The Discrete Ordinates Source

The discrete ordinates method is an implementation of multiple scattering that is enabled with

import sasktran2 as sk

config = sk.Config()

config.multiple_scatter_source = sk.MultipleScatterSource.DiscreteOrdinates

Advantages

• “exact” solution in a plane-parallel medium of stacked homogenous layers

• Correct solutions in layers of large optical depth without sub-layering

• Computationally efficient for most cases

Disadvantages

• May not be suitable for some limb-viewing applications because of errors in the plane-parallel assumption

• Only suitable for 1-D atmospheres

• May not be suitable for twilight viewing conditions (solar zenith angle > 85)

Corrections in a Spherical Atmosphere

As noted, the discrete ordinates technique is a solution to the radiative transfer equation in a plane-parallel medium, however several corrections are implemented to improve the solution in spherical atmospheres.

The first is the pesudo-spherical approximation, which accounts for sphericity when calculating the solar attenuation factor. This correction has very little computational overhead and is thus always enabled when appropriate for the given model geometry.

The second correction is more involved and attempts to correct for line of sight sphericity effects. In a spherical atmosphere, the solar zenith angle changes along any given line of sight, but the discrete ordinates solution is only valid for a single solar zenith angle. To account for this multiple discrete ordinates calculations are performed at different solar zenith angles. The resulting sources are then interpolated in cosine of solar zenith angle. The number of such calculations is controlled with the sasktran2.Config.num_sza attribute. The required value of this attribute to obtain an accurate solution is very application dependent, we recommend increasing it until the solution stops changing. A rough rule of thumb is that for all ground viewing applications, 1-2, is usually sufficient. For limb viewing applications usually somewhere in the range 1-7 is good enough.

Notes

• The discrete ordinates source is perfectly linearized, i.e., weighting functions are calculated to machine precision

Relevant Configuration Options

sasktran2.Config.multiple_scatter_source	Sets which (if any) multiple scatter source is to be used inside the calculation.
sasktran2.Config.num_streams	The number of streams to use in the discrete ordinates method.
sasktran2.Config.num_sza	The number of solar zenith angle discretizations to use when calculating the multiple scatter source.
sasktran2.Config.num_stokes	Sets the number of Stokes parameters used in the calculation.
sasktran2.Config.do_backprop	Enables backpropagation for the weighting functions when using the DO source in plane parallel or pseudo-spherical geometry.