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 radiationG Heat flow into/out of packH Sensible heat exchangeL Latent heat exchange M MeltAll 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

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

Heigh

t, cm

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

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.