Earth energy budget and balance

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1 Earth energy budget and balance 31% total reflection (3% clouds. 8% surface) 69% absorption( 0% clouds, 49% surface) Reflection is frequency dependent but will be treated as average value for visible light range.

2 i r Simplified scheme of the balance between the incident, reflected, transmitted, and absorbed radiation t a Box Model Kirchhoff s law Efficiency factors i r a t r i 1 1 Albedo, Absorption, Opacity a i t i : 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!

3 Albedo The ratio of reflected to incident solar energy is called the Albedo α At present cloud and climate conditions: 31% 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 4-1% orest 8-18% Bare soil 17% Green grass 5% Desert sand 40% New concrete 55% Ocean Ice 50-70% resh snow 80-90%

4 Albedo of Earth α ice >35% α forest 1% α agriculture 0% α desert 30% α agriculture 0% α desert 30% α forest 1% α desert 30% α ocean <10% α forest 1% α forest 1% α ocean <10% α ice >35% Tundra 0% Arctic ocean 7 % New snow 80% Melting ice 65% Melt pond 0%

5 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.

6 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.

7 Angular dependence of reflection red IR

8 Seasonal Albedo Geological map Albedo map Seasonal changes depends primarily on large area snow and ice formation!

9 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 ~5%, more sunlight is reflected decreasing temperature, but also evaporation, cloud formation and precipitation, increasing aridity. It reduces the efficiency of CO processing through the Carbon cycle increasing heat trapping!

10 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 , 1987

11 Energy absorption Solar power incident on earth: S Average solar flux incident on earth: avg S 4 R 0 Rearth 0 0 earth 4 Rearth 4 Solar power absorbed by earth: 17 S absorbed ( 1) S 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 absorbed S absorbed Rearth 4 ( m) m

12 Heat absorption and temperature change dt dt absorbed m C Heat capacity (water): v dt dt 39 m 3 C v ; J kgk Assuming surface convection of ocean depth of d=100 m m d kg m 10 3 m ater column mass mc v m kg J 400 m kgk 39 m kg s m kgk 5 kg m absorbed 7 5 assuming water world K s 7 dt 1y 10 s 17 dt K y Observed: dt dt 0.01 K y

13 Earth emission spectrum max sun earth 897 m T 897 m 0.48 m m 10.4 m 80 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.

14 Heat balance of earth Earth is stellar object with average temperature T 80K! It cools by radiation following the Stefan Boltzmann law: emitted T m 4 = erg s -1 cm - K -4 = m - K -4 K m 4 80K m Considerably lower than incident solar energy flux: Total emitted power: m S0 4 R emitted 4 10 m Compared to absorption: 17 S absorbed ( 1) S0 1.10

15 Emission temperature Balance between absorption and emission is required to maintain thermal equilibrium conditions on earth! S S T emission emission emission S absorption 4 R 4 T R 4 emission K 17 Emission temperature is lower than the average temperature General formula for radiation emission; T emission varies with albedo! High albedo translates into lower emission temperature T emission (1 ) S R 1.37 Solar constant m

16 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 41 o C =106 o =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

17 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.

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