earth energy budget and balance - university of notre damensl/lectures/phys20054/15lectur… ·...
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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
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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
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!
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!