1. GLACIAL ISOSTATIC ADJUSTMENT AND COASTLINE MODELLING Glenn Milne
Dept of Geological Sciences
University of Durham, UK

2. Outline General GIA • What is GIA? • Key observables
• General model components
• Constraining model parameters
(2) Modelling coastline evolution
• General idea
• Predicting GIA-induced sea-level change
• Example predictions

4. Oxygen Isotope Record 18O/16O(sample) - 18O/16O(standard) d18O=1000 x

5. GLACIAL ISOSTATIC ADJUSTMENT
Surface Mass Redistribution
Earth
Earth Response
Relative sea level
Geopotential
Rotation vector
3D solid surface deformation
Model
Surface load + Rotational potential
Rheological Earth model
Better understanding of GIA process
Constraints on Earth rheology
Constraints on surface mass redistribution

6. Ice history and earth rheology are the key inputs
GIA MODEL
Earth Forcing
Earth Rheology
Impulse response formalism Linear Maxwell rheology D structure
Rotational potential
Surface loading
Euler equations
Ice
Other?
Interdisciplinary approach
Ice dammed lakes Sediment redistribution
Ocean
Sea-level equation
Ice history and earth rheology are the key inputs

7. Constraining Model Parameters
Largest uncertainties associated with ice sheet histories and earth rheology
Near-field data give best constraints on local ice histories
Near-field and far-field data can be effectively used to constrain earth viscosity structure
Far-field sea-level data give best constraints on integrated ice melt signal
Both forward and inverse modelling techniques are used

10. Modelling Coastline Evolution
(Associated with GIA)
Position of coastline is influenced by rising/falling relative sea level AND advancing or retreating marine-based ice

11. Modelling Coastline Evolution Driven by GIA-Induced Sea-Level Changes
Choose optimal model parameters and predict changes in relative sea level for period of interest
Compute palaeotopography via the relation
Accuracy of prediction will depend on accuracy of the present-day topography data set and the accuracy of the relative sea-level prediction
GIA model does not include tectonic motions or sediment flux (associated with marine or fluvial processes)

12. Eustatic Sea-Level Change
Mass conservation
Earth is rigid and non-rotating
Ice and water have no mass

13. Glaciation-Induced Sea-Level Change
S(q,f,t) = G(q,f,t) – R(q,f,t)
+ HG(t)
Geoid perturbation, G(q,f,t)
geopotential perturbed directly by surface mass redistribution and changing rotational potential and indirectly by earth deformation caused by these forcings
Solid surface perturbation, R(q,f,t)
vertical earth deformation associated with surface mass redistribution and changing rotational potential
Surface mass conservation, HG(t)
VOW(t) = G(q,f,t) – R(q,f,t)  + HG(t)AO
HG(t) = VOW(t) AO-1 – AO-1 G(q,f,t) – R(q,f,t) 
“eustatic” “syphoning”

14. Sea-Level Model
● Original theory published by Farrell and Clark (1976).
● Theory extended to include:
(1) Time-dependent shorelines (Johnston 1993; Peltier
1994; Milne et al. 1999).
(2) Glaciation-induced perturbations to Earth
rotation (Han and Wahr 1989; Bills and James 1996;
Milne and Mitrovica 1996; 1998).
(3) The influence of marine-based ice sheets
(Milne 1998; Peltier 1998).

15. Some Comments on the Sea-Level Algorithm
Computing ∆G and ∆R requires knowledge of the sea-level change since this is a key component of surface load. Iterative process required at each time step in computation.
Sea loading in given by C(θ,Φ,t) S(θ,Φ,t). Continent function can only be determined when RSL is known. Iterative process required over each glacial cycle.
High spatial resolution computations are computationally intensive (CPU and disk space).

18. 20 kyr BP
10 kyr BP