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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)

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Mass balance measurements on Austfonna, Svalbard Thank you !