Why is the sky blue?

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Damon Chase
5 years ago
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1 Why is the sky blue?

2 Volcanic: June 12, 1991: Mt Pinatubo ejected 20 million tons of sulfur dioxide. Aerosols spread globally Haze lowered a drop of global temperature by 1F

5 Size parameter:

7 Rayleigh scattering Vertically polarized light Particle is so small that every part experiences simultaneously the EM field

8 Raman scattering Molecule polarized from EM field Electrons in each atom wobble Atomic bonds wobble too à Scattered light is a different color à At the level of 1 in a million photons

9 Particle experiences a separation of charge It then oscillates with the incident E field Radiates like a vibrating dipole

10 E of vibrating dipole α 1/λ 2 I α E 2 α 1/λ 4

13 Incident Vertically polarized light Polarization of Scattered light is shown in blue Incident Horizontally polarized light Degree of polarization: Phase function: Incident Nonpolarized light Polarized light

14 Direction of the Sun Polarized filter

16 Light travels 1.33 times faster in a vacuum than in water

17 Imaginary index of refraction, n, Attenuation coefficient: k = 2πn/λ 0 From Khare et al. 1984

$effects such as diffraction and interference.$ $Interference Diffraction pattern of red laser beam made on a$ magnified image of a colored interference pattern in a soap

magnified image of a colored interference pattern in a soap

20 Geometrical optics does not account for certain optical effects such as diffraction and interference. Interference Diffraction pattern of red laser beam made on a plate after passing a small circular hole in another plate A magnified image of a colored interference pattern in a soap film. The "black holes" are areas of almost total destructive interference, (antiphase). Ray tracing treat spherical and non-spherical particles with sizes much larger than the wavelength of light.

21 Scattering of spherical particles n i = 0 From Hansen & Travis 1974

23 n i is Related to the absorption coefficient κ= 4πn i /λ No absorption: n i = 0: 50% of light scattered / 3% reflected / 47% refracted Strong absorption: n i = 100: 50% of light scattered / 3% reflected / 0% refracted

25 Forward scattering Mean value of the cosine of scattering angle, weighted by phase function Maximum values of g result from diffraction & transmission - L=0 and L=2 of light through a spherical particle Equal forward & backward scattering Smoothed over a size range. Still can see primary interference pattern

28 Interference between diffracted (l=0) and transmitted light (l=2) n r =1.33 The phase shift in light passing through the diameter is 2x(n r -1). Constructive & destructive interference occurs in intervals of 2pi, and thus here in intervals of x = 2pi/2(n r -1) ~ 9.5 for n r =1.33 Efficiency of scattering for one particle size

29 Forward scattering Where: Weight radius by πr 2 (Qsca too cumborous) because each particle scatters proportional to πr 2 Q sca

30 Standard size distributions Large spread in radius dampens the wobbles

31 Indices of refraction of soot particles Dombrovsky, Leonid A.

32 Determining the UV imaginary index of refraction of Saharan dust particles from Total Ozone Mapping Spectrometer data using a three-dimensional model of dust transport A three-dimensional model has been developed for simulating Saharan dust emissions and transport over the tropical North Atlantic Ocean. The computed dust fields are constrained by data from ACE-2, and we use a radiative transfer code to simulate the Total Ozone Mapping Spectrometer on the Earth Probe satellite (EP-TOMS) aerosol index (AI). Using the observed relationship between AI and aerosol optical depth, we determine from our simulations the UV refractive index for dust particles at Dakar, Sal, and Tenerife. We find that the dust imaginary refractive index at Sal and Tenerife is approximately k = ( ) at 331 nm and k = ( ) at 360 nm. At Dakar the dust imaginary refractive index is approximately k = ( ) at 331 nm and k = ( ) at 360 nm. These values are considerably less absorbing than the refractive index currently used in the TOMS retrievals of dust optical depth and single scatter albedo. Once the dust refractive index has been constrained, we calculate the single scatter albedo by integrating across the particle size distribution. We find that the particle single scatter albedo at 331 nm is ϖ 0 = 0.81 ( ) at Dakar, ϖ 0 = 0.84 ( ) at Sal, and ϖ 0 = 0.86 ( ) at Tenerife. The refractive index determined in this study should be useful for future retrievals using the TOMS data, as well as for energy balance studies that incorporate the radiative effects of mineral dust aerosols. Colarco Journal of Geophysical Research: Atmospheres ( ) Volume 107, Issue D16, pages AAC 4-1 AAC 4-18, 27 August 2002

33 Phase Function: Single scattering albedo: Particulate number density: N How many variables does this make?

$reflector diffraction Which constitutes$ $Large particles absorb all refracted n r$

34 Approaching Rayleigh regime Perfect reflector diffraction Which constitutes half the scattered light. Large particles absorb all refracted n r =1.33 Note as ωè1 Q è2

35 Fractal particles

38 Blue contour plot at 88 km. The observations are inside the narrow red box. The models are for 3000 monomers of radius 0.05 mm. The model and data contours are in reasonably good agreement. Blue contour plot at 88 km. The observations are inside the narrow red box. The models are for 3000 monomers of radius 0.05 mm. The model and data contours are in reasonably good agreement.

41 We know: phase function P(θ, z, λ, t) and ssa ω(z, λ, t) and density N(z) At the landing site. How do we figure it out for all time and all latitudes? Fortunately Titan has fast zonal winds that uniforms the haze with longitude

The scattering behavior of particles are usually couched in terms of their single scattering albedo, the phase function polarization and particle density.

42 The scattering behavior of particles are usually couched in terms of their single scattering albedo, the phase function polarization and particle density. The former two properties depend on the composition, shape and size of the particle. Large particles tend to scatter more in the forward direction and Rayleigh scattering scatters equally in the forward and backward directions. Efficiency of Rayleigh scattering depends on λ -4 Efficiency of Mie scattering decreases as the wavelength approaches the particle size The sky is blue because the EM field induces a dipole moment in atmospheric molecules that nudges the negative electrons away from the positive charges. The electrons, as they are smaller, accelerate tracing out the shape of the light s electric field. The blue photons have a higher frequency thus accelerates the electrons faster. The power radiated depends on the acceleration squared. Since the blue photons make the electrons accelerate the fastest, they radiate more than do the other colors.

p(θ,φ,θ,φ) = we have: Thus:

p(θ,φ,θ,φ) = we have: Thus: 1. Scattering RT Calculations We come spinning out of nothingness, scattering stars like dust. - Jalal ad-din Rumi (Persian Poet, 1207-1273) We ve considered solutions to the radiative transfer equation