Seinfeld-Pandis

ModelingToolkit implementation of the aerodynamic resistance to dry deposition from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 19 (Dry Deposition), Eq. 19.14. Computes the aerodynamic resistance r_a [s/m] -- the resistance to turbulent transport of a depositing species through the surface layer, from the reference height z down to the roughness height z_0 -- under neutral atmospheric stability. Eq. 19.14, r_a = ln(z/z_0)/(kappa*u_star), is the integral of the neutral-stability logarithmic wind profile: r_a falls inversely with the friction velocity u_star (stronger turbulence carries the species down faster) and with the logarithm of the height ratio z/z_0 (a rougher surface, larger z_0, is more efficiently coupled to the atmosphere and presents less aerodynamic resistance). Migrated from AtmosphericDeposition.jl@e4468c79 src/seinfeld_pandis_ch19.jl:106 (the AerodynamicResistance @component). Purely algebraic: no differential states, a single explicit equation.

Combined aerosol population dynamics: condensation growth (DiameterGrowthRate) and Brownian coagulation (BrownianCoagulationCoefficient + MonodisperseCoagulation), coupled so that the Fuchs-form coagulation coefficient K_12 drives the number-concentration ODE and the shared temperature T and particle density ρ_p parameterize both growth and coagulation. Implements Seinfeld & Pandis (2006) Ch. 13 Eqs. 13.11-13.13 (condensation), 13.47 and Table 13.1 (coagulation coefficient), and 13.65-13.67 (number-concentration dynamics). Migrated from Aerosol.jl src/dynamics.jl:279 (esm-540).

Correction factor Q for the aqueous-phase reaction rate when intra-droplet diffusion limits access to the reactive interior (Seinfeld & Pandis 2006, Chapter 12, Eqs. 12.105 and 12.110). Computes the dimensionless Hatta number q = R_p √(k_rxn/D_aq) and the corresponding correction factor Q = 3(q·coth q − 1)/q², which scales the effective reaction rate from the well-mixed limit (Q = 1) down toward zero as the droplet becomes increasingly diffusion-limited. Migrated from Aerosol.jl src/aqueous_transport.jl:14.

Coupled gas-aqueous chemical equilibrium for cloud droplets and aerosol water. Migrated from Aerosol.jl@c8c640bb src/aqueous_equilibria.jl:642. Composes WaterEquilibrium, CO2Equilibria, SO2Equilibria, NH3Equilibria, HNO3Equilibria, H2O2Equilibria, and O3Equilibria via a quadratic charge-balance approximation for H+. Reference: Seinfeld & Pandis (2016) Ch. 7 §7.3.

Fundamental mass-conservation (budget) equation for an atmospheric species in a single reservoir, from Seinfeld & Pandis (2006) Ch. 2 (Atmospheric Trace Constituents), Eqs. 2.1-2.2, pp. 25-30. The reservoir mass Q evolves under the balance of transport (inflow minus outflow) and chemistry (production minus removal): dQ/dt = (F_in - F_out) + (P - R_removal) — the most basic statement of a trace-species budget, on which the lifetime, multiple-removal and tropospheric-budget formulations of the same chapter are built. The component additionally computes two diagnostic decomposition terms: the net transport contribution net_transport = F_in - F_out and the net chemistry contribution net_chemistry = P - R_removal; their sum is dQ/dt, and the steady-state condition (Eq. 2.2) dQ/dt = 0 ⇔ F_in + P = F_out + R_removal is reached when net_transport = -net_chemistry. One time-resolved ODE state (the reservoir mass Q) plus two observed (algebraic) diagnostic states (net_transport, net_chemistry); the four flux terms F_in, F_out, P, R_removal are externally-supplied inputs encoded as parameters. Migrated from GasChem.jl@8c12c048 src/AtmosphericLifetime.jl:64 (`AtmosphericBudget` @component); the upstream removal-rate @variable `R` is renamed `R_removal` here because the ESS schema reserves the bare name `R` for the ideal gas constant.

Atmospheric eddy-diffusivity and wind-profile parameterizations from Seinfeld & Pandis (2006) Ch. 18, Sec. 18.12. Given a height z above ground, the component computes the mean wind speed u_wind from a power-law profile (Eq. 18.118) and the vertical and horizontal eddy diffusivities K_zz, K_yy that govern turbulent transport of trace species in the planetary boundary layer. K_zz is selected by atmospheric stability from the Monin-Obukhov length L_MO: an unstable four-piece convective profile (Eq. 18.121, Lamb & Duran 1977), a neutral profile (Eq. 18.122, Myrup & Ranzieri 1976), or a stable profile (Eq. 18.125, Businger & Arya 1974). K_yy is 0.1*w_star*z_i under unstable conditions (Eq. 18.128) and equals K_zz otherwise. Three purely-algebraic equations, no time integration. Migrated from AtmosphericDynamics.jl@816cc391 src/atmospheric_diffusion.jl:30 (`AtmosphericDiffusion` @component).

Atmospheric pressure, density, and vertical pressure gradient as a function of altitude for an isothermal atmosphere. Couples the hydrostatic equation with the ideal gas law: the scale height H = R*T/(M_air*g) (Eq. 1.4) sets the e-folding altitude, the barometric formula p = p_0*exp(-z/H) (Eq. 1.5) gives pressure, the ideal gas law rho = M_air*p/(R*T) (Eq. 1.2) gives density, and the hydrostatic equation dpdz = -rho*g (Eqs. 1.1/1.3) gives the pressure gradient. Migrated from AtmosphericDynamics.jl@816cc391 src/seinfeld_pandis_ch1.jl:151 (`AtmosphericPressureProfile` @component). Implements Seinfeld & Pandis (2006) Chapter 1 Equations 1.1-1.5 for an isothermal atmosphere — the integrated, constant-scale-height form; a non-isothermal atmosphere would require numerical integration of Eq. 1.3. Parameterized as observed-only: altitude z and temperature T are inputs (parameters in standalone form, with R, M_air, g, p_0 as further parameter inputs carrying their upstream @constant values), and H, p, rho, dpdz are the four algebraic outputs. The upstream `5.3 AtmosphericPressureProfile Compilation` test compiles the component with `inputs = [app_nns.T]`, confirming T is an input.

Atmospheric static-stability diagnostics from Seinfeld & Pandis (2006) Ch. 16 (Meteorology of the Local Scale). Given the air temperature T and pressure p at a height z, the air temperature T_below one layer below, and the layer spacing delta_z, the component computes the potential temperature theta = T*(p_0/p)^(R_air/c_p) (Eq. 16.14), the actual temperature lapse rate dT_dz = (T - T_below)/delta_z, the potential-temperature gradient dtheta_dz = dT_dz + Gamma_d (Eqs. 16.16-16.18), and the static-stability parameter S = dtheta_dz: S > 0 stable, S = 0 neutral, S < 0 unstable. Four purely-algebraic equations, no time integration. Migrated from AtmosphericDynamics.jl@816cc391 src/local_scale_meteorology.jl:32 (`AtmosphericStability` @component).

Atmospheric thermodynamic profile for an isothermal atmosphere: given altitude and temperature it computes the scale height H = R*T/(M_air*g) (Eq. 1.4), the atmospheric pressure p = p_0*exp(-z/H) from the barometric formula (Eq. 1.5), the air density rho = M_air*p/(R*T) from the ideal gas law (Eq. 1.2), and the total molar concentration c_total = p/(R*T) (Eq. 1.7). Migrated from AtmosphericDynamics.jl@816cc391 src/seinfeld_pandis_ch1.jl:479 (`AtmosphericThermodynamics` @component). Implements Seinfeld & Pandis (2006) Chapter 1 Equations 1.2, 1.4, 1.5, 1.7. Despite the upstream docstring describing it as 'combining' equations from other components, the Julia @component is a flat model — it re-derives the four equations directly via `System(eqs, t; name)` with no MTK subsystems — so it is migrated here as a flat algebraic model (not subsystem-composed), mirroring the structurally identical sibling pressure_profile.esm. Parameterized as observed-only: altitude z and temperature T are inputs (parameters in standalone form, with R, M_air, g, p_0 as further parameter inputs carrying their upstream @constant values), and H, p, rho, c_total are the four algebraic outputs. The upstream `5.9 AtmosphericThermodynamics Compilation` test compiles the component with `inputs = [at_nns.T]`, confirming T is an input.

Barometric formula for an isothermal atmosphere: p(z) = p_0 * exp(-z/H). Gives the pressure at altitude z from the sea-level pressure p_0 and the atmospheric scale height H. Migrated from AtmosphericDynamics.jl@816cc391 src/seinfeld_pandis_ch1.jl:201 (`BarometricFormula` @component). Implements Seinfeld & Pandis Ch 1 Eq. 1.5 — the integrated form of the hydrostatic equation for an isothermal atmosphere. Parameterized as observed-only: z, H, and p_0 are inputs (parameters in standalone form), pressure_ratio and p are the algebraic outputs.

Irreversible below-cloud (washout) scavenging of a gas-phase species by falling raindrops, from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 20 (Wet Deposition), Eqs. 20.22, 20.24, 20.25. The gas scavenging coefficient Λ_gas = 6·p₀·K_c/(D_p·U_t) (Eq. 20.25) for monodisperse drops is constant in time, so the below-cloud gas concentration decays exponentially via dC_g/dt = −Λ_gas·C_g (Eq. 20.24) and the below-cloud scavenging flux is F_bc = Λ_gas·h·C_g (Eq. 20.22). 'Irreversible' means the gas is assumed to be taken up and not re-released — the limiting case opposite to the reversible (Henry's-law-equilibrium) treatment of the sibling ReversibleGasScavenging component. Migrated from AtmosphericDeposition.jl@e4468c79 src/seinfeld_pandis_2006_ch20.jl:234 (`BelowCloudGasScavenging` @component). ODE system: C_g is the single differential state; Λ_gas and F_bc are algebraic outputs (upstream `@variables`, serialized as type `state` with explicit algebraic equations); K_c, U_t, D_p, h, p₀ are input parameters.

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.

Brownian coagulation coefficient K_12 for two particles using the Fuchs interpolation formula (Seinfeld & Pandis 2006, Table 13.1). Valid across the continuum, transition, and free-molecular regimes. Computes Knudsen numbers, Cunningham slip corrections, Brownian diffusion coefficients, mean thermal velocities, particle mean free paths, and the Fuchs interpolation parameters g_1, g_2 as intermediate observed variables before assembling K_12. Migrated from Aerosol.jl src/dynamics.jl:75.

Stratospheric bromine catalytic ozone-destruction cycle (BrOx). Three ODEs (Br, BrO, HOBr) and two algebraic family identities (BrOx = Br + BrO; Bry = Br + BrO + HOBr). Reactions: Br + O3 → BrO + O2 (Arrhenius); BrO + O → Br + O2; BrO + ClO → Br + Cl + O2 (constant rate); BrO + HO2 → HOBr + O2; HOBr + hν → OH + Br (photolysis). Unlike chlorine, bromine has no stable HBr reservoir because Br + CH4 is endothermic (Seinfeld & Pandis Page 169). Bromine is approximately 50× more effective than chlorine in destroying ozone on an atom-for-atom basis. Migrated from GasChem.jl@8c12c048 src/StratosphericChemistry.jl:390 (`BrOxCycle` @component). Rate coefficients converted CGS → SI: cm³/molec/s × 1e-6 → m³/s.

Seven-reservoir model of the global carbon cycle from Schmitz (2002), as presented in Seinfeld & Pandis (2006) Ch. 22 (Global Cycles: Sulfur and Carbon), Table 22.1 and Fig. 22.6, pp. 1009-1015. Carbon is tracked as a mass (kg) in seven reservoirs — atmosphere (M1), warm ocean surface waters (M2), cool ocean surface waters (M3), deep ocean waters (M4), terrestrial biota (M5), soils and detritus (M6), and fossil fuel reserves (M7) — plus a dimensionless land-use-change scaling factor G that modulates biotic uptake (Eq. 22.21). Inter-reservoir transport uses first-order exchange coefficients k_ij (Table 22.1), except three nonlinear fluxes carried as auxiliary algebraic variables: the saturating atmosphere-to-biota photosynthetic uptake F15 (Eq. 22.19) and the carbonate-buffer power-law ocean-to-atmosphere outgassing fluxes F21 and F31 (Eq. 22.18). Three external forcing parameters drive the anthropogenic perturbation — fossil fuel emissions Ff, deforestation Fd, and reforestation Fr — all zero by default, recovering the preindustrial (~1850) steady state. The system is an 11-unknown ODE model (8 time-differentiated reservoir states M1-M7,G + 3 algebraic flux states F15/F21/F31) with 11 equations and 25 parameters (22 first-order/derived constants + 3 forcing fluxes). All quantities are SI (kg for mass, s for time); the source material's Pg C (1 Pg = 1e12 kg) and years (1 yr = 31557600 s) are converted to maintain unit consistency. Migrated from AtmosphericDynamics.jl@816cc391 src/global_cycles.jl:115 (`CarbonCycle` @component).

Stratospheric Chapman mechanism for ozone production and destruction (Seinfeld & Pandis 2006 Ch. 5, §5.2, Eqs. 5.1-5.17). Two-state ODE on atomic oxygen O and ozone O3 driven by the four canonical Chapman reactions: O2 photolysis (j_O2), three-body recombination O + O2 + M → O3 + M (k2 with power-law T-dependence (T_ref/T)^2.4), O3 photolysis (j_O3), and the O + O3 → 2 O2 odd-oxygen sink (k4 with Arrhenius temperature dependence). Odd oxygen Ox = O + O3 is *not* exactly conserved — the Chapman cycle has a net Ox source (2·j_O2·O2·M from O2 photolysis) balanced against an Ox sink (2·k4·O·O3 from the O+O3 reaction) — but on short timescales (≲ 10 s under default mid-stratosphere conditions) the net change is small (~4e-5 relative drift) and the upstream test treats it as quasi-conserved at rtol=1e-4. Migrated from GasChem.jl@8c12c048 src/StratosphericChemistry.jl:51 (`ChapmanMechanism` @component). Rate coefficients carry SI units throughout, converted from Seinfeld & Pandis CGS values via cm^6/molec^2/s × 1e-12 → m^6/s for the 3-body k2 and cm^3/molec/s × 1e-6 → m^3/s for the bimolecular k4.

Simplified single-component classical nucleation rate (Eq. 11.47) from Seinfeld & Pandis (2006), Chapter 11. Computes only the steady-state nucleation rate J from the Zeldovich pre-exponential factor and the free-energy-barrier exponential. Use this component when the critical-cluster properties (i*, r*, ΔG*) are not needed; see the Nucleation component for the full coupled system.

Climate-feedback diagnostic (Seinfeld & Pandis 2006 Ch. 23 §23.4 Eqs. 23.1-23.4 and Eq. 23.7 p. 1045) — the linear-response relation between a top-of-atmosphere radiative forcing perturbation ΔF and the equilibrium surface temperature change ΔT_s through the feedback-amplified climate sensitivity λ. Six observed-only algebraic equations on six state variables (ΔT_s the feedback-amplified equilibrium response, ΔT_0 the no-feedback Planck response, λ_0 the no-feedback sensitivity factor, ΔF_e the efficacy-weighted effective forcing, ΔF_r the forcing equivalent of realized warming, ΔT_unrealized the warming commitment) driven by five input parameters (ΔF the forcing perturbation, λ the feedback-amplified sensitivity, λ_CO2 the CO₂-doubling sensitivity reference, E_i the efficacy of the forcing agent, ΔT_r the realized warming to date) and two reference constants (ΔF_2xCO2 the CO₂-doubling radiative forcing, ΔT0_2xCO2 the no-feedback temperature change for CO₂ doubling). No time derivatives, no PDE, no coupling. Migrated from GasChem.jl@8c12c048 src/climate_forcing.jl:32 (`ClimateFeedback` @component). The component extends the no-feedback Planck response of the sibling `ClimateSensitivity` model (components/gaschem/radiation/climate_sensitivity.esm, S&P §4.2 Eqs. 4.8-4.10) by introducing the feedback-amplified sensitivity factor λ and the warming-commitment relation ΔT_unrealized = (ΔF - ΔF_r)·λ that captures the lag between achieved (ΔT_r) and equilibrium (ΔT_s) warming under a non-zero forcing perturbation. At Earth's nominal 2×CO₂ forcing ΔF = 3.7 W/m² and λ = 0.8 K·m²/W (IPCC AR4 central estimate), the component reproduces the textbook canonical ΔT_s ≈ 2.96 K equilibrium warming (S&P Page 1040), λ_0 ≈ 0.338 K·m²/W no-feedback Planck response, and ΔT_unrealized ≈ 0.49 K warming commitment for the present-day p. 1045 scenario (λ = 0.7, ΔF = 1.7, ΔT_r = 0.7).

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.

Stratospheric ClOx catalytic ozone destruction cycle (Seinfeld & Pandis 2006, Ch. 5 §5.5.1). Migrated from GasChem.jl@8c12c048 src/StratosphericChemistry.jl:272 (`ClOxCycle` @component). Implements 4 ODEs (Cl, ClO, HCl, ClONO2) coupled to 2 algebraic family sums (ClOx = Cl + ClO, Cly = Cl + ClO + HCl + ClONO2). Rate coefficients are Arrhenius (k = A·exp(C/T)) for the five binary reactions and a (T_ref/T)^3.4 form for the termolecular ClO + NO2 + M → ClONO2 channel. All upstream `@constants` are encoded as parameters with their literal SI defaults; physical-condition `@parameters` (T, M, photolysis rates, fixed-bath species O, O3, NO, NO2, OH, CH4) are also parameters so the cycle can be exercised at different atmospheric conditions.

CO2 dissolution and dissociation equilibria with van't Hoff temperature dependence (Seinfeld & Pandis Ch 7 §7.3.2, Eqs 7.14–7.24). Migrated from Aerosol.jl@c8c640bb src/aqueous_equilibria.jl:140 (`CO2Equilibria` @component). Parameterized as observed-only: T, H_plus, p_CO2 are inputs and the carbonate-system species (CO2_aq, HCO3-, CO3^2-, total dissolved C, effective Henry constant) are algebraic outputs.

CO oxidation chemistry diagnostics from Seinfeld & Pandis (2006) Ch. 6 §6.3 Eqs. 6.9-6.18, pp. 212-219. CO oxidation is the simplest hydrocarbon-oxidation mechanism and illustrates the catalytic HOx cycling that drives tropospheric ozone production (net: CO + 2O₂ + hν → CO₂ + O₃, with OH regenerated through HO₂ + NO). This observed-only algebraic component implements six diagnostic relations: the OH loss rate L_OH (to CO, NO₂, O₃), the HO₂ loss rate L_HO2 (to NO, the HO₂ self-reaction, and O₃), the HOx radical-termination loss rate L_HOx (OH+NO₂→HNO₃ plus the HO₂ self-reaction), the high-NOx HO₂ steady-state concentration HO2_ss (Eq. 6.18), the net ozone production rate P_O3 (HO₂+NO production minus the OH+O₃ and HO₂+O₃ loss channels), and the HOx chain length (propagation rate over termination rate — the number of OH-HO₂ cycles before radical termination). Observed-only algebraic system (no time derivatives): twelve variables (six inputs CO/OH/HO₂/NO/NO₂/O₃ encoded as parameters, six outputs L_OH/L_HO2/L_HOx/HO2_ss/P_O3/chain_length as state), six rate-constant parameters (k_CO_OH, k_HO2_NO, k_HO2_HO2, k_OH_NO2, k_HO2_O3, k_OH_O3), one dimensionless stoichiometric constant (two), and six algebraic equations. Migrated from GasChem.jl@8c12c048 src/co_oxidation.jl:88 (`COOxidation` @component).

Critical cluster properties for classical homogeneous nucleation theory following Seinfeld & Pandis (2006), Chapter 11, Equations 11.27, 11.35, 11.52, and 11.53. Computes the dimensionless surface tension parameter (theta), critical cluster size (i*), critical radius (r*), and free energy barrier (ΔG*) as purely algebraic functions of temperature, saturation ratio, surface tension, and molecular volume. Use this component for parameter sensitivity studies or when the full nucleation rate (ClassicalNucleationRate) is not needed.

Dahneke transition-regime correction factor f_D for gas-particle mass transfer. f_D is the ratio J/J_c of the actual particle-surface flux to the continuum-regime flux (Seinfeld & Pandis 2006, Chapter 12, Eq. 12.42): f_D = (1 + Kn) / (1 + 2 Kn(1 + Kn) / α). In the continuum limit (Kn ≪ 1) f_D → 1, recovering J_c with no correction; in the free-molecular limit (Kn ≫ 1) f_D ≈ α / (2 Kn) → 0, reflecting strong reduction in flux for very small particles or very long mean free paths. Migrated from Aerosol.jl src/mass_transfer.jl `Dahneke`.

Diameter growth rate due to vapor condensation in the continuum regime (Seinfeld & Pandis 2006, Ch. 13, Eq. 13.11-13.13). Algebraic growth parameter A = 4·D_diff·M_i·Δp / (R_gas·T·ρ_p), algebraic growth rate I_D = A/D_p, ODE D(D_p) = I_D. Source: Aerosol.jl@c8c640bb:src/dynamics.jl:22.

5-bin discrete coagulation model for a monodisperse initial distribution with constant coagulation coefficient (Seinfeld & Pandis 2006, Ch. 13, Eqs. 13.59, 13.67, 13.71). Tracks the evolution of five k-mer bins (N1..N5) under Brownian coagulation. Source: Aerosol.jl@c8c640bb:src/dynamics.jl:221 (n_bins=5 instantiation, esm-isv).

ModelingToolkit implementation of particle (aerosol) dry deposition from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 19 (Dry Deposition), Eq. 19.7. Computes the particle dry deposition velocity v [m/s] for a single aerosol size and the corresponding first-order deposition rate k = v/z [1/s], as a resistance network: v = 1/(R_a + R_b + R_a*R_b*V_s) + V_s, where R_a is the aerodynamic resistance (Eqs. 19.13-19.14), R_b is the quasi-laminar sublayer resistance (Eq. 19.27), and V_s is the gravitational settling velocity (Eq. 9.42). R_b combines Brownian diffusion (Schmidt number), inertial impaction (Stokes number) and interception, with land-use-dependent collector geometry from the Seinfeld & Pandis Table 19.2 characteristic-radius table. Migrated from AtmosphericDeposition.jl@e4468c79 src/dry_deposition.jl:1040 (the DryDepositionAerosol builder); its DryDepParticle kernel (src/dry_deposition.jl:272) and the whole helper chain (ra, mu, mfp, cc, vs, dParticle, sc, stSmooth/stVeg, RbParticle) are inlined. Purely algebraic: no differential states -- the 27 computed quantities are observed variables defined by inline expressions.

ModelingToolkit implementation of the complete gas dry-deposition velocity model from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 19 (Dry Deposition), Eq. 19.2 (deposition velocity) and Eq. 19.1 (deposition flux). The gas dry-deposition velocity follows the resistance-in-series model: a depositing gas crosses three resistances stacked in series between the reference height and the surface -- the aerodynamic resistance r_a (turbulent transport through the surface layer, Eq. 19.14), the quasi-laminar resistance r_b (molecular diffusion across the thin stagnant sublayer in contact with the surface, Eq. 19.17), and the surface resistance r_c (uptake by the canopy along four parallel pathways, Wesely 1989, Eq. 19.50). The deposition velocity is the reciprocal of their sum, v_d = 1/(r_a + r_b + r_c), and the downward deposition flux is F = -v_d*C for a gas concentration C at the reference height. Migrated from AtmosphericDeposition.jl@e4468c79 src/seinfeld_pandis_ch19.jl:416 (`DryDepositionGas` @component), which composes three MTK subsystems via `System(eqs, t; systems=[aero, qlam, surf])` plus its own coupling equations. Represented here as a subsystem-composed ESS model (spec section 4.7): the `aero` subsystem inlines the already-migrated AerodynamicResistance component (aerodynamic_resistance.esm, esm-x8pg), `qlam` inlines QuasiLaminarResistanceGas (quasi_laminar_gas.esm, esm-t3wp), and `surf` inlines SurfaceResistance (surface_resistance.esm, esm-ug1i), wired together by seven top-level coupling equations. Algebraic (no time derivative): u_star, C, G and T_s are input parameters; r_t, v_d and F are algebraic state outputs.

Composite particle dry-deposition model from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 19 (Dry Deposition). Given the surface-layer friction velocity and an aerosol particle's properties it computes the particle dry deposition velocity v_d (Eq. 19.7) and the resulting downward deposition flux F (Eq. 19.1). Eq. 19.7, v_d = 1/(r_a + r_b + r_a*r_b*v_s) + v_s, combines the resistance-network pathway -- turbulent transport through the aerodynamic resistance r_a and the quasi-laminar boundary-layer resistance r_b, with the r_a*r_b*v_s cross term capturing gravitational settling acting inside the resistance network -- with a direct gravitational-settling term v_s; the flux F = -v_d*C (Eq. 19.1) is negative for downward transport. The competition between Brownian diffusion (efficient for sub-0.1 um particles) and inertial impaction (efficient for super-um particles) leaves a deposition-velocity minimum at accumulation-mode sizes. Migrated from AtmosphericDeposition.jl@e4468c79 src/seinfeld_pandis_ch19.jl:479 (the DryDepositionParticle @component), which composes three MTK subsystems via System(eqs, t; systems=[aero, settling, qlam]). Represented here as a subsystem-composed ESS model (spec §4.7): the aero subsystem inlines the already-migrated AerodynamicResistance component (aerodynamic_resistance.esm, esm-x8pg), settling inlines ParticleSettling (particle_settling.esm, esm-egwt) and qlam inlines QuasiLaminarResistanceParticle (quasi_laminar_particle.esm, esm-brbr), wired by six top-level coupling equations. Purely algebraic (no D() time-derivative anywhere): u_star and C are input parameters; v_d and F are algebraic state outputs.

Fuchs-Sutugin transition-regime correction factor for aerosol mass transfer. f_FS = J/J_c is the ratio of the actual flux to the continuum-regime flux J_c; it interpolates between f_FS → 1 in the continuum limit (Kn ≪ 1) and f_FS → 0 in the free-molecular limit (Kn ≫ 1). The formula f_FS = 0.75α(1+Kn)/(Kn²+Kn+0.283Kn·α+0.75α) (Seinfeld & Pandis 2006, Chapter 12, Eq. 12.43) is the most widely used semi-empirical interpolation across the full Knudsen number range, and extends the original Fuchs (1934) result with an explicit accommodation-coefficient correction due to Sutugin. Migrated from Aerosol.jl src/mass_transfer.jl `FuchsSutugin`.

Below-cloud gas scavenging coefficient for irreversible uptake of a gas-phase species by falling monodisperse raindrops, from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 20 (Wet Deposition), Eq. 20.25. The scavenging coefficient Λ_gas = 6·p₀·K_c/(D_p·U_t) sets the first-order loss rate (s⁻¹) of a soluble gas to rain: it rises linearly with the precipitation rate p₀ and the gas-phase mass transfer coefficient K_c, and falls inversely with the raindrop diameter D_p and terminal velocity U_t. 'Irreversible' uptake assumes the gas is captured and not re-released — the limiting case opposite to the Henry's-law-equilibrium treatment of the sibling ReversibleGasScavenging component. Migrated from AtmosphericDeposition.jl@e4468c79 src/seinfeld_pandis_2006_ch20.jl:116 (`GasScavengingCoeff` @component). Observed-only algebraic model: K_c, U_t, D_p, p₀ are input parameters and Λ_gas is the single algebraic output, fixed by one equation with no time derivative.

General circulation of the atmosphere — Coriolis parameter, tangential speed, geostrophic wind, and thermal-wind relations from Seinfeld & Pandis (2006) Chapter 21. Migrated from AtmosphericDynamics.jl@816cc391 src/general_circulation.jl:60 (`GeneralCirculation` @component).

Greenhouse-gas radiative forcing budget for the well-mixed industrial-era GHGs plus tropospheric ozone (Seinfeld & Pandis 2006 Ch. 23 §23.3, p. 1038-1042, IPCC TAR 2001 baseline reproduced in S&P Figure 23.6 / Table 23.4). The component aggregates the five canonical anthropogenic radiative-forcing channels — CO₂, CH₄, N₂O, tropospheric O₃, and the halocarbon family — and exposes per-channel and total radiative forcing as observable outputs. Each channel is parameterized as a dimensionless scaling factor f_X applied to a fixed IPCC TAR reference forcing ΔF_X_ref: ΔF_X = f_X · ΔF_X_ref. The total ΔF_total = Σ ΔF_X is the headline anthropogenic radiative-forcing diagnostic. Observed-only algebraic component: six equations on six state variables (ΔF_CO2, ΔF_CH4, ΔF_N2O, ΔF_O3, ΔF_halo, ΔF_total) driven by five scaling-factor parameters (f_CO2, f_CH4, f_N2O, f_O3, f_halo) and five reference-forcing constants (ΔF_CO2_ref = 1.46, ΔF_CH4_ref = 0.48, ΔF_N2O_ref = 0.15, ΔF_O3_trop_ref = 0.4, ΔF_halo_ref = 0.34, all in W/m^2). No time derivatives, no PDE, no coupling. Migrated from GasChem.jl@8c12c048 src/climate_forcing.jl:104 (`GHGForcing` @component). The scaling-factor design lets a downstream consumer adjust each individual channel without forking the component — useful for (i) reproducing the IPCC AR4/AR5/AR6 revisions to the industrial-era forcing values (e.g., AR5 CO₂ ≈ 1.82 W/m² vs TAR 1.46), (ii) sensitivity studies that probe each channel's contribution to the total, and (iii) attribution scenarios that zero out individual channels (f_X = 0 ⇒ ΔF_X = 0). At the defaults (all f_X = 1), ΔF_total = 1.46 + 0.48 + 0.15 + 0.4 + 0.34 = 2.83 W/m² which matches the upstream IPCC TAR 2001 industrial-era forcing total (S&P p. 1039, sum of the five well-mixed-GHG + O3 channels excluding aerosols).

Global Warming Potential (GWP) for atmospheric trace species with first-order exponential-decay perturbation lifetimes (Seinfeld & Pandis 2006 Ch. 23, Eqs. 23.5-23.6 and Problem 23.3, p. 1050). The GWP is defined as the ratio of the time-integrated radiative forcing from a pulse emission of 1 kg of species A to that of 1 kg of CO₂ over a specified time horizon t_f. For species whose atmospheric perturbation decays exponentially as exp(-t/τ_A), the time-integrated forcing reduces to the closed-form expression τ_A · (1 - exp(-t_f/τ_A)), so the GWP becomes GWP = a_A · τ_A · (1 - exp(-t_f/τ_A)) / [a_CO2 · τ_CO2 · (1 - exp(-t_f/τ_CO2))]. The component is observed-only: five algebraic equations on five state variables (decay_integral_A, decay_integral_CO2, AGWP_A, AGWP_CO2, GWP) driven by three input parameters (τ_A the species lifetime, a_A the radiative efficiency relative to CO₂, t_f the time horizon) and two CO₂-reference constants (τ_CO2 the effective CO₂ lifetime, a_CO2 the reference radiative efficiency). No time derivatives, no PDE, no coupling. Migrated from GasChem.jl@280ee50f src/climate_forcing.jl:182 (`GlobalWarmingPotential` @component). The GWP framework is the IPCC standard for comparing the climate impact of different greenhouse gases on a common (CO₂-equivalent) scale and underlies the conversion between mass emissions of CH₄, N₂O, halocarbons, and other well-mixed GHGs to their CO₂-equivalent emissions for policy and inventory accounting. Canonical GWP₁₀₀ values (IPCC AR4 Table 23.1, S&P p. 1042): CH₄ ≈ 23, N₂O ≈ 296, SF₆ ≈ 22800 — the framework's three-order-of-magnitude span anchors the design choice of representing GWP as a derived ratio rather than a hardcoded table.

H2O2 gas-aqueous dissolution and (weak) dissociation equilibria with van't Hoff temperature dependence. Migrated from Aerosol.jl@c8c640bb src/aqueous_equilibria.jl:519 (`H2O2Equilibria` @component). Implements Seinfeld & Pandis Ch 7 §7.3.6: K_H(H2O2, 298 K) = 1.0×10⁵ M/atm, ΔH_sol = −14.5 kcal/mol; K_h1(H2O2, 298 K) = 2.2×10⁻¹² M (temperature-independent, very weak). Parameterized as observed-only: T, H_plus, and p_H2O2 are inputs; H_H2O2, K_h1, H2O2_aq, HO2_minus, H2O2_total, H_H2O2_eff are algebraic outputs.

Basic Henry's law equilibrium at fixed temperature (Seinfeld & Pandis 2006, Chapter 7, Eq. 7.3). Computes the aqueous-phase concentration C_aq = H_A × p_A, where H_A is the Henry's law constant at the reference temperature and p_A is the gas-phase partial pressure of species A. Migrated from Aerosol.jl src/henrys_law.jl `HenrysLaw` (esm-3ro).

HNO3 gas-aqueous dissolution and dissociation equilibria. Migrated from Aerosol.jl@c8c640bb src/aqueous_equilibria.jl:438 (`HNO3Equilibria` @component). Implements Seinfeld & Pandis Ch 7 §7.3.5 (Eq 7.53–7.54, 7.58, 7.61): K_H(HNO3, 298 K) = 2.1×10⁵ M/atm (temperature-independent, dH≈0), K_n1(HNO3, 298 K) = 15.4 M (temperature-independent). HNO3 is a strong acid (pKa ≈ −1.2) that essentially completely dissociates at all atmospheric pH values. Parameterized as observed-only: T, H_plus, and p_HNO3 are inputs; H_HNO3, K_n1, HNO3_aq, NO3_minus, HNO3_total, H_HNO3_eff are algebraic outputs.

Stratospheric HOx catalytic ozone destruction cycle (Seinfeld & Pandis 2006 Ch. 5, §5.4, Eqs. 5.23-5.28). Two-state ODE on the radicals OH and HO2 driven by reactions with O3, atomic O, and NO; HOx = OH + HO2 is exactly conserved by construction (D(OH) + D(HO2) ≡ 0). Migrated from GasChem.jl@8c12c048 src/StratosphericChemistry.jl:187 (`HOxCycle` @component). All rate coefficients are temperature-dependent Arrhenius forms k_X = k_X_A · exp(C_X / T) with the Seinfeld & Pandis bimolecular CGS pre-factors converted to SI via the cm³/molec/s × 1e-6 → m³/s factor; SI rates and SI number-density concentrations (m^-3) are preserved verbatim from upstream.

Ideal gas law for atmospheric air density: rho = M_air * p / (R * T). Migrated from AtmosphericDynamics.jl@816cc391 src/seinfeld_pandis_ch1.jl:68 (`IdealGasLaw` @component). Implements Seinfeld & Pandis Ch 1 Eq 1.2. Parameterized as observed-only: T and p are inputs (parameters in standalone form), rho is the algebraic output. Upstream the Julia @component declares T and p as @variables for composition into a parent system; for standalone serialization (3 unknowns vs 1 equation otherwise), they are declared as parameters here, mirroring the WaterEquilibrium serialization pattern.

Knudsen number Kn = λ/R_p — the ratio of the gas mean free path λ to the particle radius R_p. Kn determines the transport regime: Kn ≪ 1 (continuum, Fick's law applies), Kn ≫ 1 (free-molecular, kinetic theory applies), Kn ~ 1 (transition regime, interpolation formulas such as Fuchs-Sutugin required). At standard atmospheric conditions λ ≈ 65 nm; Kn ≈ 0.65 for a 100 nm particle and Kn ≈ 0.0065 for a 10 µm droplet. Migrated from Aerosol.jl src/mass_transfer.jl `KnudsenNumber`.

Local-scale boundary-layer meteorology from Seinfeld & Pandis (2006) "Atmospheric Chemistry and Physics", 2nd ed., Chapter 16 "Meteorology of the Local Scale". A flat observed-only algebraic component that combines atmospheric static-stability analysis, Monin-Obukhov surface-layer similarity theory and Pasquill stability-class estimation: from the air temperature and pressure, the surface-layer geometry, the friction velocity u_star and the surface sensible heat flux q_z it computes the potential temperature θ (Eq. 16.14), the actual and potential-temperature lapse rates dT_dz and dθ_dz (Eqs. 16.16-16.18), the Monin-Obukhov length L and its inverse L_inv (Eq. 16.70), the stability parameter ζ = z/L, the Businger-Dyer stability functions φ_m, φ_h and their integrated forms ψ_m, ψ_h (Eqs. 16.75, 16.78-16.79), the stability-corrected mean wind speed ū (Eq. 16.66) and the Pasquill stability class (1=A to 6=F) via the Golder (1972) correlation (Eq. 16.83). Twelve purely-algebraic equations, no time integration. Migrated from AtmosphericDynamics.jl@816cc391 src/local_scale_meteorology.jl:234 (`LocalScaleMeteorology` @component).

Complete transition-regime mass transfer model combining mean molecular speed, air density, mean free path, Knudsen number, Fuchs-Sutugin correction, and continuum-regime flux to produce the transition-regime corrected molar flow rate J for particle growth/evaporation across all Knudsen number regimes (Seinfeld & Pandis 2006, Chapter 12, Sections 12.1.1–12.1.4, Eqs. 12.12, 12.24, 12.31, 12.43). Migrated from Aerosol.jl src/mass_transfer.jl `MassTransfer` (esm-44h).

Gas-phase mass transfer coefficient K_c to a falling raindrop, from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 20 (Wet Deposition), Eq. 20.12. K_c is computed from a Sherwood-number correlation K_c = (D_g/D_p)·[2 + 0.6·Re^(1/2)·Sc^(1/3)], where the drop Reynolds number Re = ρ_air·U_t·D_p/μ_air measures the convective flow past the falling drop and the gas Schmidt number Sc = μ_air/(ρ_air·D_g) is the ratio of the momentum to the mass boundary-layer thickness. The leading 2 is the still-air diffusive limit (Sh→2 for an isolated sphere); the 0.6·Re^(1/2)·Sc^(1/3) term is the ventilation enhancement from the drop's fall. K_c sets the gas-uptake rate at the raindrop surface and feeds the below-cloud gas scavenging coefficient computed by the sibling GasScavengingCoeff / BelowCloudGasScavenging components. Migrated from AtmosphericDeposition.jl@e4468c79 src/seinfeld_pandis_2006_ch20.jl:60 (`MassTransferCoeff` @component). Algebraic (observed-only) system: K_c is the single algebraic output (the upstream component's lone `@variable`); D_g, D_p, U_t are input parameters and ρ_air_sp, μ_air_sp are the migrated upstream module `@constants`.

Combined gas-phase and interfacial mass transfer coefficient k_mt for gas-particle exchange. k_mt is the inverse of the total resistance to mass transfer, which is the sum of two resistances in series: (1) gas-phase diffusion resistance tau_g = R_p²/(3 D_g), and (2) interfacial resistance tau_i = (R_p/3α) √(2πM_A/(RT)) arising from the finite accommodation probability and molecular speed. The reciprocal relation k_mt = 1/(tau_g + tau_i) (Seinfeld & Pandis 2006, Chapter 12, Eq. 12.116) determines the overall rate at which a gaseous species is transferred to or from the particle surface. Migrated from Aerosol.jl src/mass_transfer.jl `MassTransferCoefficient`.

Mass transport limitation criteria for aqueous-phase chemistry (Seinfeld & Pandis 2006, Chapter 12, Eqs. 12.85, 12.86, 12.93). Computes the threshold values of k₁H* and k₁ below which gas-phase diffusion, aqueous-phase diffusion, and interfacial mass transfer do not limit the aqueous-phase reaction rate by more than 10%. Migrated from Aerosol.jl src/aqueous_transport.jl:53.

Continuum-regime molar flux of a gas species to a spherical particle. In the continuum limit (Kn ≪ 1) the steady-state diffusive flux is governed by Fick's law on a spherical geometry: J_c = 4πR_p D_g (c_∞ − c_s) (Seinfeld & Pandis 2006, Chapter 12, Eq. 12.12). A positive J_c indicates net uptake (c_∞ > c_s); a negative value indicates net evaporation or desorption (c_s > c_∞). Migrated from Aerosol.jl src/mass_transfer.jl `MaxwellianFlux`.

Mean free path of gas molecules in air for aerosol mass transfer. Uses the kinetic-theory relation λ = 2μ/(ρ_air c̄_air) where μ is the dynamic viscosity, ρ_air = PM_air/(RT) is the ideal-gas air density, and c̄_air = √(8RT/(πM_air)) is the mean molecular speed of air (S&P 2006, Chapter 12, Section 12.1.3). The resulting λ is the mean free path used to compute the Knudsen number Kn = λ/R_p (see knudsen.esm) and hence the appropriate mass-transfer regime (continuum, transition, or free-molecular). At standard conditions (T=298.15 K, P=101325 Pa) λ ≈ 65 nm. Migrated from Aerosol.jl src/mass_transfer.jl `MeanFreePathMassTransfer`.

Mean molecular speed of gas molecules using kinetic theory (Seinfeld & Pandis 2006, Chapter 12, Eq. 12.24). Computes c̄ = √(8kT/(πm_A)) where m_A = M_A/N_Av is the molecular mass and k_B, N_Av are folded as numeric literals. Migrated from Aerosol.jl src/mass_transfer.jl `MeanMolecularSpeed` (esm-1i9).

Methane oxidation reaction-rate diagnostics from Seinfeld & Pandis (2006) Ch. 6 §6.4, Table 6.1, pp. 219-227. Methane oxidation is the archetypal VOC oxidation mechanism in the troposphere, proceeding CH₄ → CH₃O₂ → CH₃O → HCHO → HCO → CO → CO₂. This observed-only algebraic component computes the 17 individual reaction rates R1-R17 of the complete Table 6.1 mechanism (10 bimolecular, 3 termolecular, 4 photolysis reactions) plus three diagnostic aggregates: the gross ozone production rate P_O3_gross = R15 + R3 (the two peroxy-radical + NO channels), the formaldehyde production rate P_HCHO = R6 + R8, and the methane loss rate L_CH4 = R1. Each reaction rate is the product of a 298 K rate constant and the reactant concentrations (R = k·[A]·[B] bimolecular, k·[M]·[A]·[B] termolecular, j·[A] photolysis). The fate of the methylperoxy radical CH₃O₂ — the O₃-producing NO channel R3 versus the chain-terminating HO₂ channel R4 — sets the ozone yield per CH₄ oxidized and is the central NOx-regime diagnostic of the mechanism. Purely algebraic (no time derivatives): 52 variables (15 input species and 17 rate constants encoded as parameters, 20 output diagnostics as state) and 20 equations. Migrated from GasChem.jl@8c12c048 src/methane_oxidation.jl:77 (`MethaneOxidation` @component).

Full time-resolved ODE system for the methane oxidation mechanism in the polluted-continental troposphere (Seinfeld & Pandis 2006 Ch. 6 §6.4 Table 6.1, pp. 219-227). Eighteen-state stiff ODE on the methane oxidation chain CH₄ → CH₃ → CH₃O₂ → CH₃O → HCHO → HCO → CO → (CO₂) plus the supporting NOx/HOx radical chemistry that recycles OH and converts NO ↔ NO₂. The reaction network has 22 reactions: the 17 canonical Table 6.1 reactions covering the Cl-skeleton oxidation chain through HCHO and ozone-formation chemistry via the peroxy + NO channels, plus 5 auxiliary reactions (CO + OH, OH + NO₂ → HNO₃ termination, HO₂ + HO₂ → H₂O₂ termination, NO + O₃ titration, and a zero-order external OH source representing primary OH production from O(¹D) + H₂O that is implicit in the upstream model). Eight termolecular reactions (R2, R6, R13, R14, R17) and the bimolecular cross-reactions have their O₂ and M dependence folded into effective rate constants k6_eff, k13_eff and the explicit k2_0·M·O₂, k14_0·M·O₂, k17_0·M·O₂ products with M_fixed, O2_fixed parameters at fixed STP-tropospheric values (M = 2.5e25 m⁻³, O₂ = 5.25e24 m⁻³). Migrated from GasChem.jl@8c12c048 src/methane_oxidation.jl:213 (`MethaneOxidationODE` @component / @network_component → Catalyst.ode_model). The reaction-network DSL form upstream is converted to explicit ODE equations here because the migration tracker classifies this as `Model` with `variables, parameters, equations` features (not a ReactionSystem-shaped migration — those go to a separate path; see sibling superfast.esm).

Volume (mole) mixing ratio of an atmospheric species: xi = c_i / c_total, the ratio of the species molar concentration to the total molar concentration of air. Migrated from AtmosphericDynamics.jl@816cc391 src/seinfeld_pandis_ch1.jl:278 (`MixingRatio` @component). Implements Seinfeld & Pandis (2006) Chapter 1 Equation 1.6. The mixing ratio is dimensionless (stored with unit 1) and in the atmosphere spans roughly twelve orders of magnitude — from ~0.78 for the dominant gas N2 down to parts-per-trillion (~1e-12) trace species — so it is conventionally quoted in ppm, ppb, or ppt. Parameterized as observed-only: c_i and c_total are inputs (parameters in standalone form), xi is the algebraic output. Upstream the Julia @component declares c_i, c_total, and xi as @variables for composition into a parent system; for standalone serialization (3 unknowns vs 1 equation otherwise) c_i and c_total are declared as parameters here, mirroring the IdealGasLaw / ScaleHeight / RelativeHumidity serialization pattern in this directory.

Total aerosol number concentration evolution for a monodisperse aerosol undergoing Brownian coagulation with constant coagulation coefficient (Seinfeld & Pandis 2006, Ch. 13, Eqs. 13.65-13.67). ODE: dN/dt = -K·N²/2; algebraic characteristic coagulation time τ_c = 2/(K·N₀). Source: Aerosol.jl@c8c640bb:src/dynamics.jl:178.

Combined atmospheric lifetime from parallel removal pathways — Seinfeld & Pandis (2006) Ch. 2 (Atmospheric Trace Constituents), Eqs. 2.7-2.9. When a trace species is removed by two independent first-order processes acting simultaneously (rate constants k_1 and k_2), the removal rates add: the inverse lifetimes (1/τ) sum while the lifetimes themselves combine harmonically. This observed-only algebraic component implements four relations: the two individual pathway lifetimes tau_1 = 1/k_1 and tau_2 = 1/k_2 (Eq. 2.6 applied per pathway), the summed inverse lifetime inverse_tau = k_1 + k_2 = 1/tau_1 + 1/tau_2 (Eqs. 2.7-2.8), and the combined lifetime tau_combined = (tau_1·tau_2)/(tau_1+tau_2) = 1/(k_1+k_2) (Eq. 2.9). The combined lifetime is always shorter than either individual pathway lifetime, and the faster (shorter-lifetime) pathway dominates: a fast removal process sets the overall atmospheric lifetime even when a slow pathway is also present; when the two pathways are equal the combined lifetime is exactly half of either. Observed-only algebraic system (no time derivatives): four state variables (tau_1, tau_2, tau_combined in s; inverse_tau in s⁻¹) computed from two rate-constant parameters (k_1, k_2 in s⁻¹) by four algebraic equations. Migrated from GasChem.jl@280ee50f src/AtmosphericLifetime.jl:204 (`MultipleRemovalLifetime` @component).

Ammonia gas-aqueous dissolution and dissociation equilibria with van't Hoff temperature dependence. Migrated from Aerosol.jl@c8c640bb src/aqueous_equilibria.jl:345 (`NH3Equilibria` @component). Implements Seinfeld & Pandis Ch 7 §7.3.4 (Eq 7.46–7.51) and Table 7.4. Parameterized as observed-only: T, H_plus, and p_NH3 are inputs; H_NH3, K_a1, K_w, OH_minus, NH3_aq, NH4_plus, NH3_total, H_NH3_eff are algebraic outputs.

Stratospheric NOx catalytic ozone destruction cycle (Seinfeld & Pandis 2006 Ch. 5 §5.3.2, Eqs. 5.20-5.22). Two-state ODE on the NOx radicals NO and NO2 driven by reactions with O3 and atomic O, plus daytime NO2 photolysis; NOx = NO + NO2 is exactly conserved by construction (D(NO) + D(NO2) ≡ 0). Migrated from GasChem.jl@8c12c048 src/StratosphericChemistry.jl:118 (`NOxCycle` @component). Rate coefficients are temperature-dependent Arrhenius forms k_X = k_X_A · exp(C_X / T) with the Seinfeld & Pandis bimolecular CGS pre-factors converted to SI via the cm³/molec/s × 1e-6 → m³/s factor; SI rates and SI number-density concentrations (m^-3) preserved verbatim from upstream.

The NOx (NO + NO₂) photochemical cycle that governs tropospheric ozone — Seinfeld & Pandis (2006) Ch. 6 §6.2, Eqs. 6.5-6.8, pp. 207-212. During daytime three reactions cycle rapidly between NO, NO₂ and O₃: NO₂ + hν → NO + O (λ < 424 nm), O + O₂ + M → O₃ + M, and NO + O₃ → NO₂ + O₂. In the absence of other oxidants this cycle reaches a photostationary state (the Leighton relationship). Implements four algebraic diagnostic relations: (Eq. 6.5) ground-state O-atom steady-state concentration O = j_NO2·[NO₂] / (k_O_O2_M·[O₂]·[M]), (Eq. 6.6) photostationary-state ozone O3_pss = j_NO2·[NO₂] / (k_NO_O3·[NO]) — the Leighton relationship, (Eq. 6.7) the photostationary-state parameter Φ = j_NO2·[NO₂] / (k_NO_O3·[NO]·[O₃]) which is 1 at exact PSS and deviates when peroxy radicals perturb the cycle, and (Eq. 6.8) the net ozone production rate P_O3 = j_NO2·[NO₂] − k_NO_O3·[NO]·[O₃]. Observed-only algebraic system (no time derivatives): nine variables (five inputs NO/NO2/O3/O2/M encoded as parameters, four outputs O/O3_pss/Φ/P_O3 encoded as state) plus three rate-constant parameters (j_NO2, k_O_O2_M, k_NO_O3). Migrated from GasChem.jl@8c12c048 src/nox_photochemistry.jl:88 (`NOxPhotochemistry` @component). Sibling component PhotostationaryState (src/nox_photochemistry.jl:145) migrates separately to photostationary.esm.

Full coupled homogeneous nucleation system following classical nucleation theory from Seinfeld & Pandis (2006), Chapter 11. Derives saturation ratio and monomer concentration from partial pressures, then computes critical cluster properties (size, radius, free-energy barrier) and the nucleation rate J. Use this component when the full coupled system is needed; see ClassicalNucleationRate for a lighter variant that takes S and N_1 as direct parameters.

Ozone (O3) aqueous dissolution equilibrium via temperature-dependent Henry's law. Migrated from Aerosol.jl@c8c640bb src/aqueous_equilibria.jl:589 (`O3Equilibria` @component). Implements Seinfeld & Pandis Ch 7 Table 7.3: K_H(O3, 298 K) = 1.1×10⁻² M/atm, ΔH_sol = −5.04 kcal/mol. O3 does not ionize in water; dissolution is purely described by Henry's law with van't Hoff temperature dependence.

Tropospheric OH radical production from O₃ photolysis — Seinfeld & Pandis (2006) Ch. 6 §6.1 Eqs. 6.1, 6.3, 6.4, pp. 204-207. The dominant source of OH in the troposphere is O₃ photolysis below 320 nm producing electronically excited O(¹D), which either reacts with H₂O to yield two OH radicals or is collisionally quenched back to ground-state O(³P) by N₂/O₂. Implements three algebraic relations: (Eq. 6.1) O(¹D) steady-state concentration [O(¹D)] = j_O₃·[O₃] / (k₃[M] + k₄[H₂O]), (Eq. 6.4) OH yield ε_OH = 2·k₄[H₂O] / (k₃[M] + k₄[H₂O]) as the fraction of O(¹D) producing OH (the factor of 2 accounts for the 2 OH produced per O(¹D)+H₂O encounter — ε_OH ranges 0..2), (Eq. 6.3) OH production rate P_OH = j_O₃·[O₃]·ε_OH. The effective quenching rate k₃_eff = f_N₂·k₃,N₂ + f_O₂·k₃,O₂ is the air-composition-weighted average of the N₂ and O₂ quenching channels. Observed-only algebraic system (no time derivatives): six variables (three inputs O₃/H₂O/M as parameters, three outputs O₁D/ε_OH/P_OH as state) plus six rate-parameter inputs (j_O₃, k₃_N₂, k₃_O₂, k₄, f_N₂, f_O₂) and one stoichiometric constant (two=2). Migrated from GasChem.jl@8c12c048 src/oh_production.jl:88 (`OHProduction` @component).

Atmospheric lifetime against reaction with the hydroxyl radical (OH), from Seinfeld & Pandis (2006) Atmospheric Chemistry and Physics Ch. 2, Eq. 2.12: tau = 1/(k_OH*[OH]). OH is the dominant daytime oxidant of the troposphere, so the OH-reaction lifetime sets how long most reactive trace gases — methane, carbon monoxide, non-methane VOCs — persist in the atmosphere. This observed-only algebraic component implements two relations: an effective pseudo-first-order loss rate constant k_eff = k_OH*OH_conc (the second-order reaction X + OH collapsed onto the approximately constant ambient OH), and the lifetime tau_OH = 1/k_eff. The lifetime is jointly controlled by the species' intrinsic reactivity (k_OH, spanning four-plus decades across tropospheric trace gases) and the ambient oxidising capacity ([OH], varying with season, latitude and pollution): a species may persist for years in clean remote air and only hours in a polluted daytime plume. Purely algebraic system (no time derivatives): four variables — one parameter k_OH, one input OH_conc encoded as a parameter, two outputs k_eff and tau_OH as state — and two equations. Migrated from GasChem.jl@280ee50f src/AtmosphericLifetime.jl:264 (`OHReactionLifetime` @component).

Ozone Production Efficiency (OPE) diagnostic from Seinfeld & Pandis (2006) Ch. 6 §6.3 Eqs. 6.21-6.24, pp. 212-219. OPE = Δ[O₃]/Δ[NOx] is the number of ozone molecules produced per molecule of NOx consumed — a central diagnostic for the NOx-VOC-O₃ regime structure of tropospheric photochemistry. This observed-only algebraic component implements three relations: gross ozone production rate P_O3 = k_HO2_NO·[HO₂]·[NO] + k_RO2_NO·[RO₂]·[NO] (the two peroxy-radical + NO channels — each peroxy+NO reaction makes an NO₂ whose photolysis yields an O₃), NOx loss rate L_NOx = k_OH_NO2·[OH]·[NO₂] (the OH + NO₂ + M → HNO₃ termination, the dominant daytime NOx sink), and OPE = P_O3 / L_NOx. High OPE (low-NOx, NOx-limited regime) means each NOx molecule cycles through many O₃-producing reactions before it is lost as nitric acid; low OPE (high-NOx, VOC-limited regime) means NOx is removed before it can drive much O₃ production. Observed-only algebraic system (no time derivatives): eight variables (five inputs OH/HO₂/RO₂/NO/NO₂ encoded as parameters, three outputs P_O3/L_NOx/OPE as state) plus three rate-constant parameters (k_HO2_NO, k_RO2_NO, k_OH_NO2) and three algebraic equations. Migrated from GasChem.jl@280ee50f src/co_oxidation.jl:183 (`OzoneProductionEfficiency` @component).

Relates the volume mixing ratio of an atmospheric species to its partial pressure: xi = p_i / p (Seinfeld & Pandis, Atmospheric Chemistry and Physics, Ch. 1, Eq. 1.8). The mixing ratio equals the ratio of the species' partial pressure to the total atmospheric pressure. Migrated from AtmosphericDynamics.jl@816cc391 src/seinfeld_pandis_ch1.jl:308 (`PartialPressureMixingRatio` @component). Parameterized as observed-only: the partial pressure p_i and total pressure p are inputs (parameters in standalone form), xi is the algebraic output. Upstream the Julia @component declares p_i, p, and xi as @variables for composition into a parent system; for standalone serialization (3 unknowns vs 1 equation otherwise), p_i and p are declared as parameters here, mirroring the IdealGasLaw / ScaleHeight serialization pattern in the same module.

Slinn (1983) semi-empirical collision (collection) efficiency E between a falling raindrop and an aerosol particle, the kernel of below-cloud particle scavenging (Eqs. 20.53-20.54, Seinfeld & Pandis, 2006). E is the sum of three collection mechanisms — Brownian diffusion (E_diff, important for sub-0.1 µm particles), interception (E_int), and inertial impaction (E_imp, important for super-µm particles, switched on only when the Stokes number exceeds the critical Stokes number S* of Eq. 20.54) — and is clamped to a maximum of 1. The competition between the diffusion and impaction mechanisms produces the Greenfield gap: a collection-efficiency minimum at accumulation-mode (~0.1-1 µm) particle sizes. Migrated from AtmosphericDeposition.jl@e4468c79 src/seinfeld_pandis_2006_ch20.jl:365 (`ParticleCollectionEfficiency` @component). The upstream component carries the single equation E ~ slinn_collection_efficiency(D_p, U_t, d_p, ρ_p, T); the helper function and its sub-helpers (particle_diffusivity, particle_relaxation_time, particle_terminal_velocity) are decomposed here into 18 named intermediate algebraic states (Re, D_diff, Sc, τ, St, S_star, E_diff, E_int, E_imp, ...) mirroring the helper's local variables, so each equation maps to one source line. Observed-only: all 18 equations are algebraic — the five raindrop/aerosol/thermodynamic inputs and six physical constants are parameters, and Re through E are the algebraic outputs.

Rate of change of particle radius due to condensation or evaporation of a trace gas. Models diffusion-limited radial growth in the continuum regime via Eq. 12.14 of Seinfeld & Pandis (2006): dR_p/dt = (D_g M_A / (ρ_p R_p)) (c_∞ − c_s). The quadratic-in-R_p growth law R_p(t)² = R_p0² + 2Kt (K = D_g M_A (c_∞ − c_s)/ρ_p) is the classical result for condensation onto an absorbing sphere in the continuum limit. Migrated from Aerosol.jl src/mass_transfer.jl `ParticleGrowthRate`.

Below-cloud scavenging coefficient Λ_particle for an aerosol particle collected by monodisperse raindrops (Seinfeld & Pandis 2006, Chapter 20, Eq. 20.57): Λ_particle = (3/2)·E·p₀/D_p, where E is the Slinn (1983) raindrop-aerosol collision (collection) efficiency of Eqs. 20.53-20.54, p₀ the precipitation rate and D_p the raindrop diameter. E sums three collection mechanisms — Brownian diffusion, interception, and inertial impaction (switched on only when the Stokes number exceeds the critical Stokes number S*) — and is clamped to a maximum of 1; their competition produces the Greenfield gap, a scavenging minimum at accumulation-mode (~0.1-1 µm) particle sizes. Migrated from AtmosphericDeposition.jl@e4468c79 src/seinfeld_pandis_2006_ch20.jl:414 (`ParticleScavengingCoeff` @component). The upstream slinn_collection_efficiency helper and its diffusivity / relaxation-time / settling-velocity sub-helpers are decomposed into 18 named intermediate algebraic states (Re, D_diff, Sc, τ, St, S_star, E_diff, E_int, E_imp, ...) — identical to the sibling component particle_collection_eff.esm — and a 19th equation applies Eq. 20.57. The five raindrop/aerosol/thermodynamic inputs, the precipitation rate, and six physical constants are parameters; Re through E and Λ_particle are the algebraic outputs.

Gravitational settling velocity and Brownian diffusivity of an aerosol particle, from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 19 (Dry Deposition). Two algebraic outputs are computed from the particle and air properties. The settling (terminal) velocity v_s = rho_p*D_p^2*g*C_c/(18*mu) (Eq. 19.18) is the steady gravitational drift speed of a particle in the Stokes (low-Reynolds-number) regime, where aerodynamic drag balances gravity; the Cunningham slip correction factor C_c (>= 1) accounts for the non-continuum reduction in drag when the particle diameter approaches the mean free path of air. The Brownian diffusivity D_diff = k_B*T*C_c/(3*pi*mu*D_p) (Eq. 19.20) is the Stokes-Einstein diffusion coefficient describing the particle's thermal random walk. The two quantities have opposite size dependence -- v_s grows as D_p^2 while D_diff falls as 1/D_p -- which is the physical origin of the dry-deposition-velocity minimum for accumulation-mode (~0.1-1 um) aerosol: such particles settle too slowly to deposit gravitationally yet are too large to diffuse efficiently to the surface. Both quantities feed the Zhang et al. (2001) quasi-laminar resistance and the overall particle dry deposition velocity computed by the sibling sp_ch19 components. Migrated from AtmosphericDeposition.jl@e4468c79 src/seinfeld_pandis_ch19.jl:182 (`ParticleSettling` @component). Observed-only algebraic model: rho_p, D_p, mu, T, C_c are input parameters, g/k_B/pi_val are physical-constant parameters, and v_s and D_diff are the two algebraic outputs, each fixed by one equation with no time derivative.

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.

Photostationary-state diagnostic for the NO-NO₂-O₃ Leighton cycle — Seinfeld & Pandis (2006) Ch. 6 §6.2, Eqs. 6.6-6.7, pp. 207-212. Computes the photostationary-state parameter Φ = j_NO2·[NO₂] / (k_NO+O₃·[NO]·[O₃]) and its deviation from unity Φ_deviation = Φ - 1. Φ = 1 is the exact Leighton photostationary state (pure NO-NO₂-O₃ cycling, zero net ozone production); Φ > 1 indicates additional oxidants (peroxy radicals HO₂/RO₂ converting NO→NO₂ and producing ozone), Φ < 1 indicates net ozone loss. This observed-only algebraic component is the simplified companion to NOxPhotochemistry (the full Eqs. 6.5-6.8 diagnostic): five variables (three inputs NO/NO₂/O₃ encoded as parameters, two outputs Φ/Φ_deviation as state), two rate parameters (j_NO2, k_NO_O3) plus the dimensionless unity constant `one`, and two algebraic equations. No time derivatives. Migrated from GasChem.jl@8c12c048 src/nox_photochemistry.jl:145 (`PhotostationaryState` @component).

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).

ModelingToolkit implementation of the quasi-laminar (boundary-layer) resistance to gaseous dry deposition from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 19 (Dry Deposition), Eq. 19.17. The quasi-laminar resistance r_b [s/m] is the second of the three series resistances of the gas dry-deposition resistance model (r_a aerodynamic + r_b quasi-laminar + r_c surface) and represents molecular diffusion of the depositing gas across the thin, quasi-laminar sublayer of stagnant air in direct contact with the surface. It is computed as r_b = 5*Sc^(2/3)/u_star, where the Schmidt number Sc = nu/D_g is the ratio of the kinematic viscosity of air nu to the molecular diffusivity D_g of the gas, and u_star is the friction velocity. Slower-diffusing (higher-Sc) gases face a larger boundary-layer resistance, and stronger surface turbulence (higher u_star) thins the sublayer and lowers r_b. Migrated from AtmosphericDeposition.jl@e4468c79 src/seinfeld_pandis_ch19.jl:143 (`QuasiLaminarResistanceGas` @component). Algebraic (no time derivative) two-equation system: Sc and r_b are the algebraic outputs (the upstream component's computed @variables, migrated as type:state); nu and D_g are the input @parameters and u_star is the upstream input @variable (migrated as type:parameter -- it carries no defining equation and the upstream test suite compiles the component with u_star declared as an input).

Zhang et al. (2001) quasi-laminar (boundary-layer) resistance r_b for particle dry deposition, Seinfeld & Pandis (2006) Ch. 19 Eq. 19.27. r_b = 1/(3*u_star*(E_B+E_IM+E_IN)*R_1) sums three size-dependent collection mechanisms — Brownian diffusion E_B (Eq. 19.21), inertial impaction E_IM (Eq. 19.22), and interception E_IN (Eq. 19.25) — scaled by the friction velocity u_star and the rebound-correction sticking fraction R_1 (Eq. 19.26). The competition between diffusion (efficient for sub-0.1 um particles) and impaction (efficient for super-um particles) leaves a deposition minimum at accumulation-mode sizes. Migrated from AtmosphericDeposition.jl@e4468c79 src/seinfeld_pandis_ch19.jl:234 (`QuasiLaminarResistanceParticle` @component). The seven upstream equations are migrated verbatim and one-to-one; the five input @parameters, the @constant g, and the three externally-supplied input @variables (u_star, v_s, D_diff) are all parameters, and the seven equation-defined quantities (Sc, St, E_B, E_IM, E_IN, R_1, r_b) are the algebraic outputs.

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).

Relative humidity from water-vapor partial pressure and saturation vapor pressure: RH = 100 * p_H2O / p_sat. Migrated from AtmosphericDynamics.jl@816cc391 src/seinfeld_pandis_ch1.jl:397 (`RelativeHumidity` @component). Implements Seinfeld & Pandis Ch 1 Eq. 1.9. Relative humidity is expressed as a percentage (0-100 for subsaturated air, >100 under transient supersaturation), stored as a dimensionless ratio scaled by 100. Parameterized as observed-only: p_H2O and p_sat are inputs (parameters in standalone form), RH is the algebraic output. Upstream the Julia @component declares p_H2O and p_sat as @variables for composition into a parent system; for standalone serialization (3 unknowns vs 1 equation otherwise), they are declared as parameters here, mirroring the IdealGasLaw / ScaleHeight serialization pattern in this directory.

Parameters-preset model representing typical remote/background tropospheric conditions with low NOx. Migrated from GasChem.jl@8c12c048 src/combined_system.jl:261 (`RemoteConditions` @component). Eleven species concentrations are declared as parameters in SI units (m⁻³); the model exposes them as algebraic outputs (`*_out`) so a parent system or test harness can read presets without depending on MTK parameter-introspection APIs. Based on Seinfeld & Pandis Chapter 6 background conditions: ~30 ppb O₃, ~10 ppt NO, ~20 ppt NO₂, ~80 ppb CO.

Saturation vapor pressure of water over liquid water as a function of temperature: p_sat = p_std * exp(c1*a - c2*a^2 - c3*a^3 - c4*a^4) with a = 1 - T_boil/T (Seinfeld & Pandis Eq. 1.10). An empirical fit valid for liquid water (T > 273 K). Migrated from AtmosphericDynamics.jl@816cc391 src/seinfeld_pandis_ch1.jl:351 (`SaturationVaporPressure` @component). Algebraic (observed-only): T is an input parameter; a and p_sat are algebraic state outputs fixed by two explicit equations. Pressure is reported in Pa (the upstream module uses P_0 = 101325 Pa = 1013.25 mbar).

Atmospheric scale height H = R*T/(M_air*g) — the altitude increase over which atmospheric pressure decreases by a factor of e (~2.718) for an isothermal atmosphere. Migrated from AtmosphericDynamics.jl@816cc391 src/seinfeld_pandis_ch1.jl:109 (`ScaleHeight` @component). Implements Seinfeld & Pandis Eq. 1.4. Parameterized as observed-only: T is an input parameter, H is the algebraic observed output.

SO2 gas-aqueous dissolution and dissociation equilibria with van't Hoff temperature dependence. Migrated from Aerosol.jl@c8c640bb src/aqueous_equilibria.jl:240 (`SO2Equilibria` @component). Implements Seinfeld & Pandis Ch 7 §7.3.3 (Eq 7.33-7.35, 7.39, 7.41, 7.43-7.45) and Table 7.4. Parameterized as observed-only: T, H_plus, and p_SO2 are inputs; H_SO2, K_s1, K_s2, SO2_aq, HSO3_minus, SO3_2minus, S_IV_total, H_SO2_eff, alpha_0, alpha_1, alpha_2 are algebraic outputs.

Atmospheric-lifetime calculator for a trace species, from Seinfeld & Pandis (2006) Ch. 2 (Atmospheric Trace Constituents), Eqs. 2.3-2.6. The component is observed-only: four algebraic equations, no time derivative, expressing the four textbook definitions of atmospheric lifetime as functions of the species burden Q and the removal/production/outflow rates. tau_general = Q/(R_removal + F_out) is the general lifetime accounting for both chemical removal R_removal and outflow F_out to other reservoirs (Eq. 2.3); tau_removal = Q/R_removal is the global-atmosphere limit with no outflow (Eq. 2.4); tau_production = Q/P is the production-based lifetime, equal to tau_removal at steady state (Eq. 2.5); and tau_first_order = 1/lambda is the lifetime when removal follows first-order kinetics R_removal = lambda*Q (Eq. 2.6). The four definitions interlock: Eq. 2.3 reduces to Eq. 2.4 as F_out -> 0, Eqs. 2.4 and 2.5 coincide when production balances removal, and Eq. 2.6 coincides with Eq. 2.4 when lambda is the consistent first-order rate constant R_removal/Q. Migrated from GasChem.jl@280ee50f src/AtmosphericLifetime.jl:132 (`SpeciesLifetime` @component). Every equation is a closed-form algebraic expression in the parameters, so every inline-test expected value below is the exact arithmetic evaluation of the textbook formula.

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.

Comprehensive stratospheric ozone chemistry (Seinfeld & Pandis 2006, Chapter 5) — a monolithic 15-state ODE plus 5 algebraic family sums combining the Chapman mechanism, O(1D) photochemistry, the N2O NOx source, and the NOx / HOx / ClOx / BrOx catalytic ozone-destruction cycles. Migrated from GasChem.jl@8c12c048 src/StratosphericChemistry.jl:497. SI units throughout.

Monin-Obukhov surface-layer similarity theory for the atmospheric surface layer, from Seinfeld & Pandis (2006) "Atmospheric Chemistry and Physics", 2nd ed., Chapter 16 "Meteorology of the Local Scale". Observed-only algebraic component: from the friction velocity u_star, surface sensible heat flux q_z, and surface-layer geometry it computes the Monin-Obukhov length L (Eq. 16.70), the dimensionless stability parameter ζ = z/L, the Businger-Dyer stability functions φ_m and φ_h (Eq. 16.75), their integrated forms ψ_m and ψ_h (Eq. 16.78-16.79), and the stability-corrected mean wind speed ū (Eq. 16.66 with the Eq. 16.77 correction). Migrated from AtmosphericDynamics.jl@816cc391 src/local_scale_meteorology.jl:107 (`SurfaceLayerProfile` @component); the 4 upstream @constants (g, κ, ĉ_p, ε_q) are declared as fixed-default parameters.

ModelingToolkit implementation of the surface (canopy) resistance to gaseous dry deposition from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 19 (Dry Deposition), Eqs. 19.50-19.52 -- the Wesely (1989) resistance model. Computes the total surface resistance r_c [s/m] as four parallel deposition pathways (Eq. 19.50): the combined stomatal+mesophyll pathway, the cuticular/outer-surface pathway r_lu, the lower-canopy pathway r_dc+r_cl, and the ground pathway r_ac+r_gs. The stomatal resistance r_st (Eq. 19.51) responds to solar irradiance G and surface temperature T_s through dimensionless light and temperature factors; the mesophyll resistance r_m (Eq. 19.52) is set by the gas's effective Henry's-law solubility H_star and reactivity f_0. Migrated from AtmosphericDeposition.jl@e4468c79 src/seinfeld_pandis_ch19.jl:311 (the SurfaceResistance @component). Purely algebraic: no differential states, six explicit equations evaluated as a triangular cascade.

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.

Total molar concentration of air from the ideal gas law: c_total = N/V = p / (R * T) (Seinfeld & Pandis Eq. 1.7). Migrated from AtmosphericDynamics.jl@816cc391 src/seinfeld_pandis_ch1.jl:244 (`TotalMolarConcentration` @component). Algebraic (observed-only): T and p are input parameters; c_total is the algebraic output fixed by one explicit equation. Upstream the Julia @component declares T and p as @variables for composition into a parent system; for standalone serialization (3 unknowns vs 1 equation otherwise), they are declared as parameters here, mirroring the sibling ideal_gas.esm / sat_vapor_pressure.esm pattern.

Complete tropospheric mass-budget model for a trace species, from Seinfeld & Pandis (2006) Ch. 2 §2.3, Eqs. 2.13-2.17. A single linear first-order ODE on the species burden Q drives the dynamics: dQ/dt = (P_n + P_a + P_c) - (k_d + k_w + k_c + k_t)·Q — total production from natural emissions, anthropogenic emissions, and in-troposphere chemical production, balanced against first-order removal by dry deposition, wet deposition, chemical loss, and cross-tropopause transport to the stratosphere. The model also reports the algebraic diagnostics that the textbook builds on this budget: the total production rate P_total and removal rate R_total, the total first-order removal rate constant k_total, the per-pathway lifetimes tau_dry/tau_wet/tau_chem/tau_transport = 1/k_X, the total atmospheric lifetime tau_total = 1/k_total (Eq. 2.15), and the production-based lifetime tau_production = Q/P_total (Eqs. 2.16-2.17), which equals tau_total once the burden has relaxed to steady state. Migrated from GasChem.jl@280ee50f src/AtmosphericLifetime.jl:336 (`TroposphericBudget` @component). The system is linear with constant coefficients, so the burden has the exact closed form Q(t) = Q_ss + (Q_0 - Q_ss)·exp(-k_total·t) with steady state Q_ss = P_total/k_total; every inline-test expected value below is that analytic solution.

Combined tropospheric chemistry diagnostic system (Seinfeld & Pandis 2006, Chapter 6) — couples three photochemical subsystems into a comprehensive steady-state diagnostic model of tropospheric photochemistry: OH production from O3 photolysis (§6.1), the NOx photochemical cycle (§6.2), and CO oxidation chemistry (§6.3). Migrated from GasChem.jl@8c12c048 src/combined_system.jl:54 (`TroposphericChemistrySystem` @component). The three subsystems — `oh` (OHProduction), `nox` (NOxPhotochemistry), `co` (COOxidation) — are inlined verbatim (ESS spec §4.7 subsystem composition) from their already-migrated standalone .esm files; the parent supplies 14 coupling equations feeding the shared species (O3, NO, NO2, OH, HO2, CO, CH3O2, H2O, M, O2) into the subsystems and 9 combined-diagnostic equations (total/net O3 production, ozone production efficiency, NOx loss rate, HOx chain length). Purely algebraic — a steady-state diagnostic system with no time derivatives. SI units throughout (m^-3 for concentrations, m^3/s for bimolecular rate constants).

Effective uptake coefficient γ for gas-particle mass transfer. γ is the net probability that a gas molecule striking the particle surface is irreversibly taken up; it accounts for three resistances in series: (1) gas-phase diffusion to the surface (term_diff), (2) surface accommodation (term_acc), and (3) aqueous-phase reaction-diffusion within the droplet (term_rxn). The reciprocal relation 1/γ = term_diff + term_acc + term_rxn (Seinfeld & Pandis 2006, Chapter 12, Eq. 12.121) expresses resistances additively, analogous to resistors in series. Migrated from Aerosol.jl src/mass_transfer.jl `UptakeCoefficient`.

Parameter-preset condition system representing typical urban-air-quality lower-troposphere conditions with elevated NOx, CO, and reduced HOx, following Seinfeld & Pandis (2006) Chapter 6. Migrated from GasChem.jl@8c12c048 src/combined_system.jl:219 (`UrbanConditions` @component). The component declares 11 species number-density parameters (M, O2, H2O, O3, NO, NO2, CO, CH4, OH, HO2, CH3O2) with urban-regime defaults in SI units (m^-3) and 11 corresponding `_out` output state variables, one per parameter, defined by identity equations `*_out ~ *`. The component is a sibling preset to `TypicalConditions` (background-air defaults) and `RemoteConditions` (clean-remote defaults); together they parametrize the three canonical regimes the upstream `TroposphericChemistrySystem` is exercised against. Compared to TypicalConditions: NO is 100x higher (10 vs 0.1 ppb), NO2 is 30x higher (30 vs 1 ppb), CO is 20x higher (2000 vs 100 ppb), and OH/HO2 are reduced 2x (titrated by the elevated NOx and CO oxidation chain). All concentrations are positive number densities at standard temperature and pressure; the `_out` indirection lets downstream consumers wire the preset values into the canonical tropospheric-chemistry input interface without renaming.

Visibility calculation from extinction coefficient. Computes visual range using the Koschmeider equation (Eq. 15.36) and related visibility metrics. Visual range is the distance at which a black object against a white background reaches the threshold contrast of 0.02.

Water autoionization equilibrium with van't Hoff temperature dependence. Migrated from Aerosol.jl@c8c640bb src/aqueous_equilibria.jl:76 (`WaterEquilibrium` @component). Serialized via EarthSciAST.mtk2esm. Implements Seinfeld & Pandis Ch 7 Eq 7.10–7.13 and Table 7.4. Parameterized as observed-only: T and [H+] are inputs, K_w/[OH-]/pH are algebraic outputs.

Temperature-dependent physical properties of water for nucleation calculations following Seinfeld & Pandis (2006), Chapter 11, Tables 11.1 and 11.4. Provides surface tension, molecular volume, molecular mass, and saturation vapor pressure as functions of temperature.

Composite water-vapor thermodynamics system from Seinfeld & Pandis (2006) Chapter 1: given air temperature and water-vapor partial pressure it computes the saturation vapor pressure of water over liquid water (Eq. 1.10) and the relative humidity (Eq. 1.9). Migrated from AtmosphericDynamics.jl@816cc391 src/seinfeld_pandis_ch1.jl:433 (`WaterVaporThermodynamics` @component), which composes two MTK subsystems via `System(eqs, t; systems=[sat, rh])`. Represented here as a subsystem-composed ESS model (spec §4.7): the `sat` subsystem inlines the already-migrated SaturationVaporPressure component (sat_vapor_pressure.esm, esm-zuku) and the `rh` subsystem inlines RelativeHumidity (relative_humidity.esm, esm-vann), wired together by five top-level coupling equations. Algebraic (observed-only): T and p_H2O are input parameters; p_sat and RH are algebraic state outputs. The flattened chain T -> sat.a -> sat.p_sat -> rh.p_sat -> rh.RH is fully explicit and triangular.

Net wet deposition diagnostics — wet deposition flux, washout ratio, and wet deposition velocity — for a trace species removed from the atmosphere by falling rain, from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 20 (Wet Deposition), Eqs. 20.6-20.9. Given the species concentration in ground-level rainwater (C_rain), its gas-phase concentration in air (C_air), and the precipitation rate (p₀), the component evaluates three quantities: the wet deposition flux F_w = C_rain·p₀ (Eq. 20.7) — the downward species mass flux carried to the surface by rain; the dimensionless washout ratio w_r = C_rain/C_air (Eq. 20.6) — a measure of how strongly the species partitions into rainwater; and the wet deposition velocity u_w = F_w/C_air (Eq. 20.8), equivalently w_r·p₀ (Eq. 20.9) — the flux normalized by the air-phase concentration. Migrated from AtmosphericDeposition.jl@e4468c79 src/seinfeld_pandis_2006_ch20.jl:451 (`WetDepositionFlux` @component). Flat observed-only algebraic model: C_rain, C_air and p₀ are the input parameters and F_w, w_r, u_w are the algebraic outputs, each fixed by one equation with no time derivative. The upstream @component is a single flat System with no subsystems; the migration-tracker `coupling.couple` feature tag and `depends_on: ParticleScavengingCoeff, GasScavengingCoeff` describe a conceptual relationship that the source code does not implement, so this is migrated as a standalone flat model.

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.