1 MET 60 Chapter 4: Radiation & Radiative Transfer

2 The layout of chapter 4 is: Basics of radiation Scattering, Absorption & Emission of radiation Radiative Transfer

3 Basics of radiation Properties of radiation (pp ) –wavelength, frequency etc. –Intensity vs. flux –Blackbody radiation

4 Basics of radiation cont. Basic Radiation Laws (pp ) –Wien’s Law & Stefan-Boltzman Law –About the type and amount of radiation emitted

5 Scattering, Absorption & Emission of radiation Emissivity, absorptivity, transmissivity, reflectivity (p. 120) –All relate to things that can happen to radiation as it passes through the atmosphere The Greenhouse Effect (p.121) The physics of scattering (pp ) –Type & amount of scattering depends on number, size & shape of particles in the air

6 Scattering, Absorption & Emission of radiation contd. The physics of absorption –Lots of details! (pp ).

7 Radiative Transfer Putting it all together to follow a beam of incident radiation: From top of atmosphere to the surface And back up With interactions along the beam (scattering, absorption etc.)

8 Radiative Transfer contd. With the result being: A vertical profile of heating rates due to radiation e.g., in the form of the values of Remember that radiative heating drives the atmosphere! –Vertical distribution (here) –Horizontal distribution (climatology-related)

9 Basics of Radiation The sun emits radiation (type? amount?) Earth intercepts it and also emits its own radiation (type? amount?) Radiation is characterized by: –Frequency ( ) … measured in “per sec” –Wavelength ( ) … measured in micrometers (µm) or microns –Wavenumber ( -1 ) Note: all EM radiation travels at the speed of light (c) with c =

10 The EM spectrum…

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12 Solar radiation consists mainly of: uv radiation (? – 0.38 µm) visible radiation (0.38 – 0.75 µm) IR radiation ( ? µm) –Near-IR has < 4 µm –Far-IR has > 4 µm

13 Terms… Monochromatic intensity of radiation is the amount of energy at wavelength passing through a unit area (normal to area) in unit time I Adding over all wavelengths (all values of ), we get radiance, or intensity: I I is also called radiance

14 Terms… Monochromatic flux density (irradiance) is the rate of energy transfer through a plane surface per unit area due to radiation with wavelength F For, say, a horizontal surface in the atmosphere: Monochromatic radiance Accounts for radiation arriving in slanted direction Integrate over ½ sphere

15 Note…on confusion!

16 Inverse Square Law… Flux density (F) obeys the inverse square law: F  1/d 2 where d = distance from source (sun!) sunearthmars 149 million km million km

17 Blackbody Radiation… A surface that absorbs ALL incident radiation is called a blackbody All radiation absorbed – none reflected etc. Hypothetical but useful concept

18 Blackbody Radiation… Radiation emitted by a blackbody is given by: c 1 and c 2 are constants T Planck Function

19 Blackbody Radiation…

20 Blackbody Radiation… Fig. 4.6 shows how emission varies with for different temperatures Choosing T values representative of the sun and of earth gives Fig. 4.7 (upper)

21 Wavelength of peak emission? Wien’s Displacement Law… or

22 Solar radiation … Peaks in the visible Concentrated in uv-vis-IR Terrestrial radiation … Peaks in the IR (15-20  m) All in IR (far IR)

23 Maximum intensity of emission? Stefan-Boltzmann Law… So the sun emits much more radiation than earth since T sun >> T earth

24 Example 4.6 Calculate blackbody temperature of earth (T e ). Assume: earth is in radiative equilibrium  energy in = energy out Assume: albedo = 0.3 (fraction reflected back to space) Assume: solar constant = 1368 W/m 2 = incoming irradiance/flux top of atmosphere

25 Incoming energy: Given by solar constant spread over area of Earth = area the beam intercepts area =  R e 2 Thus incoming = 1368 x (1 – 0.3) x  R e 2

26 Outgoing energy: Given by F e =  T e 4 where we need to find T e Now this is per unit area, so the total outgoing energy is F e = 4  R e 2  T e 4

27 Equating: 4  R e 2  T e 4 = 1368 x (1 – 0.3) x  R e 2  4  T e 4 = 1368 x (1 – 0.3)  T e = {1368 x 0.7 / 4  } ¼  T e = 255 K

28 Non-blackbody radiation A blackbody absorbs ALL radiation A non-blackbody can also reflect and transmit radiation Example – the atmosphere! Actually, the gases that make up the atmosphere!

29 Definitions: emissivity actual radiation emitted / BB radiation BB has  = 1 absorptivity radiation absorbed / radiation incident

30 reflectivity radiation reflected / radiation incident transmissivity radiation transmitted / radiation incident

31 incident reflection absorption transmission absorption

32 incident reflection absorption transmission absorption scattering

33 Kirchoff’s Law emissivity = absorptivity (at E m )

34 An example regarding the greenhouse effect… 1)Pretend the atmosphere can be represented as a single isothermal slab The slab is transparent to solar radiation (all gets through!) The slab is opaque to terrestrial radiation (none gets through!) Everything is in E m.

35 z=0 “top” incoming = F units outgoing = F units for balance F units emitted downwards Surface receives 2F units Surface must emit 2F units for balance F F F 2F

36 Now use the 2F units of radiation emitted by the surface to compute T e via Stefan-Boltzman. F = 1368 W/m 2 modified by albedo result: T e = 303 K  Greenhouse effect delivers 48 K of “warming” (single slab model)

37 2)Pretend the atmosphere can be represented as two isothermal slabs…or three etc. – see text per p.122, T e = 335 K etc. Note: include more layers → steeper lapse rate in lower atmosphere eventually …  >  d … unstable atmosphere “predicted” → use a Radiative-convective model instead…”convective adjustment”

38 Physics of Scattering, Absorption & Emission Need to understand physics of these processes to come up with expressions for how much radiation is scattered etc. from a beam. Scattering Consider a “tube” of incoming radiation – Fig Radiation may be scattered by: –gas molecules (tiny) –aerosol particles (small – tiny).

39 Physics of Scattering, Absorption & Emission

40 Scattering contd. Scattering amount depends on: 1)Incident radiation intensity (I ) 2)Amount of scattering gases/aerosols 3)Ability of these to scatter (size, shape etc.)

41 Scattering contd. For an incident intensity of I, an amount dI is lost by scattering, with N = number of particles (gas, aerosol) per unit volume.  = c/s area of each particle ds = path length (see diagram) K = (scattering or absorption) efficiency factor (large “K”) Note: K (total extinction) = K (scattering) + K (absorption)

42 Scattering contd. For a gas, we write: r = is the mass of the absorbing gas per unit mass of air  = air density k = mass absorption coefficient (m 2 kg -1 )(small “k”)

43 Scattering contd. For a column (“tube”) of air from height z to the top of the atmosphere, we can integrate: This represents the amount of absorbing material in the column down to height z. Called the optical depth or optical thickness (  ). Large   much extinction in the column. Note that  is wavelength-dependent.

44 Scattering is very complicated. Scattering particles have a wide range of sizes and shapes (and distributions). Start by looking at a sphere of radius r. How does this scatter? Extinction is given by Eq – need to know K - provided by theory (which we will not do!!) ???

45 First…Fig y-axis: r = scattering radius (  m) x-axis: = wavelength (  m) Plotted is: Fig shows us the different regimes of scattering that occur as a function of: -wavelength of radiation (solar vs. terrestrial) -size of scattering particle

46 Results of theory… With small particles (x << 1), we get Rayleigh Scattering And theory gives: Particles scatter radiation forward and backward equally! Fig. 4.12a.

47 As particle size increases, we get more forward scattering…Fig b,c. For larger particles with x > 1, we get Mie Scattering. In this case, values of K are oscillatory - Fig Note: an index of refraction has entered m = m r + im i m r = (speed of light in vacuum) / (speed of light through particle) m i = absorption (m i = 0  no absorption; m i = 1  complete absorption)

48 Example 4.9…the sky is blue because… Blue light is scattered 3.45 times more efficiently than red light! ALSO…p nd column …tells us that to understand satellite imaging and retrievals, as well as weather radar etc., we need to apply the ideas in this section.

49 Absorption by non-gaseous particles Not much information BUT read last sentence of p.126

50 Absorption - and emission - by gas molecules Energy arrives, is emitted and absorbed in discrete amounts called photons Having energy E = h And c =  E = hc/ h = Planck’s constant

51 Atomic energy states An atom has electrons in orbit around the nucleus

52 For the electron to jump into a higher orbit (higher energy level), a discrete amount of energy must be absorbed So only discrete orbits are allowed

53 When this discrete amount of energy (  E) is absorbed, a spectrum of absorption versus wavelength shows a spike. Finite absorption at certain wavelengths. Zero absorption otherwise (transparency). wavelength (  m) absorption

54 → line spectrum Each species → different line spectrum All overlap & combine in the atmosphere Adding molecules → additional complications

55 Energy of a molecule, E is: E = E o + E v + E r + E t Energy due to electron orbits in atoms Energy due to vibration of molecule Energy due to rotation of molecule translational energy

56 As a result, the spectrum is more complicated. Adding  E of energy (e.g., incident from the sun) can result in changes to the rotational state of the molecule, ditto vibrational, ditto electron states etc. → complex absorption spectrum (one for each species)

57 Examples:

58 Examples: Atmospheric Absorption spectra for the main gases

59 Examples: