WSM6Parameters

Scheme constants of the WRF single-moment 6-class microphysics scheme (WSM6), transcribed from the `parameter` declarations, the mp_wsm6_init products and the in-line literals of phys/physics_mmm/mp_wsm6.F90 (WRF 4.8, NCAR/MMM-physics CCPP kernel mp_wsm6_run). Mounted by the WSM6 components as subsystem `par` so that no tuning constant is written inline in the physics. Values are the nominal (decimal) values of the Fortran source; the two Gamma-function constants are the values WSM6 itself computes with its `rgmma` routine (a Weierstrass product truncated after 10000 factors), which differ from the exact Gamma function by about 7e-4 (recorded in EqWeFiC FORTRAN_BUGS.md) -- the scheme's effective constants are the rgmma values, so those are what the tests reproduce. NOTE (also in EqWeFiC FORTRAN_BUGS.md): the kernel declares its constants real(kind_phys) but initialises them from default-real literals, so a real64 build runs with single-precision roundings (bvtr = 0.800000011920929, avtr = 841.9000244); the WSM6 tests document the resulting O(1e-7) relative mismatch in their tolerances rather than reproducing the rounding here. EqWeFiC, cited here for FORTRAN_BUGS.md and couplings/, is https://github.com/EarthSciML/EqWeFiC, where these components were developed and are coupled into a WRF column.

Domain: atmospheric_dynamics
Subdomain: wsm6
Type: model
.esm schema: 1.0.0
Source: components/atmospheric_dynamics/wsm6/wsm6_parameters.esm
Tags: #atmospheric_dynamics #wsm6 #model #wrf #microphysics #scheme-constants

Description

Scheme constants of the WRF single-moment 6-class microphysics scheme (WSM6), transcribed from the parameter declarations, the mp_wsm6_init products and the in-line literals of phys/physics_mmm/mp_wsm6.F90 (WRF 4.8, NCAR/MMM-physics CCPP kernel mp_wsm6_run). Mounted by the WSM6 components as subsystem par so that no tuning constant is written inline in the physics. Values are the nominal (decimal) values of the Fortran source; the two Gamma-function constants are the values WSM6 itself computes with its rgmma routine (a Weierstrass product truncated after 10000 factors), which differ from the exact Gamma function by about 7e-4 (recorded in EqWeFiC FORTRAN_BUGS.md) – the scheme’s effective constants are the rgmma values, so those are what the tests reproduce. NOTE (also in EqWeFiC FORTRAN_BUGS.md): the kernel declares its constants real(kind_phys) but initialises them from default-real literals, so a real64 build runs with single-precision roundings (bvtr = 0.800000011920929, avtr = 841.9000244); the WSM6 tests document the resulting O(1e-7) relative mismatch in their tolerances rather than reproducing the rounding here. EqWeFiC, cited here for FORTRAN_BUGS.md and couplings/, is https://github.com/EarthSciML/EqWeFiC , where these components were developed and are coupled into a WRF column.

Reference

Hong, S.-Y., and J.-O. J. Lim (2006). The WRF single-moment 6-class microphysics scheme (WSM6). J. Korean Meteor. Soc. 42, 129-151.
Hong, S.-Y., J. Dudhia, and S.-H. Chen (2004). A revised approach to ice microphysical processes for the bulk parameterization of clouds and precipitation. Mon. Wea. Rev. 132, 103-120.
NCAR/MMM-physics mp_wsm6.F90 at commit 550b5b4 (WRF 4.8 phys/physics_mmm submodule).

Parameters

Name	Units	Default	Description
`n0r`	`1/m^4`	`8000000.0`	Intercept parameter of the Marshall-Palmer raindrop size distribution N(D) = n0r exp(-lambda D).
`avtr`	`m^(1/5)/s`	`841.9`	Coefficient a of the raindrop terminal velocity V(D) = a D^b (units m^(1-bvtr)/s).
`bvtr`	`1`	`0.8`	Exponent b of the raindrop terminal velocity V(D) = a D^b.
`r0`	`m`	`8e-06`	Critical cloud-droplet radius of the autoconversion threshold (8 micrometres).
`peaut`	`1`	`0.55`	Collection efficiency of the autoconversion rate coefficient.
`xncr`	`1/m^3`	`300000000.0`	Prescribed cloud-droplet number concentration (maritime value 3e8 m^-3).
`xmyu`	`kg/(m*s)`	`1.718e-05`	Dynamic viscosity of air used by the autoconversion rate coefficient.
`lamdarmax`	`1/m`	`80000.0`	Upper bound of the rain slope parameter lambda; below the rain threshold qcrmin the inverse slope is held at 1/lamdarmax.
`qcrmin`	`kg/kg`	`1e-09`	Minimum rain, snow and graupel mixing ratio for which a size distribution is evaluated.
`qmin`	`kg/kg`	`1e-15`	Floor on mixing ratios and saturation quantities (the kernel argument qmin, WRF epsilon).
`q_delta`	`kg/kg`	`0.0001`	Rain/snow partition threshold of the mass-conservation block: where rain (delta3) or both rain and snow (delta2) are below it, the ice-rain and rain-snow collection products are given to snow instead of graupel (WSM6’s unnamed literal 1.e-4 in ‘check mass conservation of generation terms’).
`eacrr`	`1`	`1.0`	Collection efficiency of cloud water by rain.
`g3pbr`	`1`	`4.690786833363863`	Gamma(3 + bvtr) as WSM6 evaluates it with rgmma (exact Gamma(3.8) = 4.694174205740421); enters the accretion coefficient pacrr.
`g5pbro2`	`1`	`1.8265869519788835`	Gamma(2.5 + bvtr/2) as WSM6 evaluates it with rgmma (exact Gamma(2.9) = 1.8273550806240353); enters the ventilation coefficient precr2.
`autoconv_coef`	`1`	`0.104`	Dimensionless coefficient of the autoconversion rate constant qck1 (the literal .104 in mp_wsm6_init).
`g_autoconv`	`m/s^2`	`9.8`	Gravitational acceleration hard-wired into the autoconversion rate constant qck1 (the literal 9.8, not WRF’s g = 9.81).
`vent_a`	`1`	`0.78`	Ventilation coefficient a of the rain evaporation rate f_v = a + b Sc^(1/3) Re^(1/2) (the literal .78 in precr1).
`vent_b`	`1`	`0.31`	Ventilation coefficient b of the rain evaporation rate (the literal .31 in precr2).
`es_cap`	`1`	`0.99`	The saturation vapor pressure is capped at es_cap times the pressure (the literal 0.99 p).
`ttp_offset`	`K`	`0.01`	Triple-point temperature offset above 0 C, ttp = t0c + 0.01 K.
`diffus_coef`	`m^2Pa/(sK^(181/100))`	`8.794e-05`	Coefficient of the water-vapor diffusivity Dv = diffus_coef T^diffus_exp / p.
`diffus_exp`	`1`	`1.81`	Temperature exponent of the water-vapor diffusivity.
`viscos_coef`	`kg/(msK^(1/2))`	`1.496e-06`	Coefficient of Sutherland’s law for the kinematic viscosity nu = viscos_coef T^(3/2) / (T + sutherland_T) / rho.
`sutherland_T`	`K`	`120.0`	Sutherland temperature of the air viscosity law.
`xka_coef`	`J/(kg*K)`	`1414.0`	Thermal conductivity of air as ka = xka_coef nu rho (the literal 1.414e3).
`dtcldcr`	`s`	`120.0`	Maximum length of a WSM6 minor (sub-)time step; the model step is split into ceil(delt/dtcldcr) sub-steps of dtcld.
`n0s`	`1/m^4`	`2000000.0`	Intercept parameter of the snow size distribution at 0 C; multiplied by the temperature factor snow_intercept_factor below freezing (HDC 2004 eq. 6).
`n0smax`	`1/m^4`	`100000000000.0`	Upper bound of the temperature-dependent snow intercept n0s(T) (reached near -90 C).
`alpha_n0s`	`1/K`	`0.12`	Exponential coefficient of the snow intercept temperature dependence, n0s(T) = n0s exp(alpha (T0 - T)) (the literal .12; the code comment gives .122).
`n0g`	`1/m^4`	`4000000.0`	Intercept parameter of the graupel size distribution (graupel-like setting, hail_opt = 0).
`avts`	`m^(59/100)/s`	`11.72`	Coefficient a of the snow terminal velocity V(D) = a D^b (units m^(1-bvts)/s).
`bvts`	`1`	`0.41`	Exponent b of the snow terminal velocity.
`avtg`	`m^(1/5)/s`	`330.0`	Coefficient a of the graupel terminal velocity (graupel-like setting; hail_opt = 1 uses 285).
`bvtg`	`1`	`0.8`	Exponent b of the graupel terminal velocity (equal to bvtr, so the graupel Gamma-function constants equal the rain ones).
`dens`	`kg/m^3`	`100.0`	Bulk density of snow particles (WSM6 dens).
`deng`	`kg/m^3`	`500.0`	Bulk density of graupel particles (graupel-like setting; hail_opt = 1 uses 700).
`lamdasmax`	`1/m`	`100000.0`	Upper bound of the snow slope parameter; below qcrmin the inverse slope is held at 1/lamdasmax.
`lamdagmax`	`1/m`	`60000.0`	Upper bound of the graupel slope parameter (graupel-like setting; hail_opt = 1 uses 2e4).
`dicon`	`m/kg^(1/2)`	`11.9`	Coefficient of the ice crystal diameter-mass relation D_i = dicon sqrt(m_i) (HDC 2004 eq. 5b).
`dimax`	`m`	`0.0005`	Upper bound of the ice crystal diameter (500 micrometres).
`dimin_fallout`	`m`	`1e-25`	Lower bound of the ice crystal diameter in the fallout speed only (the kernel’s max(…, 1.e-25) in the Vice block); the cold-rain diameter has no floor.
`xni_coef`	`1/(kg^(3/4)*m^(3/4))`	`53800000.0`	Coefficient of the ice number concentration N_i = 5.38e7 (rho q_i)^0.75 (HDC 2004 eq. 5c).
`xni_min`	`1/m^3`	`1000.0`	Lower bound of the diagnosed ice number concentration.
`xni_max`	`1/m^3`	`1000000.0`	Upper bound of the diagnosed ice number concentration.
`vt_ice_coef`	`1/(m^(31/100)*s)`	`14900.0`	Coefficient of the ice crystal fall speed V_i = 1.49e4 D^1.31 (HDC 2004 eq. 5a).
`vt_ice_exp`	`1`	`1.31`	Exponent of the ice crystal fall speed power law.
`eacrs_coef`	`1/K`	`0.07`	Temperature coefficient of the snow/graupel-ice collection efficiency E = exp(-0.07 (T0 - T)) (the literals 0.07 in eacrs and egi).
`wilt_exp`	`1`	`2.0`	Exponent of the collection-efficiency reduction min(max(0, q_collector/q_collected), 1)^2 (‘suggested by B. Wilt’).
`qs0`	`kg/kg`	`0.0006`	Snow mixing-ratio threshold of the snow-to-graupel autoconversion (WSM6 qs0).
`pgaut_coef`	`1/s`	`0.001`	Rate coefficient of the snow-to-graupel autoconversion alpha2 = 1e-3 exp(-0.09 (T0 - T)).
`pgaut_exp`	`1/K`	`0.09`	Temperature coefficient of the snow-to-graupel autoconversion.
`eacrc`	`1`	`1.0`	Collection efficiency of cloud water by snow (WSM6 eacrc, enters pacrc).
`vent_a_snow`	`1`	`0.65`	Ventilation coefficient a of snow deposition/melting, precs1 = 4 n0s a (the literal .65).
`vent_b_snow`	`1`	`0.44`	Ventilation coefficient b of snow deposition/melting, precs2 = 4 n0s b sqrt(avts) Gamma(2.5 + bvts/2) (the literal .44).
`xni0_coef`	`1/m^3`	`1000.0`	Ice-nuclei concentration at 0 C in the nucleation target N_i0 = 1e3 exp(0.1 (T0 - T)) (HDC 2004 eq. 7).
`xni0_exp`	`1/K`	`0.1`	Temperature coefficient of the ice-nuclei concentration.
`roqi0_coef`	`kg*m^(99/100)`	`4.92e-11`	Coefficient of the initial ice content rho q_i0 = 4.92e-11 N_i0^1.33 (HDC 2004 eq. 8).
`roqi0_exp`	`1`	`1.33`	Exponent of the initial ice content relation.
`roqimax_coef`	`kg/m^11`	`2.08e+22`	Coefficient of the maximum ice content rho q_imax = 2.08e22 dimax^8 above which ice aggregates to snow (HDC 2004 eq. 13).
`roqimax_exp`	`1`	`8.0`	Exponent of the maximum ice content relation.
`pfrz1`	`1/(m^3*s)`	`100.0`	Bigg (1953) freezing constant B’ (WSM6 pfrz1).
`pfrz2`	`1/K`	`0.66`	Bigg (1953) freezing constant B (WSM6 pfrz2).
`supcol_max`	`K`	`50.0`	Cap on the supercooling entering the Bigg freezing exponentials (the literal 50. in supcolt).
`supcol_homog`	`K`	`40.0`	Supercooling beyond which all cloud water freezes homogeneously (the literal 40. of pihmf).
`pgfrz_coef`	`1`	`20.0`	Numerical coefficient of the rain freezing rate 20 pi^2 B’ n0r … (LFO 1983 eq. 45).
`g3pbs`	`1`	`3.0115638223109507`	Gamma(3 + bvts) as WSM6 evaluates it with rgmma; enters pacrs and pacrc.
`g4pbs`	`1`	`10.265419060185165`	Gamma(4 + bvts) as WSM6 evaluates it with rgmma; enters the snow fall-speed constant pvts.
`g5pbso2`	`1`	`1.5502934809754454`	Gamma(2.5 + bvts/2) as WSM6 evaluates it with rgmma; enters precs2.
`g4pbr`	`1`	`17.817328905833126`	Gamma(4 + bvtr) as WSM6 evaluates it with rgmma (exact 17.837825 per the code comment); enters pvtr and, because bvtg = bvtr, pvtg.
`g6pbr`	`1`	`495.45956737138556`	Gamma(6 + bvtr) as WSM6 evaluates it with rgmma; enters piacr.

Raw .esm

Raw .esm JSON (this component)

{
  "variables": {
    "n0r": {
      "type": "parameter",
      "units": "1/m^4",
      "default": 8000000.0,
      "description": "Intercept parameter of the Marshall-Palmer raindrop size distribution N(D) = n0r exp(-lambda D)."
    },
    "avtr": {
      "type": "parameter",
      "units": "m^(1/5)/s",
      "default": 841.9,
      "description": "Coefficient a of the raindrop terminal velocity V(D) = a D^b (units m^(1-bvtr)/s)."
    },
    "bvtr": {
      "type": "parameter",
      "units": "1",
      "default": 0.8,
      "description": "Exponent b of the raindrop terminal velocity V(D) = a D^b."
    },
    "r0": {
      "type": "parameter",
      "units": "m",
      "default": 8e-06,
      "description": "Critical cloud-droplet radius of the autoconversion threshold (8 micrometres)."
    },
    "peaut": {
      "type": "parameter",
      "units": "1",
      "default": 0.55,
      "description": "Collection efficiency of the autoconversion rate coefficient."
    },
    "xncr": {
      "type": "parameter",
      "units": "1/m^3",
      "default": 300000000.0,
      "description": "Prescribed cloud-droplet number concentration (maritime value 3e8 m^-3)."
    },
    "xmyu": {
      "type": "parameter",
      "units": "kg/(m*s)",
      "default": 1.718e-05,
      "description": "Dynamic viscosity of air used by the autoconversion rate coefficient."
    },
    "lamdarmax": {
      "type": "parameter",
      "units": "1/m",
      "default": 80000.0,
      "description": "Upper bound of the rain slope parameter lambda; below the rain threshold qcrmin the inverse slope is held at 1/lamdarmax."
    },
    "qcrmin": {
      "type": "parameter",
      "units": "kg/kg",
      "default": 1e-09,
      "description": "Minimum rain, snow and graupel mixing ratio for which a size distribution is evaluated."
    },
    "qmin": {
      "type": "parameter",
      "units": "kg/kg",
      "default": 1e-15,
      "description": "Floor on mixing ratios and saturation quantities (the kernel argument qmin, WRF epsilon)."
    },
    "q_delta": {
      "type": "parameter",
      "units": "kg/kg",
      "default": 0.0001,
      "description": "Rain/snow partition threshold of the mass-conservation block: where rain (delta3) or both rain and snow (delta2) are below it, the ice-rain and rain-snow collection products are given to snow instead of graupel (WSM6's unnamed literal 1.e-4 in 'check mass conservation of generation terms')."
    },
    "eacrr": {
      "type": "parameter",
      "units": "1",
      "default": 1.0,
      "description": "Collection efficiency of cloud water by rain."
    },
    "g3pbr": {
      "type": "parameter",
      "units": "1",
      "default": 4.690786833363863,
      "description": "Gamma(3 + bvtr) as WSM6 evaluates it with rgmma (exact Gamma(3.8) = 4.694174205740421); enters the accretion coefficient pacrr."
    },
    "g5pbro2": {
      "type": "parameter",
      "units": "1",
      "default": 1.8265869519788835,
      "description": "Gamma(2.5 + bvtr/2) as WSM6 evaluates it with rgmma (exact Gamma(2.9) = 1.8273550806240353); enters the ventilation coefficient precr2."
    },
    "autoconv_coef": {
      "type": "parameter",
      "units": "1",
      "default": 0.104,
      "description": "Dimensionless coefficient of the autoconversion rate constant qck1 (the literal .104 in mp_wsm6_init)."
    },
    "g_autoconv": {
      "type": "parameter",
      "units": "m/s^2",
      "default": 9.8,
      "description": "Gravitational acceleration hard-wired into the autoconversion rate constant qck1 (the literal 9.8, not WRF's g = 9.81)."
    },
    "vent_a": {
      "type": "parameter",
      "units": "1",
      "default": 0.78,
      "description": "Ventilation coefficient a of the rain evaporation rate f_v = a + b Sc^(1/3) Re^(1/2) (the literal .78 in precr1)."
    },
    "vent_b": {
      "type": "parameter",
      "units": "1",
      "default": 0.31,
      "description": "Ventilation coefficient b of the rain evaporation rate (the literal .31 in precr2)."
    },
    "es_cap": {
      "type": "parameter",
      "units": "1",
      "default": 0.99,
      "description": "The saturation vapor pressure is capped at es_cap times the pressure (the literal 0.99 p)."
    },
    "ttp_offset": {
      "type": "parameter",
      "units": "K",
      "default": 0.01,
      "description": "Triple-point temperature offset above 0 C, ttp = t0c + 0.01 K."
    },
    "diffus_coef": {
      "type": "parameter",
      "units": "m^2*Pa/(s*K^(181/100))",
      "default": 8.794e-05,
      "description": "Coefficient of the water-vapor diffusivity Dv = diffus_coef T^diffus_exp / p."
    },
    "diffus_exp": {
      "type": "parameter",
      "units": "1",
      "default": 1.81,
      "description": "Temperature exponent of the water-vapor diffusivity."
    },
    "viscos_coef": {
      "type": "parameter",
      "units": "kg/(m*s*K^(1/2))",
      "default": 1.496e-06,
      "description": "Coefficient of Sutherland's law for the kinematic viscosity nu = viscos_coef T^(3/2) / (T + sutherland_T) / rho."
    },
    "sutherland_T": {
      "type": "parameter",
      "units": "K",
      "default": 120.0,
      "description": "Sutherland temperature of the air viscosity law."
    },
    "xka_coef": {
      "type": "parameter",
      "units": "J/(kg*K)",
      "default": 1414.0,
      "description": "Thermal conductivity of air as ka = xka_coef nu rho (the literal 1.414e3)."
    },
    "dtcldcr": {
      "type": "parameter",
      "units": "s",
      "default": 120.0,
      "description": "Maximum length of a WSM6 minor (sub-)time step; the model step is split into ceil(delt/dtcldcr) sub-steps of dtcld."
    },
    "n0s": {
      "type": "parameter",
      "units": "1/m^4",
      "default": 2000000.0,
      "description": "Intercept parameter of the snow size distribution at 0 C; multiplied by the temperature factor snow_intercept_factor below freezing (HDC 2004 eq. 6)."
    },
    "n0smax": {
      "type": "parameter",
      "units": "1/m^4",
      "default": 100000000000.0,
      "description": "Upper bound of the temperature-dependent snow intercept n0s(T) (reached near -90 C)."
    },
    "alpha_n0s": {
      "type": "parameter",
      "units": "1/K",
      "default": 0.12,
      "description": "Exponential coefficient of the snow intercept temperature dependence, n0s(T) = n0s exp(alpha (T0 - T)) (the literal .12; the code comment gives .122)."
    },
    "n0g": {
      "type": "parameter",
      "units": "1/m^4",
      "default": 4000000.0,
      "description": "Intercept parameter of the graupel size distribution (graupel-like setting, hail_opt = 0)."
    },
    "avts": {
      "type": "parameter",
      "units": "m^(59/100)/s",
      "default": 11.72,
      "description": "Coefficient a of the snow terminal velocity V(D) = a D^b (units m^(1-bvts)/s)."
    },
    "bvts": {
      "type": "parameter",
      "units": "1",
      "default": 0.41,
      "description": "Exponent b of the snow terminal velocity."
    },
    "avtg": {
      "type": "parameter",
      "units": "m^(1/5)/s",
      "default": 330.0,
      "description": "Coefficient a of the graupel terminal velocity (graupel-like setting; hail_opt = 1 uses 285)."
    },
    "bvtg": {
      "type": "parameter",
      "units": "1",
      "default": 0.8,
      "description": "Exponent b of the graupel terminal velocity (equal to bvtr, so the graupel Gamma-function constants equal the rain ones)."
    },
    "dens": {
      "type": "parameter",
      "units": "kg/m^3",
      "default": 100.0,
      "description": "Bulk density of snow particles (WSM6 dens)."
    },
    "deng": {
      "type": "parameter",
      "units": "kg/m^3",
      "default": 500.0,
      "description": "Bulk density of graupel particles (graupel-like setting; hail_opt = 1 uses 700)."
    },
    "lamdasmax": {
      "type": "parameter",
      "units": "1/m",
      "default": 100000.0,
      "description": "Upper bound of the snow slope parameter; below qcrmin the inverse slope is held at 1/lamdasmax."
    },
    "lamdagmax": {
      "type": "parameter",
      "units": "1/m",
      "default": 60000.0,
      "description": "Upper bound of the graupel slope parameter (graupel-like setting; hail_opt = 1 uses 2e4)."
    },
    "dicon": {
      "type": "parameter",
      "units": "m/kg^(1/2)",
      "default": 11.9,
      "description": "Coefficient of the ice crystal diameter-mass relation D_i = dicon sqrt(m_i) (HDC 2004 eq. 5b)."
    },
    "dimax": {
      "type": "parameter",
      "units": "m",
      "default": 0.0005,
      "description": "Upper bound of the ice crystal diameter (500 micrometres)."
    },
    "dimin_fallout": {
      "type": "parameter",
      "units": "m",
      "default": 1e-25,
      "description": "Lower bound of the ice crystal diameter in the fallout speed only (the kernel's max(..., 1.e-25) in the Vice block); the cold-rain diameter has no floor."
    },
    "xni_coef": {
      "type": "parameter",
      "units": "1/(kg^(3/4)*m^(3/4))",
      "default": 53800000.0,
      "description": "Coefficient of the ice number concentration N_i = 5.38e7 (rho q_i)^0.75 (HDC 2004 eq. 5c)."
    },
    "xni_min": {
      "type": "parameter",
      "units": "1/m^3",
      "default": 1000.0,
      "description": "Lower bound of the diagnosed ice number concentration."
    },
    "xni_max": {
      "type": "parameter",
      "units": "1/m^3",
      "default": 1000000.0,
      "description": "Upper bound of the diagnosed ice number concentration."
    },
    "vt_ice_coef": {
      "type": "parameter",
      "units": "1/(m^(31/100)*s)",
      "default": 14900.0,
      "description": "Coefficient of the ice crystal fall speed V_i = 1.49e4 D^1.31 (HDC 2004 eq. 5a)."
    },
    "vt_ice_exp": {
      "type": "parameter",
      "units": "1",
      "default": 1.31,
      "description": "Exponent of the ice crystal fall speed power law."
    },
    "eacrs_coef": {
      "type": "parameter",
      "units": "1/K",
      "default": 0.07,
      "description": "Temperature coefficient of the snow/graupel-ice collection efficiency E = exp(-0.07 (T0 - T)) (the literals 0.07 in eacrs and egi)."
    },
    "wilt_exp": {
      "type": "parameter",
      "units": "1",
      "default": 2.0,
      "description": "Exponent of the collection-efficiency reduction min(max(0, q_collector/q_collected), 1)^2 ('suggested by B. Wilt')."
    },
    "qs0": {
      "type": "parameter",
      "units": "kg/kg",
      "default": 0.0006,
      "description": "Snow mixing-ratio threshold of the snow-to-graupel autoconversion (WSM6 qs0)."
    },
    "pgaut_coef": {
      "type": "parameter",
      "units": "1/s",
      "default": 0.001,
      "description": "Rate coefficient of the snow-to-graupel autoconversion alpha2 = 1e-3 exp(-0.09 (T0 - T))."
    },
    "pgaut_exp": {
      "type": "parameter",
      "units": "1/K",
      "default": 0.09,
      "description": "Temperature coefficient of the snow-to-graupel autoconversion."
    },
    "eacrc": {
      "type": "parameter",
      "units": "1",
      "default": 1.0,
      "description": "Collection efficiency of cloud water by snow (WSM6 eacrc, enters pacrc)."
    },
    "vent_a_snow": {
      "type": "parameter",
      "units": "1",
      "default": 0.65,
      "description": "Ventilation coefficient a of snow deposition/melting, precs1 = 4 n0s a (the literal .65)."
    },
    "vent_b_snow": {
      "type": "parameter",
      "units": "1",
      "default": 0.44,
      "description": "Ventilation coefficient b of snow deposition/melting, precs2 = 4 n0s b sqrt(avts) Gamma(2.5 + bvts/2) (the literal .44)."
    },
    "xni0_coef": {
      "type": "parameter",
      "units": "1/m^3",
      "default": 1000.0,
      "description": "Ice-nuclei concentration at 0 C in the nucleation target N_i0 = 1e3 exp(0.1 (T0 - T)) (HDC 2004 eq. 7)."
    },
    "xni0_exp": {
      "type": "parameter",
      "units": "1/K",
      "default": 0.1,
      "description": "Temperature coefficient of the ice-nuclei concentration."
    },
    "roqi0_coef": {
      "type": "parameter",
      "units": "kg*m^(99/100)",
      "default": 4.92e-11,
      "description": "Coefficient of the initial ice content rho q_i0 = 4.92e-11 N_i0^1.33 (HDC 2004 eq. 8)."
    },
    "roqi0_exp": {
      "type": "parameter",
      "units": "1",
      "default": 1.33,
      "description": "Exponent of the initial ice content relation."
    },
    "roqimax_coef": {
      "type": "parameter",
      "units": "kg/m^11",
      "default": 2.08e+22,
      "description": "Coefficient of the maximum ice content rho q_imax = 2.08e22 dimax^8 above which ice aggregates to snow (HDC 2004 eq. 13)."
    },
    "roqimax_exp": {
      "type": "parameter",
      "units": "1",
      "default": 8.0,
      "description": "Exponent of the maximum ice content relation."
    },
    "pfrz1": {
      "type": "parameter",
      "units": "1/(m^3*s)",
      "default": 100.0,
      "description": "Bigg (1953) freezing constant B' (WSM6 pfrz1)."
    },
    "pfrz2": {
      "type": "parameter",
      "units": "1/K",
      "default": 0.66,
      "description": "Bigg (1953) freezing constant B (WSM6 pfrz2)."
    },
    "supcol_max": {
      "type": "parameter",
      "units": "K",
      "default": 50.0,
      "description": "Cap on the supercooling entering the Bigg freezing exponentials (the literal 50. in supcolt)."
    },
    "supcol_homog": {
      "type": "parameter",
      "units": "K",
      "default": 40.0,
      "description": "Supercooling beyond which all cloud water freezes homogeneously (the literal 40. of pihmf)."
    },
    "pgfrz_coef": {
      "type": "parameter",
      "units": "1",
      "default": 20.0,
      "description": "Numerical coefficient of the rain freezing rate 20 pi^2 B' n0r ... (LFO 1983 eq. 45)."
    },
    "g3pbs": {
      "type": "parameter",
      "units": "1",
      "default": 3.0115638223109507,
      "description": "Gamma(3 + bvts) as WSM6 evaluates it with rgmma; enters pacrs and pacrc."
    },
    "g4pbs": {
      "type": "parameter",
      "units": "1",
      "default": 10.265419060185165,
      "description": "Gamma(4 + bvts) as WSM6 evaluates it with rgmma; enters the snow fall-speed constant pvts."
    },
    "g5pbso2": {
      "type": "parameter",
      "units": "1",
      "default": 1.5502934809754454,
      "description": "Gamma(2.5 + bvts/2) as WSM6 evaluates it with rgmma; enters precs2."
    },
    "g4pbr": {
      "type": "parameter",
      "units": "1",
      "default": 17.817328905833126,
      "description": "Gamma(4 + bvtr) as WSM6 evaluates it with rgmma (exact 17.837825 per the code comment); enters pvtr and, because bvtg = bvtr, pvtg."
    },
    "g6pbr": {
      "type": "parameter",
      "units": "1",
      "default": 495.45956737138556,
      "description": "Gamma(6 + bvtr) as WSM6 evaluates it with rgmma; enters piacr."
    }
  },
  "equations": []
}