Download Ice in the climate system Summary so far Today The Cryosphere

Ice in the climate system
Summary so far
1.  Climate history of the Earth
2.  Paleo observations (1)
3.  Paleo observations (2)
4.  Ice ages
Radiation (Milankovitch theory) must be important
Internal Feedbacks must be important (100 kyr)
Interpretation sea level difficult
earth response
gravitational effects
5.  Climate sensitivity
6. Ice in the climate system
7. Climate Change (2105)
8. Sea level (0406)
Today
What is the cryosphere?
What are the basic features and terminology?
How do climate and ice sheets interact?
Basic physics of ice flow
The Cryosphere
• Ice sheets (Antarctica and Greenland)
• Large topogrophy covering ice
• Ice shelves
• Floating (sweet, thick, permanent)
• Glaciers
• Land based ice in mountains
• Sea ice
• Frozen ocean water (salt, thin, semi permanent)
• Snow
• % NH covered with snow in winter
• Permafrost
• Frozen ground
Basic terminology
Ice Sheet and Mass Balance
Equilibrium line
accumulation
ablation
calving
flow
lines
ice core
MASS BALANCE
Accumulation = Ablation + Calving
Differences Antarctica and
Greenland, Glaciers
Characteristics of the cryosphere
Present day estimate of:
!
!
!Antarctica !Greenland !Glaciers
!100%!
!0% !
!100%!
!100%!
!50% !
!50% !
!100%!
!80% !!
!20%!
Greenland
Glaciers
Area (106 km2)
13.8
1.7
0.68
Mean thickness (m)
2079
1707
265
(106
26.4
2.9
0.18
72.3
7.2
0.51
2246
± 86
0.163
520
± 26
0.306
670
0.985
Runoff (1012kg yr-1)
-53
-297 ± 32
-690
Ice berg discharge
(1012kg yr-1)
-2072 ± 304
-235 ± 33
-50
Ice shelf basal melt
(1012kg yr-1)
-540 ± 218
-32 ± 3
-
Volume
• Accumulation
• Ablation !
• Calving !
Antarctic ice sheet
(incl. ice shelves)
km3)
Sea level equivalent (m)
-1)
Accumulation (10
kg yr-1
(m 12
w.e.
Church et al., 2001
Time scales
Snow cover:
days-months
Sea ice:
months-10 years
Glaciers:
10-100 years
Ice shelves:
100- 1000 years
Ice sheets:
1000-100000 years
Ice and sea level time scales
Miller et al. 2005!
Albedo feedback
Albedo feedback
Temperature
lower
Absorption
less
Temperature
higher
Snow/Ice
more
Absorption
more
Snow/Ice
less
Albedo
Albedo
higher
lower
Ice leads to nonlinear
response in the climate
Hysteresis
Ice volume
Forcing
Amplitude
Linear
Nonlinear
Time
Temperature
R. Bintanja
Response ice to climate change
8
Change in annual temperature (˚C)
Cryospheric Feedbacks
6
4
(mwe/a)
glaciers and
small ice caps
Antarctica
ablation
Greenland
2
accumulation
0
spec. balance
-2
-4
-6
-8
-30
-25
-20
-15
-10
-5
annual temperature (°C)
J. Oerlemans!
0
5
Mass balance and climate change
Modelling ice flow
Elevation
0
Mass Balance (m/yr)
Steady state
Flow on a sloping surface
"H
=0
"t
Mb =
# b˙dxdy
= 0
-Ice thickness remains constant everywhere
!
-specific balance varies along the glacier/ice sheet,
but is constant in time
Shear stress:
dhs
" xz = #gH
dx
Shallow ice approximation
Reference profile Rhone
150
Mass balance height feedback implicit!
No thermodynamics!
No bedrock compensation!
3000
100
2500
50
2000
0
modelled - observed
1500
0
Non-linear diffusion equation!
Length
-50
12
Future changes Rhone
10
4
10
Volume
3.5
3
8
ELA
7
1600
1700
1800
Year AD
1900
2.5
2000
Length (km)
4.5
11
9
4
6
8
10
Distance from head (km)
12
5
12
Volume (km3) and ELA (km a.s.l.)
Green observed!
Length (km)
Time evolution Rhone
2
Difference (m)
3500
Altitude (m a.s.l.)
U=f(H,dH/dx)!
8
6
4
2
2000
0˚C
+2˚C
+2˚C en +20%
+4˚C
2020
2040 2060
Time (AD)
2080
2100
Schematic flow (1)
Schematic flow (2)
Velocity 10-100 m/yr!
Major source of complications
Temperature - flow parameter
-hypsometry
-time scale of the response
basal
melt
1.5 10-16
-3
-1
Flow parameter (Pa a )
Flow mechanisms
1 10-16
!T=10 >A'=10A
5 10-17
!T=10 > A'=3A
0
240
245
250
255
260
265
Temperature (K)
270
275
Importance
1: Change of internal energy
-Deformation rate temperature dependent!
-Criteria for Basal sliding!
dE d"e
de d"
=
= " +e
dt
dt
dt
dt
First Law of Thermodynamics:!
!Internal Energy= Work done +
!Heat Added!
!
!dE/dt !=
!dW/dt !+
!
dQ/dt!
!
!1
!2
!
!3!
!
!
!
e
cp
!
!specific internal energy =cpT!
!specific heat capacity!
!density (constant)!
dE
dT
= "C p
dt
dt
Purpose now to rewrite this as a change in temperature over time!
!
2:Work done deformation
phase change
3: Heat added~conduction
r
Fc = "k#T
k thermal conductivity
..... (flux $ unit volume)
dQ
= k# 2T
dt
Wd = "˙ij# ij
"˙ij strain rate
# ij stress
Wl = L f M f
L f Latent heat of fusion
!
M f amount that refreezes
!
!
Combining the three terms
"C p
dT
= k# 2T + $˙ij % ij + L f M f
dt
Table of thermal parameters
Thermal parameters of glacier ice (Paterson 1994)
writing the total derivative as sum of the local time change and advection!
"T
"T
"T
"T
= #u # v # w +
"t
"x
"y
"z
!
2
Cp
T 0˚C
2091 Jkg-1K-1
Latent heat of fusion
Lf
333.5 kJkg-1
(conduction)
Thermal conductivity
k
2.1 Wm-1K-1
2.76 Wm-1 K-1
(internal deformation)
Thermal diffusivity
K
1.09 10-6 m2s-1
1.73 10-6 m2s-1
(advection)
2
" T
" T
+K
+K
+
"x 2
"y 2
"z 2
1
(%˙xx& xx + %˙yy& yy + %˙zz& zz ) +
$C p
K
" T
2
Specific heat
1
(2%˙xy& xy + 2%˙xz& xz + 2%˙yz& yz ) +
$C p
Lf M f
T -50˚C
1741
34.4 m2yr-1
917 kg m-3
!
Density
(melt)
$C p
!
Robin solution
valid at ice divide!
2
"T
" T
"T
=K
#w
"t
"z
"z 2
-steady state!
-mechanical steady state > w known as function of z!
!
0
M in cm/yr
500
Depth below the surface (m)
Assumptions!
-The basal temperature is below pressure melting point.!
-Horizontal diffusion is neglected compared to the vertical diffusion. !
-Horizontal advection is neglected. !
-Frictional heat from internal deformation is included in!
the geothermal heat flux!
Effect of vertical velocity
0
5
15
30
1000
1500
ablation area Ts=Tmelt
2000
2500
3000
0
20
40
60
T(z) - Ts (˚C)
80
100
Vertical profiles
Tb-Ts for M =10 cm /yr
Ice isolates
Mind
Hor.
Advection
Purple
More or less
ELA
Large G
leads to melt
at bottom
Temperature difference
Milankovitch phasing
(Ruddiman, 2000)
J. v.d. Berg
40-100 kyr transition
100 kyr evolution of NAM
Transition 40-100 kyr
~1 m/1000 yr
merging
~0.2 m/1000 yr
Blue bar is first minimum after 100 ky interglacial (black arrow)
Orange line connects max ice volume in 100 ky cycle
Terminations
Thermodynamics
play role
In 40-100 kyr
transition
BW08
BW08
Leads and Lags in the system
Summary Thermodynamics
Central parts of ice sheets!
!cold at the top warm near the bed!
!vertical advection:!
!
! cools isothermal near the surface (~15 m)!
!vertical diffusion:!
!
!redistributes geothermal heat!
!
!linear temperature profile near the bottom !
!(Robin solution)!
Summary Ice Flow
Simple model:
-shear stress driven models
-isothermal
Slightly more complicated:
-short outline thermodynamics
Summary Thermodynamics (2)
Downstream of the divide!
!horizontal advection start to play a role!
!particularly near the bed where deformation is largest!
!-melt water penetration can be an important term!
!-in addition deformation is strongly dependent on!
!temperature!
!Simultaneous numerical solution of temperature and velocity !
Summary ice in the climate
Cryosphere important:
as part of the climate system (passive and active)
as climate archive
for sea level
Basic terminology:
Ice sheet, shelves, glaciers, sea ice
Mass balance, accumulation, ablation, equilibrium line
Difference mass balance Antarctica, Greenland, glaciers
Relation mass balance and flow
Perfect plasticity
Further reading
*W.S.B. Paterson
“The Physics of Glaciers”
*J. Oerlemans
“Glaciers and climate change”
*C. Van der Veen
“Fundamentals of Glacier Dynamics”
*R. Leb. Hooke
“Principles of Glacier Mechanics”