Non-equilibrium bulk microphysics scheme, which includes:

• condensation and evaporation of cloud liquid water and deposition and sublimation of cloud ice (relaxation to equilibrium)

τ_relax(liquid)
τ_relax(ice)

• liquid or ice - a type for cloud liquid water or ice

Returns the relaxation timescale for condensation and evaporation of cloud liquid water or the relaxation timescale for sublimation and deposition of cloud ice.

conv_q_vap_to_q_liq_ice(liquid, q_sat, q)
conv_q_vap_to_q_liq_ice(ice, q_sat, q)

• liquid or ice - a type for cloud water or ice
• q_sat - PhasePartition at equilibrium
• q - current PhasePartition

Returns the cloud water tendency due to condensation and evaporation or cloud ice tendency due to sublimation and vapor deposition. The tendency is obtained assuming a relaxation to equilibrium with a constant timescale.

Microphysics0M

Zero-moment bulk microphysics scheme that instantly removes moisture above certain threshold. This is equivalent to instanteneous conversion of cloud condensate into precipitation and precipitation fallout with infinite terminal velocity.

remove_precipitation(params_0M, q; q_vap_sat)

• params_0M - a struct with 0-moment parameters
• q - current PhasePartition
• q_vap_sat - water vapor specific humidity at saturation

Returns the q_tot tendency due to the removal of precipitation. The tendency is obtained assuming a relaxation with a constant timescale to a state with precipitable water removed. The threshold for when to remove q_tot is defined either by the condensate specific humidity or supersaturation. The thresholds and the relaxation timescale are defined in ClimaParams.

One-moment bulk microphysics scheme, which includes:

• terminal velocity of precipitation
• autoconversion of cloud liquid water into rain and of cloud ice into snow
• accretion due to collisions between categories of condensed species
• evaporation and sublimation of hydrometeors
• melting of snow into rain

get_v0(v, ρ)

• v - a struct with bulk 1-moment terminal velocity parameters
• ρ - air density (only for Rain)

Returns the proportionality coefficient in terminal velocity(r/r0).

get_n0(pdf, q_sno, ρ)

• pdf - a struct with parameters for snow, ice, and rain size distribution
• q_sno - snow specific humidity (only for Snow)
• ρ - air density (only for Snow)

Returns the intercept parameter of the assumed Marshall-Palmer distribution

lambda(pdf, mass, q, ρ)

• pdf, mass - structs with particle size distribution and mass parameters
• q - specific humidity of rain, ice or snow
• ρ - air density

Returns the rate parameter of the assumed size distribution of particles (rain drops, ice crystals, snow crystals).

radar_reflectivity(precip, q, ρ)

- `precip` - struct with rain free parameters
- `q` - specific humidity of rain
- `ρ` - air density

Returns logarithmic radar reflectivity from the assumed rain particle size distribution normalized by the reflectivty of 1 millimiter drop in a volume of one meter cube

terminal_velocity(precip, vel, ρ, q)

• precip - a struct with precipitation type (rain or snow)
• vel - a struct with terminal velocity parameters
• ρ - air density
• q - rain or snow specific humidity

Returns the mass weighted average terminal velocity assuming a Marshall-Palmer (1948) distribution of particles. Fall velocity of individual rain drops is parameterized:

• assuming an empirical power-law relations for velocity == Blk1MVelType
• following Chen et. al 2022, DOI: 10.1016/j.atmosres.2022.106171, for velocity == Chen2022VelType

conv_q_liq_to_q_rai(acnv, q_liq, smooth_transition)

• acnv - 1M autoconversion parameters
• q_liq - liquid water specific humidity
• smooth_transition - a flag to switch on smoothing

Returns the q_rai tendency due to collisions between cloud droplets (autoconversion), parametrized following Kessler (1995).

conv_q_ice_to_q_sno_no_supersat(acnv, q_ice, smooth_transition)

• acnv - 1M autoconversion parameters
• q_ice - cloud ice specific humidity
• smooth_transition - a flag to switch on smoothing

Returns the q_sno tendency due to autoconversion from ice. This is a simplified version of a snow autoconversion rate that can be used in simulations where there is no supersaturation (for example in TC.jl when using saturation adjustment).

conv_q_ice_to_q_sno(ice, aps, tps, q, ρ, T)

• ice - a struct with ice parameters
• aps - a struct with air properties
• tps - a struct with thermodynamics parameters
• q - phase partition
• ρ - air density
• T - air temperature

Returns the q_sno tendency due to autoconversion from ice. Parameterized following Harrington et al. (1996) and Kaul et al. (2015).

accretion(cloud, precip, vel, ce, q_clo, q_pre, ρ)

• cloud - type for cloud water or cloud ice
• precip - type for rain or snow
• vel - a struct with terminal velocity parameters
• ce - collision efficiency parameters
• q_clo - cloud water or cloud ice specific humidity
• q_pre - rain water or snow specific humidity
• ρ - rain water or snow specific humidity

Returns the source of precipitating water (rain or snow) due to collisions with cloud water (liquid or ice).

accretion_rain_sink(rain, ice, vel, ce, q_ice, q_rai, ρ)

• rain - rain type parameters
• ice - ice type parameters
• vel - terminal velocity parameters for rain
• ce - collision efficiency parameters
• q_ice - cloud ice specific humidity
• q_rai - rain water specific humidity
• ρ - air density

Returns the sink of rain water (partial source of snow) due to collisions with cloud ice.

accretion_snow_rain(ce, type_i, type_j, blk1m_type_i, blk1m_type_j, q_i, q_j, ρ)

• ce - collision efficiency parameters
• i - snow for temperatures below freezing or rain for temperatures above freezing
• j - rain for temperatures below freezing or snow for temperatures above freezing
• type_i, type_j - a type for snow or rain
• blk1mveltype_ti, blk1mveltype_tj - 1M terminal velocity parameters
• q_ - specific humidity of snow or rain
• ρ - air density

Returns the accretion rate between rain and snow. Collisions between rain and snow result in snow at temperatures below freezing and in rain at temperatures above freezing.

evaporation_sublimation(rain, vel, aps, tps, q, q_rai, ρ, T)
evaporation_sublimation(snow, vel, aps, tps, q, q_sno, ρ, T)

• rain - a struct with rain parameters
• snow - a struct with snow parameters
• vel - a struct with terminal velocity parameters
• aps - a struct with air parameters
• tps - a struct with thermodynamics parameters
• q - phase partition
• q_rai - rain specific humidity
• q_sno - snow specific humidity
• ρ - air density
• T - air temperature

Returns the tendency due to rain evaporation or snow sublimation.

snow_melt(snow, vel, aps, tps, q_sno, ρ, T)

• snow - snow parameters
• vel - terminal velocity parameters
• aps - air properties
• tps - thermodynamics parameters
• q_sno - snow water specific humidity
• ρ - air density
• T - air temperature

Returns the tendency due to snow melt.

Double-moment bulk microphysics parametrizations including:

• autoconversion, accretion, self-collection, breakup, mean terminal velocity of raindrops and rain evaporation rates from Seifert and Beheng 2006,
• additional double-moment bulk microphysics autoconversion and accretion rates from: Khairoutdinov and Kogan 2000, Beheng 1994, Tripoli and Cotton 1980, and Liu and Daum 2004.

A structure containing the rates of change of the specific humidities and number densities of liquid and rain water.

raindrops_limited_vars(pdf, q_rai, ρ, N_rai)

• pdf - a struct with SB2006 size distribution parameters
• q_rai - rain water specific humidity
• ρ - air density
• N_rai raindrops number density

Returns a named tupple containing the mean mass of raindrops, xr, and the rate parameter of the assumed size distribution of raindrops (based on drops diameter), λr, limited within prescribed ranges

autoconversion(scheme, q_liq, q_rai, ρ, N_liq)

• scheme - type for 2-moment rain autoconversion parameterization
• q_liq - cloud water specific humidity
• q_rai - rain water specific humidity
• ρ - air density
• N_liq - cloud droplet number density

Returns a LiqRaiRates object containing q_liq, N_liq, q_rai, N_rai tendencies due to collisions between cloud droplets (autoconversion) for scheme == SB2006Type

accretion(scheme, q_liq, q_rai, ρ, N_liq)

• scheme - type for 2-moment accretion parameterization
• q_liq - cloud water specific humidity
• q_rai - rain water specific humidity
• ρ - air density
• N_liq - cloud droplet number density

Returns a LiqRaiRates object containing q_liq, N_liq, q_rai, N_rai tendencies due to collisions between raindrops and cloud droplets (accretion) for scheme == SB2006Type

accretion(accretion_scheme, q_liq, q_rai, ρ)

• accretion_scheme - type for 2-moment rain accretion parameterization
• q_liq - cloud water specific humidity
• q_rai - rain water specific humidity
• ρ - air density (for KK2000Type and Beheng1994Type)

Returns the accretion rate of rain, parametrized following

• Khairoutdinov and Kogan (2000) for scheme == KK2000Type
• Beheng (1994) for scheme == B1994Type
• Tripoli and Cotton (1980) for scheme == TC1980Type

liquid_self_collection(scheme, q_liq, ρ, dN_liq_dt_au)

• scheme - type for 2-moment liquid self-collection parameterization
• q_liq - cloud water specific humidity
• ρ - air density
• dN_liq_dt_au - rate of change of cloud droplets number density due to autoconversion

Returns the cloud droplets number density tendency due to collisions of cloud droplets that produce larger cloud droplets (self-collection) for scheme == SB2006Type

autoconversion_and_liquid_self_collection(scheme, q_liq, q_rai, ρ, N_liq)

• scheme - type for 2-moment rain autoconversion parameterization
• q_liq - cloud water specific humidity
• q_rai - rain water specific humidity
• ρ - air density
• N_liq - cloud droplet number density

Returns a named tupple containing a LiqRaiRates object for the autoconversion rate and the liquid self-collection rate for scheme == SB2006Type

rain_self_collection(scheme, q_rai, ρ, N_rai)

• scheme - type for 2-moment rain self-collection parameterization
• q_rai - rain water specific humidity
• ρ - air density
• N_rai - raindrops number density

Returns the raindrops number density tendency due to collisions of raindrops that produce larger raindrops (self-collection) for scheme == SB2006Type

rain_breakup(scheme, q_rai, ρ, dN_rai_dt_sc)

• scheme - type for 2-moment liquid self-collection parameterization
• q_rai - rain water specific humidity
• ρ - air density
• N_rai - raindrops number density
• dN_rai_dt_sc - rate of change of raindrops number density due to self-collection

Returns the raindrops number density tendency due to breakup of raindrops that produce smaller raindrops for scheme == SB2006Type

rain_self_collection_and_breakup(SB2006, q_rai, ρ, N_rai)

• SB2006 - a struct with SB2006 parameters for size distribution self collection and breakup
• q_rai - rain water specific humidity
• ρ - air density
• N_rai - raindrops number density

Returns a named tupple containing the raindrops self-collection and breakup rates for scheme == SB2006Type

rain_terminal_velocity(SB2006, vel, q_rai, ρ, N_rai)

• SB2006 - a struct with SB2006 rain size distribution parameters
• vel - a struct with terminal velocity parameters
• q_rai - rain water specific humidity [kg/kg]
• ρ - air density [kg/m^3]
• N_rai - raindrops number density [1/m^3]

Returns a tuple containing the number and mass weigthed mean fall velocities of raindrops in [m/s]. Assuming an exponential size distribution from Seifert and Beheng 2006 for scheme == SB2006Type Fall velocity of individual rain drops is parameterized:

• assuming an empirical relation similar to Rogers (1993) for velo_scheme == SB2006VelType
• following Chen et. al 2022, DOI: 10.1016/j.atmosres.2022.106171 for velo_scheme == Chen2022Type

rain_evaporation(evap, aps, tps, q, q_rai, ρ, N_rai, T)

• evap - evaporation parameterization scheme
• aps - air properties
• tps - thermodynamics parameters
• q - phase partition
• q_rai - rain specific humidity
• ρ - air density
• N_rai - raindrops number density
• T - air temperature

Returns a tupple containing the tendency of raindrops number density and rain water specific humidity due to rain rain_evaporation, assuming a power law velocity relation for fall velocity of individual drops and an exponential size distribution, for scheme == SB2006Type

radar_reflectivity(struct, q_liq, q_rai, N_liq, N_rai, ρ_air, ρ_w)

- `struct` - type for 2-moment rain autoconversion parameterization
- `q_liq` - cloud water specific humidity 
- `q_rai` - rain water specific humidity
- `N_liq` - cloud droplet number density 
- `N_rai` - rain droplet number density 
- `ρ_air` - air density
- `ρ_w` - water density

Returns logarithmic radar reflectivity from the assumed cloud and rain particle size distribuions normalized by the reflectivty of 1 millimiter drop in a volume of one meter cube

effective_radius(struct, q_liq, q_rai, N_liq, N_rai, ρ_air, ρ_w)

- `struct` - type for 2-moment rain autoconversion parameterization
- `q_liq` - cloud water specific humidity 
- `q_rai` - rain water specific humidity
- `N_liq` - cloud droplet number density 
- `N_rai` - rain droplet number density 
- `ρ_air` - air density
- `ρ_w` - water density

Returns effective radius using the 2-moment scheme cloud and rain particle size distributions

effective_radius_Liu_Hallet_97(q_liq, q_rai, N_liq, N_rai, ρ_air, ρ_w)

- `q_liq` - cloud water specific humidity 
- `q_rai` - rain water specific humidity
- `N_liq` - cloud droplet number density 
- `N_rai` - rain droplet number density 
- `ρ_air` - air density
- `ρ_w` - water density

Returns effective radius using the "1/3" power law from Liu and Hallett (1997)

conv_q_liq_to_q_rai(acnv, q_liq, ρ, N_d; smooth_transition)

• acnv - 2-moment rain autoconversion parameterization
• q_liq - cloud water specific humidity
• ρ - air density
• N_d - prescribed cloud droplet number concentration

Returns the q_rai tendency due to collisions between cloud droplets (autoconversion), parametrized following:

• Khairoutdinov and Kogan (2000) for scheme == KK2000Type
• Beheng (1994) for scheme == B1994Type
• Tripoli and Cotton (1980) for scheme == TC1980Type
• Liu and Daum (2004) for scheme ==LD2004Type

The Beheng1994Type, TC1980Type and LD2004Type of schemes additionally accept smooth_transition flag that smoothes their thershold behaviour if set to true. The default value is false.

Flexible N-moment microphysics representation, including:

• Generalized collisional-coalescence described by a kernel K(x,y), with

default parameterization based on Long collision kernel

• Power-series representation of fall-speed
• Power-series representation of condensational growth

TODO: no representation of ventilation effects TODO: conversion back to Nrai, Nliq, qrai, qliq

A structure containing the subdistributions, their moments, and additional dynamical parameters corresponding to rates of collision, sedimentation, and condensation/evaporation

coalescence(clinfo)

• clinfo - kwarg structure containing pdists, moments, and coalescence parameters

TODO: currently implemented only for analytical coalescence style

Returns a vector of moment tendencies due to collisional coalescence

condensation(clinfo, aps, tps, q, ρ, T)

• clinfo - kwarg structure containing pdists, moments, and coalescence parameters
• aps - air properties
• tps - thermodynamics parameters
• q - phase partition
• ρ - air density
• T - air temperature

Returns a vector of moment tendencies due to condensation/evaporation

weighted_vt(clinfo)

• clinfo - kwarg structure containing pdists, moments, and coalescence parameters

Returns the moment-weighted terminal velocities corresponding to the rate of change of prognostic moments

Predicted particle properties scheme (P3) for ice, which includes:

• threshold solver
• shape parameters solver
• m(D) regime
• a(D) regime

Implementation of Morrison and Milbrandt 2015 doi: 10.1175/JAS-D-14-0065.1

Note: Particle size is defined as its maximum length (i.e. max dimesion).

thresholds(p3, ρ_r, F_r)

• p3 - a struct with P3 scheme parameters
• ρr - rime density (qrim/B_rim) [kg/m^3]
• Fr - rime mass fraction (qrim/q_i) [-]

Solves the nonlinear system consisting of Dcr, Dgr, ρg, ρd for a given rime density and rime mass fraction. Returns a named tuple containing:

• D_cr - is the threshold size separating partially rimed ice and graupel [m],
• D_gr - is the threshold size separating graupel and dense nonspherical ice [m],
• ρ_g - is the effective density of a spherical graupel particle [kg/m3],
• ρ_d - is the density of the unrimed portion of the particle [kg/m3],

distrbution_parameter_solver()

• p3 - a struct with P3 scheme parameters
• q - mass mixing ratio
• N - number mixing ratio
• ρr - rime density (qrim/B_rim) [kg/m^3]
• Fr - rime mass fraction (qrim/q_i)

Solves the nonlinear system consisting of N_0 and λ for P3 prognostic variables Returns a named tuple containing:

• N_0 - intercept size distribution parameter [1/m4]
• λ - slope size distribution parameter [1/m]

A container for information on aerosol size distribution
and chemical properties.

The size distribution is a sum of lognormal internally mixed modes.
The chemical composition can be expressed using kappa parameter
or hygroscopicity parameter B.

Mode_B

Represents the sizes and chemical composition of aerosol particles in one size distribution mode. The mode is assumed to be made up of internally mixed components and follow a lognormal size distribution. The chemical composition of aerosol particles in this mode is described using the parameters from Abdul-Razzak and Ghan 2000.

Mode_κ

Represents the sizes and chemical composition of aerosol particles in one size distribution mode. The mode is assumed to be made up of internally mixed components and follow a lognormal size distribution. The chemical composition of aerosol particles in this mode is described using the parameters from Petters and Kreidenweis 2007.

AerosolDistribution

Represents the aerosol size distribution as a tuple with different modes. All modes have to either be of type ModeB (Abdul-Razzak and Ghan 2000) or of type Modeκ (Petters and Kreidenweis 2007).

Constructors

AerosolDistribution(Modes::T)

Aerosol activation scheme, which includes:

• mean hygroscopicity for each mode of the aerosol size distribution
• critical supersaturation for each mode of the aerosol size distribution
• maximum supersaturation
• total number of particles actived
• total mass of particles actived

mean_hygroscopicity_parameter(ap, ad)

• ap - a struct with aerosol activation parameters
• ad - a struct with aerosol distribution (B or κ based)

Returns a tuple of hygroscopicity parameters (one tuple element for each aerosol size distribution mode). The tuple is computed either as mass-weighted B parameters (Abdul-Razzak and Ghan 2000) or volume weighted kappa parameters (Petters and Kreidenweis 2007). Implemented via a dispatch based on aerosol distribution mode type.

max_supersaturation(ap, ad, aip, tps, T, p, w, q)

• ap - a struct with aerosol activation parameters
• ad - a struct with aerosol distribution
• aip - a struct with air parameters
• tps - a struct with thermodynamics parameters
• T - air temperature
• p - air pressure
• w - vertical velocity
• q - phase partition

Returns the maximum supersaturation.

N_activated_per_mode(ap, ad, aip, tps, T, p, w, q)

• ap - a struct with aerosol activation parameters
• ad - aerosol distribution struct
• aip - a struct with air parameters
• tps - a struct with thermodynamics parameters
• T - air temperature
• p - air pressure
• w - vertical velocity
• q - phase partition

Returns the number of activated aerosol particles in each aerosol size distribution mode.

M_activated_per_mode(ap, ad, aip, tps, T, p, w, q)

• ap - a struct with aerosol activation parameters
• ad - a struct with aerosol distribution parameters
• aip - a struct with air parameters
• tps - a struct with thermodynamics parameters
• T - air temperature
• p - air pressure
• w - vertical velocity
• q - phase partition

Returns the mass of activated aerosol particles per mode of the aerosol size distribution.

total_N_activated(ap, ad, aip, tps, T, p, w, q)

• ap - a struct with aerosol activation parameters
• ad - aerosol distribution struct
• aip - a struct with air properties
• tps - a struct with thermodynamics parameters
• T - air temperature
• p - air pressure
• w - vertical velocity
• q - phase partition

Returns the total number of activated aerosol particles.

total_M_activated(ap, ad, aip, tps, T, p, w, q)

• ap - a struct with aerosol activation parameters
• ad - aerosol distribution struct
• aip - a struct with air properties
• tps - a struct with thermodynamics parameters
• T - air temperature
• p - air pressure
• w - vertical velocity
• q - phase partition

Returns the total mass of activated aerosol particles.

Parameterization for heterogenous ice nucleation.

dust_activated_number_fraction(dust, ip, Si, T)

• dust - a struct with dust parameters
• ip - a struct with ice nucleation parameters
• Si - ice saturation ratio
• T - air temperature [K]

Returns the number fraction of mineral dust particles acting as deposition nuclei (n ice nuclei / n dust particles). From Mohler et al 2006 Table 2 (averages from different measurements excluding those where a was not measured)

MohlerDepositionRate(dust, ip, S_i, T, dSi_dt, N_aer)

• dust - a struct with dust parameters
• ip - a struct with ice nucleation parameters
• Si - ice saturation
• T - ambient temperature
• dSi_dt - change in ice saturation over time
• N_aer - number of unactivated aerosols

Returns the ice nucleation rate from deposition. From Mohler et al 2006 equation 5.

deposition_J(dust, Δa_w)

• dust - a struct with dust parameters
• Δa_w - change in water activity [unitless].

Returns the deposition nucleation rate coefficient, J, in m^-2 s^-1 for different minerals in liquid droplets. The free parameters m and c are derived from China et al (2017) see DOI: 10.1002/2016JD025817

ABIFM_J(dust, Δa_w)

• dust - a struct with dust parameters
• Δa_w - change in water activity [unitless].

Returns the immersion freezing nucleation rate coefficient, J, in m^-2 s^-1 for different minerals in liquid droplets. The free parameters m and c are taken from Knopf & Alpert 2013 see DOI: 10.1039/C3FD00035D

P3_deposition_N_i(ip, T)

• ip - a struct with ice nucleation parameters,
• T - air temperature [K].

Returns the number of ice nucleated via deposition nucleation with units of m^-3. From Thompson et al 2004 eqn 2 as used in Morrison & Milbrandt 2015.

P3_het_N_i(ip, T, N_l, B, V_l, a, Δt)

• ip - a struct with ice nucleation parameters,
• T - air temperature [K],
• N_l - number of droplets [m^-3],
• B - water-type dependent parameter [cm^-3 s^-1],
• V_l - volume of droplets to be frozen [m^3],
• a - empirical parameter [C^-1],
• Δt - timestep.

Returns the number of ice nucleated within Δt via heterogeneous freezing with units of m^-3. From Pruppacher & Klett 1997 eqn (9-51) as used in Morrison & Milbrandt 2015.

INP_concentration_frequency(params,INPC,T)

• params - a struct with INPC(T) distribution parameters
• INPC - concentration of ice nucleating particles [m^-3]
• T - air temperature [K]

Returns the relative frequency of a given INP concentration, depending on the temperature. Based on Frostenberg et al., 2023. See DOI: 10.5194/acp-23-10883-2023

INP_concentration_mean(T)

• T - air temperature [K]

Returns the logarithm of mean INP concentration (in m^-3), depending on the temperature. Based on the function μ(T) in Frostenberg et al., 2023. See DOI: 10.5194/acp-23-10883-2023

Parameterization for homogeneous ice nucleation

homogeneous_J_cubic(ip, Δa_w)

• ip - a struct with ice nucleation parameters
• Δa_w - change in water activity [-].

Returns the homogeneous freezing nucleation rate coefficient, J, in m^-3 s^-1 for sulphuric acid solutions. Parameterization based on Koop 2000, DOI: 10.1038/35020537.

homogeneous_J_linear(ip, Δa_w)

• ip - a struct with ice nucleation parameters
• Δa_w - change in water activity [-].

Returns the homogeneous freezing nucleation rate coefficient, J, in m^-3 s^-1 for sulphuric acid solutions. Parameterization derived from a linear fit of the Koop 2000 parameterization, DOI: 10.1038/35020537.

Module for functions shared by different parameterizations.

G_func(air_props, tps, T, Liquid())
G_func(air_props, tps, T, Ice())

• air_props - struct with air parameters
• tps - struct with thermodynamics parameters
• T - air temperature
• Liquid(), Ice() - liquid or ice phase to dispatch over.

Utility function combining thermal conductivity and vapor diffusivity effects.

logistic_function(x, x_0, k)

• x - independent variable
• x_0 - threshold value for x
• k - growth rate of the curve, characterizing steepness of the transition

Returns the value of the logistic function for smooth transitioning at thresholds. This is a normalized curve changing from 0 to 1 while x varies from 0 to Inf (for positive k). For x < 0 the value at x = 0 (zero) is returned. For x_0 = 0 H(x) is returned.

logistic_function_integral(x, x_0, k)

• x - independent variable
• x_0 - threshold value for x
• k - growth rate of the logistic function, characterizing steepness of the transition

Returns the value of the indefinite integral of the logistic function, for smooth transitioning of piecewise linear profiles at thresholds. This curve smoothly transition from y = 0 for 0 < x < x0 to y = x - x0 for x_0 < x.

H2SO4_soln_saturation_vapor_pressure(prs, x, T)

• prs - a struct with H2SO4 solution free parameters
• x - wt percent sulphuric acid [unitless]
• T - air temperature [K].

Returns the saturation vapor pressure above a sulphuric acid solution droplet in Pa. x is, for example, 0.1 if droplets are 10 percent sulphuric acid by weight

a_w_xT(H2SO4_prs, tps, x, T)

• H2SO4_prs - a struct with H2SO4 solution free parameters
• tps - a struct with thermodynamics parameters
• x - wt percent sulphuric acid [unitless]
• T - air temperature [K].

Returns water activity of H2SO4 containing droplet. x is, for example, 0.1 if droplets are 10 percent sulphuric acid by weight.

a_w_eT(tps, e, T)

• tps - struct with thermodynamics parameters
• e - partial pressure of water [Pa]
• T - air temperature [K].

Returns water activity of pure water droplet. Valid when droplet is in equilibrium with surroundings.

a_w_ice(tps, T)

• tps - struct with thermodynamics parameters
• T - air temperature [K].

Returns water activity of ice.

Chen2022_vel_add(a, b, c, λ, k)

• a, b, c, - free parameters defined in Chen etl al 2022
• λ - size distribution parameter
• k - size distribution moment for which we compute the bulk fall speed

Returns the addends of the bulk fall speed of rain or ice particles following Chen et al 2022 DOI: 10.1016/j.atmosres.2022.106171 in [m/s]. We are assuming exponential size distribution and hence μ=0.

Chen2022_vel_coeffs_small(precip_type, velo_scheme, ρ)

• velo_scheme - type for terminal velocity scheme (contains free parameters)
• ρ - air density

Returns the coefficients from Appendix B in Chen et al 2022 DOI: 10.1016/j.atmosres.2022.106171

Chen2022_vel_coeffs_large(velo_scheme, ρ)

• velo_scheme - type for terminal velocity scheme (contains free parameters)
• ρ - air density

Returns the coefficients from Appendix B (table B4 for large particles) in Chen et al 2022 DOI: 10.1016/j.atmosres.2022.106171

Parameters

A module for CloudMicrophysics.jl free parameters.

ParametersType{FT}

The top-level super-type for all cloud microphysics parameters

AerosolType{FT}

The top-level super-type for all aerosol properties

AerosolDistributionType

The top-level super-type for all aerosol distribution types

CloudCondensateType{FT}

The top-level super-type for cloud condensate types (liquid and ice)

PrecipitationType{FT}

The top-level super-type for precipitation types (rain and snow)

TerminalVelocityType{FT}

The top-level super-type for terminal velocity parameterizations

Precipitation2MType

The top-level super-type for 2-moment precipitation parameterizations

AirProperties{FT}

Parameters with air properties.

Fields

• K_therm: thermal conductivity of air [w/m/K]

• D_vapor: diffusivity of water vapor [m2/s]

• ν_air: kinematic viscosity of air [m2/s]

WaterProperties{FT}

Parameters with water properties.

Fields

• ρw: density of liquid water [kg/m3]

• ρi: density of ice [kg/m3]

ArizonaTestDust{FT}

Parameters for Arizona Test Dust from Mohler et al, 2006. DOI: 10.5194/acp-6-3007-2006

Fields

• S₀_warm: S₀ for T > T_thr [-]

• S₀_cold: S₀ for T < T_thr [-]

• a_warm: a for T > T_thr [-]

• a_cold: a for T < T_thr [-]

DesertDust{FT}

Parameters for desert dust from Knopf and Alpert 2013 DOI: 10.1039/C3FD00035D and from Mohler et al, 2006 DOI: 10.5194/acp-6-3007-2006

Fields

• S₀_warm: S₀ for T > T_thr [-]

• S₀_cold: S₀ for T < T_thr [-]

• a_warm: a for T > T_thr [-]

• a_cold: a for T < T_thr [-]

• ABIFM_m: m coefficient for immersion freezing J [-]

• ABIFM_c: c coefficient for immersion freezing J [-]

Illite{FT}

Parameters for illite from Knopf and Alpert 2013 DOI: 10.1039/C3FD00035D

Fields

• ABIFM_m: m coefficient for immersion freezing J [-]

• ABIFM_c: c coefficient for immersion freezing J [-]

Kaolinite{FT}

Parameters for kaolinite from Knopf and Alpert 2013 DOI: 10.1039/C3FD00035D and China et al 2017 DOI: 10.1002/2016JD025817

Fields

• deposition_m: m coefficient for deposition nucleation J [-]

• deposition_c: c coefficient for deposition nucleation J [-]

• ABIFM_m: m coefficient for immersion freezing J [-]

• ABIFM_c: c coefficient for immersion freezing J [-]

Feldspar{FT}

Parameters for Feldspar from Alpert et al 2022 DOI: 10.1039/D1EA00077B

Fields

• deposition_m: m coefficient for deposition nucleation J [-]

• deposition_c: c coefficient for deposition nucleation J [-]

Ferrihydrite{FT}

Parameters for Ferrihydrite from Alpert et al 2022 DOI: 10.1039/D1EA00077B

Fields

• deposition_m: m coefficient for deposition nucleation J [-]

• deposition_c: c coefficient for deposition nucleation J [-]

Seasalt{FT}

Parameters for seasalt

Fields

• M: molar mass [kg/mol]

• ρ: density [kg/m3]

• ϕ: osmotic coefficient [-]

• ν: ion number [-]

• ϵ: water soluble mass fraction [-]

• κ: hygroscopicity parameter [-]

Sulfate{FT}

Parameters for sulfate aerosol

Fields

• M: molar mass [kg/mol]

• ρ: density [kg/m3]

• ϕ: osmotic coefficient [-]

• ν: ion number [-]

• ϵ: water soluble mass fraction [-]

• κ: hygroscopicity parameter [-]

AerosolActivationParameters{FT}

Parameters for Abdul-Razzak and Ghan 2000 aerosol activation scheme DOI: 10.1029/1999JD901161

Fields

• M_w: molar mass of water [kg/mol]

• R: gas constant [J/mol/K]

• ρ_w: cloud water density [kg/m3]

• σ: surface tension of water [N/m]

• g: gravitational_acceleration [m/s2]

• f1: scaling coefficient in Abdul-Razzak and Ghan 2000 [-]

• f2: scaling coefficient in Abdul-Razzak and Ghan 2000 [-]

• g1: scaling coefficient in Abdul-Razzak and Ghan 2000 [-]

• g2: scaling coefficient in Abdul-Razzak and Ghan 2000 [-]

• p1: power of (zeta / eta) in Abdul-Razzak and Ghan 2000 [-]

• p2: power of (S_m^2 / (zeta + 3 * eta)) in Abdul-Razzak and Ghan 2000 [-]

IceNucleationParameters{FT, DEP, HOM, P3_type}

Parameters for ice nucleation

Fields

• deposition

• homogeneous

• p3

Frostenberg2023{FT}

Parameters for frequency distribution of INP concentration DOI: 10.5194/acp-23-10883-2023

Fields

• σ: standard deviation

• a: coefficient

• b: coefficient

H2SO4SolutionParameters{FT}

Parameters for water activity of H2SO4 solutions from Luo et al 1995. DOI: 10.1029/94GL02988

Fields

• T_max: max temperature for which the parameterization is valid [K]

• T_min: min temperature for which the parameterization is valid [K]

• w_2: coefficient [-]

• c1: coefficient [-]

• c2: coefficient [-]

• c3: coefficient [-]

• c4: coefficient [-]

• c5: coefficient [-]

• c6: coefficient [-]

• c7: coefficient [-]

Mohler2006{FT}

Parameters for ice nucleation from Mohler et al 2006 DOI: 10.5194/acp-6-3007-2006

Fields

• Sᵢ_max: max allowed supersaturation [-]

• T_thr: threshold temperature [K]

Koop2000{FT}

Parameters for ice nucleation from Koop et al 2000 DOI: 10.1038/35020537

Fields

• Δa_w_min: min Δaw [-]

• Δa_w_max: max Δaw [-]

• c₁: coefficient [-]

• c₂: coefficient [-]

• c₃: coefficient [-]

• c₄: coefficient [-]

• linear_c₁: coefficient [-]

• linear_c₂: coefficient [-]

H2S04NucleationParameters{FT}

Parameters for pure sulfuric acid nucleation from Dunne et al 1016 DOI:10.1126/science.aaf2649

Fields

• p_b_n

• p_b_i

• u_b_n

• u_b_i

• v_b_n

• v_b_i

• w_b_n

• w_b_i

• p_t_n

• p_t_i

• u_t_n

• u_t_i

• v_t_n

• v_t_i

• w_t_n

• w_t_i

• p_A_n

• p_A_i

• a_n

• a_i

OrganicNucleationParameters{FT}

Parameters for pure organic nucleation from Kirkby 2016 DOI: 10.1038/nature17953

Fields

• a_1

• a_2

• a_3

• a_4

• a_5

• Y_MTO3

• Y_MTOH

• k_MTO3

• k_MTOH

• exp_MTO3

• exp_MTOH

MixedNucleationParameters{FT}

Parameters for mixed organic and sulfuric acid nucleation from Riccobono et al 2014 DOI:10.1126/science.1243527

Fields

• k_H2SO4org

• k_MTOH

• exp_MTOH

Parameters0M{FT}

Parameters for zero-moment bulk microphysics scheme

Fields

• τ_precip: precipitation timescale [s]

• qc_0: specific humidity precipitation threshold [-]

• S_0: supersaturation precipitation threshold [-]

ParticlePDFSnow{FT}

A struct with snow size distribution parameters

Fields

• μ: snow size distribution coefficient [1/m4]

• ν: snow size distribution coefficient [-]

ParticlePDFIceRain{FT}

A struct with snow size distribution parameters

Fields

• n0: snow size distribution coefficient [1/m4]

ParticleMass{FT}

A struct with coefficients of the assumed mass(size) relationship for particles

m(r) = m0 χm (r/r0)^(me + Δm)

Fields

• r0: particle length scale [m]

• m0: mass size relation coefficient [kg]

• me: mass size relation coefficient [-]

• Δm: mass size relation coefficient [-]

• χm: mass size relation coefficient [-]

ParticleArea{FT}

A struct with coefficients of the assumed crosssectionarea(size) relationship for particles

a(r) = a0 χa (r/r0)^(ae + Δa)

Fields

• a0: cross section size relation coefficient [m2]

• ae: cross section size relation coefficient [-]

• Δa: cross section size relation coefficient [-]

• χa: cross section size relation coefficient [-]

Ventilation{FT}

A struct with ventilation coefficients

Fields

• a: ventilation coefficient a [-]

• b: ventilation coefficient b [-]

Acnv1M{FT}

A struct with autoconversion parameters

Fields

• τ: autoconversion timescale [s]

• q_threshold: specific humidity autoconversion threshold [-]

• k: threshold smooth transition steepness [-]

CloudLiquid{FT}

The parameters and type for cloud liquid water condensate

Fields

• τ_relax: condensation evaporation non_equil microphysics relaxation timescale [s]

CloudIce{FT, MS}

The parameters and type for cloud ice condensate

Fields

• pdf: a struct with size distribution parameters

• mass: a struct with mass size relation parameters

• r0: particle length scale [m]

• r_ice_snow: ice snow threshold radius [m]

• τ_relax: deposition sublimation non_equil microphysics relaxation timescale [s]

Rain{FT, MS, AR, VT, AC}

The parameters and type for rain

Fields

• pdf: a struct with size distribution parameters

• mass: a struct with mass size relation parameters

• area: a struct with cross section size relation parameers

• vent: a struct with ventilation coefficients

• acnv1M: a struct with cloud water to rain autoconversion parameters

• r0: particle length scale [m]

Snow{FT, PD, MS, AR, VT, AC}

The parameters and type for snow

Fields

• pdf: a struct with size distribution parameters

• mass: a struct with mass size relation parameters

• area: a struct with cross section size relation parameers

• vent: a struct with ventilation coefficients

• acnv1M: a struct with ice to snow autoconversion parameters

• r0: particle length scale [m]

• T_freeze: freezing temperature of water [K]

• ρᵢ: ice density [kg/m3]

CollisionEff{FT}

Collision efficiency parameters for the 1-moment scheme

Fields

• e_liq_rai: cloud liquid-rain collision efficiency [-]

• e_liq_sno: cloud liquid-snow collision efficiency [-]

• e_ice_rai: cloud ice-rain collision efficiency [-]

• e_ice_sno: cloud ice-snow collision efficiency [-]

• e_rai_sno: rain-snow collision efficiency [-]

KK2000

The type and parameters for 2-moment precipitation formation by Khairoutdinov and Kogan (2000)

DOI:10.1175/1520-0493(2000)128<0229:ANCPPI>2.0.CO;2

Fields

• acnv: Autoconversion parameters

• accr: Accretion parameters

AcnvKK2000

Khairoutdinov and Kogan (2000) autoconversion parameters

Fields

• A: Autoconversion coefficient A

• a: Autoconversion coefficient a

• b: Autoconversion coefficient b

• c: Autoconversion coefficient c

AccrKK2000

Khairoutdinov and Kogan (2000) accretion parameters

Fields

• A: Accretion coefficient A

• a: Accretion coefficient a

• b: Accretion coefficient b

B1994

The type and parameter for 2-moment precipitation formation by Beheng (1994) DOI: 10.1016/0169-8095(94)90020-5

Fields

• acnv: Autoconversion coeff C

• accr: Autoconversion coeff a

AcnvB1994

Beheng (1994) autoconversion parameters

Fields

• C: Autoconversion coeff C

• a: Autoconversion coeff a

• b: Autoconversion coeff b

• c: Autoconversion coeff c

• N_0: Autoconversion coeff N_0

• d_low: Autoconversion coeff d_low

• d_high: Autoconversion coeff d_high

• k: Threshold for smooth tranistion steepness

AccrB1994

Beheng (1994) accretion parameters

Fields

• A: Accretion coefficient A

TC1980

The type and parameters for 2-moment precipitation formation by Tripoli and Cotton (1980)

DOI: 10.1175/1520-0450(1980)019<1037:ANIOSF>2.0.CO;2

Fields

• acnv: Autoconversion parameters

• accr: Accretion parameters

AcnvTC1980

Tripoli and Cotton (1980) autoconversion parameters

Fields

• a: Autoconversion coefficient a

• b: Autoconversion coefficient b

• D: Autoconversion coefficient D

• r_0: Autoconversion coefficient r_0

• me_liq: Autoconversion coefficient me_liq

• m0_liq_coeff: Autoconversion coefficient m0liqcoeff

• k: Threshold for smooth tranistion steepness

AccrTC1980

Tripoli and Cotton (1980) accretion parameters

Fields

• A: Accretion coefficient A

LD2004

The type and parameters for 2-moment precipitation formation by Liu and Daum (2004)

DOI: 10.1175/1520-0469(2004)061<1539:POTAPI>2.0.CO;2

Fields

• R_6C_0: Autoconversion coefficient R6C0

• E_0: Autoconversion coefficient E_0

• ρ_w: liquid water density [kg/m3]

• k: Threshold for smooth tranistion steepness

VarTimescaleAcnv

The type for 2-moment precipitation formation based on the 1-moment parameterization with variable time scale Azimi et al (2023)

Fields

• τ: Timescale [s]

• α: Powerlaw coefficient [-]

SB2006

The type and parameters for 2-moment precipitation formation by Seifert and Beheng (2006)

DOI: 10.1007/s00703-005-0112-4

Fields

• pdf: Rain particle size distribution parameters

• acnv: Autoconversion parameters

• accr: Accretion parameters

• self: Rain selfcollection parameters

• brek: Rain breakup parameters

• evap: Rain evaporation parameters

ParticlePDF_SB2006

Rain size distribution parameters from SB2006

Fields

• xr_min: Raindrop minimal mass

• xr_max: Raindrop maximum mass

• N0_min: Raindrop size distribution coefficient N0 min

• N0_max: Raindrop size distribution coefficient N0 max

• λ_min: Raindrop size distribution coefficient lambda min

• λ_max: Raindrop size distribution coefficient lambda max

• ρw: Cloud liquid water density [kg/m3]

• ρ0: Reference air density [kg/m3]

AcnvSB2006

Autoconversion parameters from SB2006

Fields

• kcc: Collection kernel coefficient

• νc: Cloud gamma distribution coefficient

• x_star: Minimum mass of rain droplets

• ρ0: Reference air density [kg/m3]

• A: Autoconversion correcting function coeff A

• a: Autoconversion correcting function coeff a

• b: Autoconversion correcting function coeff b

AccrSB2006

Accretion parameters from SB2006

Fields

• kcr: Collection kernel coefficient Kcr

• τ0: Accretion correcting function coefficient τ_0

• ρ0: Reference air density [kg/m3]

• c: Accretion correcting function coefficient c

SelfColSB2006

Rain selfcollection parameters from SB2006

Fields

• krr: Collection kernel coefficient krr

• κrr: Collection kernel coefficient kappa rr

• d: Raindrop self collection coefficient d

BreakupSB2006

Rain breakup parameters from SB2006

Fields

• Deq: Raindrop equilibrium mean diamater

• Dr_th: Raindrop breakup mean diamater threshold

• kbr: Raindrops breakup coefficient kbr

• κbr: Raindrops breakup coefficient kappa br

EvaporationSB2006

Rain evaporation parameters from SB2006

Fields

• av: Ventillation coefficient a

• bv: Ventillation coefficient b

• α: Rain evapoartion coefficient α

• β: Rain evapoartion coefficient β

• ρ0: Reference air density [kg/m3]

ParametersP3{FT}

Parameters for P3 bulk microphysics scheme from Morrison and Milbrandt 2015 doi: 10.1175/JAS-D-14-0065.1

Fields

• α_va: Coefficient in mass(size) relation [g/μm^β_va]

• β_va: Coefficient in mass(size) relation [-]

• ρ_i: Cloud ice density [kg/m3]

• ρ_l: Cloud liquid water density [kg/m3]

• γ: Coefficient in area(size) for ice side plane, column, bullet, and planar polycrystal aggregates from Mitchell 1996 [μm^(2-σ)]

• σ: Coefficient in area(size) for ice side plane, column, bullet, and planar polycrystal aggregates from Mitchell 1996 [-]

• a: Coefficient for shape parameter mu for ice. See eq 3 in Morrison and Milbrandt 2015. Units: [m^0.8]

• b: Coefficient for shape parameter mu for ice. See eq 3 in Morrison and Milbrandt 2015. Units: [-]

• c: Coefficient for shape parameter mu for ice. See eq 3 in Morrison and Milbrandt 2015. Units: [-]

• μ_max: Limiter for shape parameter mu for ice. See eq 3 in Morrison and Milbrandt 2015. Units: [-]

Blk1MVelType

The type for precipitation terminal velocity from the simple 1-moment scheme (defined for rain and snow)

Fields

• rain

• snow

Blk1MVelTypeRain

The type for precipitation terminal velocity from the simple 1-moment scheme for rain

Fields

• r0: particle length scale [m]

• ve: rain terminal velocity size relation coefficient [-]

• Δv: rain terminal velocity size relation coefficient [-]

• χv: rain terminal velocity size relation coefficient [-]

• ρw: cloud water density [kg/m3]

• C_drag: rain drop drag coefficient [-]

• grav: gravitational acceleration [m/s2]

Blk1MVelTypeSnow

The type for precipitation terminal velocity from the simple 1-moment scheme for snow

Fields

• r0: particle length scale [m]

• ve: snow terminal velocity size relation coefficient [-]

• Δv: snow terminal velocity size relation coefficient [-]

• χv: snow terminal velocity size relation coefficient [-]

• v0: snow terminal velocity size relation coefficient [m/s]

SB2006VelType

The type for precipitation terminal velocity from Seifert and Beheng 2006 (Defined only for rain)

Fields

• ρ0

• aR

• bR

• cR

Chen2022VelType

The type for precipitation terminal velocity from Chen et al 2022 DOI: 10.1016/j.atmosres.2022.106171 (defied for rain, snow and cloud ice)

Fields

• rain

• snow_ice

Chen2022VelTypeSnowIce

The type for precipitation terminal velocity from Chen et al 2022 for snow and ice. See Table B3 for parameter definitions. DOI: 10.1016/j.atmosres.2022.106171

Fields

• As

• Bs

• Cs

• Es

• Fs

• Gs

• Al

• Bl

• Cl

• El

• Fl

• Gl

• Hl

• ρᵢ: density of cloud ice [kg/m3]

Chen2022VelTypeRain

The type for precipitation terminal velocity from Chen et al 2022 for rain. See Table B1 for parameter definitions. DOI: 10.1016/j.atmosres.2022.106171

Fields

• ρ0

• a

• a3_pow

• b

• b_ρ

• c

precipitation_susceptibility_autoconversion(param_set, scheme, q_liq, q_rai, ρ, N_liq)

• scheme - type for 2-moment rain autoconversion parameterization
• q_liq - cloud water specific humidity
• q_rai - rain water specific humidity
• ρ - air density
• N_liq - cloud droplet number density

Returns the precipitation susceptibility rates due to autoconversion as a precip_susceptibility_rates object, using automatic differentiation. Works for any 2-moment scheme, as long as autoconversion is defined for it.

precipitation_susceptibility_accretion(param_set, scheme, q_liq, q_rai, ρ, N_liq)

• scheme - type for 2-moment rain autoconversion parameterization
• q_liq - cloud water specific humidity
• q_rai - rain water specific humidity
• ρ - air density
• N_liq - cloud droplet number density

Returns the precipitation susceptibility rates due to accretion as a precip_susceptibility_rates object, using automatic differentiation. Works for any 2-moment scheme, as long as accretion is defined for it.