Lecture 3Lecture 3Radiation and Radiation and

Planetary Energy Planetary Energy BalanceBalance

(provide a review and add (provide a review and add something new)something new)

Electromagnetic RadiationElectromagnetic Radiation

• Oscillating electric and magnetic fields propagate through space

• Virtually all energy exchange between the Earth and the rest of the Universe is by electromagnetic radiation

• Most of what we perceive as temperature is also due to our radiative environment

• Dual properties; may be described either as waves or as particles (photons)

• High energy photons = short waves; lower energy photons = longer waves

Electromagnetic Spectrum of the Electromagnetic Spectrum of the SunSun

Visible light band, i.e. 0.4~0.7 μm, occupies 44% of total energy

Spectrum of the sun compared with that of the earth

Blackbodies and GraybodiesBlackbodies and Graybodies

• A blackbody is a hypothetical object that absorbs all of the radiation that strikes it. It also emits radiation at a maximum rate for its given temperature.– Does not have to be black!

• A graybody absorbs radiation equally at all wavelengths, but at a certain fraction (absorptivity, emissivity) of the blackbody rate

• The energy emission rate is given by– Planck’s law (wavelength dependent emission)– Stefan Boltzmann law (total energy)– Wien’s law (peak emission wavelength)

Blackbody RadiationBlackbody Radiation

• Planck’s Law describes the rate of energy output of a blackbody as a function of wavelength

• Emission is a very sensitive function of wavelength

• Total emission is a strong function of temperature

Total Blackbody EmissionTotal Blackbody Emission• Integrating Planck's Law across all wavelengths,

and all directions, we obtain an expression for the total rate of emission of radiant energy from a blackbody:

E* = T4

• This is known as the Stefan-Boltzmann Law, and the constant is the Stefan-Boltzmann constant (5.67 x 10-8 W m-2 K-4).

• Stefan-Boltzmann says that total emission strongly depends on temperature!

• Strictly, S-B Law is true only for a blackbody. For a gray body, E = E*, where is called the emissivity.

• In general, the emissivity depends on wavelength just as the absorptivity does, for the same reasons:

RedRed isis Cool, Blue Cool, Blue isis HotHot

Take the derivative of the Planck function, set to zero, and solve for wavelength of maximum emission

Solar and Planetary RadiationSolar and Planetary Radiation• Earth receives energy from the sun at many

wavelengths, but most is in visible wavelengths• Earth emits energy back to space at much

longer (thermal) wavelengths, infrared • Because temperatures of the Earth and Sun are

so different, it's convenient to divide atmospheric radiation into solar and planetary components

Overlapped band is trivial

3 Ways to label radiation3 Ways to label radiation

• By its source– Solar radiation - originating from the sun– Terrestrial radiation - originating from the

earth

• By its proper name– ultra violet, visible, near infrared, infrared,

microwave, etc….

• By its wavelength– short wave radiation 3 micrometers– long wave radiation > 3 micrometers

Molecular Absorbers/EmittersMolecular Absorbers/Emitters

• Molecules of gas in the atmosphere interact with photons of electromagnetic radiation

• Different kinds of molecular transitions can absorb/emit very different wavelengths of radiation

• Some molecules are able to interact much more with photons than others

• Different molecular structures produce wavelength-dependent absorptivity/emissivity

facts

Molecular Absorbers/EmittersMolecular Absorbers/Emitters• permanent dipole

moment – existence of dipole pole (e.g., H2O)

• 3 modes of motions in tri-atomic molecule:

a)Symmetric vibrationb)Bendingc)Anti-symmetric

vibration

RemarksRemarks• Molecules containing two atoms of the same

element such as N2 and O2 and monatomic molecules such as Ar have NO NET change in their dipole moment when they vibrate and hence almost do not interact with infrared photon.

• Although molecules containing two atoms of different elements such as carbon monoxide (CO) or hydrogen chloride (HCl) do absorb IR, they are short-lived in the atmosphere owing to their reactivity and solubility. As a consequence their greenhouse effect is neglected.

How do greenhouse gases How do greenhouse gases (GHGs) "work"? (GHGs) "work"?

• After GHGs absorb passing IR photons, the energy of the photon is converted into various excited vibration states.

• The IR spectrum spans a range of wavelengths with different energies. Different types of GHGs absorb different wavelengths of IR photons.

• Different vibrational modes allow GHGs to absorb IR photons in more than one wavelength. This in fact causes the uncertainty as to how much of the greenhouse effect each gas produces

Remarks (cont.)Remarks (cont.)

• Relative contributions of atmos. constitutes to the greenhouse effect

water vapor, 36–72% (discussed later) carbon dioxide, 9–26% (In fact, CO2 is NOT

the BIG guy) methane, 4–9% ozone, 3–7%

Conservation of EnergyConservation of Energy• Incident radiation (Ei) upon a medium can be:

– absorbed (Ea)

– Reflected (Er)

– Transmitted (Et)

Ei = Ea + Er + Et

• Define– reflectance r = Er/Ei

– absorptance a = Ea/Ei

– transmittance = Et/Ei

• Conservation: r + a + = 1

• Emissivity ε of an object = its absorptance a (it must!!)

Ei

Ea

Er

Et

Greenhouse effectGreenhouse effect(actually, atmospheric effect is (actually, atmospheric effect is

a more proper term)a more proper term)

Heat balance of Solar-earth Heat balance of Solar-earth systemsystem

Heat flux coming from the sun = heat loss of earth

Scenario 1 Simple heat balance of the Earth

Absorbed solar radiation = emitted terrestrial radiation

This leads to

and finally to

This corresponds to

Te=255 K (= -18°C). NOT Realistic!!

factor 1/4 arises from the spherical geometry of the Earth, because only part of the Earth’s surface receives solar radiation directly.

Scenario 1

the temperature (-18C) that would occur on the Earth’s surface if it were a perfect black body, there were no atmosphere, and the temperature was the same at every point.

Scenario 2 with an atmosphere represented by a single layer, which is totally transparent to solar radiation but opaque to infrared radiations

Scenario 2Heat balance at the top of atmosphere (TOA)

Heat balance at the surface energy emitted by the surface = incoming solar fluxes + infra-red flux coming from the atmosphere

Combining two formula

Ts = 303K (30°C) NOT Realistic!! Much higher than the observed 15°C

Scenario 3 Consider the fact that our atmosphere is not a perfect blackbody but with the emissivity ε < 1, a gray body

Scenario 3Heat balance at the surface is rewritten as

energy emitted by the surface = incoming solar fluxes + infra-red flux coming from the “graybody” atmosphere

Heat balance at TOA becomes (note: transmittance is not zero, but equals to 1- ε in this scenario)

From surfaceCombining above two

formula

, and bonus

DiscussionsDiscussions

① For ε=0, corresponding to an atmosphere totally transparent to infra-red radiations (as if there exists no atmosphere),Ts =Te, we go back to scenario 1.

② For a perfect black body, ε=1, we go back to scenario 2.

Discussions (cont.)Discussions (cont.)

③ A typical ε value = 0.97 for the atmosphere,

=> Ts =1.18Te = 301 K (28°C), and

=> Ta = 255.1 K = -18.1°C

Fxxx, the ground is too warm and the air is too cold!

ConclusionConclusionOur simple radiation balance model has deficiencies

Radiation-Convection balance modelRadiation-Convection balance model

(a) 太陽短波輻射 (100)

氣體吸收 :16

雲吸收 : 3

被空氣散射回太空 : 6

被雲反射 :20

被地面反射 : 4

地面吸收 :51

(b) 長波輻射 ( 進入太空的量 )

地面放射 :21

15 被氣體吸收 ,

6 直接進入太空

大氣放射 :38

雲放射 :26

出去短波輻射

出去長波輻射

(c) 對大氣而言 :

吸收 = 16 + 3 + 15 = 34

放射 = 38 + 26 = 64

不夠的量 = 30, <= 透過對流活動，釋放潛熱 (23) 和可感熱 (7) 補充

行星能量平衡準則行星能量平衡準則 : : 長期平均後長期平均後 , , 大氣層頂處大氣層頂處 , , 淨向下太陽輻射淨向下太陽輻射通量 通量 = = 淨向上行星長波輻射淨向上行星長波輻射

Planetary AlbedoPlanetary Albedo

① Global mean ~ 30%

② Not the same as surface albedo (clouds, aerosol, solar geometry)

③ Increases with latitude

④ Lower over subtropical highs

⑤ Higher over land than oceans

⑥ Bright spots over tropical continents

⑦ Strong seasonality: clouds, sea ice and snow cover

dark shading > 40%light shading < 20%

Annual Mean

JJA

DJF

TOA Outgoing Longwave TOA Outgoing Longwave RadiationRadiation

① Given by T4 (which T?)

② Combined surface and atmosphere effects

③ Decreases with latitude

④ Maxima over subtropical highs (clear air neither absorbs or emits much)

⑤ Minima over tropical continents (cold high clouds)

⑥ Very strong maxima over deserts (hot surface, clear atmosphere)

dark shading < 240 W m-2 ; light shading > 280 W m-2

Annual Mean

JJA

DJF

TOA Net Incoming RadiationTOA Net Incoming Radiation

① Huge seasonal switch from north to south

② Tropics are always positive, poles always negative

③ Western Pacific is a huge source of energy (warm ocean, cold cloud tops)

④ Saharan atmosphere loses energy in the annual mean!

⑤ TOA net radiation must be compensated by lateral energy transport by oceans and atmosphere

dark shading < 0 W m-2 ; light shading > 80 W m-2

Annual Mean

JJA

DJF

Energy Surplus and DeficitEnergy Surplus and Deficit

① Absorbed solar more strongly “peaked” than the emitted longwave

② OLR depression at Equator due to high clouds along ITCZ

③ Subtropical maxima in OLR associated with clear air over deserts and subtropical highs

Annual Mean Zonal Mean TOA Fluxes

TOA net radiation surplus in tropics and deficits at high latitudes must be compensated by horizontal energy transports in oceans and atmosphere

Energy Budget Cross-SectionEnergy Budget Cross-Section

① Excess or deficit of TOA net radiation can be expressed as a trend in the total energy of the underlying atmosphere + ocean + land surface, or as a divergence of the horizontal flux of energy in the atmosphere + ocean

② Can’t have a trend for too long. Transport of RTOA will eventually adjust to balance trends.

aoTOA ao

ER F

t

Energy Transports Energy Transports in the Ocean and Atmospherein the Ocean and Atmosphere

① Northward energy transports in petawatts (1015 W)

② “Radiative forcing” is cumulative integral of RTOA starting at zero at the pole

③ Slope of forcing curve is excess or deficit of RTOA

④ Ocean transport dominates in subtropics

⑤ Atmospheric transport dominates in middle and high latitudes

End of Lecture 3End of Lecture 3