Earth energy budget and balance
31% total reflection (23% clouds. 8% surface) Reflection is frequency dependent but will be 69% absorption( 20% clouds, 49% surface) treated as average value for visible light range. Simplified scheme of the balance between the incident, reflected, Fi transmitted, and absorbed radiation Fr
Ft Box Model Fa
Kirchhoff’s law Efficiency factors F F F : emissivity (=absorptivity) F F F F r a t 1 i r a t α: albedo Fi Fi Fi : opacity (=1-transmittivity) 1 Black body: =1, α=0 Albedo, Absorption, Opacity 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: 31%
The Albedo depends on the Surface Albedo nature and characteristics of Asphalt 4-12% the reflecting surface, a light surface has a large Albedo Forest 8-18% (maximum 1 or 100%), a dark Bare soil 17% surface has a small Albedo Green grass 25% (minimum 0 or 0%). Desert sand 40% New concrete 55% Ocean Ice 50-70% Fresh snow 80-90% Albedo of Earth
αice >35%
αforest 12% αforest 12% αagriculture 20% αagriculture 20% αdesert 30% αdesert 30% αdesert 30%
αforest 12% αforest 12%
αocean <10% αocean <10%
αice >35% Tundra 20% Arctic ocean 7 %
New snow 80% Melting ice 65% Melt pond 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
Geological map Albedo map
Seasonal changes depends primarily on large area snow and ice formation! 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
17 Solar power incident on earth: S0 1.7510 W
2 S0 Rearth F0 F0 Average solar flux incident on earth: Favg 2 2 4 Rearth 4 Rearth 4
17 Solar power absorbed by earth: Sabsorbed (1) S0 1.22 10 W
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
17 Sabsorbed 1.22 10 W W F absorbed 2 6 2 239 2 4 Rearth 4 (6.37110 m) m Heat absorption and temperature change
dT W F mC 239 ; absorbed v dt m2 J Heat capacity (water): C 4.2103 assuming water world v kgK Assuming surface convection of ocean depth of d=100 m kg kg Water column mass m d 1000 100m 105 m3 m2 W W 239 239 dT F 2 2 K absorbed m m 5.69107 dt mC 5 kg J kg Ws s v 10 4200 100000 4200 m2 kgK m2 kgK
dT K dT K 1y 107 s 17 Observed: 0.01 dt y dt y Earth emission spectrum
2897 m max T 2897 m 0.48 m sun 6000 2897 m 10.4 m earth 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: W F T 4 5.67 108Wm2K 4 280K4 349 emitted m2 = 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: F 1370 0 m2 Total emitted power:
2 W S 4 R2 F 4 6.371106 m 349 1.781017W 0 emitted m2 17 Compared to absorption: Sabsorbed (1) S0 1.22 10 W Emission temperature
Balance between absorption and emission is required to maintain thermal equilibrium conditions on earth!
Semission Sabsorption 2 4 17 Semission 4 R Temission 1.22 10 W 1.22 1017W 4 Emission temperature is lower Temission 2 255K 4 R than the average temperature
General formula for radiation emission; Temission varies with albedo! High albedo translates into lower emission temperature 1 4 (1 ) F0 2 3 W Temission F0 S R 1.3710 4 m2 Solar constant 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 Traditional Greek (Mediterranean) slate walls which helps by low Albedo to village with chalked walls with high absorb energy and keep the houses Albedo to reflect solar energy and warm in moderate summers and cold minimize absorption to keep houses winter times. cool in hot summer months.