Earth energy budget and balance
31% total reflection (23% clouds. 8% surface)
69% absorption( 20% clouds, 49% surface)
Reflection is frequency dependent but will be
treated as average value for visible light range.
Simplified scheme of the balance
between the incident, reflected,
transmitted, and absorbed radiation
Fi
Fr
Ft
Kirchhoff’s law
Fi  Fr  Fa  Ft
Box Model
Fa
Fr Fa Ft

 1
Fi Fi Fi
    1
Albedo, Absorption, Opacity
Efficiency factors
: emissivity (=absorptivity)
α: albedo
: opacity (=1-transmittivity)
Black body:  =1, α=0
Opaque body:  =0
The incident, absorbed, reflected, and transmitted flux
depends sensitively on the wavelength  of the radiation!
Albedo
The ratio of reflected to incident solar energy is called the Albedo α
At present cloud and climate conditions:
The Albedo depends on the
nature and characteristics of
the reflecting surface, a light
surface has a large Albedo
(maximum 1 or 100%), a dark
surface has a small Albedo
(minimum 0 or 0%).
Surface
Albedo
Asphalt
4-12%
Forest
8-18%
Bare soil
17%
Green grass
25%
Desert sand
40%
New concrete
55%
Ocean Ice
50-70%
Fresh snow
80-90%
  31%
Albedo of Earth
αice >35%
αforest 12%
αagriculture 20%
αdesert 30%
αagriculture 20%
αforest 12%
αdesert 30%
αdesert 30%
αforest 12%
αforest 12%
αocean <10%
αocean <10%
αice >35%
Tundra 20%
New snow 80%
Melting ice 65%
Melt pond 20%
Arctic ocean 7 %
Clear skies versus clouds
At clear skies Albedo is relatively
low because of the high Albedo
value of water. This translates in an
overall variation of 5-10%.
Cloud Albedo varies from less than
10% to more than 90% and depends
on drop sizes, liquid water or ice
content, and the thickness of the
cloud. Low altitude, thick clouds
(stratocumulus)
primarily
reflect
incoming solar radiation, causing it to
have a high Albedo, whereas high
altitude, thin clouds (such as Cirrus)
tend to transmit it to the surface but
then trap reflected radiation, causing
it to have low Albedo.
Albedo of water surfaces
Albedo of water surfaces depend on incident angle of light.
This translates into a large variation of Albedo between
noon and evening time with impact on temperature.
Angular dependence of reflection
red
IR
Seasonal Albedo
Geological map
Seasonal changes depends primarily
on large area snow and ice formation!
Albedo map
Albedo feed back processes
 Snow has a high Albedo, average over Antarctica is about 80%.
 Snow melt lowers the Albedo, more sunlight is absorbed and
temperature increases accelerating melting process.
 If snow forms, the Albedo increases, which results into further
cooling because more light is reflected and less light is absorbed.
 Deforestation for generating agricultural land or grassland
increases Albedo from ~10 to ~25%, more sunlight is reflected
decreasing temperature, but also evaporation, cloud formation
and precipitation, increasing aridity. It reduces the efficiency of
CO2 processing through the Carbon cycle increasing heat trapping!
Seasonal Albedo for different
snow-free environments
C. L. Brest, Seasonal Albedo of an Urban/Rural Landscape from Satellite Observations,
Journal of Climate and Applied Meteorology 26 1169, 1987
Energy absorption
Solar power incident on earth:
S0  1.75  1017W
Average solar flux incident on earth: Favg
Solar power absorbed by earth:
2
S0
  Rearth
 F0 F0



2
2
4  Rearth
4  Rearth
4
Sabsorbed  (1   )  S0  1.22  1017W
Absorption of so much power will increase the surface temperature of earth!
The total power absorbed over the entire earth surface area can be computed
Sabsorbed
1.22  1017W
W
F absorbed

 239 2
2
6
2
4  (6.371  10 m)
m
4  Rearth
Heat absorption and temperature change
dT
W
Fabsorbed  m  Cv 
 239 2 ;
dt
m
Heat capacity (water): Cv  4.2  103
J
kg K
assuming water world
Assuming surface convection of ocean depth of d=100 m
kg
5 kg
Water column mass m    d  1000 3  100m  10
m
m2
dT Fabsorbed

dt
m  Cv
W
W
239 2
239 2
7 K
m
m


 5.69 10
kg
J
kg
Ws
s
105 2 4200
100000 2 4200
m
kgK
m
kgK
1 y    107 s
dT
K
 17
dt
y
Observed:
dT
K
 0.01
dt
y
Earth emission spectrum
2897
 max 
m
T
2897
 sun 
m  0.48 m
6000
2897
 earth 
m  10.4 m
280
Low temperature moves emission spectrum well into infrared range, that means that
mostly heat is radiated away from earth surface. The infrared radiation can be
absorbed in air, clouds, or aerosols, causing temperature increase of the atmosphere.
Heat balance of earth
Earth is stellar object with average temperature T  280K!
It cools by radiation following the Stefan Boltzmann law:
Femitted    T  5.67  10 Wm K  280K 
4
8
2
4
4
W
 349 2
m
 = 5.67·10-5 erg s-1 cm-2 K-4 = 5.67·10-8 W m-2 K-4
W
Considerably lower than incident solar energy flux: F0  1370 2
m
Total emitted power:
S0  4  R 2  Femitted  4  6.371  106 m  349
2
Compared to absorption:
W
 1.78  1017W
2
m
Sabsorbed  (1   )  S0  1.22  1017W
Emission temperature
Balance between absorption and emission is required
to maintain thermal equilibrium conditions on earth!
Semission  Sabsorption
4
Semission  4  R 2    Temission
 1.22  1017W
17
1
.
22

10
W
Temission  4
 255K
2
4  R  
Emission temperature is lower
than the average temperature
General formula for radiation emission; Temission varies with
albedo! High albedo translates into lower emission temperature
Temission
 (1  )  F0 


 4 
1
4
W
F0  S    R  1.37 10 2
m
2
Solar constant
3
Local temperature modifications
Asphalt areas of low Albedo, efficient absorption of incoming radiation energy is
balanced by the emission of infrared thermal radiation as shown at right hand
picture ( the equilibrium reaches 41o C =106oF=314K). River water has low Albedo
as well, but additional cooling occurs by continuous water flow. Grassy areas have
higher Albedo, less absorption and heat radiation
Tradition & Experience
Traditional German village with dark
slate walls which helps by low Albedo to
absorb energy and keep the houses
warm in moderate summers and cold
winter times.
Traditional Greek (Mediterranean)
village with chalked walls with high
Albedo to reflect solar energy and
minimize absorption to keep houses
cool in hot summer months.