Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

CH5: Radiative Properties of Natural Surfaces

BRDF: One of the most general means to characterize the reflection properties of a surface is by use of the bi-directional reflection distribution function (BRDF), a function which defines the spectral and spatial reflection characteristic of a surface. The BRDF of a surface is the ratio of reflected radiance to incident irradiance at a particular wavelength: L = reflected radiance (radiant intensity) and E is the incident irradiance (flux). From http://math.nist.gov/~FHunt/appearance/brdf.html

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

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

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

More Details on the Polarization States

Circular Polarization

Elliptical Polarization:

The most general representation.

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

Fresnel Reflection Coefficients: What is the magnitude of the light specularly reflected from an ice surface as a function of wavelength?

Medium 2

Medium 1

i

t

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

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.

Mirages can complicate the BRDF

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

Solar Wavelengths: Reflection + Absorption = Total Radiation

Incident = 1

Reflection = r()

Transmission = Absorption = a()

1 = a() + r()

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

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

What are examples of each type of reflection?

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

Reflection is Complex !!!

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

Reflection Coefficient of Various Surfaces

Notes: 1. Snow varies greatly with wavelength, especially in the IR.2. Note the straw versus alfalfa (dry dead plant versus live plant).

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

General Case: BDRF BRDF, Bidirectional Reflection Function.

Special Case: Lambertian Surface.

General Case: Why the cos and sin?

General Case: reflectivity