Boundary conditions

Upper boundary

The top boundary supplies the downward diffuse intensity at the top of the atmosphere. In thermal mode it defaults to \(B(T_0)\) (the top level temperature). Override it with top_temperature — most commonly top_temperature = 0 for cold space (no downwelling), which matches DisORT. In non-thermal mode, top_emission gives the raw isotropic downward radiance.

Lower boundary: Lambertian surface

By default the lower boundary is a Lambertian surface characterised by:

  • surface_albedo — the reflectivity in \([0, 1]\);

  • surface_temperature (thermal mode) or surface_emission (raw) — the thermal emission.

If surface_temperature is left at -1 in thermal mode, the surface emits at the bottom level temperature temperature[num_layers]. A distinct positive surface_temperature decouples the ground (skin) temperature from the lowest atmospheric level.

The surface reflects the diffuse field and, if a solar beam is present, also reflects the attenuated direct beam back upward (Boundary conditions and intensity reconstruction).

Lower boundary: diffusion approximation

For stellar-atmosphere models where the deepest level is an optically thick interior rather than a physical surface, set use_diffusion_lower_bc = true. The upward intensity at the lower boundary is then

\[I^{\uparrow}_{\text{bot},i} = B(T_\text{bot}) + \mu_i\left.\frac{\dd B}{\dd\tau}\right|_\text{bot},\]

with the Planck gradient estimated from the bottom two levels. When this is active, no surface layer is added, so surface_albedo and the surface emission fields are ignored. The condition requires Planck data (use_thermal_emission or planck_levels).

adrt::ADConfig cfg(50, 16);
cfg.use_thermal_emission   = true;
cfg.use_diffusion_lower_bc = true;
cfg.wavenumber_low  = 2000.0;
cfg.wavenumber_high = 3000.0;
cfg.allocate();
// ... fill temperatures, delta_tau, single_scat_albedo, moments ...
adrt::RTOutput r = adrt::solve(cfg);

See Boundary conditions and intensity reconstruction for the full treatment of the internal interface intensities.