Chapter 6: Blackbody Radiation: Thermal Emission

1. "Blackbody radiation" or "cavity radiation" refers to an object or system which absorbs all radiation incident upon it and re-radiates energy which is characteristic of this radiating system only, not dependent upon the type of radiation which is incident upon it. The radiated energy can be considered to be produced by standing wave or resonant modes of the cavity which is radiating. http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html Chapter 6: Blackbody Radiation: Thermal Emission Eventual Absorption: Acts like a black body (classroom also?)

2. Earth-Atmosphere Energy Balance Fig. 9.1

3. Molecules as Billiard Balls

4. Container of Photons: It really works! I=T4, =5.67e-8 W m-2 K-4 Radiation Pressure

5. DEFINITION OF THE BRIGHTNESS TEMPERATURETB Measured Radiance at wavenumber v = Theoretical Radiance of a Black Body at temperature TB

6. FTIR Radiance: Atmospheric IR Window 13 microns 8 microns FTIR Ground, Ts

7. FTIR Brightness Temperatures FTIR Ground, Ts

8. Nimbus Satellite FTIR Spectrum FTIR Ground, Ts

9. Nimbus Satellite and Ground Based FTIR Spectrum FTIR Ts Ground, Ts ≈Ts FTIR Ground, Ts

10. Planck Functions for Earth and Sun: Note some overlap (4 microns), but with log scale, can treat them separately for the most part.

11. Eye Response Evolved to Match Solar Spectrum Peak? The answer depends on how you look at the distribution functions, wavelength or wavenumber. Seems to support it Seems not to support it.

12. Blackbody Radiation: A look at the Forms:

13. Blackbody Radiation: Another look at the Forms:

14. Earth’s Surface Temperature Te Earth’s radiative temperature Ts Sun’s radiative temperature Rs Sun’s radius Rse Sun to Earth distancea Earth’s surface solar reflectancet IR transmittance of Earth’s atmosphere.

15. Simple Model for Earth’s Atmosphere: No Absorption of Sunlight by the Atmosphere.

16. Simple Surface Temperature Calculation Assuming Solar Absorption only at the surface, IR emission by the atmosphere and Earth’s surface, and IR absorption by the Atmosphere. S0 = 1376 W/m2=Solar Irradiance at the TOA and =Stefan-Boltzmann constant

17. Model with Atmosphere that absorbs solar radiation: Terrestrial IR=IR=LW, Solar = SW • A = surface albedo≈0.3 • asw = Atmosphere absorption of solar radiation • tsw = Transmission of solar by the atmosphere = (1-asw) • alw = Atmosphere absorption of IR radiation • = Atmospheric Emissivity. • tlw = Transmission of IR by the atmosphere = (1-alw) • Ts = surface temperature • Ta= atmosphere temperature • ≈ 1 = IR surface emissivity . Fluxes: F1=incident from sun F2 = tswF1 = (1-asw)F1 F3=Solar reflected to space by the earth, atmosphere=F4 transmitted by atmosphere. F4=Solar reflected by surface. F8=IR emitted by surface. F7=tlwF8=(1-alw)F8 . F5=F6=IR emitted by atmosphere. • Solar Flux Relationships: • F1= S • F2 = tswF1 = (1-asw) F1= (1-asw) S • F4=A F2 = A (1-asw) S • F3= (1-asw) F4= A(1-asw)2 S • IR Flux Relationships: • F5= F6 = alwTa4 • F8 = Ts4= Ts4 • F7= (1-alw) F8= (1-alw) Ts4

18. Radiative Equilibrium Relationships • A = surface albedo≈0.3 • asw = Atmosphere absorption of solar radiation • tsw = Transmission of solar by the atmosphere = (1-asw) • alw = Atmosphere absorption of IR radiation • = Atmospheric Emissivity. • tlw = Transmission of IR by the atmosphere = (1-alw) • Ts = surface temperature • Ta= atmosphere temperature • ≈ 1 = IR surface emissivity . Fluxes: F1=incident from sun F2 = tswF1 = (1-asw)F1 F3=Solar reflected to space by the earth, atmosphere=F4 transmitted by atmosphere. F4=Solar reflected by surface. F8=IR emitted by surface. F7=tlwF8=(1-alw)F8 . F5=F6=IR emitted by atmosphere. Fnet,toa= F3+F5+F7-F1 = Flux (Out-In)=0 Fnet,surface= F4+F8-F2-F6 = Flux (Out-In)=0

19. Sufficient Number of Equations to Solve for All Fluxes • A = surface albedo≈0.3 • asw = Atmosphere absorption of solar radiation • tsw = Transmission of solar by the atmosphere = (1-asw) • alw = Atmosphere absorption of IR radiation • = Atmospheric Emissivity. • tlw = Transmission of IR by the atmosphere = (1-alw) • Ts = surface temperature • Ta= atmosphere temperature • ≈ 1 = IR surface emissivity . S0 = 1360 W/m2

20. Resulting Temperate Example for the Simple Model

21. Calculate the microwave radiant intensity (magnitude and polarization state) measured by a satellite above a calm water surface. Ip 55 deg Is

22. Fresnel Reflection Coefficients: What is the magnitude of the light specularly reflected from a surface? (Also can get the transmitted wave magnitude). i Medium 1 Medium 2 t

23. Reflectivity of Water And Ice Brewster Angle Mid Visible (green) =0.5 microns nr = 1.339430 ni = 9.243 x 10-10 Microwave =15,000 microns nr = 6.867192 ni = 2.630

24. What drives the reflectivity? Reflectivity of Water And Ice: Normal Incidence

25. Fresnel Reflection Coefficients: What is the magnitude of the light specularly reflected from a surface? (Also can get the transmitted wave magnitude). ICE i Medium 1 Medium 2 t Transmission & Absorption: Tp=1-Rp=ap=p Ts=1-Rs =as=s a=absorption coefficient =emissivity

26. Calculate the microwave radiant intensity (magnitude and polarization state) measured by a satellite above a calm water surface. The answer. Ip0 Ip i Is0 55 deg Is What are the sources of Ip0? T t (same form for Is)

27. WHY? What if ni = 0? Rp and Rs are not 0 in that case. How could we get emission if ni=0? We have no absorption in that case! If ni=0, then abs=4ni/ = 0!

28. The transmitted wave, with absorption k2, diminishes. The total amount of radiation eventually absorbed in medium 2 is given by Tp,s = (1 - Rp,s). No matter-filled medium exists where k2=0. Ip 55 deg Is

29. See how it goes for normal incidence … Layer dz emits radiation dI at temperature T that transfers to the satellite. After emission, it is partially absorbed in distance z, and then transmitted out the boundary. m z dz

30. See how it goes for normal incidence … Layer dz emits radiation dI at temperature T that transfers to the satellite. After emission, it is partially absorbed in distance z, and then transmitted out the boundary. Interpretation of the terms. boundary transmissivity medium propagator emissivity m z dz

31. See how it goes for normal incidence … Layer dz emits radiation dI at temperature T that transfers to the satellite. After emission, it is partially absorbed in distance z, and then transmitted out the boundary. The total emission is determined by integration in the z direction. m z dz The main contribution to the emitted radiation comes from about a skin depth of the surface, /(4ni).

32. For problem 6.28, let Ip,s0=0. Calculate  for each frequency. Ip i 55 deg Is Key for remote sensing: N2(T) (why?) N1 N2 T t (same form for Is)

33. AMSR Sensor: http://wwwghcc.msfc.nasa.gov/AMSR/ NASA A-Train In support of the Earth Science Enterprise's goals, NASA's Earth Observing System (EOS) Aqua Satellite was launched from Vandenberg AFB, California on May 4, 2002 at 02:54:58 a.m. Pacific Daylight Time. The primary goal of Aqua, as the name implies, is to gather information about water in the Earth's system. Equipped with six state-of-the-art instruments, Aqua will collect data on global precipitation, evaporation, and the cycling of water. This information will help scientists all over the world to better understand the Earth's water cycle and determine if the water cycle is accelerating as a result of climate change. The Advanced Microwave Scanning Radiometer - EOS (AMSR-E) is a one of the six sensors aboard Aqua. AMSR-E is passive microwave radiometer, modified from the Advanced Earth Observing Satellite-II (ADEOS-II) AMSR, designed and provided by JAXA (contractor: Mitsubishi Electric Corporation).It observes atmospheric, land, oceanic, and cryospheric parameters, including precipitation, sea surface temperatures, ice concentrations, snow water equivalent, surface wetness, wind speed, atmospheric cloud water, and water vapor.

34. Geometrical Optics: Interpret Most Atmospheric Optics from Raindrops and lawn sprinklers (from Wallace and Hobbs CH4) Rainbow from raindrops Primary Rainbow Angle: Angle of Minimum Deviation (turning point) for rays incident with 2 chords in raindrops. Secondary Rainbow Angle: Angle of Minimum Deviation (turning point) for rays incident with 3 chords in raindrops.

35.  Rainbow Optics scattering angle nr See http://www.philiplaven.com/p8e.html, and atmospheric optics.

36. Geometrical Optics: Rainbow (from Petty) x Angle of minimum deviation from the forward direction. Focusing or confluence of rays. Distance x is also known as the impact parameter. (Height above the sphere center.)

37. Geometrical Optics: Interpret Most Atmospheric Optics from Ice Crystals (from Wallace and Hobbs CH4) 22 deg and 45 deg Halos from cirrus crystals of the column or rosette (combinations of columns) types. Both are angle of deviation phenomena like the rainbow. Crystal orientation important. 22 deg halo, more common, thumb rule to measure size of arc.

38. Light Scattering Basics (images from Wallace and Hobbs CH4). Angular Distribution of scattered radiation (phase function) x x Sphere, radius r, complex refractive index n=mr + imi Dipole scattering x x mr=1.5 x Qs x