Energy balance and warming
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Energy balance and warming
Ned Bair US Army Corps of Engineers Cold Regions Research and Engineering
LaboratoryEarth Research Institute, UC - Santa Barbara
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Heat transfer
• Radiation– Energy transfer via photons
• Sensible– Heat exchange from a change in temperature– 2 types:
• Conduction– Direct exchange of kinetic energy
• Conduction– Heat carried by bulk flow, i.e. wind
– Heat exchange from a change of temperature• Latent
– Heat exchange from a change of phase
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Radiation• All bodies emit electromagnetic radiation as a
function of their temperature• This can be modeled by the Steffan-Boltzman
equation
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Electromagnetic spectrum
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Energy balance for dry snow
R Net radiation
G Heat flow into/out of pack
H Sensible heat exchange
L Latent heat exchange
M Melt
All units in W m-2
• Dry snow– M=0
• Wet, ripe snow– G=0, because T is
uniform
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G, heat flow, Fourier’s Law
Thermal conductivities0.045 fiberglass0.05-0.25 dry snow0.56-0.61 water16-24 stainless steel
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Periodic: 0 10C, 10T T
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R, Net radiation
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H, Sensible heat
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H, Latent heat
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Convective energy transfers
mixing
warm dry air
cold humid air
warm humid air
sensible heat
sensible heat
latent heat
latent heat
sensible and latent heat
windcold dry airlatent heat
sensible heat
Negative net
turbulent transfer
Positive net
turbulent transfer
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131 cal 80 cal 720 cal
Cooling 1 g 1 C water to 0 C
Freezing 1 g water
Condensing and freezing 1 g water vaporPhase changes of water
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Negative radiation balance
Positive radiation balance
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Warming effects
• Generally, the effects of warming on avalanche formation are minor
• Not affected:– Layers deeper than 20-30 cm (e.g. the failure layer)– The stress bulb depth
• Affected:– E modulus of upper 20 cm of slab (increased
bending)– PST and ECT results
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The stress bulb and layers deeper than 20-30 cm are not affected
Exner, T., and B. Jamieson, 2008: The effect of snowpack warming on the stress bulb below a skier. International Snow Science Workshop.
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Warming effect on E modulus• No change in weak layer (wf) or layers in the slab deeper than 20
cm.• E modulus (stiffness) in layers < 20 cm decreased.• PST cut length decreased after cumulative energy inputs of 400 kJ
m-2.
Reuter, B. and Schweizer, J., 2012. The effect of surface warming on slab stiffness and the fracture behavior of snow. Cold Reg. Sci. Technol.: in press, doi: 10.1016/j.coldregions.2012.06.001.
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Warming case study, Hammil Bowl 3/11/13
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• Triggered at 10,550 ft on 38° N aspect at 11:30AM on 3/11/13• 2 skiers in old skin track, crown formed 200 vertical feet above
them• R2D2.5, crown 80 cm at deepest • HS 285cm
fist 4 finger 1 finger pencil
Heig
ht, c
m
Hardness
010
2030
4050
e(f)2-3 mm
38°
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Avalanche triggered here
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Weather Summary• March 6-9: 15.5” inches of new snow, 1.5” SWE, ~10% water at
MMSP’s Sesame site (9,014 ft).• Temperature change at CUES (9,645 ft) from low of -8 °C on March 10
to +6 °C at time of the accident, 11:30 AM on March 11.
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The E modulus in the upper 20-30 cm and PST cut lengths can be reduced
Reuter, B. and Schweizer, J., 2012. The effect of surface warming on slab stiffness and the fracture behavior of snow. Cold Reg. Sci. Technol.: in press, doi: 10.1016/j.coldregions.2012.06.001.
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Energy fluxes at CUES
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1000 W/m2
700 W/m2
Aspect and slope effects
Fresno
BowlVarmint’s
300 W/m2
Direct Shortwave
Longwave
300 W/m2
300 W/m2
Negative net
radiation
Positive net radiation
(Reflected: 500-950 W/m2)
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Steps to adjust net solar flux for TJ Bowl
• Calculate solar declination δ and solar longitude λ from measurement dates & times
• Calculate solar zenith angle μ0 and solar azimuth φ0 (i.e. local sun position on flat surface) from lat/lon, δ, and λ
• Calculate illumination angle μ from μ0 , φ0, slope angle, and slope azimuth
• Calculate ratio of sun on flat surface to slope s=μ/μ0
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CUES
TJ Bowl
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Cumulative heat flow at snow surface (G)
Increases:Sat 3/9 – 475 kJSun 3/10 – 751 kJMon 3/11 – 245 kJ
Increases:Sat 3/9 – 1761 kJSun 3/10 – 3822 kJMon 3/11 – 1017 kJ
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32Reuter, B. and Schweizer, J., 2012. The effect of surface warming on slab stiffness and the fracture behavior of snow. Cold Reg. Sci. Technol.: in press, doi: 10.1016/j.coldregions.2012.06.001.