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.