Surface energy balance (2)
Review of last lecture
–
What is energy? 3 methods of energy transfer
–
The names of the 6 wavelength categories in the
electromagnetic radiation spectrum. The wavelength range
of Sun (shortwave) and Earth (longwave) radition
–
Earth’s energy balance at the top of the atmosphere.
Incoming shortwave = Reflected Shortwave + Emitted longwave
–
Earth’s energy balance at the surface.
Incoming shortwave + Incoming longwave = Reflected shortwave
+ Emitted longwave + Latent heat flux + Sensible heat flux
+ Subsurface conduction
Surface energy balance
Incoming shortwave + Incoming longwave = Reflected shortwave + Emitted longwave
+ Latent heat flux + Sensible heat flux + Subsurface conduction
SWdn
SWup
LWdn
LWup
LH
SH
dT/dt
Fc
Incoming solar radiation
SWdn = S cos
where
S is solar constant S=1366 Watts/m2
 is solar zenith angle, which is the angle between the
local zenith and the line of line of sight to the sun
Reflected solar radiation
SWup = SWdn 
where  is albedo, which is the ratio of
reflected flux density to incident flux density,
referenced to some surface.
Global map of surface albedo 
Incoming and surface emitted
longwave radiation
• Incoming longwave radiation can be
estimated from air temperature using the
blackbody approximation
• Surface emitted longwave radiation can be
estimated from surface temperature using
the blackbody approximation
Physical Representation of
Radiation
• Blackbodies: purely hypothetical bodies that absorb
and emit the maximum radiation at all wavelengths
• The Earth and the sun are close to blackbodies.
• The atmosphere is not close to blackbody, but it can
served as the first order approximation
Stefan-Boltzmann Law
• States that radiation emitted from a blackbody is
a function ONLY of temperature
• Hotter bodies emit more energy than colder bodies
I=T4
where I is the intensity of the radiation, T is the
temperature in K, and  is the Stefan-Boltzmann
constant, 5.67 x 10-8 W m-2 K-4)
• So, double T, 16x more radiation
• Earth (290K)= 401 Wm-2, Sun (6000K) = 7.3 x 106
Wm-2. So ISun >> Iearth
• Incoming LW (air-emitted):
LWdn = Tair4
• Surface emitted LW:
LWup=Ts4
Net longwave radiation
( LWdn - Lwup = Tair4 - Ts4 )
• Is generally small because air temperature is often
close to surface temperature
• Is generally smaller than net shortwave radiation
even when air temperature is not close to surface
temperature
• Important during the night when there is no
shortwave radiation
Surface “Sensible” and
“Latent” heat transfers
First, recall 2 other methods of
energy transfer in addition to
radiation:
1. Conduction
–
This is how excess heat in ground
is transferred to the atmosphere
via an extremely thin layer of air in
contact with the surface
2. Convection
–
Once the heat is transferred from
the surface to the air via
conduction, convection takes over
from here via “sensible” and
“latent” heat transfers
Sensible heat flux
• Sensible heat: heat energy which is readily detected
• Sensible heat flux
SH =  Cd Cp V (Tsurface - Tair)
Where  is the air density, Cd is flux transfer coefficient, Cp is
specific heat of air (the amount of energy needed to increase
the temperature by 1 degree for 1 kg of air), V is surface wind
speed, Tsurface is surface temperature, Tair is air temperature
• Magnitude is related surface wind speed
– Stronger winds cause larger flux
• Sensible heat transfer occurs from warmer to cooler areas
(i.e., from ground upward)
• Cd needs to be measured from complicated eddy flux
instrument
Latent Heat
• Energy required to induce changes of
state in a substance
• In atmospheric processes, invariably
involves water
• When water is present, latent heat of
evaporation redirects some energy
which would be used for sensible heat
– Wet environments are cooler
relative to their insolation amounts
• Latent heat of evaporation is stored in
water vapor
– Released as latent heat of
condensation when that change of
state is induced
Latent heat flux
• LH =  Cd L V (qsurface - qair)
Where  is the air density, Cd is flux transfer coefficient, L is
latent heat of water vapor, V is surface wind speed, qsurface
is surface specific humidity, qair is surface air specific
humidity
• Magnitude is related surface wind speed
– Stronger winds cause larger flux
• Latent heat transfer occurs from wetter to drier areas (i.e.,
from ground upward)
• Cd needs to be measured from complicated eddy flux
instrument
Seasonal variation of surface energy
budget
Storage change = net radiation - latent heat flux sensible heat flux
Summary: Surface energy balance
Incoming shortwave + Incoming longwave = Reflected shortwave + Emitted longwave
+ Latent heat flux + Sensible heat flux + Subsurface conduction
SWdn
=Scos
SWup
=SWdn 
LWdn
LWup
=Tair4 =Ts4
LH=CdLV(qsurface- qair)
SH=CdCpV(TsurfaceTair)

dT/dt
Fc = -  dT/dz