How does snow melt? Principles of snow melt. Energy balance. GEO4430 snow hydrology Energy flux onto a unit surface:

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1 Principles of snow melt How does snow melt? We need energy to melt snow/ ice. GEO443 snow hydrology E = m L h we s K = ρ h = w w we f E ρ L L f f Thomas V. Schuler t.v.schuler@geo.uio.no E energy (J) ρ w density (kg m-3) of water m s mass (kg) of snow h we height of snow (m w.e.) L f latent heat of fusion = 3334 J kg -1 Energy flux onto a unit surface: Energy balance = Q + Q + Q + Q + Q + Q R H Q R L G P = S S + L L M Q (Wm -2 ) = E (J) / t (s) ATMOSPHERE Precipitation Amount of energy per unit time S L Sensible heat flux & latent heat flux S L Wind Where does the energy come from? Snow surface MELTING Conduction (snow & ice) ground 1

2 Radiation Radiation Black body radiation (Stefan-Boltzmann law) Q = σ T 4 σ = 5.673*1-8 Wm -2 K -1 )))))) )))))) Electromagnetic radiation Wien s law: T )))))) Real world: Gray body radiation Q = ε σ T4 ε emissivity [,1] λ max = 2.88*1-3 T -1 [m] [m K] [K] Electromagnetic spectrum 2

3 Radiation DEM of 25m resolution GLOBAL RADIATION S:.15-5 µm Direct / diffuse component Engabreen 8 POTENTIAL DIRECT SOLAR RADIATION Jul 11-Jul 21-Jul 31-Jul 1-Aug 2-Aug 3-Aug MEASURED GLOBAL RADIATION 1-Jul 11-Jul 21-Jul 31-Jul 1-Aug 2-Aug 3-Aug 1994 Longwave radiation 4-12µm Emitted by atmosphere (water vapour, CO 2, ozone) Function of air temperature and humidity (cloudiness) L =εσt 4 Max = 316 Wm 2 L acts day & night G R MELTING L L ATMOSPHERE Precipitation Sensible heat flux & latent heat flux SNOW Wind Conduction (snow & ice) 3

4 Cloud effect: reflexion shortwave reflectance = albedo new snow old snow glacier ice soil, dark grass rain forest snow looks white!! Why?? Why are values positive in polar regions??? Longwave reflectance of snow: <.1 reflectance = 1 - emissivity snow is dark on IR image! snow emits a lot L Turbulent heat fluxes Sensible heat flux Function of temperature gradient Function of wind speed Latent heat flux Function of vapour pressure gradient Function of wind speed Fluxes also affected by Surface roughness Atmospheric stability G R MELTING L L Precipitation Sensible heat flux & latent heat flux Wind GLACIER Conduction (snow & ice) wind speed Turbulent exchange turbulent mixing surface roughness 4

5 Melt physics Dry conditions: Sublimation of snow occurs L s = 8*L f 8x less ablation than under wet conditions To melt 1 kg snow/ice requires 334 J kg -1 Latent heat of fusion To sublimate 1 kg of snow requires 2 6 J kg -1 Latent heat of sublimation (8x L f!!!) To warm 1 kg of snow 1 K requires 29 J kg -1 K -1 ; ice: 297 J kg -1 K -1 Specific heat capacity Refreezing of 1 g water warms 16 g snow by 1 K Melt physics To melt 1 kg snow/ice requires 334 J kg -1 Latent heat of fusion To sublimate 1 kg of snow requires 2 6 J kg -1 Latent heat of sublimation (8x L f!!!) To warm 1 kg of snow 1 K requires 29 J kg -1 K -1 ; ice: 297 J kg -1 K -1 Specific heat capacity Refreezing of 1 g water warms 16 g snow by 1 K melt-water snow Removing cold content T w = C V s = 1 m 3 T s = -1 C Condition for melt: snow must be at melting temperature, otherwise refreezing will occur Cold content = energy needed to bring the snow / ice to C. In the given example, refreezing of 2.5 l melt-water is needed to compensate for the cold content of the snow pack (snow density, ρ s =4 kg m -3 ). 5

6 Cold content Precipitation snow Snö temp Djup depth Energy partinioning in [%] out [%] Niwot Ridge, Colorado, USA 6

7 Energy partitioning (%) Glacier Q R Q H Q L Q G Q M high windspeed, dry & warm air, low cloudiness Aletschgletscher, Switzerland Hintereisferner, Austria Peytoglacier, Canada Storglaciären, Sweden Summary Austfonna 25 wind speed & direction Ice and snow melt are determined by the energy balance Do not necessarily melt at air temperature >= C Snow/ice surface temperature must be raised to C before melting can occur (2 steps: warming, melting) Fixed maximum surface temperature ( C) under melting conditions: constant L = 316 Wm 2, surface vapour pressure = 611 Pa Often net radiation dominant source of energy Sublimation reduces energy available for melt radiation components (S, S, L, L ) temperature humidity 7

8 Meteo data surface lowering (melt) snow/ ice temperature alternative use: limbo championship 8