Notation
AnalyticBandRadiation follows the NumericalEarth.jl notation guide for symbolic names in math, in docstring equations, and in plot labels. Julia struct fields stay descriptive snake_case (matching Breeze's public API convention), but the mapping to the symbolic notation is always unambiguous.
Radiative fluxes
| Math | Where it appears in code | NumericalEarth symbol |
|---|---|---|
ℐꜜˡʷ at surface | LongwaveDiagnostics .surface_longwave_down | \scrI\^downarrow\^l\^w |
ℐꜛˡʷ at surface | LongwaveDiagnostics .surface_longwave_up, .ocean_surface_longwave_up, .land_surface_longwave_up | \scrI\^uparrow\^l\^w |
ℐꜛˡʷ at TOA (OLR) | LongwaveDiagnostics .outgoing_longwave | \scrI\^uparrow\^l\^w at top of atmosphere |
ℐꜜˢʷ at surface | ShortwaveDiagnostics .surface_shortwave_down | \scrI\^downarrow\^s\^w |
ℐꜛˢʷ at surface | ShortwaveDiagnostics .surface_shortwave_up | \scrI\^uparrow\^s\^w |
ℐꜛˢʷ at TOA | ShortwaveDiagnostics .outgoing_shortwave | reflected-to-space shortwave |
State and surface variables
| Math | Code | Description |
|---|---|---|
T | AtmosphereProfile.temperature | Layer air temperature (K) |
q | AtmosphereProfile.humidity | Specific humidity (kg kg⁻¹) |
p | AtmosphereProfile.surface_pressure; ColumnGrid.σ_*·pₛ in-code | Pressure (Pa) |
α | SurfaceState.ocean_albedo, land_albedo | Surface albedo |
ϵ | SurfaceState.ocean_emissivity, land_emissivity | Surface emissivity |
σ (Stefan–Boltzmann) | PhysicalConstants.stefan_boltzmann | W m⁻² K⁻⁴ |
g | PhysicalConstants.gravity | m s⁻² |
cₚ | PhysicalConstants.heat_capacity | Isobaric specific heat (J kg⁻¹ K⁻¹) |
Sigma-coordinate vertical grid
The vertical grid is stored in ColumnGrid using the pressure-normalized σ = p / pₛ convention inherited from SpeedyWeather.
| Math | Code | Description |
|---|---|---|
σₖ at midpoints | σ_full | Length nlayers |
σₖ₊½ at interfaces | σ_half | Length nlayers + 1, monotonic from 0 (TOA) to 1 (surface) |
Δσₖ | σ_thick | Layer thickness, = diff(σ_half) |
Note: the package uses σ for the vertical coordinate and σ in context for the Stefan–Boltzmann constant (e.g. PhysicalConstants.stefan_boltzmann). Local variables in the solvers disambiguate with σ_SB.
Longwave spectroscopy
| Math | Code | Description |
|---|---|---|
ν̃ | ν̃ | Wavenumber (cm⁻¹) |
B(T, ν̃) | planck_wavenumber | Spectral Planck radiance |
κ_line^ref(ν̃) | h2o_line_kappa_ref | Reference H₂O line absorption |
κ_cnt^ref(ν̃) | h2o_cont_kappa_ref | Reference H₂O continuum absorption |
κ_CO₂^ref(ν̃) | co2_kappa_ref | Reference CO₂ absorption |
τ(p) | integrated internally | Optical depth |
D | AnalyticBandLongwave.diffusivity | Two-stream diffusivity factor (≈ 1.5) |
Loop-internal scalar accumulators in solve_longwave! use compact names U and D for ℐꜛ and ℐꜜ in the spectral sweep. Comments in the solver tie them to the math.