Energy balance and warming Ned Bair US Army Corps of Engineers Cold Regions Research and Engineering Laboratory Earth Research Institute, UC - Santa Barbara
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
Radiation • All bodies emit electromagnetic radiation as a function of their temperature • This can be modeled by the Steffan-Boltzmanequation
Energy balance for dry snow • Dry snow • M=0 • Wet, ripe snow • G=0, because T is uniform R Net radiation G Heat flow into/out of pack H Sensible heat exchange L Latent heat exchange MMelt All units in W m-2
G, heat flow, Fourier’s Law Thermal conductivities 0.045 fiberglass 0.05-0.25 dry snow 0.56-0.61 water 16-24 stainless steel
Convective energy transfers warm dry air wind latent heat cold dry air cold humid air latent heat sensible heat sensible heat warm humid air mixing Negative net turbulent transfer Positive net turbulent transfer latent heat sensible heat sensible and latent heat
Condensing and freezing 1 g water vapor Phase changes of water Freezing 1 g water Cooling 1 g 1 C water to 0 C 1 cal 80 cal 720 cal
Positive radiation balance Negative radiation balance
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
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.
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.
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 0 10 38° 20 30 40 e(f) Height, cm 2-3 mm 50 pencil 4 finger fist 1 finger Hardness
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.
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.
Aspect and slope effects Direct Shortwave 300 W/m2 300 W/m2 Longwave 300 W/m2 (Reflected: 500-950 W/m2) 700 W/m2 1000 W/m2 Negative net radiation Positive net radiation Varmint’s Fresno Bowl
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
CUES TJ Bowl
Cumulative heat flow at snow surface (G) Increases: Sat 3/9 – 1761 kJ Sun 3/10 – 3822 kJ Mon 3/11 – 1017 kJ Increases: Sat 3/9 – 475 kJ Sun 3/10 – 751 kJ Mon 3/11 – 245 kJ
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.