pat arnott, atms 749 atmospheric radiation transfer ch4: reflection and refraction in a homogenous...

$: Pat Arnott, ATMS 749 Atmospheric Radiation Transfer CH4: Reflection and Refraction in a Homogenous Medium$
Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

CH4: Reflection and Refraction in a Homogenous Medium.


Polarization States: A reminder

Wave/Photon boson: Polarization.

Linear Polarization: E-field in one direction.

Circular, elliptical polarization: E-Efield rotates due to phase difference between horizontal and vertical components.From: http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/polclas.html


More Details on the Polarization States

Circular Polarization

Elliptical Polarization:

The most general representation.


Three Choices for Solar Radiation

Emissivity is the same as absorptivity. Source can be visible or infrared radiation, or other wavelengths as well, microwave, etc.

Transmission + Reflection + Absorption = 1


Reflection, Refraction, and Transmission


Radiant Intensity and Flux: How do we deal with reflected radiation?

What are examples of each type of reflection?


Trace velocity matching principle: Snell’s law (continuity of the wavefront at a boundary)

“slow is more normal”Here assume n1=n1r, n1i=0, n2=n2r, n2i=0.

MIRAGES

n1sin(1)= n2sin(2)

For a gas, (nr-1) ≈ =gas density.

d/dz > 0 for this type or mirage.

What does this say about the likelihood of convection?

z

Another type of reflection without a real interface.


Snell’s Law: Kinematics


Complex Refractive Index for Water and Ice


Some Basics, Electromagnetic Skin Depth


Wave Penetration Depth in Water and Ice


Boundary Conditions at Interfaces: Used with Plane Wave Solutions of Maxwell’s Equations for E and H to get the Fresnel Coefficients.

• Used along with boundary conditions to calculate the single scattering properties of aerosols and hydrometeors (cloud droplets, rain drops, ice crystals, snow flakes, etc), from first principles if possible. {Mie theory for homogeneous spheres, coupled dipole theory for general particles, T-Matrix method, etc}

• Are not used to calculate the radiation field arriving at the surface from the complex atmosphere. Multiple scattering theory is used.


Fresnel Reflection Coefficients: What is the magnitude of the light specularly reflected from a surface? (Also can get the transmitted wave magnitude).

Medium 2

Medium 1

i

t


Reflectivity of Water And Ice

BrewsterAngle

Microwave =15,000 microns nr = 6.867192 ni = 2.630

Mid Visible (green) =0.5 microns nr = 1.339430 ni = 9.243 x 10-10


Reflectivity of Water And Ice: Normal Incidence

What drives the reflectivity?


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.


Rainbow Optics

scattering angle

See http://www.philiplaven.com/p8e.html, and atmospheric optics.

nr


Geometrical Optics: Rainbow (from Petty)

Angle of minimum deviation from the forward direction. Focusing or confluence of rays.

x

Distance x is also known as the impact parameter. (Height above the sphere center.)


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.


Light Scattering Basics (images from Wallace and Hobbs CH4).

Sphere, radius r, complex refractive index n=mr + imi

x

xxLines :

r= x2π

Dimensionless Parameters

SizeParameter≡x=2πr

ScatteringEfficiency≡Qs=σscaπr2

mr=1.5

Qs

Angular Distribution of scattered radiation (phase function)

x x

xDipole scattering

pat arnott, atms 749 atmospheric radiation transfer ch4: reflection and refraction in a homogenous...

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