Earth energy budget and balance II

EmissivityAbsorbed incoming radiation flux heats up surface material, which in turn emits thermal radiation. The emissivity of a surface is its effectiveness in emitting its energy as thermal radiation into the outer space!

FiFe

e

a

e

a

e

a

e

tate F

FFF

FF

FFFFF 11

As higher the absorption for emitted radiation in atmosphere as lower is the emissivity ε

Fe

FtFa We ignore reflection back

No absorption: ε=1 (black body) 

Emissivity

sTBF

Emissivity in IR range >0.8(=4m – 100m)

For =8m – 12m

Flux in a fixed wavelength range

White paint 0.60-0.75Black paint, tar 0.9-1.0

Emissivity, , is defined as the ratio of the emitted radiation at a specificwavelength and temperature to the emitted radiation from a black bodyat the same wavelength and temperature.

Microwave to infrared range

Day Night Emissivity

More emission during evening night, when earth is cooling

CO2

O3H2O

CH4

Wave length dependence of emissivityEmissivity spectra are a function of surface types including water, old snow, fresh snow,soil, tilled soil, sand, rock, irrigated low vegetation, meadow grass, scrub, broadleaf forest,pine forest, tundra, grass soil, broadleaf pine forest, grass scrub, oil grass, urban concrete,pine brush, broadleaf brush, wet soil, scrub soil, broadleaf 70‐pine 30, and new ice.

red infrared

Broad leaf forests Gras savannaNeedle forest

Arid bare soil Ice and snowOrganic bare soil

William G. Snyder et al. 2005

Uncertainty range of emissivity predictions for remote sensing

infrared red

Impact of emissivity on equilibrium temperature

FRS

TF

TBF

emitted

s

2

4

4

1

4 0

40

42

02

0

4)1(

4)1(

4

)1()1(

FT

TF

TRS

FRSS

SS

emission

emission

emissionemission

absorption

absorptionemission

Averaging over the wavelength dependence: 

r

a

i

a

FF

FF

approximate assumption

Emission temperature of dark asphalt on a sunny summer day

= 5.67∙10‐8 W m‐2 K‐42

30

41

0 1037.14

)1(mWFFTasphalt

24 308

274

mWTF

KT

asphalt

asphalt

White roof top; α = 0.8,  = 0.68

Asphalt surface or black tar roof; α = 0.1,  = 0.97

24 5.68

205

mWTF

KT

white

white

“The picture above depicts a hot summer day in California. The roof pictured is a Duro‐Lastroof. The yellow, orange and red colors are the areas of the highest temperatures in the photo(blue and violet correspond to cooler environments). Compare the roof of the building to theleft of the Duro‐Last roof. Notice it's colors are yellow, orange and red, while the Duro‐Last roofcolors are primarily blue.” Compare also the temperature range of the trees, it beats Duro‐last!

Insulation commercials

4 0

4)1(

FTemission

Wavelength averaged values of albedo:    α=31%Wavelength averaged value of emissivity: =80%

K

smKJ

mW

Temission 2701067.58.04

1370)31.01(4

248

2

Closer to average temperature of T=280 K but still coldA change of the solar constant by 1.4% or the average albedo 3.3%, or theaverage emissivity by 1.4% will change the average temperature by 1oC !!!

ε(8.3m)

Maintaining equilibriumConstant temperature requires balance between absorption and emission ofenergy. Changing ratio will have consequences for local and possibly globaltemperature conditions. Most discussed change is CO2 increase, whichincreases the absorption of emitted infrared radiation in the earthatmosphere, reducing the emissivity!

Impact of CO2 abundance

http://climatemodels.uchicago.edu/modtran/

Absorption in the atmosphereInfrared radiation from the earth surface of temperature TS is partiallyabsorbed in atmosphere, generating a temperature TA. Atmosphere isconsidered opaque to infrared but transparent to other wavelength.

Incoming net solar flux:

AT

FF

aa

in

4

0

4)1(

Flux A↑ radiated to space depends on atmospheric temperature Ta : ATA aa

4

Flux F↑ radiated from surface with terrestrial temperature Ts

4ss TF

For thermal equilibrium:  0 groundatnetfluxAFF in

F↑

F0F0

Greenhouse effectThe thermal equilibrium requires:

AFFAFF

in

in 0

as

aas

as

aaaass

assuming

TTT

TTFT

19.12

24)1(

4

4404

With the calculated emission temperature Ta=255K (withoutemissivity corrections) we obtain a increased surface temperatureof Ts=303K. Overshooting, model is too simplified, more later!

CO2 Impact on energy budget

...then it loses as much energy as it gains.

http://climatemodels.uchicago.edu/rrtm/