VLIDORT-QS Model

In essence, VLIDORT-QS ("VLIDORT Quasi-Spherical" or VQS for short) is an "approximately spherical" RT model designed to work in a spherically curved atmosphere. Single scattering (SS) is treated accurately in full spherical manner, while multiple scattering (MS) RT is done using a modified version of the standard VLIDORT. The VQS model has three geometrical configurations:

• Regime I - the standard "nadir-upwelling" scenario where the light path originates at the surface, which includes surface reflectance as well as atmospheric scattering;
• Regime II - the "limb-view" scenario where the light path passes through a tangent point separating near- and far-side path segments;
• Regime III - the "nadir-downwelling" scenario where the light path originates at the top of the atmosphere.

In a stratified atmosphere, VQS makes separate calculations of the SS and MS source term contributions in each segment of the light path, and segment source terms are computed by integrating the SS and MS radiation fields using an accurate Gaussian quadrature scheme. The final radiation field at the viewing camera is then computed using a recursion calculation which propagates these source terms along the light path from its origin to its destination. Although MS fields at any point on the path are calculated using the usual VLIDORT plane-parallel scattering solutions, the variation in geometrical configuration along the light path allows for a much more accurate assessment of the MS field when compared to the single-geometry calculation from the standard VLIDORT model.

VQS, also has a full linearization facility. It can generate (in addition to the radiation field itself) a complete range of analytically-derived radiance or Stokes-vector Jacobians (weighting or sensitivity functions) with respect to any atmospheric parameter (for example, plume aerosol loading parameters). The model also has the ability to generate actinic and regular fluxes (integrated radiation fields) at all segment boundaries and the code has been made thread-safe for use in parallel-computing environments such as OpenMP.

VLIDORT-QS is a recent development, started in 2015. A detailed description of the VQS model is in [Spurr et al., 2022]. This includes a number of validations of VQS against a 3-D Monte-Carlo (MC) RT model operating in a spherical medium.

2-Stream Model

The 2-stream model provides fast multiple-scatter (MS) low-stream radiance and Jacobian output at TOA (upwelling) and BOA (downwelling) geometries. The Jacobian facility is the same as that for the main LIDORT family of models (with respect to profile/column atmospheric or surface properties). 2S does not include the primary scatter RT contribution (it is MS only!).

2S has the pseudo-spherical treatment for the incoming solar beam. It also has thermal and surface emission, a BRDF supplement, and additional options for different geometrical inputs. This code is designed to run in tandem with LIDORT; it is validated against the latter model.

The 2-stream model was written in 2009-2010, with thermal emission treatment completed in 2011, and the model given a BRDF supplement and the observational geometry option in 2012. More recently, the code has received a number of performance enhancements to make it faster, and it has a conservative-scattering option for exoplanet studies. The code is in Fortran 90 and is currently at Version 1.5.

First-Order Models

These models are single-scatter and (except for LIDORT-RRS) direct-thermal-emission codes that can be used either for stand-alone calculations, or in conjunction with LIDORT, VLIDORT and LIDORT-RRS. All of the parent models have the ability to ingest their corresponding FO code inputs. All FO models have profile/bulk atmospheric and surface-property Jacobians.

The observational geometry option is also standard. The FO codes are fully compatible with the multiple-scatter options in the main codes; in particular, output is available at arbitrary vertical heights. The solar single-scattering FO codes incorporate the Nakajima-Tanaka ansatz to deal with the use of the delta-M scaling approximation in the main RTE treatment with multiple scatter.

The FO codes were created in 2011 (for use with LIDORT) and 2012 (for use with VLIDORT and LIDORT-RRS), and recently upgraded to Version 1.5 to include output away from layer boundaries, and to incorporate pre-calculated phase-functions and F-matrices (instead of expansion coefficients). All FO codes are in Fortran 90.

Electromagnetic Scattering Models

In 2011, a linearization of the NASA-GISS T-matrix scattering code was carried out. [Mie code was linearized independently in 2004]. In 2012, two packages were prepared for public availability. These are the linearized Mie and T-matrix code packages; they are both in Fortran 90 and are currently at Version 1.4.

Both electromagnetic scattering packages will work in either mono-disperse or poly-disperse modes; for the latter there are the usual choices of particle size distributions (PSDs): log-normal, standard and modified Gamma, power-law, etc. Both packages have a full bimodal aerosol capability. Aerosol "microscopic" optical property derivatives are available with respect to the real and imaginary parts of the refractive index, the non-spherical "deformation parameter" (T-matrix only, restricted to spheroids, cylinders and Chebyshev particles), and PSD parameters such as mode or effective radius.

Fast-PCA Model

In recent years, RT Solutions has worked closely with V. Natraj (NASA-JPL) and others on the development of a number of fast radiative transfer tools based on PCA (Principal Component Analysis) applied to optical property data sets. Within the hyperspectral modeling context, PCA exploits redundancy in grouped optical data, and enables computationally expensive full-stream multiple-scatter (MS) LIDORT calculations to be done for just a few PCA-derived optical profiles; correction factors for MS fields can then be derived from comparing LIDORT and 2-stream MS output for this information-rich set of optical profiles; the corrections are based on second-order central finite-differencing using the Principal Component arising from the PCA. Full-wavelength calculations are then done only for fast 2-stream and single scatter contributions, with the correction factors applies to the 2-stream MS part.

Fast-PCA RT can achieve speed-ups of more than 50 for many applications in the UV/Vis/SWIR out to 3.0 Microns; the accuracy is better than 0.1% everywhere, with RMS accuracy overall at the 0.01% level. A number of other Fast-PCA RT applications using LIDORT, 2-stream and SS codes have been constructed, and it is now possible to generate accurate fields of profile and surface Jacobians (as well as radiances) with speed and accuracy, not only for solar sources but also for the thermal regime. The PCA method has been extended recently to VLIDORT and the fast generation of all Stokes vector components.

Other Models

In 2004/2005, LIDORT linearization methods were successfully applied to a coupled atmosphere-ocean discrete ordinate model. This model was given polarization treatment in 2006-2007 and a rough-surface capability introduced.

LIDORT linearization methods have also been applied to a hybrid RT model with discrete-ordinate layer RTE solutions, and matrix-operator (adding method) completion of the radiation field at TOA.

Research is continuing on the development of a Twilight model of LIDORT, for use in high solar-zenith-angle simulations with and without shadowing.