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Snow Energy Balance T.H. Painter, NSIDC

Snow Energy Balance T.H. Painter, NSIDC. Energy Balance. Conservation of Energy. Energy Balance. Energy Balance Equation. where  = albedo S = solar irradiance L * = net longwave flux Q s = sensible heating flux Q v = latent heating flux Q g = ground heating flux

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Snow Energy Balance T.H. Painter, NSIDC

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  1. Snow Energy BalanceT.H. Painter, NSIDC

  2. Energy Balance Conservation of Energy

  3. Energy Balance

  4. Energy Balance Equation where  = albedo S = solar irradiance L* = net longwave flux Qs = sensible heating flux Qv = latent heating flux Qg = ground heating flux Qm = melting energy flux dU/dT = change in internal energy

  5. Snowpack Energy and Melt • Bring snowpack to 0 C (remove “cold content”) • Melt snow (overcome latent heat of fusion) • Get the water into and through the snowpack (complicated) • Melt enough that water drains when surface melt occurs (make the pack “ripe”)

  6. Solar Irradiance, S • TOA controlled by • Temperature of Sun • Emissivity of Sun • Planck’s Law • Locally controlled by • Atmospheric optical depth • Solar zenith angle (latitude and time of day) • Local slope and aspect

  7. Planck Equation where Mis the radiant exitance (W m-2m-1), h is Planck’s constant, c is the speed of light, k is Boltzmann’s constant,  is wavelength, T is temperature.

  8. Planck Curves

  9. Peak Wavelength of Emission Wien’s Displacement Law Willhelm Wien  in micrometers T in Kelvin

  10. Albedo • Controlled by snow grain size • Controlled by snow impurities • Controlled by snow density? • Controlled by irradiance spectrum dist, geometry, etc. • Range: 0.35 – 0.9

  11. Snow Albedo

  12. Spectral albedo  = 0.72  = 0.43

  13. Net Shortwave • Winter  = 0.85: (1-0.85)*700 = 105 W m-2 • Spring  = 0.55: (1-0.55)*1100 = 495 W m-2 Winter Spring

  14. Longwave (Terrestrial) Radiation • Controlled by temperature • Controlled by emissivity • Stefan-Boltzmann’s Law • Range of Emissivity: 0.97-0.99

  15. Planck Curves again

  16. Integrate Planck’s Equation where  is emissivity,  is the Stefan Boltzmann constant, and T is temperature in Kelvin

  17. Shortwave versus Longwave

  18. Longwave from Snow • Dry Snow • Ts = 253.15 K • M = 0.98 x 5.67 x 10-8 x 253.154 • M = 228 W m-2 • Melting Snow • Ts = 273.15 K • M = 0.98 x 5.67 x 10-8 x 273.154 • M = 309 W m-2

  19. Longwave Irradiance • Incoming longwave depends on atmospheric optical depth, cloud height, and temperature, as well as field of view (vegetation, etc.) Winter Spring

  20. Net Longwave • Dry Snow • Clear Sky L - L = 138 – 228 = -90 W m-2 • Cloudy L - L = 240 – 228 = 12 W m-2 • Wet Snow • Clear Sky L - L = 220 – 309 = -89 W m-2 • Cloudy L - L = 280 – 309 = -29 W m-2

  21. Sensible Heating • Turbulent exchange of atmospheric heat • Qs DS uz (Ta-Ts) • DS is the convective heat bulk transfer coefficient • uz is the wind speed at height z above the snow • Ta is the air temperature at height z • Ts is the snow surface temperature • Controlled by vertical gradient in temperature, surface roughness • Best measured through eddy-correlation

  22. Sensible Heating Senator Beck Alpine Study Plot, San Juan Mountains, CO

  23. Latent Heating • Turbulent exchange of latent release associated with sublimation or condensation • Qv Dv uz (ea-es) • Dv is the latent heat bulk transfer coefficient • uz is the wind speed at height z above the snow • ea is the water vapor pressure at height z • es is the snow surface vapor pressure • Controlled by vertical gradient in vapor, surface roughness • Best measured through eddy-correlation

  24. Latent Heating Senator Beck Alpine Study Plot, San Juan Mountains, CO

  25. Ground Heating • Ground heating flux due to temperature gradient, respective thermal conductivities, and infiltration of meltwater into soils • Generally small component of snowpack energy balance Where K is the thermal conductivity.

  26. Change in Internal Energy • AKA ‘Cold Content’ • Richard Armstrong will discuss the details of snowpack metamorphism and therein will discuss internal energy

  27. Melting Energy Flux • Residual in Energy Balance equation

  28. Spectral albedo Snowmelt flux SWE Snowmelt Modeling clean 0.72 dirty 0.43 SNTHERM.89 (CRREL- Jordan, 1990) Met inputs from 3500 m, Tokopah Basin, Sierra Nevada, CA

  29. Alpine Site Sub-alpine Site

  30. Energy Balance Sites • Solar irradiance (K&Z CM21) • Reflected solar (K&Z CM21) • Terrestrial irradiance (K&Z CG4) • Terrestrial emission (Everest IR) • Relative humidity • Wind speed and direction • Air temperature • Snow temperatures in stratigraphy

  31. Slope Correction to Albedo

  32. Energy Balance - 2005

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