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