Photo Ilulissat Ice Fjord, Greenland courtesy of Tina Rolf

Phillip Blakey. Summer Internship. Dr. Peltier. Physics Department. University of Toronto.

Relative Sea Level Response to a Sudden Removal of the Greenland Ice Sheet

AbstractThe sudden removal of an Ice Sheet releases a large volume of

water into the ocean; However the redistribution of the ocean

water after such an event is not straight forward. Changes in the

bathymetry of the ocean and Ice loading values perturb the

gravitational field of the earth. The ocean surface is fixed at the

geoid so the perturbations directly impact the relative sea level of

the ocean basins. The relative sea-level change 𝑆(𝜃, 𝜆, 𝑡) is

predicted by solutions to the Sea Level Equation

• 𝐶(𝜃, 𝜆, 𝑡) is the ocean function, defined as 1 over the oceans

and zero over land.

• 𝐿 𝜃, 𝜆, 𝑡 is the surface mass load per unit area.

• 𝜙 is the angle between the source point (𝜃′, 𝜆′) and the field

point 𝜃, 𝜆• Ψ𝑅(𝜃, 𝜆, 𝑡) is the variation of the centrifugal potential from

the changing rotational state of the Earth.

• 𝐺𝜙𝐿 𝜙, 𝑡 − 𝑡′ and 𝐺𝜙

𝑇(𝜙, 𝑡 − 𝑡′) are the surface mass loading

and tidal potential loading Green functions.

The Sea Level Equation𝑆 𝜃, 𝜆, 𝑡

= 𝐶(𝜃, 𝜆, 𝑡)

න

−∞

𝑡

𝑑𝑡′නන𝑑Ω′൛

ൟ

𝐿 𝜃′, 𝜆′, 𝑡′ 𝐺𝜙𝐿 𝜙, 𝑡 − 𝑡′

+Ψ𝑅 𝜃′, 𝜆′, 𝑡′ 𝑅𝐺𝜙𝑇(𝜙, 𝑡 − 𝑡′) +

ΔΦ(𝑡)

𝑔

ModificationsThe original ice loading history spanned from 122.5kybp to

-1kybp. This was modified to span from 2kybp to -30kybp

with all values after 0kybp to remain constant. Further one

time step before present the Greenland Ice sheet was

zeroed.

The program to calculate relative sea level was then

modified to populate a grid of latitude longitude points

rather than one.

The purpose of starting the simulation closer to present is

to avoid adding noise from Pleistocene deglaciation events

to the effects of melting the Greenland Ice sheet.

Graphic of how simulator works

Data AnalysisUsing the ice loading history

the water volume in the

Greenland Ice Sheet

0.25kybp was calculated to

be

𝑉𝑤 = 2.8338 ⋅ 1015𝑚3

Area of Ocean

𝐴𝑂 = 3.619 ⋅ 1014𝑚2

Average Ocean Rise

𝑑𝐻 =𝑉𝑤𝐴𝑜

= 7.830 𝑚

Relative Sea Level Variation in meters at present and 14ky in the future after the Removal of the Greenland Ice Sheet.

Year

(kyap)

Integral of RSL

Over the Oceans

(𝑚3)

Percent

Difference

from 𝑉𝑤-0.75 6.88148 ⋅ 1011 NA

-0.5 6.58413 ⋅ 1011 NA

-0.25 6.32418 ⋅ 1011 NA

0 2.787718 ⋅ 1015 −1.626%

1 2.784731 ⋅ 1015 −1.732%

2 2.781901 ⋅ 1015 −1.831%

3 2.782448 ⋅ 1015 −1.812%

4 2.778447 ⋅ 1015 −1.953%

5 2.775669 ⋅ 1015 −2.051%

6 2.770945 ⋅ 1015 −2.218%

7 2.769907 ⋅ 1015 −2.255%

⋮

⋮

⋮

⋮

⋮

⋮

30 2.766388 ⋅ 1015 −2.379%

The chart to the right contains the output from

integrating relative sea level over the ocean

basins as well as the percent difference between

the integral and the expected water volume. As

can be seen the error is small and stabilizes

around −2.4% as time goes on indicating that

mass is indeed conserved in the model.

In the figure for 0 kyap the loss

of mass in Greenland from the

removal of the ice sheet has

caused the relative sea level in

the far field to increase more

than the close field. This is

caused by a reduction in the

gravitational attraction of the

Greenland surface load to the

oceans.

In the second figure isostatic

rebound has caused subsidence

in the the solid surface around

Greenland Increasing the

relative sea level. The increase in

mass has also caused the relative

sea level to increase in the near

field.

Variables References• Eakins, B.W. and G.F. Sharman, Volumes of the World's

Oceans from ETOPO1, NOAA National Geophysical

Data Center, Boulder, CO, 2010.

• Peltier W.R The History of the Earth's Rotation: Impacts

of Deep Earth Physics and Surface Climate Variability. In:

Gerald Schubert (editor-in-chief) Treatise on Geophysics,

2nd edition, Vol 9. Oxford: Elsevier; 2015. p. 221-279.

Ice Editing Tool. This ice editing tool allows for some

ice loading samples to be zeroed by selecting them as

demonstrated in the above figure.

The rebound of the continental crust over Greenland is caused by mantle material flowing

into the region of depression caused by the weight of ice mass. As the mantle material

flows into the depression from the edge of where the ice sheet was, the new mass exerts a

gravitational attraction on the ocean water, causing it to flow towards Greenland and

Increase the relative sea level further.