5 · Surfaces — the bottom-most AddedLayer

For: users configuring scenes with land, ocean, or canopy surfaces; method developers adding a new BRDF.
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In MOM language, the surface is just another layer. Specifically, the bottom-most AddedLayer — built once for the lower boundary of the atmospheric column, then composed with the accumulated atmosphere using the same interaction! machinery that stacks atmospheric layers in Concepts/04.

Surfaces in MOM language

Each BRDF type is a Julia struct subtyping AbstractSurfaceType, plus a method of create_surface_layer! that fills the r⁻⁺, r⁺⁻, t⁺⁺, t⁻⁻, j₀⁺, j₀⁻ matrices of the bottom AddedLayer from the BRDF's parameters. After the atmosphere has been composed TOA → BOA, the loop calls interaction! one more time with the surface layer underneath the accumulated atmosphere. Then interaction_hdrf! (src/CoreRT/CoreKernel/interaction_hdrf.jl:1–42) runs to extract hemispherical-directional reflectance products for m=0.

   CompositeLayer (after final iz=Nz)        Surface BRDF
        │                                          │
        │                                  create_surface_layer!
        │                                          │
        │                                  AddedLayer (bottom)
        │                                          │
        └──────────────► interaction!  ◄───────────┘
                              │
                              ▼
                       interaction_hdrf!
                       HDRF + BHR products
                              │
                              ▼
                       postprocessing_vza!
                              │
                              ▼
                  R, T, hdr, bhr  per (VZA, Stokes, λ)

Surface gallery

The implemented BRDFs and where to find them:

BRDF	Parameters	Use case	File
`LambertianSurfaceScalar`	albedo (single)	featureless reference, calibration scenes	`Surfaces/lambertian_surface.jl`
`LambertianSurfaceSpectrum`	albedo vector	spectrally-varying surface	same
`rpvSurfaceScalar`	ρ₀, ρ_c, k, Θ	semi-arid land with hot-spot	`Surfaces/rpv_surface.jl`
`RossLiSurfaceScalar`	f_iso, f_vol, f_geo	MODIS-style kernel-driven BRDF	`Surfaces/rossli_surface.jl`
`CoxMunkSurface`	wind speed, n_water	sun glint over ocean (polarized)	`Surfaces/coxmunk_surface.jl`
`CanopySurface`	LAI, leaf R/T, soil, n_layers	vegetation canopies	`Surfaces/canopy_surface.jl`

Linearized variants (*_lin.jl files) exist for Lambertian, RPV, Ross-Li, and Cox-Munk; canopy linearization is a work in progress.

Polarized surfaces (Cox–Munk)

For ocean glint, vSmartMOM uses the Cox & Munk (1954) wave-slope distribution for wind-roughened sea surfaces, plus full Fresnel reflection to populate the polarized 4×4 Mueller matrix on each facet. The polarized r⁻⁺ blocks are not zero in Stokes_IQUV — they couple through the Fresnel angle dependence.

Optional refinements:

Whitecaps: wind-speed-dependent Lambertian contribution from breaking waves (Koepke 1984).
Shadowing: Mishchenko-Travis shadowing function for grazing geometries.

Canopy surfaces

CanopySurface is a pre-solver — it solves a discrete-ordinate problem within the vegetation layer (LAI-weighted leaf reflectance/transmittance, soil at the bottom) before presenting an effective lower-boundary AddedLayer to the atmospheric MOM solver. This keeps the canopy physics (specular leaf scattering, dark soil background, vertical heterogeneity in LAI) decoupled from the atmospheric pass while reusing the same matrix-operator language.

HDRF and BHR products

Many remote-sensing applications report hemispherical-directional reflectance factor (HDRF) and bi-hemispherical reflectance (BHR) instead of (or alongside) per-VZA radiances. interaction_hdrf!:

julia

# src/CoreRT/CoreKernel/interaction_hdrf.jl:1–42
hdr_J₀⁻ = r⁻⁺ ⊠ J₀⁺ .+ j₀⁻                     # HDRF (per quadrature node)
if m == 0
    bhr_J₀⁻[i, λ] = sum( hdr_J₀⁻[j, λ] * w[j] * μ[j]  for j in nodes )  # BHR
end

HDRF is the per-VZA (or per-quadrature) reflectance into the upper hemisphere normalized by incident solar flux; BHR is its hemispherical integral, only well-defined for m=0.

Code anchors

Concept	Source
Surface BRDF kernels	`src/CoreRT/Surfaces/` (10 files)
`create_surface_layer!` interface	implemented per BRDF in `Surfaces/*.jl`
Surface coupling step	`src/CoreRT/CoreKernel/interaction_hdrf.jl:1–42`
Polarized Cox–Munk Mueller blocks	`src/CoreRT/Surfaces/coxmunk_surface.jl` + `fresnel.jl`
Canopy pre-solver	`src/CoreRT/Surfaces/canopy_surface.jl`
Surface BRDF map (YAML)	`src/IO/Parameters.jl::BRDF_MAP`
Linearized Cox–Munk	`src/CoreRT/Surfaces/coxmunk_surface_lin.jl`

To add a new surface BRDF, see the developer guide Add a Surface BRDF.

Hands-on tutorials

Runnable examples with Plotly figures:

References

Sanghavi et al. (2014), JQSRT 133:412–433, doi:10.1016/j.jqsrt.2013.09.004. Eqs. (33)–(37) — surface boundary conditions for MOM.
Wanner, Li, Strahler (1995), On the derivation of kernels for kernel-driven models of bidirectional reflectance, JGR 100:21077. (Ross-thick / Li-dense.)
Cox, C. & Munk, W. (1954), Measurement of the roughness of the sea surface from photographs of the sun's glitter, J. Opt. Soc. Am. 44:838.
Rahman, Pinty, Verstraete (1993), Coupled surface-atmosphere reflectance (CSAR) model (RPV).
Koepke, P. (1984), Effective reflectance of oceanic whitecaps, Appl. Opt. 23:1816.
Crib sheet: docs/dev_notes/theory_references.md §C (S2014 Eqs 33–37).

5 · Surfaces — the bottom-most AddedLayer ​

Surfaces in MOM language ​

Surface gallery ​

Polarized surfaces (Cox–Munk) ​

Canopy surfaces ​

HDRF and BHR products ​

Code anchors ​

Hands-on tutorials ​

References ​