Lifetime

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.

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).

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).

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.

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.