The “Shallow Ice Approximation” - University of Michigan

AOSS 605 (004)

Climate and Gla

Define ice sheet bed:

Define balance rate: The e

Steady-state mass balance dictates:

aciers Revisited

equilibrium line elevation

AOSS 605 (004)

Climate and Gla

Define ice sheet bed:

Define balance rate: The e

Steady-state mass balance dictates:

aciers Revisited

equilibrium line elevation

AOSS 605 (004)

Climate and Gla

Define ice sheet bed:

Define balance rate: The e

Steady-state mass balance dictates:

aciers Revisited

equilibrium line elevation

AOSS 605 (004)

Climate and Gla

aciers Revisited

AOSS 605 (004)

Climate and Gla

aciers Revisited

AOSS 605 (004)

Climate and Gla

aciers Revisited

AOSS 605 (004)

Climate and Gla

aciers Revisited

AOSS 605 (004)

Climate and Gla

aciers Revisited

AOSS 605 (004)

Climate and Gla

Assume plastic in a global sense:

aciers Revisited

AOSS 605 (004)

Climate and Gla

Assume plastic in a global sense:

aciers Revisited

Steady-state length (km)AOSS 605 (004)

Climate and Gla

120

τ0 = 100 kPa

z0 - E = 500 m
60

0
0
Sl

aciers Revisited

a

m

0.1 0.2
lope

Steady-state length (km)AOSS 605 (004)

Climate and Gla

120

τ0 = 100 kPa

z0 - E = 500 m
60

0
0
Sl

aciers Revisited

Small slopes - large glacier?

a

m

0.1 0.2
lope

AOSS 605 (004)

Climate and Gla

Small slope means glacier has to g
drop beneath the equilibrium line

Equilibrium line

aciers Revisited

Small slopes - large glacier?

grow large to

AOSS 605 (004)

Climate and Gla

Large slope means that as th
moves beneath the equilibrium

Equilibrium line

aciers Revisited

Small slopes - large glacier?

he glacier grows it
m line quickly

AOSS 605 (004)

A first look at cl

limate sensitivity

AOSS 605 (004)

A first look at cl

limate sensitivity

AOSS 605 (004)

A first look at cl

Glaciers on a be
sensitive than gl
slope

limate sensitivity

ed with a small slope are more
laciers on a bed with a large

AOSS 605 (004)

A first look at cl

Glaciers on a be
sensitive than gl
slope
Fractional change in length:

limate sensitivity

ed with a small slope are more
laciers on a bed with a large

AOSS 605 (004)

Climate sensitivit

Recall: E = elevati

ty and lapse rate

ion of equilibrium line

AOSS 605 (004)

Climate sensitivit

Recall: E = elevati
Lapse rate

ty and lapse rate

ion of equilibrium line (z)

AOSS 605 (004)

Climate sensitivit

Recall: E = elevati
Lapse rate
Change in equilibri

ty and lapse rate

ion of equilibrium line (z)
ium line with temp.

AOSS 605 (004)

Climate sensitivit

Recall: E = elevati
Lapse rate
Change in equilibri

ty and lapse rate

ion of equilibrium line (z)
ium line with temp.

dL/dTa (km/K)AOSS 605 (004)

Climate sensitivit

0

γ = -4 K/km
γ = -6 K/km
γ = -10 K/km

-5

-100 Slope

ty and lapse rate

e 0.2