1. Page 1 Vijay Natraj Polarization November 9, 2007

2. Page 2 Stokes Parameters Electromagnetic radiation can be described in terms of the Stokes parameters: I, Q, U and V –I - total intensity –Q & U - linear polarization –V - circular polarization Degree of Polarization (if U = V = 0)

3. Page 3 Importance of Polarization Polarization is a result of scattering Atmospheric scatterers –molecules –aerosols –clouds Surfaces can also polarize, in some cases significantly (e.g., ocean) The ground-based/satellite instrument could be sensitive to polarization

4. Page 4 Radiative Transfer Equation (RTE) Z: phase matrix; describes scattering of radiation from one direction to another

5. Page 5 Solution of RTE Atmosphere stratified into homogeneous layers Expand phase matrix in generalized spherical functions Fourier expansion for Stokes vector Integrals replaced by Gaussian quadrature RTE splits up into individual equation for each Fourier component

6. Page 6 Solution Techniques Discrete Ordinates –Treat RTE as BVP –boundary conditions at TOA and surface –continuity at interface between layers Doubling-Adding –Compute reflection and transmission properties for very thin sub-layer assuming single scattering –Add two such identical sub-layers by computing successive reflections back and forth between the layers (doubling) –Repeat process until layer properties computed –Add contiguous layers using same technique (adding) –Repeat process until all layers treated –Start with reflection properties of surface and build up Successive Orders of Scattering –Reflection and transmission computed individually for photons scattered once, twice, thrice … –Stokes parameters obtained as sum over all orders of scattering –(n-1) th order of scattering is the source for the n th order of scattering