From Alfred de Quervain's From Alfred de Quervain's observations toobservations to

modern ice-sheet modelsmodern ice-sheet models

Johannes OerlemansIMAU, Universiteit Utrecht

j.oerlemans@uu.nl

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• crevassed marginal zone

• 'terraces' with large meltwater lakes

up to 1530 m asl

• very smooth surface over hundreds of kms

• steeper melt zone without lakes

• high mountains in coastal zone

Crossing from Jakobshavn to Angmagssalik

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De Quervain (1914)

The early explorers had no means to determine the ice thickness.

De Quervain suspected that at the east coast the fjord system was penetrating inland under the ice for at least 100 km.

Small irregularities in the smooth surface were supposed to be expressions of bedrock undulations.

The thickness of the ice sheet was grossly underestimated !

accumulation

and runoff

melt

icebergs

iceb

ergs

iceb

ergs

accumulation – runoff – icebergs ≈ 0?

equilibrium line

• in the west: equilibrium line at 1450 – 1500 m asl

• in the east: equilibrium line at 1000 – 1100 m asl

• annual accumulation in the interior of the inland ice: 0.35 m water eq

In the expedition report, the following factors are mentioned to explain the relatively large altitude of the equilibrium line:

- decreasing precipitation towards the interior

- greater brightness of the sun

- general anti-cyclonic weather

About the surface mass balance

De Quervain's expedition

R S W van de Wal,  W Boot, C J P P Smeets, H Snellen, M R van den Broeke and J Oerlemans (2012): Twenty-one years of mass balance observations along the K-transect, West Greenland. Earth System Science Data 4, 31-35.

Ablation in the western melt zone:

Ideas on the total mass budget

• averaged precipitation in the 'accumulator': 0.36 mwe

• averaged ablation in the 'dissipator': 0.95 mwe

• a budget calculation showed that the ice sheet was in good shape, and should have a production of icebergs equivalent to 0.08 mwe

Ideas on the stability of the ice sheet

'We may ask whether such a glacier could start under present general climatic and

topographic conditions'

De Quervain (1914):

The influence of heavier precipitation would preponderate over that of the higher temperature and result in the formation of a new ice sheet

Brooks (1923):

It does not seem likely that the ice could have started forming in the interior, for the snowfall on an upland so far from the coast would be insufficient to survive the summer melting.

Early theory of ice sheets

Bodvarsson (1955), Robin (1955), Vialov (1958), Nye (1959), and, above all,

Johannes WEERTMAN

• glaciers always try to reduce the spatial variations in internal stresses

• the basal shear stress dominates and is proportional to slope and ice thickness

-> steep surface means small thickness and the other way around

=> application of perfect plasticity theory

shear concentrated at base:perfect

plasticity

surface height h

ice thickness H

x

shear concentrated at base:

ice cap on a flat bed:

perfectplasticity

=> glacier profile is parabolic

in agreement withfield obervations...

J. Alean

equilibrium line

E

an ice sheet can only exist if !

mean elevation

equilibrium states:Hysteresis

17

Vatnajökull

equilibrium states:

GISAIS

Semi-bounded domain and sloping equilibrium line (Weertman, 1976):

equilibrium states:

Perfect plasticity: parabolic profile

Does this differ much from a profile with simple shear and Glen’s law?

Ice sheet profile for simple shear with Glen's law (Vialov, 1958):

constant accumulation rate b

ice sheet radius R

.

Ice sheet profile for simple shear with Glen's law (Vialov):.

Taylor-expansion to see how sensitive ice thickness is for for changes in:

- accumulation rate

- ice viscosity

- ice-sheet radius

Some basic numbers

area volume accumulation time scale(x1000 km2) (x1000 km3) (m/yr) (yr)

-------------------------------------------------------------------------------------------------------Antarctica 12000 26500 0.15 14722

Greenland 1700 2900 0.35 4873

glacier 0.02 0.002 1.50 67

-------------------------------------------------------------------------------------------------------

time scale = volume / (area x precipitation)

Numerical ice sheet models

(1) Climatic variations during the Pleistocene were relatively large, with big ice sheets waxing and waning all the time.Do we understand this?

(2) The global climate is warming, and will probably continue to do so.Will the Greenland and Antarctic ice sheets make a significant contribution to sea-level rise in the next 100-200 years?

PI

LGM

Glacial Interglacial

Take the Milankovitch insolation variations…

….and force a climate model (which includes ice sheets).

IPC

C (

2007

)

It needs much ‘calibration’# to get ‘reasonable results’# tuning, fiddling

• making an ice age start during an insolation minimum is difficult

• hard to get fast deglaciation

• too much ice in Asia

• little generation of 100 kyr power

(1) Ice ages

• our diagnosis of the present state is poor• hard to quantify the ‘background signal’=> we have an initialization problem

• uplift data

• satellite (gravity anomalies, ice velocities, grounding line)

• ice/snow radar (isochrones)

• boreholes and ice/firn cores

• sediment cores

(2) Global warming – sea level

How to achieve further progress in ice-sheet modelling ?

It is all about the interfaces !

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Thank you !Thank you !

Antarctic ice sheet

Greenland ice sheet glaciers

Sea level rise due to melting land ice, scaled with the global mean.

Mitrovica (2006)

AD 2000

AD 2100

AD 90 000

AD 5 000 000

0

+3 °C

-5 °C

-30 °C

…een mogelijk scenario…

Arctic O. south

Arctic O.

Arctic O.

Arctic O.

• summer insolation in NH decreases• ice sheet starts to grow• height-mass balance feedback effective

• albedo-feedback becomes effective

• atmospheric CO2 concentration decreases

• strong sinking of bed (delays growth)

• ice sheet warms up (more sliding)• precip in the northern part decreases

• summer insolation increases• ice sheet is thinner because of extensive sliding

• atmospheric CO2 concentration increases

• high calving rates due to delayed bed response• full decay

time

Van den Berg et al (2006)

mm w.e.

surface balance rate

it is gorgeoushere!

yeah, but I worry…it seems that CO2-emissions

decline dramatically!

Greenland, 2100 AD