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CoreRT Starter Tutorial: Elemental -> Doubling -> Interaction ​

Goal: understand the execution workflow of the core matrix-operator solver and how it maps to code.

This tutorial is intentionally lightweight. It shows:

  1. how to run a minimal RT case,

  2. where the core operators are applied, and

  3. how to connect runtime steps to equations in the references.

1) Minimal run ​

julia
using vSmartMOM
using vSmartMOM.CoreRT

Load a simple pure-Rayleigh test case (no aerosols, no gas absorption).

julia
params = read_parameters(
    joinpath(pkgdir(vSmartMOM),
             "test", "test_parameters", "PureRayleighParameters.yaml"))
params.architecture = vSmartMOM.Architectures.CPU()
params.max_m = 2
params.l_trunc = 20

Build the model and run.

julia
model = model_from_parameters(params)
R, T = rt_run(model)

R is the top-of-atmosphere reflected Stokes field [nVZA × nStokes × nSpec].

julia
println("R shape: ", size(R))
println("R(nadir, I, λ₁) = ", R[1, 1, 1])

The generated docs include a Plotly view of this pure-Rayleigh scene across the signed viewing-angle sweep in the YAML file. The first trace is Stokes I; the second trace is Stokes Q.

2) What happens internally ​

The layer loop is implemented in src/CoreRT/rt_run.jl. For each Fourier mode and each atmospheric layer, rt_kernel! in src/CoreRT/CoreKernel/rt_kernel.jl applies:

  1. elemental!: builds elemental r/t/j operators from layer optical properties.

  2. doubling!: recursively doubles the elemental layer to the target optical thickness.

  3. interaction!: adds the new (doubled) layer to the existing composite atmosphere.

For the first layer (iz == 1), the added layer is copied directly into the composite layer (no interaction yet). For iz > 1, adding is applied.

3) Equation provenance quick map ​

  • Elemental layer: infinitesimal/elemental operator form in Sanghavi et al. (2014), Eq. (19) family.

  • Doubling/adding recursions: Sanghavi et al. (2014), Eq. (23)-(28) (scalar precursor in Sanghavi et al. (2013), Eq. (22)-(27)).

  • D-matrix symmetry (diag(1,1,-1,-1) per stream): Sanghavi et al. (2014), Eq. (29)-(32).

  • SFI single-scattering source terms (J₀⁺, J₀⁻) in get_elem_rt_SFI!: Fell (1997), Eq. (1.52)-(1.54), with thin-layer limits Eq. (1.55)-(1.56).

  • Truncation updates used by scattering optics: Sanghavi and Stephens (2015), Eq. (38a)-(38d).

For a detailed symbol-to-code mapping, see the documentation page: vSmartMOM -> Core RT Theory (Doubling/Adding).

This page was generated using Literate.jl.