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
Qs = sensible heating flux
Qv = latent heating flux
Qg = ground heating flux
Qm = melting energy flux
dU/dT = change in internal energy
dT
dUQQQLSQ gvsm *1
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”)
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
Planck Equation
1
2
5
2
Tk
hc
e
hcM
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.
Planck Curves
Wien’s Displacement
LawWillhelm Wien
in micrometers
T in Kelvin
Peak Wavelength of Emission
T
79.2897max
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
Snow Albedo
Spectral albedo
= 0.72 = 0.43
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
Longwave (Terrestrial) Radiation
• Controlled by temperature• Controlled by emissivity• Stefan-Boltzmann’s Law• Range of Emissivity: 0.97-0.99
Planck Curves again
Integrate Planck’s Equation
where is emissivity, is the Stefan Boltzmann constant, and T is temperature in Kelvin
4
05
2
1
2
T
d
e
hc
Tk
hc
Shortwave versus Longwave
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
Longwave Irradiance• Incoming longwave depends on atmospheric
optical depth, cloud height, and temperature, as well as field of view (vegetation, etc.)
Winter Spring
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
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
Sensible Heating
Senator Beck Alpine Study Plot, San Juan Mountains, CO
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
Latent Heating
Senator Beck Alpine Study Plot, San Juan Mountains, CO
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
dz
dTKQg
Where K is the thermal conductivity.
Change in Internal Energy
• AKA ‘Cold Content’• Richard Armstrong will
discuss the details of snowpack metamorphism and therein will discuss internal energy
dt
dU
Melting Energy Flux
• Residual in Energy Balance equation
Snowmelt ModelingSpectral albedo
SWESnowmelt flux
SNTHERM.89 (CRREL- Jordan, 1990)
Met inputs from 3500 m, Tokopah Basin, Sierra
Nevada, CA
clean 0.72
dirty 0.43
Alpine Site Sub-alpine Site
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
Slope Correction to Albedo
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
70.3 70.35 70.4 70.45 70.5 70.55 70.6 70.65 70.7 70.75
Day of Year 2005
Alb
edo
Uncorrected
Corrected
aspectE
slopeS
ESS sunsunsun
)cos(sinsincoscoscos 0
Energy Balance - 2005