Reaction of Glaciers due to Climate Changes What is a glacier? Findelengletscher (Valais) A glacier is a river of ice flowing under its own weight. It pushes large amounts of silt, gravel, and rock as it travels. Over a pe- riod of many years snow accumulations become deep enough to form glacier ice, which flows because of its own weight. Glaciers form in conditions where snow accumulates in suc- cessive years and does not completely melt during summer months. Eventually the snow crystals are subject to pressure metamorphism from the growing weight of the overlying snow and melt - freeze metamorphism from fluctuating warmer and cooler temperatures. The change from small individual ice grains to the very large, dense, and compressed glacial ice crystals forms a mass of ice through the process known as firnification. Reaction of Glaciers due to Climate Changes Basics of glacier flow Flowlines in a glacier Glaciers accumulate new ice from snowfall in winter months and lose ice during melting that occurs in summer months. Accumulation of ice occurs in the higher altitudes in a region called the accumulation zone, and loss occurs at the lower lat- itudes, in a region called the ablation zone. The point where these two regions meet is called the equilibrium line (ELA) and marks the highest level of retreat of winter snow. The equilib- rium line varies from place to place and from year to year de- pending on the climate. If accumulation is greater than abla- tion, the glacier will grow or advance, and if ablation is greater than accumulation the glacier will shrink or retreat. Whether a glacier is growing or shrinking is determined at the equilibrium line, not at the terminus. A glacier moves downhill under the force of gravity and the weight of the large ice mass. Distances from centimeters to meters per day are common. The bottom surface of the glacier slides along the bedrock aided by lubricating melt water in a process know as basal sliding. The ice mass itself also flows internally without breaking in a process called ductile deforma- tion. Friction is greatest on the bottom and the sides because these are the surfaces contacting rock. Friction explains why glaciers move more quickly on the surface. One can visual- ize the layers flowing at different rates similar to the way cards slide past one another as you spread a deck.
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Reaction of Glaciers due to Climate Changes
What is a glacier?
Findelengletscher (Valais)
A glacier is a river of ice flowing under its own weight. It pusheslarge amounts of silt, gravel, and rock as it travels. Over a pe-riod of many years snow accumulations become deep enoughto form glacier ice, which flows because of its own weight.
Glaciers form in conditions where snow accumulates in suc-cessive years and does not completely melt during summermonths. Eventually the snow crystals are subject to pressuremetamorphism from the growing weight of the overlying snowand melt - freeze metamorphism from fluctuating warmer andcooler temperatures. The change from small individual icegrains to the very large, dense, and compressed glacial icecrystals forms a mass of ice through the process known asfirnification.
Reaction of Glaciers due to Climate Changes
Basics of glacier flow
Flowlines in a glacier
Glaciers accumulate new ice from snowfall in winter monthsand lose ice during melting that occurs in summer months.Accumulation of ice occurs in the higher altitudes in a regioncalled the accumulation zone, and loss occurs at the lower lat-itudes, in a region called the ablation zone. The point wherethese two regions meet is called the equilibrium line (ELA) andmarks the highest level of retreat of winter snow. The equilib-rium line varies from place to place and from year to year de-pending on the climate. If accumulation is greater than abla-tion, the glacier will grow or advance, and if ablation is greaterthan accumulation the glacier will shrink or retreat. Whether aglacier is growing or shrinking is determined at the equilibriumline, not at the terminus.A glacier moves downhill under the force of gravity and theweight of the large ice mass. Distances from centimeters tometers per day are common. The bottom surface of the glacierslides along the bedrock aided by lubricating melt water in aprocess know as basal sliding. The ice mass itself also flowsinternally without breaking in a process called ductile deforma-tion. Friction is greatest on the bottom and the sides becausethese are the surfaces contacting rock. Friction explains whyglaciers move more quickly on the surface. One can visual-ize the layers flowing at different rates similar to the way cardsslide past one another as you spread a deck.
Reaction of Glaciers due to Climate Changes
Some important questions:
• How big are glaciers? (area, volume, sea-levelequivalent)
• How fast do glaciers move?
• How much water runs off? (hydrology)
• How do glaciers erode old landscape or buildup new landscape? (geomorphology)
• How do glaciers change with climate? (sensi-tivity to climate change, response time)
Reaction of Glaciers due to Climate Changes
Tongue of Aletschgletscher 1885 (S. Coutterand)
Tongue of Aletschgletscher 2000
Reaction of Glaciers due to Climate Changes
”Procès du Léman” (legal action, 1877-1884) due to damagesat the shore of lake Léman because of high lake water level
F.A. Forel (1841-1912) professor of medicine. He pioneeredthe study of lakes: founder of limnology. He acted as expertin the legal actions and suggested that the increased glaciermelt in the preceeding years could be the reason for the highlake level.
Reaction of Glaciers due to Climate Changes
Glacier Monitoring in Switzerland (GLAMOS)
1
2
3
45
6
7
8
910111213
141516
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18
19 20
21
22
2324
2526
27282930
3132
33
3435
3637
38
39404142
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4445
46
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49
505152
535455
5657
5859
6061
6263
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65
6667
6869 70
7172
7374
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8081
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109111
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117 118
119120 352
Network of glacier length change
Network of glacier volume change
Reaction of Glaciers due to Climate Changes
Glacier length changes
0
20406080
100120
Mea
sure
men
ts
1900 1950 2000
0
20
40
60
80
100
Fra
ctio
n (
%)
retreating
stationary
advancing
Percentage of advancing, retreating and stationary glaciers inSwitzerland since 1879
1900 1950 2000−3000
−2000
−1000
0
Cum
ulat
ive
leng
th c
hang
e (
m)
Grosser Aletsch (22.7 km)
Rhone (7.8 km)
Trient (4.0 km)
Pizol (0.5 km)
Cumulative length changes of Grosser Aletschgletscher,Rhonegletscher und Trientgletscher
Reaction of Glaciers due to Climate Changes
Glacier volume change
Rhonegletscher 1856 (left) and today
1900 1950 2000
−40
−30
−20
−10
0
Mas
s ch
ange
(m
w.e
.)
−1000
−500
0
Leng
th v
aria
tion
(m
)
Left: Cumulative length change (up) and cumulative mass bal-ance change (bottom). Blue dots are computed yearly val-ues. Red dots are values inferred from surface topographychanges.Right: Topographic map of Rhonegletscher for 1880.
Reaction of Glaciers due to Climate Changes
Glacier changes in Switzerland (area and volume)(Farinotti et al., 2009, An estimate of the glacier ice volume in the Swiss
Alps, Global and Planetary Change, 68, 225-231)
km2 km3 km3/a %
1850 1621 ≈1101999 1063 74 ≈-0.25 -352008 65 -1.00 -41
Climate change in the last century
Summer temperature (deviations from long-term mean)
1880 1900 1920 1940 1960 1980 2000
−20
0
20
Abw
eich
ung
des
Nie
ders
chla
gs (
%)
Annual precipitation (deviations from long-term mean in %)
Reaction of Glaciers due to Climate Changes
Processes governing the mass balance of a glacier:
1. Accumulation (snow deposition)
• Air-mass characteristics
• Topography
• Wind/avalanche redistribution of snow
2. Ablation (melting from heat)
• Solar input
• Surface reflectivity (albedo)
• Clouds
• Wind
• Air temperature and humidity
Reaction of Glaciers due to Climate Changes
Mass balance of a glacier: definitions
t1: 1. October; t2: 30. September; hydrological year
Mass balance rate (point): b(x, y, t) = c(x, y, t) + a(x, y, t)
unit: [ kgm2
1s] or [m water equivalent 1
s]
Mass balance (point): b(x, y) =t∫
t1
(c(x, y) + a(x, y)) dt
unit: [ kgm2 ] or [m water equivalent]
Annual mass balance (point): ba = bw + bs (1.10 - 30.9)bw: winter balance (1. October - 30. April)bs: summer balance (1. Mai - 30. September)
Reaction of Glaciers due to Climate Changes
Glacier wide mass balance: B =∫
Sb(x, y)dS
unit: [kg] or [m3 water equivalent]
S: glacier surface area
Mean specific mass balance: b = BS
unit: [m water equivalent] or [kgm2 ]
(glacier-wide ice volume change)
English term Symbol Unit Deutscher Ausdruckmass balance rate b kg
m2 sms
Massenbilanzrate
mass balance b kgm2 m Massenbilanz
annual mass balance bakgm2 m Jahres-Massenbilanz
glacier wide mass balance B kg m3 gesamte Massenbilanz
glacier wide annual mass balance Ba kg m3 gesamte Jahres-Massenbilanz
average specific mass balance b kgm2 m spezifische Massenbilanz
average specific annual mass balance bakgm2 m spezifische Jahres-Massenbilanz
Reaction of Glaciers due to Climate Changes
Determination of the mass balance of a glacier: in-situ mea-surement at a point.
right: in the accumulation arealeft: in the ablation area
Reaction of Glaciers due to Climate Changes
Mass balance of glaciers: results for 4 glaciers
(Huss et al. (2008), Determination of the seasonal mass balance of fourAlpine glaciers since 1865, Journal of Geophysical Research, 113, F01015)
Silvretta, 3 km2 Rhone, 16 km2 Aletsch, 86 km2 Gries, 6 km2
Reaction of Glaciers due to Climate Changes
Long term changes of the melt rates in the Swiss Alps(Huss et al. (2009), Strong glacier melt in the 1940s due to enhanced solarradiation, Geophysical Research Letters, 36, L23501)
Säntis
Davos
Aletsch
Clariden
Silvretta
Glacier siteMeteo (T)Meteo (P)Radiation (1936−)Radiation (1981−)0 10 20 30 40 50
km
SWITZERLAND
Seasonal point mass balance records since 1914
19472003
−20
0
20
40
60
80
00 500
600
700
Rel
ativ
e m
elt a
nom
aly
(%)
Pos
tive
Deg
ree
Day
s (
oC
)
a
1920 1940 1960 1980 2000
Melt anomalySmoothed anomalyPositive Degree Days
Period mean melting anomaly
+17.0%
1942−1952−18.5%
1971−1981 +13.4%
1998−2008
Ano
mal
y (%
)
−10
0
10
00
−20
−10
0
10
20
30
0
Glo
bal r
adia
tion
anom
aly
(W m
−2)
b
243 W m−2
218 W m−2 225 W m−2
Jun−Aug globalradiation at Davos
1920 1940 1960 1980 2000
Four-site average of annual glacier melt anomaly and sum of daily air tem-peratures above 0◦C over the year at the study sites (dashed), low-passfiltered using 11-year running means. Glacier melt anomalies for extremedecadal periods are shown by bars. (b) June to August anomaly in mea-sured global radiation at Davos. Period means are given.
Reaction of Glaciers due to Climate Changes
Equilibrium Line Altitude (ELA): sensitivity to precip-itation (P) and temperature (T)
Function of P und T at the ELA: f(P, T) = 0
P = a+ bT + cT2 (a=645, b=296, c=9)
A climate change means that a change ∆P and∆T will occur at an elevation z
—> zELA will move from z to z +∆z
Reaction of Glaciers due to Climate Changes
∆T + ∂T∂z
∆z =(∂P∂T
)
z
(
∆P + ∂P∂z
∆z)
—> ∆z =
(
∆T −∆P(∂P∂T
)−1
z
)
1
∂P∂z
(∂P∂T
)−1
z−∂T
∂z
∆z = 111∆T − 0.33∆N(T(summer); [
oC]; Na; [mma])
∆T = +1oC → ∆N = +336mma
(Ohmura et al. (1992), Climate at the equilibrium line altitude of glaciers,Journal of Glaciology, 38(130), 397-411)
Reaction of Glaciers due to Climate Changes
We assume a glacier in a steady state. At time to we perturbeinstantaneously the climate. Before and after to the climate isconstant. Given a climate perturbation inducing a mass bal-ance perturbation ∆b:
• What will be the length change of the glacier?
• How long will the glacier need to reach a new staedystate?
A glacier is in a steady state when: Ba =∫
S
ba · dS =
Because of the climate change at to Ba 6= 0 for t > to
Reaction of Glaciers due to Climate Changes
We assume a glacier with a constant width and a surface mass
balance only dependent on x: ba(x):
l0∫
0ba(x) · dx =
Reaction of Glaciers due to Climate Changes
We perturb ba(x) at time to with ∆b uniformly overthe whole glacier
The new steady state will be reached when:
l0+∆l∫
0(ba(x) +∆b(x))dx =
The new steady state will be reached at time tG.
tG − to = tR: reaction time of the glacier
Reaction of Glaciers due to Climate Changes
l0+∆l∫
0(ba(x) +∆b(x))dx =
l0∫
0
ba(x)dx
︸ ︷︷ ︸
+
l0∫
0
∆b(x)dx
︸ ︷︷ ︸
+
l0+∆l∫
l0
ba(x)dx
︸ ︷︷ ︸
+
l0+∆l∫
l0
∆b(x)dx
︸ ︷︷ ︸
=
∆b = 1l0
l0∫
0∆b(x)dx
bz = 1∆l
l0+∆l∫
l0
ba(x)dx (mass balance at the glacier terminus)
l0∆b+ bz ∆l ≈ 0
—> ∆l ≈l0∆b
−bz
Reaction of Glaciers due to Climate Changes
How much time is needed to reach the new steady state, or to
fill the volume difference ∆V between the two steady states?
tV = volume differencemass balance perturbation = ∆V
l0∫
0
∆b(x) dx
Reaction of Glaciers due to Climate Changes
tV = ∆Vl0∫
0
∆b(x)dx
= ∆V
l0∆b
How can we determine ∆V ?We assume that most of the glacier geometry change occursin the ablation area
We assume that the new steady state geometry can be ob-
tained by moving the glacier below the ELA by ∆l:
∆V ≈ hmax∆l
Reaction of Glaciers due to Climate Changes
Unteraargletscher,1841-1845 (upper picture) andtoday
Reaction of Glaciers due to Climate Changes
These 2 pictures confirm the assumption that most of the ge-
ometry changes occur in the glacier tongue area
Reaction of Glaciers due to Climate Changes
tV ≈ hmax∆l
l0∆b≈ hmax∆l
−bz ∆l≈ −hmax
bz
tR ≈ tV
For Alpine glaciers:
typical ice thickness: hmax ≈ 200m
typical mass balance at the glacier terminus: bz ≈ −5 ma
→ tR ≈ 40 years
→ The typical reaction time of Alpine glacier tR is some decades
Reaction of Glaciers due to Climate Changes
No dependance of the mass balance on elevation has beentaken into account into volume time scale τvJ
Total mass balance as a function of volume and area: B(V,A, t)
Linear expansion around an arbitrary reference state (A′, V ′):
B(V,A, t) = B(V ′, A′, t) + ∂B∂V
(V − V ′) + ∂B∂A
(A− A′)
= B′ +∂B
∂V︸︷︷︸ge
∆V +∂B
∂A︸︷︷︸
be
∆A
We define the effective ice thickness as: He =∂V∂A
(constant)
With:
∆V = ∂V∂A
∆A
and
B = ∂V∂t
= d(∆V )dt
It follows that:
d(∆V )dt
= ge∆V + be∆A+B′
= ge∆V + beHe∆V +B′
=
(
ge +be
He
)
︸ ︷︷ ︸
−(τvH)−1
∆V +B′
d(∆V )dt
= − 1τvH
∆V +B′
With
ge = g = d ˙b(z)dz
be = bt
We obtain the ”Harrison time scale” τvH:
τvH =
(
g + btHe
)−1= 1
−btHe
−g= He
−bt−gHe
Reaction of Glaciers due to Climate Changes
Integration of:
d(∆V )dt
= − 1τvH
∆V +B′
reads:
∆V (t) = B′ τvH
(
1− e− t
τvH
)
= ∆V∞
(
1− e− t
τvH
)
The final glacier volume change is: ∆V∞ = B′τvH
• if τvH > 0, ∆V is finite
• if τvH < 0, ∆V is unstable
– if B′ > 0 ∆V grows without limit
– if B′ < 0 ∆V decreases and the glacier vanishes
τvH = He
−bt−gHe
bt is always < 0 –> −bt is always > 0
gHe ist always > 0
–> −bt − gHe can be > 0 or < 0 depending onthe magnitude of both terms
bt is stabilizing the glacier response
gHe is destabilizing the glacier response
• Melting at the tongue limits glacier growth
• Feedback ”surface elevation (ice thickness)” and ”accu-mulation” (through g) can lead to unlimited glacier growth
Reaction of Glaciers due to Climate Changes
References:
• Farinotti, D., Huss, M., Bauder, A., and Funk, M. (2009).An estimate of the glacier ice volume in the Swiss Alps.Global and Planetary Change, 68(3):225–231.
• Huss, M., Bauder, A., Funk, M., and Hock, R. (2008). De-termination of the seasonal mass balance of four Alpineglaciers since 1865. Journal of Geophysical Research,113(F1):F01015.
• Huss, M., Funk, M., and Ohmura, A. (2009). StrongAlpine glacier melt in the 1940s due to enhanced so-lar radiation. Geophysical Research Letters, 36(L23501).doi:10.1029/2009GL040789.
• Jóhannesson, T., Raymond, C. F., and Waddington, E. W.(1989). Time-scale for adjustment of glaciers to changesin mass balance. Journal of Glaciology, 35(121):355–369.
• Lüthi, M. P. (2009). Transient response of idealized glaciersto climate variations. Journal of Glaciology, 55(193):918–930.
• Ohmura, A., Kasser, P., and Funk, M. (1992). Climateat the equilibrium line of glaciers. Journal of Glaciology,38(130):397–411.
• W.D. Harrison, D.H. Elsberg, K.A. Echelmeyer, R. M. Krim-mel (2001), On the characterization of glacier responseby a single time-scale, Journal of Glaciology, 659–664,(47) 159
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