Wet-Scavenging

Air refreshing limitation on wet scavenging from Luo & Yu (2023), Eqs. 2, 5, 10, 11. The air refreshing limited removal rate R_A accounts for the finite time needed for species in subgrid cloud-free (rain-free) air to mix into cloudy (rainy) air before being subject to wet scavenging; the standard well-mixed assumption overestimates wet scavenging when the subgrid air mixing time scale is comparable to the model time step. When turbulent mixing is strong (large TKE) the grid refreshing time goes to zero and R_A approaches f*Rᵢ (the standard model); when mixing is weak R_A falls below f*Rᵢ. Migrated from AtmosphericDeposition.jl@e4468c79 src/luo2023.jl:210 (`AirRefreshingLimitation` @component). Observed-only algebraic system: cloud fraction f, in-cloud removal rate Rᵢ, turbulence kinetic energy TKE, and the grid spacings Δx/Δy/Δz are input parameters; Kᵢ, τ_A, and R_A are the algebraic outputs fixed by three explicit equations.

Cloud ice uptake limitation on cold-cloud wet scavenging from Luo & Yu (2023), Eqs. 12-15. In cold clouds, water-soluble aerosols are captured by ice crystals via coagulation and then removed by precipitation; this component computes the cold-cloud rainout efficiency F_I from ice-crystal properties, turbulence, grid geometry, and temperature. The cloud ice uptake rate R_U is approximated by the HNO3 uptake rate of Jacob (2000) (Eq. 14); the temperature-dependent uptake efficiency gamma follows Hudson et al. (2002) (Eq. 15: gamma = 0.003 at T >= 220 K rising linearly to 0.007 at T <= 209 K); the cloudy-air refreshing rate Ki comes from turbulence kinetic energy and grid spacing (Eq. 11); the air-refreshing limited uptake rate R_AU applies the Eq. 2 refreshing-limit structure to R_U (Eq. 13); and F_I = 1 - exp(-R_AU*dt) (Eq. 12). Migrated from AtmosphericDeposition.jl@e4468c79 src/luo2023.jl:260 (`CloudIceUptakeLimitation` @component). Observed-only: the 5 equations are algebraic, so gamma, R_U, Ki, R_AU, F_I are the algebraic outputs while the 12 ice/turbulence/grid inputs and 9 module constants are parameters.

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.

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.

Below-cloud scavenging of a reversibly-absorbed (Henry's-law) trace gas by falling raindrops, from Chapter 20 (Wet Deposition) of Seinfeld & Pandis (2006). Unlike the irreversible-uptake parameterizations used for highly soluble species such as HNO3, this component retains the equilibrium (Henry's law) ceiling: a raindrop falling through polluted air relaxes toward -- but cannot exceed -- the aqueous concentration in equilibrium with the local gas phase, and a drop entering the layer already overloaded (C_aq0 above equilibrium) instead desorbs gas back to the air. Two algebraic outputs: C_aq_ground (Eq. 20.33, which is Eq. 20.28 evaluated at the cloud-base fall distance h) is the aqueous-phase concentration in a drop arriving at the ground; F_bc (Eq. 20.35) is the total below-cloud scavenging flux. Both are governed by the single dimensionless exponent alpha = 6*K_c*h/(D_p*U_t*HRT): the drop relaxes from its initial aqueous concentration C_aq0 toward the Henry's-law equilibrium C_eq = C_g*HRT, and (1 - exp(-alpha)) is the fraction of that equilibrium uptake realised over the fall. Migrated from AtmosphericDeposition.jl@e4468c79 src/seinfeld_pandis_2006_ch20.jl:194 (`ReversibleGasScavenging` @component). The upstream component is a flat MTK System whose two equations call the module helper functions reversible_drop_conc (Eq. 20.28) and reversible_scavenging_flux (Eq. 20.35); both helpers are inlined into the equation ASTs here. The eight upstream @parameters (C_g, HRT, K_c, D_p, U_t, h, C_aq0, p0) map directly to type:parameter and the two upstream @variables(t) (C_aq_ground, F_bc) to type:state, each fixed by one explicit algebraic equation. HRT is the dimensionless product H* x R x T x 1000 (effective Henry's law coefficient x gas constant x temperature x unit conversion); for HNO3 at 298 K, HRT = 2.1e5 x 8.206e-5 x 298 x 1000 is approximately 5.14e6 (the declared default). Observed-only algebraic system: both equations are algebraic (no D operator), so the two outputs are the algebraic solution while the gas-phase, drop, and precipitation inputs are parameters; system_kind is left unset.

Combined air refreshing and cloud ice uptake limitations on wet scavenging from Luo & Yu (2023). This component unifies the two novel parameterizations of the paper into a single algebraic system: (1) the air refreshing limitation (Section 2.1, Eqs. 2/5/10/11), which reduces the wet-scavenging removal rate R_A when subgrid cloud-free (rain-free) air mixes into cloudy (rainy) air slower than the model time step; and (2) the cloud ice uptake limitation (Section 2.2, Eqs. 12-15), which limits the cold-cloud rainout efficiency F_I by the rate R_U at which water-soluble aerosols are captured by ice crystals -- the HNO3 ice uptake rate of Jacob (2000), with the temperature-dependent uptake efficiency gamma of Hudson et al. (2002). Migrated from AtmosphericDeposition.jl@e4468c79 src/luo2023.jl:326 (`WetScavengingLimitations` @component). The upstream component is a flat MTK System that inlines the equations of both AirRefreshingLimitation and CloudIceUptakeLimitation -- it does not `couple` them -- so this migration is the union of air_refreshing.esm (esm-1i3m) and cloud_ice_uptake.esm (esm-3hh9): 13 input parameters, 9 module constants, and 7 algebraic state variables (Kᵢ, τ_A, R_A, gamma, R_U, R_AU, F_I) fixed by 7 explicit equations. Observed-only: every equation is algebraic, so the 7 outputs are the algebraic solution while the ice/turbulence/grid/temperature inputs and module constants are parameters.