Principles of snow melt How does snow melt?€¦ · Principles of snow melt GEO4430 snow hydrology...
Transcript of Principles of snow melt How does snow melt?€¦ · Principles of snow melt GEO4430 snow hydrology...
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Principles of snow melt
GEO4430 snow hydrology21.03.2006
Thomas V. [email protected]
How does snow melt?
• We need energy to melt snow/ ice.
fwwe
fwew
fs
LEh
Lh
LmE
ρ
ρ
=
⋅=
⋅=
K
E – energy (J) ρw – density (kg m-3) of waterms – mass (kg) of snow hwe – height of snow (m w.e.)Lf – latent heat of fusion
= 333400 J kg-1
• Energy flux onto a unit surface:
Q (Wm-2) = E (J) / t (s)
Amount of energy per unit time
Where does the energy come from?
S↓
S↑ L↑
L↓
Sensible heat flux& latent heat flux
Wind
Precipitation
Snow surface
ATMOSPHERE
Conduction (snow & ice)
ground
MELTING
MPGLHR QQQQQQ +++++=0
↑−↓+↑−↓= LLSSQR
Energy balance
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Radiation
• Black body radiation (Stefan-Boltzmann law)Q = σ T4
σ = 5.6703*10-8 W m-2 K-1
T))))))
)))))))))
))) Electromagnetic radiation
Real world:Gray body radiationQ = ε σ T4ε – emissivity [0,1]
Radiation
Wien’s law:
λmax = 2.88*10-3 T-1
[m] [m K] [K]
Electromagneticspectrum
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Radiation
GLOBAL RADIATION
• S: 0.15-5 µm• Direct / diffuse component
DEM of 25m resolution
Engabreen
1-Jul 11-Jul 21-Jul 31-Jul 10-Aug 20-Aug 30-Aug0
200
400
600
800
1-Jul 11-Jul 21-Jul 31-Jul 10-Aug 20-Aug 30-Aug0
200
400
600
800MEASURED GLOBAL RADIATION
POTENTIAL DIRECT SOLAR RADIATION
1994
Longwave radiation• 4-120µm• Emitted by atmosphere
(water vapour, CO2, ozone)• Function of air temperature
and humidity (cloudiness)
G
R L↑
L↓
Sensible heat flux& latent heat flux
Wind
Precipitation
SNOW
ATMOSPHERE
Conduction (snow & ice)
MELTING
L↑=εσT4
Max = 316 Wm2
L acts day & night
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Cloud effect:
Why are values positive in polar regions???
reflexion
0.15rain forest0.2grass0.1soil, dark0.3 – 0.45glacier ice0.4 – 0.7old snow0.75 – 0.95new snow
shortwave reflectance = albedo
snow looks white!!
Longwave reflectance of snow: < 0.1 snow is dark on IR image!
reflectance = 1 - emissivity snow emits a lot L↑
Why??
Turbulent heat fluxesSensible heat flux• Function of temperature gradient• Function of wind speed
G
R L↑
L↓
Sensible heat flux& latent heat flux
Wind
Precipitation
GLACIERConduction (snow & ice)
MELTING
Latent heat flux• Function of vapour pressure gradient• Function of wind speed
Fluxes also affected by• Surface roughness• Atmospheric stability
Turbulent exchange
wind speed
surface roughness
turb
ulen
t mix
ing
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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
Refreezing of 1 g water warms 160 g snow by 1 K
Dry conditions: Sublimation of snow occursLs = 8*Lf 8x less ablation than under wet conditions
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
Refreezing of 1 g water warms 160 g snow by 1 K
Removing cold content
Vs = 1 m3
Ts = -1 °C
Tw = 0 °Cmelt-water
snow
Condition for melt: snow must be at meltingtemperature, otherwise refreezing will occur
Cold content = energy needed to bring the snow / ice to 0 °C.
In the given example, refreezing of 2.5 l melt-water is needed to compensatefor the cold content of the snow pack (snow density, ρs=400 kg m-3 ).
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Cold content
-8.0 -4.0 0.0Snö temp
-0.8
-0.4
0.0
Dju
p
-0.8
-0.4
0.0
-0.8
-0.4
0.0
snow temp
dept
h
Precipitation…
Energy partinioning
in [%] out [%]
5892
0.211
318
7076
0.43
2724
Niwot Ridge, Colorado, USA
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high windspeed, dry & warm air, low cloudiness
Energy partitioning (%)
-97-353066Storglaciären, Sweden
-100084844Peytoglacier, Canada
-980-21090Hintereisferner, Austria
-940-6892Aletschgletscher, Switzerland
QMQGQLQHQRGlacier
Summary
•• IceIce and and snowsnow meltmelt are are determineddetermined by the by the energyenergy balancebalanceDo not Do not necessarilynecessarily meltmelt at air at air temperaturetemperature >= 0>= 0°° CC
•• SnowSnow//iceice surface temperaturesurface temperature must be must be raisedraised to 0to 0°°C C beforebefore meltingmelting cancan occuroccur (2 steps: (2 steps: warmingwarming, , meltingmelting))
•• FixedFixed maximum maximum surfacesurface temperaturetemperature (0(0°°C) C) under under meltingmelting conditionsconditions: : constantconstant LL↑↑ = 316 Wm= 316 Wm22,,surfacesurface vapourvapour pressurepressure = 611 = 611 PaPa
•• OftenOften netnet radiationradiation dominant dominant sourcesource of of energyenergy
•• SublimationSublimation reducesreduces energyenergy availableavailable for for meltmelt
Austfonna 2005
radiation components(S↓, S↑, L ↓, L↑)
temperaturehumidity
wind speed & direction
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surface lowering (melt)
alternative use: limbo championship…☺
snow/ ice temperature
Meteo data