Lecture 3Radiation and Planetary Energy Balance (provide a review and add something new)
Electromagnetic 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 Sun 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 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 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 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* = sT4 • This is known as the Stefan-Boltzmann Law, and the constant s 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 = eE*, where e is called the emissivity. • In general, the emissivity depends on wavelength just as the absorptivity does, for the same reasons: el = El/E*l
Redis Cool, Blue isHot Take the derivative of the Planck function, set to zero, and solve for wavelength of maximum emission
Solar 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 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/Emitters facts • Molecules of gas in the atmosphere interactwithphotons 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
Molecular Absorbers/Emitters • permanent dipole moment – existence of dipole pole (e.g., H2O) • 3 modes of motions in tri-atomic molecule: • Symmetric vibration • Bending • Anti-symmetric vibration
Remarks • Molecules containing two atoms of the same element such as N2 and O2 and monatomic molecules such as Ar have NONET 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 (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.) • 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%
Er Ea Ei Et Conservation 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 t = Et/Ei • Conservation: r + a + t = 1 • Emissivity ε of an object = its absorptance a (it must!!)
Heat balance of Solar-earth system Heat flux coming from the sun = heat loss of earth
Scenario 1 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. 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 2 Heat 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 NOT Realistic!! Much higher than the observed 15°C Ts = 303K (30°C)
Scenario 3 Consider the fact that our atmosphere is not a perfect blackbody but with the emissivity ε < 1, a gray body
Scenario 3 Heat 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 surface Combining above two formula bonus , and
Discussions • 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. • For a perfect black body, ε=1, we go back to scenario 2.
Discussions (cont.) • 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! Conclusion Our simple radiation balance model has deficiencies
(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 出去長波輻射 出去短波輻射 行星能量平衡準則: 長期平均後, 大氣層頂處, 淨向下太陽輻射通量 = 淨向上行星長波輻射 (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
Planetary Albedo Annual Mean • Global mean ~ 30% • Not the same as surface albedo (clouds, aerosol, solar geometry) • Increases with latitude • Lower over subtropical highs • Higher over land than oceans • Bright spots over tropical continents • Strong seasonality: clouds, sea ice and snow cover dark shading > 40%light shading < 20% JJA DJF
TOA Outgoing Longwave Radiation Annual Mean • Given by esT4 (which T?) • Combined surface and atmosphere effects • Decreases with latitude • Maxima over subtropical highs (clear air neither absorbs or emits much) • Minima over tropical continents (cold high clouds) • Very strongmaxima over deserts (hot surface, clear atmosphere) JJA DJF dark shading < 240 W m-2 ; light shading > 280 W m-2
TOA Net Incoming Radiation Annual Mean • Huge seasonal switch from north to south • Tropics are always positive, poles always negative • Western Pacific is a huge source of energy (warm ocean, cold cloud tops) • Saharan atmosphere loses energy in the annual mean! • TOA net radiation must be compensated by lateral energy transport by oceans and atmosphere JJA DJF dark shading < 0 W m-2 ; light shading > 80 W m-2
Energy Surplus and Deficit Annual Mean Zonal Mean TOA Fluxes • Absorbed solar more strongly “peaked” than the emitted longwave • OLR depression at Equator due to high clouds along ITCZ • Subtropical maxima in OLR associated with clear air over deserts and subtropical highs 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-Section • 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 • Can’t have a trend for too long. Transport of RTOA will eventually adjust to balance trends.
Energy Transports in the Ocean and Atmosphere Northward energy transports in petawatts (1015 W) “Radiative forcing” is cumulative integral of RTOA starting at zero at the pole Slope of forcing curve is excess or deficit of RTOA Ocean transport dominates in subtropics Atmospheric transport dominates in middle and high latitudes