Radiation

Planck's blackbody radiation law (Seinfeld & Pandis 2006 Ch. 4, Eq. 4.2) — the monochromatic emissive power F_B_λ of a blackbody at temperature T as a function of wavelength λ via Planck's constant h, the speed of light c, and the Boltzmann constant k_B: F_B_λ = 2π·c²·h·λ⁻⁵ / (exp(c·h/(k_B·λ·T)) - 1). The component is observed-only: one algebraic equation on one state variable (F_B_λ the monochromatic emissive power per unit wavelength in W/m³) driven by two input parameters (T temperature in K, λ wavelength in m) and four constants (h Planck's constant, c speed of light, k_B Boltzmann constant, π_val mathematical π as a Float64 value). No time derivatives, no PDE, no coupling. Migrated from GasChem.jl@8c12c048 src/radiation_fundamentals.jl:73 (`BlackbodyRadiation` @component). The Planck function is the spectral energy density of thermal radiation from an opaque, non-reflective body in thermodynamic equilibrium — the foundational equation of quantum radiative transfer. Integrating F_B_λ over all wavelengths gives the Stefan-Boltzmann total flux σT⁴ (see stefan_boltzmann.esm); the wavelength where F_B_λ peaks is λ_max = b/T from Wien's displacement law (see wien.esm). At the default T=5800 K (Sun's effective surface temperature) and λ=500 nm (visible green, the canonical solar-peak wavelength), F_B_λ ≈ 8.46e13 W/m³ — the peak intensity that anchors the Sun's irradiance at Earth's distance and the solar-driven photochemistry of the atmosphere. At T=300 K (Earth surface) and λ=10 μm (thermal-IR), F_B_λ ≈ 3.12e7 W/m³ — the canonical longwave outgoing radiation peak that drives the planetary energy balance.

Climate-sensitivity diagnostic (Seinfeld & Pandis 2006 Ch. 4, Eqs. 4.8-4.10) — the linear-response relation between a top-of-atmosphere radiative-forcing perturbation ΔF_net and the resulting change in planetary equilibrium temperature ΔT_e through the no-feedback climate-sensitivity factor λ_0 = 1 / (4·σ·T_e^3) = T_e / (4·F_L). The component is observed-only: four algebraic equations on four state variables (ΔF_net the net forcing, λ_0 the sensitivity factor, ΔT_e the temperature response, F_L the reference longwave flux) driven by three input parameters (T_e the reference equilibrium temperature, ΔF_S the forcing-side perturbation, ΔF_L the longwave-side perturbation) and one constant (σ the Stefan-Boltzmann constant). No time derivatives, no PDE, no coupling. Migrated from GasChem.jl@8c12c048 src/radiation_fundamentals.jl:268 (`ClimateSensitivity` @component). The blackbody reference state (F_L = σ·T_e^4) and the analytic differentiation of Stefan-Boltzmann (dF_L/dT_e = 4·σ·T_e^3 → λ_0 = 1 / (4·σ·T_e^3)) together encode the no-feedback Planck response — the only baseline against which feedback-amplified climate sensitivities (water vapor, lapse rate, albedo, cloud) are conventionally reported in IPCC assessments. At Earth's nominal T_e = 255 K the component reproduces the textbook λ_0 ≈ 0.27 K·m^2/W and a CO2-doubling ΔT_e ≈ 1.22 K (S&P Page 105) using a forcing-doubling estimate of 4.6 W/m^2.

Photon energy equation (Seinfeld & Pandis 2006 Ch. 4, Eq. 4.1) — the energy Δε and frequency ν of a photon as a function of wavelength λ via Planck's constant h and the speed of light c: ν = c/λ and Δε = hν, equivalently the chained form Δε = hc/λ. The component is observed-only: two algebraic equations on two state variables (Δε the photon energy in J and ν the frequency in Hz) driven by one input parameter (λ the wavelength) and two constants (h Planck's constant and c the speed of light). No time derivatives, no PDE, no coupling. Migrated from GasChem.jl@8c12c048 src/radiation_fundamentals.jl:25 (`PhotonEnergy` @component). The photon energy equation is the foundational quantum-radiative bridge that maps continuous-wave radiation to the discrete photon picture: paired with the Planck spectral distribution (BlackbodyRadiation), Stefan-Boltzmann total flux (StefanBoltzmann), and Wien peak displacement (WienDisplacement), it lets a radiative-transfer model convert spectral irradiance to photon fluxes and back — the quantity needed for actinic-flux / photolysis-rate calculations that drive atmospheric photochemistry (e.g., O2 + hν → 2 O at ~242 nm and O3 + hν → O + O2 at ~310 nm, the two Chapman-cycle photolysis channels). The defaults (λ = 500 nm) give ν ≈ 600 THz and Δε ≈ 3.97e-19 J ≈ 2.48 eV — visible green light, the canonical solar-peak wavelength matching Wien's law applied to T_sun ≈ 5800 K.

Planetary equilibrium temperature from the top-of-atmosphere energy balance (Seinfeld & Pandis 2006 Ch. 4 Eqs. 4.5-4.7). The absorbed solar flux F_S = S_0/4 * (1 - R_p), the emitted longwave flux F_L = sigma * T_e^4 (Stefan-Boltzmann law), and at equilibrium F_S = F_L. Solving the constraint gives T_e = (S_0/4 * (1-R_p) / sigma)^(1/4). At canonical Earth values (S_0 = 1370 W/m^2, R_p = 0.3), F_S = F_L = 239.75 W/m^2 and T_e = 255 K (S&P p. 101). Migrated from GasChem.jl@8c12c048 src/radiation_fundamentals.jl:211 (`PlanetaryEnergyBalance` @component).

Composed radiation-fundamentals system from Seinfeld & Pandis (2006) Chapter 4 (Eqs. 4.1-4.11). A pure structural aggregation (no coupling equations) of seven independent components: PhotonEnergy (photon energy-frequency-wavelength relations, Eq. 4.1), BlackbodyRadiation (Planck's law, Eq. 4.2), WienDisplacement (peak emission wavelength, Eq. 4.3), StefanBoltzmann (total emissive power, Eq. 4.4), PlanetaryEnergyBalance (Earth's equilibrium temperature, Eqs. 4.5-4.7), ClimateSensitivity (temperature response to forcing, Eqs. 4.8-4.10), and TOARadiativeForcing (net top-of-atmosphere flux, Eq. 4.11). Each component is inlined as a named subsystem; variables are dot-namespaced (RadiationFundamentals.<subsystem>.<var>). Migrated from GasChem.jl@8c12c048 src/radiation_fundamentals.jl:367 (`RadiationFundamentals` @component).

Stefan-Boltzmann law for blackbody radiation — Seinfeld & Pandis (2006) Ch. 4 Eq. 4.4. Total emissive power F_B of a blackbody at temperature T integrated over all wavelengths: F_B = σ·T^4, where σ = 5.671×10⁻⁸ W·m⁻²·K⁻⁴. Migrated from GasChem.jl@8c12c048 src/radiation_fundamentals.jl:164 (`StefanBoltzmann` @component). One observed binding (F_B) over two parameters (T input + σ as a fixed-default parameter encoding the upstream `@constants` block per the rig convention of translating `@constants` to fixed-default parameters so units flow through MTK's unit checker — matches sibling clmu_atmosphere.esm/surface_energy_flux.esm). Closed-form algebraic: after mtkcompile the system has zero ODE states and the inline-test runner exercises F_B at its observed algebraic value.

Top-of-atmosphere (TOA) radiative-flux balance for a 0-D planetary climate model, following Seinfeld & Pandis (2006) Chapter 4 Eq. 4.11. Implements the net incoming flux F_net = S_0/4 · (1 - R_p) - F_L as a single algebraic relation between the absorbed shortwave flux F_S = S_0/4 · (1 - R_p) (Eq. 4.5, the spherical-projection factor of 1/4 accounts for the planet receiving solar flux over its cross-section πR² but emitting over its full surface 4πR²) and the outgoing longwave flux F_L (input parameter, typically supplied by the sibling PlanetaryEnergyBalance / StefanBoltzmann components in this domain). Sign convention: positive F_net means the planet is gaining energy (warming); negative F_net means losing energy (cooling). At default parameters (S_0=1370 W/m², R_p=0.3, F_L=239.75 W/m²) the planet is in exact radiative equilibrium (F_net = 0). Migrated from GasChem.jl@8c12c048 src/radiation_fundamentals.jl:327 (`TOARadiativeForcing` @component). Sibling component to PhotonEnergy (Eq. 4.1), BlackbodyRadiation (Eq. 4.2), WienDisplacement (Eq. 4.3), StefanBoltzmann (Eq. 4.4), PlanetaryEnergyBalance (Eqs. 4.5-4.7), ClimateSensitivity (Eqs. 4.8-4.10) — together they compose the upstream RadiationFundamentals (radiation_fundamentals.jl:367) system.

Wien's displacement law (Seinfeld & Pandis 2006 Ch. 4, Eq. 4.3) — the peak emission wavelength λ_max of a blackbody at temperature T is given by the simple inverse relation λ_max = b / T where b is Wien's displacement constant (2.897×10⁻³ m·K). The component is observed-only: one algebraic equation on one state variable (λ_max the peak wavelength) driven by one input parameter (T the temperature) and one constant (b the displacement constant). No time derivatives, no PDE, no coupling. Migrated from GasChem.jl@8c12c048 src/radiation_fundamentals.jl:121 (`WienDisplacement` @component). Wien's law is one half of the radiative-transfer toolkit for blackbody emission: paired with the Stefan-Boltzmann law σT⁴ (total emitted power) and the Planck function (spectral distribution), it lets a radiative-transfer model identify which spectral region a body's emission concentrates in. The 5800 K Sun peaks at ~500 nm (visible green); the 255 K Earth peaks at ~10 μm (thermal infrared); the 3 K cosmic microwave background peaks at ~1 mm (microwave). The temperature-inverse scaling means hotter sources emit at shorter wavelengths — the canonical fact behind the visible spectrum of stars (red giants vs blue dwarfs) and the separation of solar (shortwave) from terrestrial (longwave) radiation that anchors the planetary energy balance.