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Glacier mass balance
Jon Ove Hagen
Department of geosciences
University of Oslo www.ice2sea.eu
IPCC 2013, WGI Fig 4.25
Ice-loss from glaciers and ice sheets
2005–2010 (6-year) 1.04 ±0.37 mm/yr
1993–2010 (18-year) 0.60 ±0.18 mm/yr
Relative contributions 2003 – 2010 Combined GRACE - ICESat - SMB from Gardner et al. 2013 and Shepard et al. 2012
174
85
220 Gt/yr
70
Greenland
Antarctica
Arctic GIC
Rest of GIC
Gt/yr
IPCC AR5 Modeled sea level rise 2100 0.26 to 0.82 m (incl. dynamics)
0.2 m
0.4 m
0.6 m
1.0 m
(from IPCC 2013, SPM Fig.8)
0.8 m
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Global glacier mass budget
Greenland:
Antarctica:
Himalaya, Alps, Norway:
From Cogley et.al. (2011)
Mass balance components
Mass balance components of a floating ice shelf
From Cogley et.al. (2011)
Recommended notations from Glossary of Mass Balance
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Global glacier mass budget
Greenland:
Antarctica:
Himalaya, Alps, Norway:
Mainly caused by Antarctica !
Mass balance methods
1. The direct glaciological method
2. The geodetic method (
3. The gravity
4. The hydrological method
5. The ice flux method
6. Modelling
Selected glaciers: Simultaneous –
ground-based – airborne and satellite
data
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3 main methods ∆Mnet = ∆Ma - ∆Mm – ∆Mc
1) Geodetic - Geometry h/t:
h1 DEM1 [Δh] DEM1 – DEMn = ΔV ∆Mnet = V/a *ρ
2) Gravity ∆Mnet direct mass change GRACE
3) Budget Each component Ma - Mm – Mc
A
thV /
Glaciers response on Climate
change
• Two climatic parameters: – Winter precipitation (snow)
– Summer temperature (melting)
• Climatic response (fast – immediate response)
↓ • Dynamic response (slow - velocity and ice flux
changes)
SMB Mn = Ma - Mm
Ablation area
Accumulation
area
ELA
Storglaciären,
Sweden
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Mass balance bn = bw - bs Stratigraphic method
Accumulation area
Ablation area
Stake measurements
Snow
Ice
swn bbb Specific point measurements:
Mass balance definitions
In each point: bn = bw - bs
Tower - “stake” on top of the ice cap Svartisen, Norway
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Mass balance
• Winter balance Total Bw (m3 w.eq.); Specific bw (m w.eq.), postive: mass gain
• Summer Balance Bs (m
3 w.eq.); bs (m w.eq.), negative: mass loss
• Net balance (= mass balance) Bn (m
3 w. eq.); bn (m w.eq.)
• Bn = Bw - Bs
• bn = bw - bs
Glacier mass balance points
Specific balance: bw = Δh ∙ ρ [ m ∙ kg/m3 = kg/m2 or: m water eq. ] Density measurements
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Shallow
ice core
for
density
Density - depth
0 200 400 600 800 1000
Snow depth (cm)
400
300
200
100
0
Wate
r E
quvale
nt (c
m H
2O
)
Fit Results 1998
Fit 1: Second order polynomialEquation Y = AX2+BX+CA = 0.0002833314232B = 0.364455157C = -0.9440859055
Number of data points used = 45Average X = 156.578Average Y = 67.4249
Residual sum of squares = 98.9089Coef of determination, R-squared = 0.999411
Fit Results
Fit 1: Second order polynomialEquation Y = AX2+BX+CA = 1.44627197E-005B = 0.4387409143C = -5.954281681
Number of data points used = 56Average X = 229.411Average Y = 96.013
Residual sum of squares = 608.289Coef of determination, R-squared = 0.998598
0.0 0.2 0.4 0.6
Density (g/cm3)
700
600
500
400
300
200
100
0
Depth
belo
w s
urf
ace (
cm
)
Stake 29
Winter balance map
Mass balance table
i
ii AbB )(.
iii AbB A
Bb
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50
100
150
200
250
300
350
400
450
500
550
600
-4 -3 -2 -1 0 1 2
Balance (m w.eq.)
Ele
va
tio
n (
m a
.s.l.)
W inter soundings
2
3
4
5
6
7
8
9
10
11
50
100
150
200
250
300
350
400
450
500
550
600
-4 -3 -2 -1 0 1 2
Balance (m w.eq.)
Ele
va
tio
n (
m a
.s.l.)
W inter acc.
W inter soundings
2
3
4
5
6
7
8
9
10
11
50
100
150
200
250
300
350
400
450
500
550
600
-4 -3 -2 -1 0 1 2
Balance (m w.eq.)
Ele
va
tio
n (
m a
.s.l.)
W inter acc.
W inter soundings
2
3
4
5
6
7
8
9
10
11
50
100
150
200
250
300
350
400
450
500
550
600
-4 -3 -2 -1 0 1 2
Balance (m w.eq.)
Ele
va
tio
n (
m a
.s.l.)
W inter acc.
Summer ablation
W inter soundings
2
3
4
5
6
7
8
9
10
11
50
100
150
200
250
300
350
400
450
500
550
600
-4 -3 -2 -1 0 1 2
Balance (m w.eq.)
Ele
va
tio
n (
m a
.s.l.)
W inter acc.
Summer ablation
W inter soundings
2
3
4
5
6
7
8
9
10
11
50
100
150
200
250
300
350
400
450
500
550
600
-4 -3 -2 -1 0 1 2
Balance (m w.eq.)
Ele
va
tio
n (
m a
.s.l.)
W inter accumulation
Summer ablation
Net balance
W inter soundings
2
3
4
5
6
7
8
9
10
11
50
100
150
200
250
300
350
400
450
500
550
600
-4 -3 -2 -1 0 1 2
Balance (m w.eq.)
Ele
vatio
n (
m a
.s.l.
)
W inter accumulation
Summer ablation
Net balance
W inter soundings
0 0.5 1
50-100
100-150
150-200
200-250
250-300
300-350
350-400
400-450
450-500
500-550
550-600
Ele
vatio
n in
terv
al (
m a
.s.l.
)
Area (km2)
iii AbB
dAbAbB
A
w
i
iiww 0
)(
Calculating mass balance
Total mass balance
dAbAbB
A
w
i
iiww 0
)(
Overall specific mass balances
ABb ww / ABb ss /
ABb nn /
Mass balance curves - specific balance per altitude (b(z)) and volume balance ( B(z)) B = ∑ bi (z) • Ai [109 m3]
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Mass balance by elevation - Engabreen
High elevation range - negative “winter” balance in
lower elevations
Engabreen, Norway
Ablation by elevation - linear: bs = a ∙ h + c
1200 1300 1400 1500 1600 1700Elevation (m a.s.l.)
0
1
2
3
4
Ab
latio
n (
m w
.eq
.)
Equation Y = -0.007X + 11.9Number of data points used = 49
Coef of determination, R2 = 0.90
Net balance curves varies from year to year
bn (z)
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Long-term yearly mass balance on Nigardsbreen
Mass balance is measured on 10 glaciers in Norway
West - East transect of mass balance Cumulative mass balance 1963 - 2008
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Glaciated area ~ 35 000 km2, 60% glaciated
Svalbard archipelago 77-81 °N 11-26 °E
Glacier area ~ 36 000 km2
Long-term mass balance A < 0,5 % of all
• Ny - Ålesund
0 10 km
BRG
MLB
Austre Brøggerbreen (BRG)
Midre Lovénbreen (MLB)
(~5 km2) since 1966
Kongsvegen (KNG) (100 km2) 1987
KNG
NP mass balance
From J. Kohler
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From J. Kohler
Cumulative mass balance 1965-2012
-25
-20
-15
-10
-5
0
5
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
Cu
mu
la
tive
ba
la
nc
e (m
)
Year
Austre Brøggerbreen
Midre Lovénbreen
Kongsvegen
Kronebreen-Holtedahlfonna
Yearly cumulative mass changes
Huss et al. 2009
Greenland mass balance 2003 - 2008
1) Surface mass balance (SMB) modelling and calving (D) (Ma – Mm) – Mc
2) GRACE gravity data ∆M © van den Broeke et al. 2009
(Ma - Mm) – Mc
∆M
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Mass balance gradients
• Budget gradient: bn/z
• High - wet maritime
• Low - cold, dry
0 + –
z
High
Low
z
bn
ELA
Svalbard Mean surface mass balance
Bn = ∑ bni (z) • Ai [109 m3]
Bn - 1 0,1 Gt/y
bni (z)
bn/z
Mass balance stake net on Austfonna (~8000 km2)
100 km
Ground-based field measurements
800 MHz GPR + GPS-elev. Shallow cores Neutron probe
Snow probing AWS Snow pits
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800 MHz GPR shielded antenna
GPR control unit & laptop dGPS (GNSS) receiver
Speed: 5 m/s Sampling rate: 20 Hz Trace interval: 25 cm
Ground-based monitoring of snowcover and glacier facies of Austfonna, Svalbard
W E
Snow accumulation measured in multiple years
Schuler et al. 2006
Accumulation index map
Uncertainties
• Density variability
• Internal refreezing – densification
• Percolation and deep refreezing below LSS
• Superimposed ice
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The mass balance of a column of glacier ice, firn and snow.
From Cogley et.al. (2011) Cuffey and Paterson, 2010 based on Benson (1961) and Müller (1962). ©2010 Elsevier, Inc.
König et al., 2004
Variations in surface mass balance (end of summer)
a) snowline equals firnline
b) negative anomaly; snowline retreats into firn area c) positive anomaly; snowline extents into SI/GI area
Radarzones associated with “glacier facies”
30 km
800 m asl 340 m asl
F1 SI GI F2 F3
firn superimposed ice “glacier ice”
12
m
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Greenland – melt areas increase
Greenland – melt areas (from Steffen and Huff)
In 2012 the entire Greenland experienced surface melt
2007 2012
550 610 250 350 330 430 -30 -160 Gt/yr Gt/yr Gt/yr Gt/yr
Grey: 1990ies Black: 2005-2010
GRACE
Velicogna, GRL, 2009
0.1 0.5 mm/yr
1.8 3.4 mm/yr
---50 Gt/yr
---100 Gt/yr ------------
---200 Gt/yr ---------------
1990 2010 1995 From D.D.Jensen-COP15
?
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Greenland 1960 – 2010 Cumulative mass anomalies
Broeke et al. 2009
Greenland 1960 – 2010 Cumulative mass anomalies
Broeke et al. 2009
Greenland 1960 – 2010 Cumulative mass anomalies
Broeke et al. 2009
70 % or
c. 1500 Gt
of melt to runoff
30 % or
c. 600 Gt
of melt to
refreezing
Greenland conclusions
• Fairly constant mass until early 1990ies
• Accelerating mass loss 1990 – 2012
• Current mass loss ~ 250 Gt/year
• The surface melt processes will dominate future mass loss
• The future Calving flux remains almost constant
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gradhuwbt
hssn
Volume change is derived from altitude spot
change: h1 → DEM1 [Δh] DEM1 – DEMn = Δ V
M/t =
A
thV /
M/t = V/a * ρ
Airborne laser
Geodetic mass balance
Ice surface elevation changes
A
thV /
By GPS
1) Ground-based GPS-profiles
2) Repeated mapping (aerial photos)
3) Airborne lidar/laser altimetry
4) Satellite borne altimeter sensors;
– IceSat – laser altimetry
– CryoSat – radar altimetry
– Envisat - Radarsat – Terra SAR
M/t = V/a * ρ
Austfonna - ICESat repeat tracks 2003-2008 interior thickening - peripheral thinning
Moholdt 2011
Austfonna elevation change rates (m/y) 2003-2008
Measured
mean bn ~ - 0.1 m
Mean total net balance:
Bn = ∑ bni (z) • Ai [109 m3]
~ 0,4 Gt/y
Mean specific net balance:
bn = Bn/A ~ 0.05 m 0,1m
1
2
3
Moholdt 2011
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ICESat elevation changes
(2003-2008)
∆M = V/t * ρ
∆M = - 240 ± 28 Gt/yr
or 0,66 mm SLR/yr
from Pritchard et al., 2009
A
thV /
In 2012 the entire Greenland experienced surface melt
2007 2012
4. Hydrological method Water balance equation
Q = P - E ± M (Bn)
or Bn = P - Q - E
Q = Discharge - Runoff
P = Precipitation
E = Evaporation
M (Bn) = Storage term = Glacier net mass balance
Water balance
Qtot = Qs + Qp + Qi + Qc + Qg + Ql – Qe,
Where:
Qtot the potential total runoff,
Qs snowmelt from ice-free areas,
Qp runoff from rainfall in the whole basin,
Qi the glacial component of discharge which includes icemelt,
firnmelt and snowmelt from the ice-covered areas,
Qc freshwater from icebergs calving from the glaciers,
Qg groundwater discharge,
Ql condensed water vapour and
Qe evaporation.
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5. Ice flux method
)(xSuQv j
n
j
jb bAQ
1
Continuity: The ice flux Qv = Balance flux Qb
jj bAxSu )(
Idealized glacier
Accumulation
Ablation
j
n
j
jb bAQ
1
Q u S xv ( )
Balance flux = volume of snow/ice accumulation above a cross section
of the glacier
dttbtWxQ
x
sb )()()(0
j
n
j
jb bAQ
1
Or – simpler: Area (A) times the mean net accumulation (b):
Balance velocity and mass balance
jj bAxSu )(
)(xSbAu jjj
jj AxSub )(
Balance velocity:
Mass balance:
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6. Modelling Indirect method - ELA/bn Degree-day methods empirical models Energy balance modelling physical models
Modelling Indirect method - ELA/bn Net balance curves varies from year to year - but same shape so bn = a ∙ ELA + c
•
•
•
C0T
dtTPDD
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Positive degree-day model
• Simplest PDD model uses single factor to represent ablation of ice.
PDD factor α
(typically 0.004 – 0.008 m deg-1 day-1)
PDD
Wind, speed,
direction
Temp, RH Radiation:
K&Z CNR-1
Logger:
Campbell Scientific
Snow depth
sensor
Solar panel
Automatic
Weather
Stations
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krefkkP
k
krefkkTm PPCTTCB ,,
12
1
,, 1
kkT TBC ,
krefkkP PPBC ,,
Oerlemans and Reichert, 2000
Seasonal sensitivity
CT and CP in m w.eq. K-1
Monthly sensitivities
+1 K, + 10 % P
(from ICEMASS, Oerlemans)
Future response – annual sensitivity
+ 1K, + 10 % P (from ICEMASS Oerlemans)