variable lithosphere thickness and mantle viscosity that matter for regions like Antarctica, yet runs orders of magnitude faster than a 3-D model by reducing the problem from three dimensions to two and solving it with a hybrid Fourier / finite-difference scheme (Swierczek-Jereczek et al., 2024). This makes it well suited to fast prototyping, long paleo runs, coupling with ice-sheet models and parameter/data-assimilation studies. The Analytical benchmark and the other worked examples show how to set up a simulation in a few lines of code, and the Public API documents the available options.