How does snow melt?
Principles of snow melt
• We need energy to
melt snow/ ice.
GEO4430 snow hydrology
21.03.2006
E = ms ⋅ L f
K = ρ w hwe ⋅ L f
hwe =
Thomas V. Schuler
t.v.schuler@geo.uio.no
E
ms
Lf
E
ρwLf
– energy (J)
– mass (kg) of snow
– latent heat of fusion
= 333400 J kg-1
ρw
hwe
– density (kg m-3) of water
– height of snow (m w.e.)
Energy balance
0 = QR + QH + QL + QG + QP + QM
• Energy flux onto a unit surface:
Q (Wm-2) = E (J) / t (s)
QR = S ↓ −S ↑ + L ↓ − L ↑
ATMOSPHERE
Amount of energy per unit time
Precipitation
L↑
S↑
S↓
L↓
Sensible heat flux
& latent heat flux
Wind
Snow surface
Where does the energy come from?
MELTING
Conduction
(snow & ice)
ground
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Radiation
Radiation
))))
))
• Black body radiation (Stefan-Boltzmann law)
Q = σ T4
σ = 5.6703*10-8 W m-2 K-1
)
)))))
T
))))
Electromagnetic radiation
Wien’s law:
))
Real world:
Gray body radiation
Q = ε σ T4
ε – emissivity [0,1]
λmax = 2.88*10-3 T-1
[m]
[m K]
[K]
Electromagnetic
spectrum
2
Radiation
DEM of 25m
resolution
Engabreen
GLOBAL RADIATION
• S: 0.15-5 µm
• Direct / diffuse component
800
POTENTIAL DIRECT SOLAR RADIATION
Longwave radiation
• 4-120µm
• Emitted by atmosphere
(water vapour, CO2, ozone)
• Function of air temperature
and humidity (cloudiness)
ATMOSPHERE
600
400
200
0
1-Jul
11-Jul
21-Jul
31-Jul
10-Aug
20-Aug
30-Aug
MEASURED GLOBAL RADIATION
800
L↑=εσT4
Max = 316 Wm2
Precipitation
L↑
R
G
Sensible heat flux
& latent heat flux
L↓
Wind
600
SNOW
400
L acts day & night
200
0
1-Jul
11-Jul
21-Jul
31-Jul
1994
10-Aug
20-Aug
30-Aug
Conduction
(snow & ice)
MELTING
3
Cloud effect:
reflexion
shortwave reflectance = albedo
snow looks white!!
Why??
Why are values positive in polar regions???
new snow
0.75 – 0.95
old snow
0.4 – 0.7
glacier ice
0.3 – 0.45
soil, dark
0.1
grass
0.2
rain forest
0.15
Longwave reflectance of snow: < 0.1
snow is dark on IR image!
reflectance = 1 - emissivity
snow emits a lot L↑
Turbulent heat fluxes
Turbulent exchange
Sensible heat flux
• Function of temperature gradient
• Function of wind speed
Latent heat flux
Precipitation
Fluxes also affected by
• Surface roughness
• Atmospheric stability
L↑
R
G
turbulent mixing
wind speed
• Function of vapour pressure gradient
• Function of wind speed
Sensible heat flux
& latent heat flux
surface roughness
Wind
L↓
GLACIER
Conduction
(snow & ice)
MELTING
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Melt physics
Dry conditions:
Sublimation of snow occurs
Ls = 8*Lf
8x less ablation than under wet conditions
• To melt 1 kg snow/ice requires
334 000 J kg-1
Latent heat of fusion
• To sublimate 1 kg of snow requires
2 600 000 J kg-1
Latent heat of sublimation (8x Lf !!!)
• To warm 1 kg of snow 1 K requires 2009 J kg-1 K-1;
ice: 2097 J kg-1 K-1
Specific heat capacity
Refreezing of 1 g water
warms 160 g snow by 1 K
Melt physics
• To melt 1 kg snow/ice requires
334 000 J kg-1
Latent heat of fusion
• To sublimate 1 kg of snow requires
2 600 000 J kg-1
Latent heat of sublimation (8x Lf !!!)
• To warm 1 kg of snow 1 K requires 2009 J kg-1 K-1;
ice: 2097 J kg-1 K-1
Specific heat capacity
Removing cold content
melt-water
snow
Tw = 0 °C
Vs = 1 m3
Ts = -1 °C
Condition for melt: snow must be at melting
temperature, otherwise refreezing will occur
Cold content = energy needed to bring the snow / ice to 0 °C.
Refreezing of 1 g water
warms 160 g snow by 1 K
In the given example, refreezing of 2.5 l melt-water is needed to compensate
for the cold content of the snow pack (snow density, ρs=400 kg m-3 ).
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Cold content
Precipitation…
snow
temp
Snö temp
-4.0
0.0
0.0
-0.4
-0.8
Djup
depth
-8.0
0.0
0.0
-0.4
-0.4
-0.8
-0.8
Energy partinioning
in [%]
out [%]
58
92
0.2
11
31
8
70
76
0.4
3
27
24
Niwot Ridge, Colorado, USA
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Energy partitioning (%)
high windspeed, dry & warm air, low cloudiness
Summary
• Ice and snow melt are determined by the energy balance
Do not necessarily melt at air temperature >= 0°
0° C
Glacier
QR
QH
QL
QG
QM
Aletschgletscher,
Switzerland
92
8
-6
0
-94
Hintereisferner,
Austria
90
10
-2
0
-98
Peytoglacier, Canada
44
48
8
0
-100
Storglaciären, Sweden
66
30
5
-3
-97
Austfonna 2005
radiation components
(S↓, S↑, L ↓, L↑)
wind speed & direction
temperature
humidity
• Snow/
Snow/ice surface temperature must be raised to 0°
0°C
before melting can occur (2 steps: warming,
warming, melting)
melting)
• Fixed maximum surface temperature (0°
(0°C)
under melting conditions:
conditions: constant L↑ = 316 Wm2,
surface vapour pressure = 611 Pa
• Often net radiation dominant source of energy
• Sublimation reduces energy available for melt
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Meteo data
surface lowering (melt)
snow/ ice temperature
alternative use: limbo championship…☺
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