1. 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

2. 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:

3. More Details on the Polarization States
Elliptical Polarization:
The most general representation.
Circular Polarization

4. Fresnel Reflection Coefficients: What is the magnitude of the light specularly reflected from an ice surface as a function of wavelength? i
Medium 1
Medium 2 t

5. Mirages can complicate the BRDF
Here assume
n1=n1r, n1i=0,
n2=n2r, n2i=0.
Another type of reflection without a real interface.
n1sin(1)= n2sin(2)
MIRAGES z
For a gas, (nr-1) ≈ 
=gas density.
d/dz > 0 for this type or mirage.
What does this say about the likelihood of convection?

6. Solar Wavelengths: Reflection + Absorption = Total Radiation
Incident = 1
Reflection = r()
Transmission = Absorption = a()
1 = a() + r()

7. Radiant Intensity and Flux: How do we deal with reflected radiation?
What are examples of each type of reflection?

8. Reflection is Complex !!!

9. Reflection Coefficient of Various Surfaces
Notes:
Snow varies greatly with wavelength, especially in the IR.
Note the straw versus alfalfa (dry dead plant versus live plant).

10. General Case: BDRF BRDF, Bidirectional Reflection Function.
General Case: Why the cos and sin?
Special Case: Lambertian Surface.
General Case: reflectivity