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.

Earth energy budget and balance

Simplified scheme of the balance between the incident, reflected, transmitted, and absorbed radiation

1

1

i

t

i

a

i

rtari

F

F

F

F

F

FFFFF

The incident, absorbed, reflected, and transmitted flux depends sensitively on the wavelength of the radiation!

Black body: =1, α=0 Opaque body: =0

Fi

Fr

Ft Fa

Box Model

Albedo, Absorption, Opacity

Efficiency factors Kirchhoff’s law

: emissivity (=absorptivity) α: albedo : opacity (=1-transmittivity)

Albedo

The ratio of reflected to incident solar energy is called the Albedo α

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%).

%31At present cloud and climate conditions:

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%

Albedo of Earth

New snow 80% Melting ice 65% Melt pond 20%

Tundra 20% Arctic ocean 7 %

αocean <10%

αice >35%

αice >35%

αocean <10%

αforest 12%

αforest 12%

αforest 12%

αdesert 30% αdesert 30%

αdesert 30%

αagriculture 20% αforest 12%

αagriculture 20%

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

Seasonal changes depends primarily on large area snow and ice formation!

Geological map 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: WS 17

0 1075.1

Solar power absorbed by earth: WSSabsorbed

17

0 1022.1)1(

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

226

17

2239

)10371.6(4

1022.1

4 m

W

m

W

R

SF

earth

absorbedabsorbed

Average solar flux incident on earth: 444

0

2

0

2

2

0 F

R

FR

R

SF

earth

earth

earth

avg

Heat absorption and temperature change

;2392m

W

dt

dTCmF vabsorbed

Heat capacity (water): Kkg

JCv

3102.4

Assuming surface convection of ocean depth of d=100 m Water column mass

2

5

3101001000

m

kgm

m

kgdm

s

K

kgK

Ws

m

kgm

W

kgK

J

m

kgm

W

Cm

F

dt

dT

v

absorbed 7

2

2

2

5

2

1069.5

4200100000

239

420010

239

y

K

dt

dTsy 17101 7 Observed:

y

K

dt

dT01.0

assuming water world

Earth emission spectrum

mm

mm

mT

earth

sun

4.10280

2897

48.06000

2897

2897max

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:

= 5.67·10-5 erg s-1 cm-2 K-4 = 5.67·10-8 W m-2 K-4

2

44284 3492801067.5m

WKKWmTFemitted

Considerably lower than incident solar energy flux: 20 1370

m

WF

Total emitted power:

Wm

WmFRS emitted

17

2

262

0 1078.134910371.644

WSSabsorbed

17

0 1022.1)1( Compared to absorption:

Emission temperature

Balance between absorption and emission is required to maintain thermal equilibrium conditions on earth!

KR

WT

WTRS

SS

emission

emissionemission

absorptionemission

2554

1022.1

1022.14

42

17

1742

2

32

0

4

1

0 1037.14

)1(

m

WRSF

FTemission

General formula for radiation emission; Temission varies with albedo! High albedo translates into lower emission temperature

Solar constant

Emission temperature is lower than the average temperature

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.