WSM6IceDeposition

Vapor-exchange and conversion process rates of the ice phase of the WRF single-moment 6-class microphysics scheme (WSM6; Hong and Lim 2006; Hong, Dudhia and Chen 2004), transcribed from the cold-rain block of mp_wsm6_run in phys/physics_mmm/mp_wsm6.F90 (WRF 4.8, NCAR/MMM-physics): deposition/sublimation of vapor on cloud ice (pidep, HDC eq. 9), snow (psdep, HDC eq. 14) and graupel (pgdep, HL A21) below 0 C; ice nucleation from vapor (pigen, HDC eqs. 7-8); aggregation of ice to snow (psaut, HDC eq. 12) and of snow to graupel (pgaut, LFO eq. 37); and evaporation of melting snow (psevp, HL A35) and graupel (pgevp, HL A25) above 0 C. The UNLIMITED rates are the physics: pidep = 4 D_i N_i (rh_i - 1)/F_i, psdep/pgdep/psevp/pgevp the ventilated diffusional growth (rh - 1)(c1 lambda^-2 + c2 f_v coeres)/F, pgaut = alpha2(T) max(0, qs - qs0). Two processes are instantaneous adjustments that the kernel writes as rates: nucleation relaxes the ice content to the target q_i0(T) = 4.92e-11 N_i0(T)^1.33/rho and ice-to-snow aggregation removes the excess of q_i over q_imax = 2.08e22 D_max^8/rho; here the physical quantities are the targets q_i0 and q_imax (observeds qi_nucleation_target, qi_max) and the rates pigen, psaut carry the sub-step dtcld as a parameter (EqWeFiC FORTRAN_BUGS.md N3). WSM6 limits the deposition processes SEQUENTIALLY against the vapor budget: after the rain evaporation prevp of the warm-rain block (an INPUT here, from warm_rain.esm), each of pidep, psdep, pgdep may take at most half the supersaturation over ice per sub-step (satdt/2) and at most what the earlier processes left (supice), a sublimating species may not lose more than it holds, and once the running sum of the limited rates reaches satdt the flag ifsat closes the remaining processes and the nucleation; that chain is transcribed pointwise as the <rate>_lim observeds and the ifsat_* indicators, all time-step artefacts kept apart from the physics. The saturation state over water and ice (qsat_w, rh_w, qsat_i, rh_i, xl) is an INPUT from saturation.esm evaluated at the start of the sub-step (EqWeFiC FORTRAN_BUGS.md N4); the size distributions, N_i, D_i come from hydrometeor_slopes.esm mounted as subsystem `sd`; the deposition coefficients precs1/2, precg1/2, the transport properties of air, the ventilation factor and the ventilation moments live there too; the diffusional-growth denominators over water and ice are computed here with the same template as warm_rain.esm. Constants: wsm6_parameters.esm (`par`), lib/wrf_constants.esm (`wrf`). Consumer-supplied inputs are the rewrite-target ops `input_<name>` lowered in the inline tests through a per-test template library extracted from kernel dumps of the instrumented WRF fork ctessum-claude/WRF, commit e42a269 (v4.8.0-2-ge42a269e). 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.

.esm schema: 1.2.0
Source: components/atmospheric_dynamics/wsm6/ice_deposition.esm

Description

Vapor-exchange and conversion process rates of the ice phase of the WRF single-moment 6-class microphysics scheme (WSM6; Hong and Lim 2006; Hong, Dudhia and Chen 2004), transcribed from the cold-rain block of mp_wsm6_run in phys/physics_mmm/mp_wsm6.F90 (WRF 4.8, NCAR/MMM-physics): deposition/sublimation of vapor on cloud ice (pidep, HDC eq. 9), snow (psdep, HDC eq. 14) and graupel (pgdep, HL A21) below 0 C; ice nucleation from vapor (pigen, HDC eqs. 7-8); aggregation of ice to snow (psaut, HDC eq. 12) and of snow to graupel (pgaut, LFO eq. 37); and evaporation of melting snow (psevp, HL A35) and graupel (pgevp, HL A25) above 0 C. The UNLIMITED rates are the physics: pidep = 4 D_i N_i (rh_i - 1)/F_i, psdep/pgdep/psevp/pgevp the ventilated diffusional growth (rh - 1)(c1 lambda^-2 + c2 f_v coeres)/F, pgaut = alpha2(T) max(0, qs - qs0). Two processes are instantaneous adjustments that the kernel writes as rates: nucleation relaxes the ice content to the target q_i0(T) = 4.92e-11 N_i0(T)^1.33/rho and ice-to-snow aggregation removes the excess of q_i over q_imax = 2.08e22 D_max^8/rho; here the physical quantities are the targets q_i0 and q_imax (observeds qi_nucleation_target, qi_max) and the rates pigen, psaut carry the sub-step dtcld as a parameter (EqWeFiC FORTRAN_BUGS.md N3). WSM6 limits the deposition processes SEQUENTIALLY against the vapor budget: after the rain evaporation prevp of the warm-rain block (an INPUT here, from warm_rain.esm), each of pidep, psdep, pgdep may take at most half the supersaturation over ice per sub-step (satdt/2) and at most what the earlier processes left (supice), a sublimating species may not lose more than it holds, and once the running sum of the limited rates reaches satdt the flag ifsat closes the remaining processes and the nucleation; that chain is transcribed pointwise as the lim observeds and the ifsat* indicators, all time-step artefacts kept apart from the physics. The saturation state over water and ice (qsat_w, rh_w, qsat_i, rh_i, xl) is an INPUT from saturation.esm evaluated at the start of the sub-step (EqWeFiC FORTRAN_BUGS.md N4); the size distributions, N_i, D_i come from hydrometeor_slopes.esm mounted as subsystem sd; the deposition coefficients precs1/2, precg1/2, the transport properties of air, the ventilation factor and the ventilation moments live there too; the diffusional-growth denominators over water and ice are computed here with the same template as warm_rain.esm. Constants: wsm6_parameters.esm (par), lib/wrf_constants.esm (wrf). Consumer-supplied inputs are the rewrite-target ops input_<name> lowered in the inline tests through a per-test template library extracted from kernel dumps of the instrumented WRF fork ctessum-claude/WRF, commit e42a269 (v4.8.0-2-ge42a269e). 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., 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 (eqs. 7-9, 12-14).
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 (appendix A eqs. A4, A21, A25, A35, eq. 50).
Lin, Y.-L., R. D. Farley, and H. D. Orville (1983). Bulk parameterization of the snow field in a cloud model. J. Climate Appl. Meteor. 22, 1065-1092 (eqs. 37, 46).
Rutledge, S. A., and P. V. Hobbs (1983). The mesoscale and microscale structure and organization of clouds and precipitation in midlatitude cyclones. VIII. J. Atmos. Sci. 40, 1185-1206 (eq. A27).
NCAR/MMM-physics mp_wsm6.F90 at commit 550b5b4 (WRF 4.8 phys/physics_mmm submodule), cold-rain block lines 1142-1245; diffac, venfac helper functions.

Parameters

Name	Units	Default	Description
`qv_in`	`kg/kg`	`0.0`	Coupling-target parameter (additive): receives the vapor mixing ratio from the upstream stage through a document coupling (EqWeFiC couplings/microphysics_column*.esm), where the mount-edge template library lowers `input_qv` to this name. Unused by the standalone inline tests, which lower `input_qv` to a dumped column profile instead.
`qsat_w_in`	`kg/kg`	`0.0`	Coupling-target parameter (additive): receives the start-of-sub-step saturation mixing ratio over water from the upstream stage through a document coupling (EqWeFiC couplings/microphysics_column*.esm), where the mount-edge template library lowers `input_qsat_w` to this name. Unused by the standalone inline tests, which lower `input_qsat_w` to a dumped column profile instead.
`rh_w_in`	`1`	`0.0`	Coupling-target parameter (additive): receives the start-of-sub-step relative humidity over water from the upstream stage through a document coupling (EqWeFiC couplings/microphysics_column*.esm), where the mount-edge template library lowers `input_rh_w` to this name. Unused by the standalone inline tests, which lower `input_rh_w` to a dumped column profile instead.
`qsat_i_in`	`kg/kg`	`0.0`	Coupling-target parameter (additive): receives the start-of-sub-step saturation mixing ratio over ice from the upstream stage through a document coupling (EqWeFiC couplings/microphysics_column*.esm), where the mount-edge template library lowers `input_qsat_i` to this name. Unused by the standalone inline tests, which lower `input_qsat_i` to a dumped column profile instead.
`rh_i_in`	`1`	`0.0`	Coupling-target parameter (additive): receives the start-of-sub-step relative humidity over ice from the upstream stage through a document coupling (EqWeFiC couplings/microphysics_column*.esm), where the mount-edge template library lowers `input_rh_i` to this name. Unused by the standalone inline tests, which lower `input_rh_i` to a dumped column profile instead.
`xl_in`	`J/kg`	`0.0`	Coupling-target parameter (additive): receives the start-of-sub-step latent heat of vaporization from the upstream stage through a document coupling (EqWeFiC couplings/microphysics_column*.esm), where the mount-edge template library lowers `input_xl` to this name. Unused by the standalone inline tests, which lower `input_xl` to a dumped column profile instead.
`prevp_in`	`kg/kg/s`	`0.0`	Coupling-target parameter (additive): receives the rain evaporation rate that opens WSM6’s sequential vapor budget from the upstream stage through a document coupling (EqWeFiC couplings/microphysics_column*.esm), where the mount-edge template library lowers `input_prevp` to this name. Unused by the standalone inline tests, which lower `input_prevp` to a dumped column profile instead.
`dtcld`	`s`	`60.0`	Length of the WSM6 sub-time step; enters the limiters and the adjustment rates only.

Observed

Name	Units	Description
`qv`	`kg/kg`	Water-vapor mixing ratio (WSM6 q).
`qsat_w`	`kg/kg`	Saturation mixing ratio over water at the start-of-step state (saturation.esm).
`rh_w`	`1`	Relative humidity over water at the start-of-step state (saturation.esm).
`qsat_i`	`kg/kg`	Saturation mixing ratio over ice at the start-of-step state (saturation.esm).
`rh_i`	`1`	Relative humidity over ice at the start-of-step state (saturation.esm).
`xl`	`J/kg`	Latent heat of vaporization at the start-of-step temperature (saturation.esm).
`prevp`	`kg/kg/s`	Rain evaporation/condensation rate as applied by the kernel (warm_rain.esm prevp_lim); the first entry of the sequential vapor budget.
`roqimax`	`kg/m^3`	Maximum ice content rho q_imax = 2.08e22 D_max^8 before aggregation to snow (WSM6 roqimax).
`supcol`	`K`	Supercooling T0 - T (WSM6 supcol).
`supsat`	`kg/kg`	Supersaturation over ice, max(qv, qmin) - qsat_i (WSM6 supsat).
`satdt`	`kg/kg/s`	Supersaturation over ice per sub-step, supsat/dtcld (WSM6 satdt).
`f_diff_w`	`s/m^2`	Diffusional-growth denominator over water, rho xl^2/(ka r_v T^2) + 1/(qsat_w Dv) (WSM6 work1(:,:,1)).
`f_diff_i`	`s/m^2`	Diffusional-growth denominator over ice with the sublimation enthalpy xls (WSM6 work1(:,:,2)).
`pidep`	`kg/kg/s`	Deposition (positive) / sublimation of vapor on cloud ice below 0 C (HDC 9), unlimited; zero without ice or above 0 C.
`supice_i`	`kg/kg/s`	Vapor budget left for cloud ice after rain evaporation, satdt - prevp (WSM6 supice before pidep).
`pidep_lim`	`kg/kg/s`	pidep after the sequential saturation limiter (WSM6 pidep as applied).
`ifsat_i`	`1`	1 where \|prevp + pidep_lim\| >= \|satdt\| has closed the vapor budget (WSM6 ifsat after pidep), else 0.
`psdep`	`kg/kg/s`	Deposition / sublimation of vapor on snow below 0 C (HDC 14), n0s(T)/n0s (rh_i - 1)(precs1 lambda_s^-2 + precs2 f_v coeres_s)/F_i, unlimited.
`supice_s`	`kg/kg/s`	Vapor budget left for snow, satdt - prevp - pidep_lim.
`psdep_lim`	`kg/kg/s`	psdep after the sequential saturation limiter; zero where ifsat_i has closed the budget (WSM6 psdep as applied).
`ifsat_s`	`1`	1 where the budget is closed after psdep (WSM6 ifsat after psdep).
`pgdep`	`kg/kg/s`	Deposition / sublimation of vapor on graupel below 0 C (HL A21, LFO 46), unlimited.
`supice_g`	`kg/kg/s`	Vapor budget left for graupel, satdt - prevp - pidep_lim - psdep_lim.
`pgdep_lim`	`kg/kg/s`	pgdep after the sequential saturation limiter; zero where ifsat_s has closed the budget (WSM6 pgdep as applied).
`ifsat_g`	`1`	1 where the budget is closed after pgdep (WSM6 ifsat after pgdep).
`supice_n`	`kg/kg/s`	Vapor budget left for nucleation, satdt - prevp - pidep_lim - psdep_lim - pgdep_lim.
`qi_nucleation_target`	`kg/kg`	Ice mixing ratio the nucleation relaxes towards, q_i0(T) = 4.92e-11 (1e3 exp(0.1 (T0 - T)))^1.33/rho (HDC 7-8; WSM6 roqi0/den).
`pigen`	`kg/kg/s`	Ice nucleation rate max(0, (q_i0 - q_i)/dtcld) below 0 C where supersaturated over ice (HL 50, HDC 7-8): an adjustment written as a rate, so it scales with 1/dtcld.
`pigen_lim`	`kg/kg/s`	pigen after the vapor-budget limiter min(pigen, satdt, supice_n); zero where ifsat_g has closed the budget (WSM6 pigen as applied).
`qi_max`	`kg/kg`	Maximum ice mixing ratio before aggregation to snow, roqimax/rho (HDC 13; WSM6 qimax).
`psaut`	`kg/kg/s`	Aggregation of cloud ice to snow, max(0, (q_i - q_imax)/dtcld) below 0 C (HDC 12): an adjustment written as a rate (WSM6 psaut, no further limiter).
`pgaut`	`kg/kg/s`	Aggregation of snow to graupel below 0 C, 1e-3 exp(-0.09 (T0 - T)) max(0, qs - qs0) (LFO 37, HL A4), unlimited.
`pgaut_lim`	`kg/kg/s`	pgaut after the limiter min(pgaut, qs/dtcld).
`psevp`	`kg/kg/s`	Evaporation of melting snow above 0 C where subsaturated over water (HL A35, RH83 A27), n0s(T)/n0s (rh_w - 1)(precs1 lambda_s^-2 + precs2 f_v coeres_s)/F_w (negative), unlimited.
`psevp_lim`	`kg/kg/s`	psevp after the limiter min(max(psevp, -qs/dtcld), 0).
`pgevp`	`kg/kg/s`	Evaporation of melting graupel above 0 C where subsaturated over water (HL A25, RH84 A19), unlimited.
`pgevp_lim`	`kg/kg/s`	pgevp after the limiter min(max(pgevp, -qg/dtcld), 0).

Observed expressions

$$ qv = \mathrm{input_qv}\left(\right) $$

Water-vapor mixing ratio (WSM6 q).

$$ qsat_{w} = \mathrm{input_qsat_w}\left(\right) $$

Saturation mixing ratio over water at the start-of-step state (saturation.esm).

$$ rh_{w} = \mathrm{input_rh_w}\left(\right) $$

Relative humidity over water at the start-of-step state (saturation.esm).

$$ qsat_{i} = \mathrm{input_qsat_i}\left(\right) $$

Saturation mixing ratio over ice at the start-of-step state (saturation.esm).

$$ rh_{i} = \mathrm{input_rh_i}\left(\right) $$

Relative humidity over ice at the start-of-step state (saturation.esm).

$$ xl = \mathrm{input_xl}\left(\right) $$

Latent heat of vaporization at the start-of-step temperature (saturation.esm).

$$ prevp = \mathrm{input_prevp}\left(\right) $$

Rain evaporation/condensation rate as applied by the kernel (warm_rain.esm prevp_lim); the first entry of the sequential vapor budget.

$$ roqimax = par.roqimax_{coef} \cdot par.dimax^{par.roqimax_{exp}} $$

Maximum ice content rho q_imax = 2.08e22 D_max^8 before aggregation to snow (WSM6 roqimax).

$$ supcol = wrf.svpt0 - sd.T $$

Supercooling T0 - T (WSM6 supcol).

$$ supsat = \mathrm{max}\left(qv, par.qmin\right) - qsat_{i} $$

Supersaturation over ice, max(qv, qmin) - qsat_i (WSM6 supsat).

$$ satdt = \frac{supsat}{dtcld} $$

Supersaturation over ice per sub-step, supsat/dtcld (WSM6 satdt).

$$ f_{diff\,w} = \mathrm{diffusional_growth_denominator}\left(L=xl, T=sd.T, rho=sd.rho, ka=sd.ka, r_{v}=wrf.r_{v}, qsat=qsat_{w}, Dv=sd.Dv\right) $$

Diffusional-growth denominator over water, rho xl^2/(ka r_v T^2) + 1/(qsat_w Dv) (WSM6 work1(:,:,1)).

$$ f_{diff\,i} = \mathrm{diffusional_growth_denominator}\left(L=wrf.xls, T=sd.T, rho=sd.rho, ka=sd.ka, r_{v}=wrf.r_{v}, qsat=qsat_{i}, Dv=sd.Dv\right) $$

Diffusional-growth denominator over ice with the sublimation enthalpy xls (WSM6 work1(:,:,2)).

$$ pidep = \mathrm{ifelse}\left(\mathrm{and}\left(\mathrm{>}\left(supcol, 0\right), \mathrm{>}\left(sd.qi, 0\right)\right), \mathrm{ice_deposition_rate}\left(D=sd.D_{i}, xni=sd.xni, rh_{i}=rh_{i}, f_{diff\,i}=f_{diff\,i}\right), 0\right) $$

Deposition (positive) / sublimation of vapor on cloud ice below 0 C (HDC 9), unlimited; zero without ice or above 0 C.

$$ supice_{i} = satdt - prevp $$

Vapor budget left for cloud ice after rain evaporation, satdt - prevp (WSM6 supice before pidep).

$$ pidep_{lim} = \mathrm{ifelse}\left(\mathrm{and}\left(\mathrm{>}\left(supcol, 0\right), \mathrm{>}\left(sd.qi, 0\right)\right), \mathrm{saturation_limited_deposition}\left(rate=pidep, satdt=satdt, supice=supice_{i}, q=sd.qi, dt=dtcld\right), 0\right) $$

pidep after the sequential saturation limiter (WSM6 pidep as applied).

$$ ifsat_{i} = \mathrm{ifelse}\left(\mathrm{and}\left(\mathrm{>}\left(supcol, 0\right), \mathrm{>}\left(sd.qi, 0\right), \mathrm{>=}\left(\left|prevp + pidep_{lim}\right|, \left|satdt\right|\right)\right), \mathrm{const}\left(\right), \mathrm{const}\left(\right)\right) $$

1 where |prevp + pidep_lim| >= |satdt| has closed the vapor budget (WSM6 ifsat after pidep), else 0.

$$ psdep = \mathrm{ifelse}\left(\mathrm{and}\left(\mathrm{>}\left(supcol, 0\right), \mathrm{>}\left(sd.qs, 0\right)\right), sd.n0sfac \cdot \mathrm{ventilated_diffusional_growth}\left(rh=rh_{i}, rslope2=sd.rslope2_{s}, coeres=sd.coeres_{s}, f_{vent}=sd.f_{vent}, f_{diff}=f_{diff\,i}, c1=sd.precs1, c2=sd.precs2\right), 0\right) $$

Deposition / sublimation of vapor on snow below 0 C (HDC 14), n0s(T)/n0s (rh_i - 1)(precs1 lambda_s^-2 + precs2 f_v coeres_s)/F_i, unlimited.

$$ supice_{s} = supice_{i} - pidep_{lim} $$

Vapor budget left for snow, satdt - prevp - pidep_lim.

$$ psdep_{lim} = \mathrm{ifelse}\left(\mathrm{and}\left(\mathrm{>}\left(supcol, 0\right), \mathrm{>}\left(sd.qs, 0\right), ifsat_{i} = 0\right), \mathrm{saturation_limited_deposition}\left(rate=psdep, satdt=satdt, supice=supice_{s}, q=sd.qs, dt=dtcld\right), 0\right) $$

psdep after the sequential saturation limiter; zero where ifsat_i has closed the budget (WSM6 psdep as applied).

$$ ifsat_{s} = \mathrm{ifelse}\left(\mathrm{or}\left(ifsat_{i} = 1, \mathrm{and}\left(\mathrm{>}\left(supcol, 0\right), \mathrm{>}\left(sd.qs, 0\right), \mathrm{>=}\left(\left|prevp + pidep_{lim} + psdep_{lim}\right|, \left|satdt\right|\right)\right)\right), \mathrm{const}\left(\right), \mathrm{const}\left(\right)\right) $$

1 where the budget is closed after psdep (WSM6 ifsat after psdep).

$$ pgdep = \mathrm{ifelse}\left(\mathrm{and}\left(\mathrm{>}\left(supcol, 0\right), \mathrm{>}\left(sd.qg, 0\right)\right), \mathrm{ventilated_diffusional_growth}\left(rh=rh_{i}, rslope2=sd.rslope2_{g}, coeres=sd.coeres_{g}, f_{vent}=sd.f_{vent}, f_{diff}=f_{diff\,i}, c1=sd.precg1, c2=sd.precg2\right), 0\right) $$

Deposition / sublimation of vapor on graupel below 0 C (HL A21, LFO 46), unlimited.

$$ supice_{g} = supice_{s} - psdep_{lim} $$

Vapor budget left for graupel, satdt - prevp - pidep_lim - psdep_lim.

$$ pgdep_{lim} = \mathrm{ifelse}\left(\mathrm{and}\left(\mathrm{>}\left(supcol, 0\right), \mathrm{>}\left(sd.qg, 0\right), ifsat_{s} = 0\right), \mathrm{saturation_limited_deposition}\left(rate=pgdep, satdt=satdt, supice=supice_{g}, q=sd.qg, dt=dtcld\right), 0\right) $$

pgdep after the sequential saturation limiter; zero where ifsat_s has closed the budget (WSM6 pgdep as applied).

$$ ifsat_{g} = \mathrm{ifelse}\left(\mathrm{or}\left(ifsat_{s} = 1, \mathrm{and}\left(\mathrm{>}\left(supcol, 0\right), \mathrm{>}\left(sd.qg, 0\right), \mathrm{>=}\left(\left|prevp + pidep_{lim} + psdep_{lim} + pgdep_{lim}\right|, \left|satdt\right|\right)\right)\right), \mathrm{const}\left(\right), \mathrm{const}\left(\right)\right) $$

1 where the budget is closed after pgdep (WSM6 ifsat after pgdep).

$$ supice_{n} = supice_{g} - pgdep_{lim} $$

Vapor budget left for nucleation, satdt - prevp - pidep_lim - psdep_lim - pgdep_lim.

$$ qi_{nucleation\,target} = \mathrm{ice_nucleation_target}\left(T=sd.T, t0=wrf.svpt0, rho=sd.rho, n_{coef}=par.xni0_{coef}, n_{exp}=par.xni0_{exp}, m_{coef}=par.roqi0_{coef}, m_{exp}=par.roqi0_{exp}\right) $$

Ice mixing ratio the nucleation relaxes towards, q_i0(T) = 4.92e-11 (1e3 exp(0.1 (T0 - T)))^1.33/rho (HDC 7-8; WSM6 roqi0/den).

$$ pigen = \mathrm{ifelse}\left(\mathrm{and}\left(\mathrm{>}\left(supcol, 0\right), \mathrm{>}\left(supsat, 0\right)\right), \mathrm{adjustment_towards_target_rate}\left(q_{target}=qi_{nucleation\,target}, q=\mathrm{max}\left(sd.qi, 0\right), dt=dtcld\right), 0\right) $$

Ice nucleation rate max(0, (q_i0 - q_i)/dtcld) below 0 C where supersaturated over ice (HL 50, HDC 7-8): an adjustment written as a rate, so it scales with 1/dtcld.

$$ pigen_{lim} = \mathrm{ifelse}\left(\mathrm{and}\left(\mathrm{>}\left(supcol, 0\right), \mathrm{>}\left(supsat, 0\right), ifsat_{g} = 0\right), \mathrm{min}\left(pigen, satdt, supice_{n}\right), 0\right) $$

pigen after the vapor-budget limiter min(pigen, satdt, supice_n); zero where ifsat_g has closed the budget (WSM6 pigen as applied).

$$ qi_{max} = \frac{roqimax}{sd.rho} $$

Maximum ice mixing ratio before aggregation to snow, roqimax/rho (HDC 13; WSM6 qimax).

$$ psaut = \mathrm{ifelse}\left(\mathrm{and}\left(\mathrm{>}\left(supcol, 0\right), \mathrm{>}\left(sd.qi, 0\right)\right), \mathrm{excess_conversion_rate}\left(q=sd.qi, q_{max}=qi_{max}, dt=dtcld\right), 0\right) $$

Aggregation of cloud ice to snow, max(0, (q_i - q_imax)/dtcld) below 0 C (HDC 12): an adjustment written as a rate (WSM6 psaut, no further limiter).

$$ pgaut = \mathrm{ifelse}\left(\mathrm{and}\left(\mathrm{>}\left(supcol, 0\right), \mathrm{>}\left(sd.qs, 0\right)\right), \mathrm{snow_to_graupel_aggregation}\left(qs=sd.qs, qs0=par.qs0, T=sd.T, t0=wrf.svpt0, coef=par.pgaut_{coef}, expn=par.pgaut_{exp}\right), 0\right) $$

Aggregation of snow to graupel below 0 C, 1e-3 exp(-0.09 (T0 - T)) max(0, qs - qs0) (LFO 37, HL A4), unlimited.

$$ pgaut_{lim} = \mathrm{sink_rate_limiter}\left(rate=pgaut, q=sd.qs, dt=dtcld\right) $$

pgaut after the limiter min(pgaut, qs/dtcld).

$$ psevp = \mathrm{ifelse}\left(\mathrm{and}\left(\mathrm{<}\left(supcol, 0\right), \mathrm{>}\left(sd.qs, 0\right), \mathrm{<}\left(rh_{w}, 1\right)\right), sd.n0sfac \cdot \mathrm{ventilated_diffusional_growth}\left(rh=rh_{w}, rslope2=sd.rslope2_{s}, coeres=sd.coeres_{s}, f_{vent}=sd.f_{vent}, f_{diff}=f_{diff\,w}, c1=sd.precs1, c2=sd.precs2\right), 0\right) $$

Evaporation of melting snow above 0 C where subsaturated over water (HL A35, RH83 A27), n0s(T)/n0s (rh_w - 1)(precs1 lambda_s^-2 + precs2 f_v coeres_s)/F_w (negative), unlimited.

$$ psevp_{lim} = \mathrm{negative_sink_limiter}\left(rate=psevp, q=sd.qs, dt=dtcld\right) $$

psevp after the limiter min(max(psevp, -qs/dtcld), 0).

$$ pgevp = \mathrm{ifelse}\left(\mathrm{and}\left(\mathrm{<}\left(supcol, 0\right), \mathrm{>}\left(sd.qg, 0\right), \mathrm{<}\left(rh_{w}, 1\right)\right), \mathrm{ventilated_diffusional_growth}\left(rh=rh_{w}, rslope2=sd.rslope2_{g}, coeres=sd.coeres_{g}, f_{vent}=sd.f_{vent}, f_{diff}=f_{diff\,w}, c1=sd.precg1, c2=sd.precg2\right), 0\right) $$

Evaporation of melting graupel above 0 C where subsaturated over water (HL A25, RH84 A19), unlimited.

$$ pgevp_{lim} = \mathrm{negative_sink_limiter}\left(rate=pgevp, q=sd.qg, dt=dtcld\right) $$

pgevp after the limiter min(max(pgevp, -qg/dtcld), 0).

Raw .esm

Raw .esm JSON (this component)

{
  "expression_template_imports": [
    {
      "ref": "./microphysics_templates.esm"
    }
  ],
  "subsystems": {
    "wrf": {
      "ref": "../../../lib/wrf_constants.esm"
    },
    "par": {
      "ref": "./wsm6_parameters.esm"
    },
    "sd": {
      "ref": "./hydrometeor_slopes.esm",
      "bindings": {
        "NLEV": "NLEV"
      }
    }
  },
  "variables": {
    "qv_in": {
      "type": "parameter",
      "units": "kg/kg",
      "shape": [
        "lev"
      ],
      "default": 0.0,
      "description": "Coupling-target parameter (additive): receives the vapor mixing ratio from the upstream stage through a document coupling (EqWeFiC couplings/microphysics_column*.esm), where the mount-edge template library lowers `input_qv` to this name. Unused by the standalone inline tests, which lower `input_qv` to a dumped column profile instead."
    },
    "qsat_w_in": {
      "type": "parameter",
      "units": "kg/kg",
      "shape": [
        "lev"
      ],
      "default": 0.0,
      "description": "Coupling-target parameter (additive): receives the start-of-sub-step saturation mixing ratio over water from the upstream stage through a document coupling (EqWeFiC couplings/microphysics_column*.esm), where the mount-edge template library lowers `input_qsat_w` to this name. Unused by the standalone inline tests, which lower `input_qsat_w` to a dumped column profile instead."
    },
    "rh_w_in": {
      "type": "parameter",
      "units": "1",
      "shape": [
        "lev"
      ],
      "default": 0.0,
      "description": "Coupling-target parameter (additive): receives the start-of-sub-step relative humidity over water from the upstream stage through a document coupling (EqWeFiC couplings/microphysics_column*.esm), where the mount-edge template library lowers `input_rh_w` to this name. Unused by the standalone inline tests, which lower `input_rh_w` to a dumped column profile instead."
    },
    "qsat_i_in": {
      "type": "parameter",
      "units": "kg/kg",
      "shape": [
        "lev"
      ],
      "default": 0.0,
      "description": "Coupling-target parameter (additive): receives the start-of-sub-step saturation mixing ratio over ice from the upstream stage through a document coupling (EqWeFiC couplings/microphysics_column*.esm), where the mount-edge template library lowers `input_qsat_i` to this name. Unused by the standalone inline tests, which lower `input_qsat_i` to a dumped column profile instead."
    },
    "rh_i_in": {
      "type": "parameter",
      "units": "1",
      "shape": [
        "lev"
      ],
      "default": 0.0,
      "description": "Coupling-target parameter (additive): receives the start-of-sub-step relative humidity over ice from the upstream stage through a document coupling (EqWeFiC couplings/microphysics_column*.esm), where the mount-edge template library lowers `input_rh_i` to this name. Unused by the standalone inline tests, which lower `input_rh_i` to a dumped column profile instead."
    },
    "xl_in": {
      "type": "parameter",
      "units": "J/kg",
      "shape": [
        "lev"
      ],
      "default": 0.0,
      "description": "Coupling-target parameter (additive): receives the start-of-sub-step latent heat of vaporization from the upstream stage through a document coupling (EqWeFiC couplings/microphysics_column*.esm), where the mount-edge template library lowers `input_xl` to this name. Unused by the standalone inline tests, which lower `input_xl` to a dumped column profile instead."
    },
    "prevp_in": {
      "type": "parameter",
      "units": "kg/kg/s",
      "shape": [
        "lev"
      ],
      "default": 0.0,
      "description": "Coupling-target parameter (additive): receives the rain evaporation rate that opens WSM6's sequential vapor budget from the upstream stage through a document coupling (EqWeFiC couplings/microphysics_column*.esm), where the mount-edge template library lowers `input_prevp` to this name. Unused by the standalone inline tests, which lower `input_prevp` to a dumped column profile instead."
    },
    "qv": {
      "type": "unknown",
      "units": "kg/kg",
      "shape": [
        "lev"
      ],
      "description": "Water-vapor mixing ratio (WSM6 q)."
    },
    "qsat_w": {
      "type": "unknown",
      "units": "kg/kg",
      "shape": [
        "lev"
      ],
      "description": "Saturation mixing ratio over water at the start-of-step state (saturation.esm)."
    },
    "rh_w": {
      "type": "unknown",
      "units": "1",
      "shape": [
        "lev"
      ],
      "description": "Relative humidity over water at the start-of-step state (saturation.esm)."
    },
    "qsat_i": {
      "type": "unknown",
      "units": "kg/kg",
      "shape": [
        "lev"
      ],
      "description": "Saturation mixing ratio over ice at the start-of-step state (saturation.esm)."
    },
    "rh_i": {
      "type": "unknown",
      "units": "1",
      "shape": [
        "lev"
      ],
      "description": "Relative humidity over ice at the start-of-step state (saturation.esm)."
    },
    "xl": {
      "type": "unknown",
      "units": "J/kg",
      "shape": [
        "lev"
      ],
      "description": "Latent heat of vaporization at the start-of-step temperature (saturation.esm)."
    },
    "prevp": {
      "type": "unknown",
      "units": "kg/kg/s",
      "shape": [
        "lev"
      ],
      "description": "Rain evaporation/condensation rate as applied by the kernel (warm_rain.esm prevp_lim); the first entry of the sequential vapor budget."
    },
    "dtcld": {
      "type": "parameter",
      "units": "s",
      "default": 60.0,
      "description": "Length of the WSM6 sub-time step; enters the limiters and the adjustment rates only."
    },
    "roqimax": {
      "type": "unknown",
      "units": "kg/m^3",
      "description": "Maximum ice content rho q_imax = 2.08e22 D_max^8 before aggregation to snow (WSM6 roqimax)."
    },
    "supcol": {
      "type": "unknown",
      "units": "K",
      "shape": [
        "lev"
      ],
      "description": "Supercooling T0 - T (WSM6 supcol)."
    },
    "supsat": {
      "type": "unknown",
      "units": "kg/kg",
      "shape": [
        "lev"
      ],
      "description": "Supersaturation over ice, max(qv, qmin) - qsat_i (WSM6 supsat)."
    },
    "satdt": {
      "type": "unknown",
      "units": "kg/kg/s",
      "shape": [
        "lev"
      ],
      "description": "Supersaturation over ice per sub-step, supsat/dtcld (WSM6 satdt)."
    },
    "f_diff_w": {
      "type": "unknown",
      "units": "s/m^2",
      "shape": [
        "lev"
      ],
      "description": "Diffusional-growth denominator over water, rho xl^2/(ka r_v T^2) + 1/(qsat_w Dv) (WSM6 work1(:,:,1))."
    },
    "f_diff_i": {
      "type": "unknown",
      "units": "s/m^2",
      "shape": [
        "lev"
      ],
      "description": "Diffusional-growth denominator over ice with the sublimation enthalpy xls (WSM6 work1(:,:,2))."
    },
    "pidep": {
      "type": "unknown",
      "units": "kg/kg/s",
      "shape": [
        "lev"
      ],
      "description": "Deposition (positive) / sublimation of vapor on cloud ice below 0 C (HDC 9), unlimited; zero without ice or above 0 C."
    },
    "supice_i": {
      "type": "unknown",
      "units": "kg/kg/s",
      "shape": [
        "lev"
      ],
      "description": "Vapor budget left for cloud ice after rain evaporation, satdt - prevp (WSM6 supice before pidep)."
    },
    "pidep_lim": {
      "type": "unknown",
      "units": "kg/kg/s",
      "shape": [
        "lev"
      ],
      "description": "pidep after the sequential saturation limiter (WSM6 pidep as applied)."
    },
    "ifsat_i": {
      "type": "unknown",
      "units": "1",
      "shape": [
        "lev"
      ],
      "description": "1 where |prevp + pidep_lim| >= |satdt| has closed the vapor budget (WSM6 ifsat after pidep), else 0."
    },
    "psdep": {
      "type": "unknown",
      "units": "kg/kg/s",
      "shape": [
        "lev"
      ],
      "description": "Deposition / sublimation of vapor on snow below 0 C (HDC 14), n0s(T)/n0s (rh_i - 1)(precs1 lambda_s^-2 + precs2 f_v coeres_s)/F_i, unlimited."
    },
    "supice_s": {
      "type": "unknown",
      "units": "kg/kg/s",
      "shape": [
        "lev"
      ],
      "description": "Vapor budget left for snow, satdt - prevp - pidep_lim."
    },
    "psdep_lim": {
      "type": "unknown",
      "units": "kg/kg/s",
      "shape": [
        "lev"
      ],
      "description": "psdep after the sequential saturation limiter; zero where ifsat_i has closed the budget (WSM6 psdep as applied)."
    },
    "ifsat_s": {
      "type": "unknown",
      "units": "1",
      "shape": [
        "lev"
      ],
      "description": "1 where the budget is closed after psdep (WSM6 ifsat after psdep)."
    },
    "pgdep": {
      "type": "unknown",
      "units": "kg/kg/s",
      "shape": [
        "lev"
      ],
      "description": "Deposition / sublimation of vapor on graupel below 0 C (HL A21, LFO 46), unlimited."
    },
    "supice_g": {
      "type": "unknown",
      "units": "kg/kg/s",
      "shape": [
        "lev"
      ],
      "description": "Vapor budget left for graupel, satdt - prevp - pidep_lim - psdep_lim."
    },
    "pgdep_lim": {
      "type": "unknown",
      "units": "kg/kg/s",
      "shape": [
        "lev"
      ],
      "description": "pgdep after the sequential saturation limiter; zero where ifsat_s has closed the budget (WSM6 pgdep as applied)."
    },
    "ifsat_g": {
      "type": "unknown",
      "units": "1",
      "shape": [
        "lev"
      ],
      "description": "1 where the budget is closed after pgdep (WSM6 ifsat after pgdep)."
    },
    "supice_n": {
      "type": "unknown",
      "units": "kg/kg/s",
      "shape": [
        "lev"
      ],
      "description": "Vapor budget left for nucleation, satdt - prevp - pidep_lim - psdep_lim - pgdep_lim."
    },
    "qi_nucleation_target": {
      "type": "unknown",
      "units": "kg/kg",
      "shape": [
        "lev"
      ],
      "description": "Ice mixing ratio the nucleation relaxes towards, q_i0(T) = 4.92e-11 (1e3 exp(0.1 (T0 - T)))^1.33/rho (HDC 7-8; WSM6 roqi0/den)."
    },
    "pigen": {
      "type": "unknown",
      "units": "kg/kg/s",
      "shape": [
        "lev"
      ],
      "description": "Ice nucleation rate max(0, (q_i0 - q_i)/dtcld) below 0 C where supersaturated over ice (HL 50, HDC 7-8): an adjustment written as a rate, so it scales with 1/dtcld."
    },
    "pigen_lim": {
      "type": "unknown",
      "units": "kg/kg/s",
      "shape": [
        "lev"
      ],
      "description": "pigen after the vapor-budget limiter min(pigen, satdt, supice_n); zero where ifsat_g has closed the budget (WSM6 pigen as applied)."
    },
    "qi_max": {
      "type": "unknown",
      "units": "kg/kg",
      "shape": [
        "lev"
      ],
      "description": "Maximum ice mixing ratio before aggregation to snow, roqimax/rho (HDC 13; WSM6 qimax)."
    },
    "psaut": {
      "type": "unknown",
      "units": "kg/kg/s",
      "shape": [
        "lev"
      ],
      "description": "Aggregation of cloud ice to snow, max(0, (q_i - q_imax)/dtcld) below 0 C (HDC 12): an adjustment written as a rate (WSM6 psaut, no further limiter)."
    },
    "pgaut": {
      "type": "unknown",
      "units": "kg/kg/s",
      "shape": [
        "lev"
      ],
      "description": "Aggregation of snow to graupel below 0 C, 1e-3 exp(-0.09 (T0 - T)) max(0, qs - qs0) (LFO 37, HL A4), unlimited."
    },
    "pgaut_lim": {
      "type": "unknown",
      "units": "kg/kg/s",
      "shape": [
        "lev"
      ],
      "description": "pgaut after the limiter min(pgaut, qs/dtcld)."
    },
    "psevp": {
      "type": "unknown",
      "units": "kg/kg/s",
      "shape": [
        "lev"
      ],
      "description": "Evaporation of melting snow above 0 C where subsaturated over water (HL A35, RH83 A27), n0s(T)/n0s (rh_w - 1)(precs1 lambda_s^-2 + precs2 f_v coeres_s)/F_w (negative), unlimited."
    },
    "psevp_lim": {
      "type": "unknown",
      "units": "kg/kg/s",
      "shape": [
        "lev"
      ],
      "description": "psevp after the limiter min(max(psevp, -qs/dtcld), 0)."
    },
    "pgevp": {
      "type": "unknown",
      "units": "kg/kg/s",
      "shape": [
        "lev"
      ],
      "description": "Evaporation of melting graupel above 0 C where subsaturated over water (HL A25, RH84 A19), unlimited."
    },
    "pgevp_lim": {
      "type": "unknown",
      "units": "kg/kg/s",
      "shape": [
        "lev"
      ],
      "description": "pgevp after the limiter min(max(pgevp, -qg/dtcld), 0)."
    }
  },
  "equations": [
    {
      "lhs": "qv",
      "rhs": {
        "op": "input_qv",
        "args": []
      }
    },
    {
      "lhs": "qsat_w",
      "rhs": {
        "op": "input_qsat_w",
        "args": []
      }
    },
    {
      "lhs": "rh_w",
      "rhs": {
        "op": "input_rh_w",
        "args": []
      }
    },
    {
      "lhs": "qsat_i",
      "rhs": {
        "op": "input_qsat_i",
        "args": []
      }
    },
    {
      "lhs": "rh_i",
      "rhs": {
        "op": "input_rh_i",
        "args": []
      }
    },
    {
      "lhs": "xl",
      "rhs": {
        "op": "input_xl",
        "args": []
      }
    },
    {
      "lhs": "prevp",
      "rhs": {
        "op": "input_prevp",
        "args": []
      }
    },
    {
      "lhs": "roqimax",
      "rhs": {
        "op": "*",
        "args": [
          "par.roqimax_coef",
          {
            "op": "^",
            "args": [
              "par.dimax",
              "par.roqimax_exp"
            ]
          }
        ]
      }
    },
    {
      "lhs": "supcol",
      "rhs": {
        "op": "-",
        "args": [
          "wrf.svpt0",
          "sd.T"
        ]
      }
    },
    {
      "lhs": "supsat",
      "rhs": {
        "op": "-",
        "args": [
          {
            "op": "max",
            "args": [
              "qv",
              "par.qmin"
            ]
          },
          "qsat_i"
        ]
      }
    },
    {
      "lhs": "satdt",
      "rhs": {
        "op": "/",
        "args": [
          "supsat",
          "dtcld"
        ]
      }
    },
    {
      "lhs": "f_diff_w",
      "rhs": {
        "op": "apply_expression_template",
        "args": [],
        "name": "diffusional_growth_denominator",
        "bindings": {
          "L": "xl",
          "T": "sd.T",
          "rho": "sd.rho",
          "ka": "sd.ka",
          "r_v": "wrf.r_v",
          "qsat": "qsat_w",
          "Dv": "sd.Dv"
        }
      }
    },
    {
      "lhs": "f_diff_i",
      "rhs": {
        "op": "apply_expression_template",
        "args": [],
        "name": "diffusional_growth_denominator",
        "bindings": {
          "L": "wrf.xls",
          "T": "sd.T",
          "rho": "sd.rho",
          "ka": "sd.ka",
          "r_v": "wrf.r_v",
          "qsat": "qsat_i",
          "Dv": "sd.Dv"
        }
      }
    },
    {
      "lhs": "pidep",
      "rhs": {
        "op": "ifelse",
        "args": [
          {
            "op": "and",
            "args": [
              {
                "op": ">",
                "args": [
                  "supcol",
                  0
                ]
              },
              {
                "op": ">",
                "args": [
                  "sd.qi",
                  0
                ]
              }
            ]
          },
          {
            "op": "apply_expression_template",
            "args": [],
            "name": "ice_deposition_rate",
            "bindings": {
              "D": "sd.D_i",
              "xni": "sd.xni",
              "rh_i": "rh_i",
              "f_diff_i": "f_diff_i"
            }
          },
          0
        ]
      }
    },
    {
      "lhs": "supice_i",
      "rhs": {
        "op": "-",
        "args": [
          "satdt",
          "prevp"
        ]
      }
    },
    {
      "lhs": "pidep_lim",
      "rhs": {
        "op": "ifelse",
        "args": [
          {
            "op": "and",
            "args": [
              {
                "op": ">",
                "args": [
                  "supcol",
                  0
                ]
              },
              {
                "op": ">",
                "args": [
                  "sd.qi",
                  0
                ]
              }
            ]
          },
          {
            "op": "apply_expression_template",
            "args": [],
            "name": "saturation_limited_deposition",
            "bindings": {
              "rate": "pidep",
              "satdt": "satdt",
              "supice": "supice_i",
              "q": "sd.qi",
              "dt": "dtcld"
            }
          },
          0
        ]
      }
    },
    {
      "lhs": "ifsat_i",
      "rhs": {
        "op": "ifelse",
        "args": [
          {
            "op": "and",
            "args": [
              {
                "op": ">",
                "args": [
                  "supcol",
                  0
                ]
              },
              {
                "op": ">",
                "args": [
                  "sd.qi",
                  0
                ]
              },
              {
                "op": ">=",
                "args": [
                  {
                    "op": "abs",
                    "args": [
                      {
                        "op": "+",
                        "args": [
                          "prevp",
                          "pidep_lim"
                        ]
                      }
                    ]
                  },
                  {
                    "op": "abs",
                    "args": [
                      "satdt"
                    ]
                  }
                ]
              }
            ]
          },
          {
            "op": "const",
            "args": [],
            "value": 1,
            "units": "1"
          },
          {
            "op": "const",
            "args": [],
            "value": 0,
            "units": "1"
          }
        ]
      }
    },
    {
      "lhs": "psdep",
      "rhs": {
        "op": "ifelse",
        "args": [
          {
            "op": "and",
            "args": [
              {
                "op": ">",
                "args": [
                  "supcol",
                  0
                ]
              },
              {
                "op": ">",
                "args": [
                  "sd.qs",
                  0
                ]
              }
            ]
          },
          {
            "op": "*",
            "args": [
              "sd.n0sfac",
              {
                "op": "apply_expression_template",
                "args": [],
                "name": "ventilated_diffusional_growth",
                "bindings": {
                  "rh": "rh_i",
                  "rslope2": "sd.rslope2_s",
                  "coeres": "sd.coeres_s",
                  "f_vent": "sd.f_vent",
                  "f_diff": "f_diff_i",
                  "c1": "sd.precs1",
                  "c2": "sd.precs2"
                }
              }
            ]
          },
          0
        ]
      }
    },
    {
      "lhs": "supice_s",
      "rhs": {
        "op": "-",
        "args": [
          "supice_i",
          "pidep_lim"
        ]
      }
    },
    {
      "lhs": "psdep_lim",
      "rhs": {
        "op": "ifelse",
        "args": [
          {
            "op": "and",
            "args": [
              {
                "op": ">",
                "args": [
                  "supcol",
                  0
                ]
              },
              {
                "op": ">",
                "args": [
                  "sd.qs",
                  0
                ]
              },
              {
                "op": "==",
                "args": [
                  "ifsat_i",
                  0
                ]
              }
            ]
          },
          {
            "op": "apply_expression_template",
            "args": [],
            "name": "saturation_limited_deposition",
            "bindings": {
              "rate": "psdep",
              "satdt": "satdt",
              "supice": "supice_s",
              "q": "sd.qs",
              "dt": "dtcld"
            }
          },
          0
        ]
      }
    },
    {
      "lhs": "ifsat_s",
      "rhs": {
        "op": "ifelse",
        "args": [
          {
            "op": "or",
            "args": [
              {
                "op": "==",
                "args": [
                  "ifsat_i",
                  1
                ]
              },
              {
                "op": "and",
                "args": [
                  {
                    "op": ">",
                    "args": [
                      "supcol",
                      0
                    ]
                  },
                  {
                    "op": ">",
                    "args": [
                      "sd.qs",
                      0
                    ]
                  },
                  {
                    "op": ">=",
                    "args": [
                      {
                        "op": "abs",
                        "args": [
                          {
                            "op": "+",
                            "args": [
                              "prevp",
                              "pidep_lim",
                              "psdep_lim"
                            ]
                          }
                        ]
                      },
                      {
                        "op": "abs",
                        "args": [
                          "satdt"
                        ]
                      }
                    ]
                  }
                ]
              }
            ]
          },
          {
            "op": "const",
            "args": [],
            "value": 1,
            "units": "1"
          },
          {
            "op": "const",
            "args": [],
            "value": 0,
            "units": "1"
          }
        ]
      }
    },
    {
      "lhs": "pgdep",
      "rhs": {
        "op": "ifelse",
        "args": [
          {
            "op": "and",
            "args": [
              {
                "op": ">",
                "args": [
                  "supcol",
                  0
                ]
              },
              {
                "op": ">",
                "args": [
                  "sd.qg",
                  0
                ]
              }
            ]
          },
          {
            "op": "apply_expression_template",
            "args": [],
            "name": "ventilated_diffusional_growth",
            "bindings": {
              "rh": "rh_i",
              "rslope2": "sd.rslope2_g",
              "coeres": "sd.coeres_g",
              "f_vent": "sd.f_vent",
              "f_diff": "f_diff_i",
              "c1": "sd.precg1",
              "c2": "sd.precg2"
            }
          },
          0
        ]
      }
    },
    {
      "lhs": "supice_g",
      "rhs": {
        "op": "-",
        "args": [
          "supice_s",
          "psdep_lim"
        ]
      }
    },
    {
      "lhs": "pgdep_lim",
      "rhs": {
        "op": "ifelse",
        "args": [
          {
            "op": "and",
            "args": [
              {
                "op": ">",
                "args": [
                  "supcol",
                  0
                ]
              },
              {
                "op": ">",
                "args": [
                  "sd.qg",
                  0
                ]
              },
              {
                "op": "==",
                "args": [
                  "ifsat_s",
                  0
                ]
              }
            ]
          },
          {
            "op": "apply_expression_template",
            "args": [],
            "name": "saturation_limited_deposition",
            "bindings": {
              "rate": "pgdep",
              "satdt": "satdt",
              "supice": "supice_g",
              "q": "sd.qg",
              "dt": "dtcld"
            }
          },
          0
        ]
      }
    },
    {
      "lhs": "ifsat_g",
      "rhs": {
        "op": "ifelse",
        "args": [
          {
            "op": "or",
            "args": [
              {
                "op": "==",
                "args": [
                  "ifsat_s",
                  1
                ]
              },
              {
                "op": "and",
                "args": [
                  {
                    "op": ">",
                    "args": [
                      "supcol",
                      0
                    ]
                  },
                  {
                    "op": ">",
                    "args": [
                      "sd.qg",
                      0
                    ]
                  },
                  {
                    "op": ">=",
                    "args": [
                      {
                        "op": "abs",
                        "args": [
                          {
                            "op": "+",
                            "args": [
                              "prevp",
                              "pidep_lim",
                              "psdep_lim",
                              "pgdep_lim"
                            ]
                          }
                        ]
                      },
                      {
                        "op": "abs",
                        "args": [
                          "satdt"
                        ]
                      }
                    ]
                  }
                ]
              }
            ]
          },
          {
            "op": "const",
            "args": [],
            "value": 1,
            "units": "1"
          },
          {
            "op": "const",
            "args": [],
            "value": 0,
            "units": "1"
          }
        ]
      }
    },
    {
      "lhs": "supice_n",
      "rhs": {
        "op": "-",
        "args": [
          "supice_g",
          "pgdep_lim"
        ]
      }
    },
    {
      "lhs": "qi_nucleation_target",
      "rhs": {
        "op": "apply_expression_template",
        "args": [],
        "name": "ice_nucleation_target",
        "bindings": {
          "T": "sd.T",
          "t0": "wrf.svpt0",
          "rho": "sd.rho",
          "n_coef": "par.xni0_coef",
          "n_exp": "par.xni0_exp",
          "m_coef": "par.roqi0_coef",
          "m_exp": "par.roqi0_exp"
        }
      }
    },
    {
      "lhs": "pigen",
      "rhs": {
        "op": "ifelse",
        "args": [
          {
            "op": "and",
            "args": [
              {
                "op": ">",
                "args": [
                  "supcol",
                  0
                ]
              },
              {
                "op": ">",
                "args": [
                  "supsat",
                  0
                ]
              }
            ]
          },
          {
            "op": "apply_expression_template",
            "args": [],
            "name": "adjustment_towards_target_rate",
            "bindings": {
              "q_target": "qi_nucleation_target",
              "q": {
                "op": "max",
                "args": [
                  "sd.qi",
                  0
                ]
              },
              "dt": "dtcld"
            }
          },
          0
        ]
      }
    },
    {
      "lhs": "pigen_lim",
      "rhs": {
        "op": "ifelse",
        "args": [
          {
            "op": "and",
            "args": [
              {
                "op": ">",
                "args": [
                  "supcol",
                  0
                ]
              },
              {
                "op": ">",
                "args": [
                  "supsat",
                  0
                ]
              },
              {
                "op": "==",
                "args": [
                  "ifsat_g",
                  0
                ]
              }
            ]
          },
          {
            "op": "min",
            "args": [
              "pigen",
              "satdt",
              "supice_n"
            ]
          },
          0
        ]
      }
    },
    {
      "lhs": "qi_max",
      "rhs": {
        "op": "/",
        "args": [
          "roqimax",
          "sd.rho"
        ]
      }
    },
    {
      "lhs": "psaut",
      "rhs": {
        "op": "ifelse",
        "args": [
          {
            "op": "and",
            "args": [
              {
                "op": ">",
                "args": [
                  "supcol",
                  0
                ]
              },
              {
                "op": ">",
                "args": [
                  "sd.qi",
                  0
                ]
              }
            ]
          },
          {
            "op": "apply_expression_template",
            "args": [],
            "name": "excess_conversion_rate",
            "bindings": {
              "q": "sd.qi",
              "q_max": "qi_max",
              "dt": "dtcld"
            }
          },
          0
        ]
      }
    },
    {
      "lhs": "pgaut",
      "rhs": {
        "op": "ifelse",
        "args": [
          {
            "op": "and",
            "args": [
              {
                "op": ">",
                "args": [
                  "supcol",
                  0
                ]
              },
              {
                "op": ">",
                "args": [
                  "sd.qs",
                  0
                ]
              }
            ]
          },
          {
            "op": "apply_expression_template",
            "args": [],
            "name": "snow_to_graupel_aggregation",
            "bindings": {
              "qs": "sd.qs",
              "qs0": "par.qs0",
              "T": "sd.T",
              "t0": "wrf.svpt0",
              "coef": "par.pgaut_coef",
              "expn": "par.pgaut_exp"
            }
          },
          0
        ]
      }
    },
    {
      "lhs": "pgaut_lim",
      "rhs": {
        "op": "apply_expression_template",
        "args": [],
        "name": "sink_rate_limiter",
        "bindings": {
          "rate": "pgaut",
          "q": "sd.qs",
          "dt": "dtcld"
        }
      }
    },
    {
      "lhs": "psevp",
      "rhs": {
        "op": "ifelse",
        "args": [
          {
            "op": "and",
            "args": [
              {
                "op": "<",
                "args": [
                  "supcol",
                  0
                ]
              },
              {
                "op": ">",
                "args": [
                  "sd.qs",
                  0
                ]
              },
              {
                "op": "<",
                "args": [
                  "rh_w",
                  1
                ]
              }
            ]
          },
          {
            "op": "*",
            "args": [
              "sd.n0sfac",
              {
                "op": "apply_expression_template",
                "args": [],
                "name": "ventilated_diffusional_growth",
                "bindings": {
                  "rh": "rh_w",
                  "rslope2": "sd.rslope2_s",
                  "coeres": "sd.coeres_s",
                  "f_vent": "sd.f_vent",
                  "f_diff": "f_diff_w",
                  "c1": "sd.precs1",
                  "c2": "sd.precs2"
                }
              }
            ]
          },
          0
        ]
      }
    },
    {
      "lhs": "psevp_lim",
      "rhs": {
        "op": "apply_expression_template",
        "args": [],
        "name": "negative_sink_limiter",
        "bindings": {
          "rate": "psevp",
          "q": "sd.qs",
          "dt": "dtcld"
        }
      }
    },
    {
      "lhs": "pgevp",
      "rhs": {
        "op": "ifelse",
        "args": [
          {
            "op": "and",
            "args": [
              {
                "op": "<",
                "args": [
                  "supcol",
                  0
                ]
              },
              {
                "op": ">",
                "args": [
                  "sd.qg",
                  0
                ]
              },
              {
                "op": "<",
                "args": [
                  "rh_w",
                  1
                ]
              }
            ]
          },
          {
            "op": "apply_expression_template",
            "args": [],
            "name": "ventilated_diffusional_growth",
            "bindings": {
              "rh": "rh_w",
              "rslope2": "sd.rslope2_g",
              "coeres": "sd.coeres_g",
              "f_vent": "sd.f_vent",
              "f_diff": "f_diff_w",
              "c1": "sd.precg1",
              "c2": "sd.precg2"
            }
          },
          0
        ]
      }
    },
    {
      "lhs": "pgevp_lim",
      "rhs": {
        "op": "apply_expression_template",
        "args": [],
        "name": "negative_sink_limiter",
        "bindings": {
          "rate": "pgevp",
          "q": "sd.qg",
          "dt": "dtcld"
        }
      }
    }
  ],
  "tests": [
    {
      "id": "qss_step250_row23_col24_mixed_phase_deposition",
      "description": "Reference: WRF 4.8 em_quarter_ss idealized supercell (GNU real32 build, dx = 2 km, dt = 12 s, 40 layers, WSM6 only) dumped by the instrumented ctessum-claude/WRF fork (module_esm_dump with esm_dump_inner hooks inside mp_wsm6_run of the ctessum-claude/MMM-physics fork, commit 52cfbd7) and replayed through the real64 (kind_phys = real64) standalone kernels/wsm6_driver at the WRF step. POINTWISE and step-free: the inputs are the state at which the kernel evaluates its process rates (t_rates, q/qi/qr/qs/qg_rates after the sub-step's sedimentation, melting, freezing and slope update; den, p; the start-of-sub-step saturation block qsat_w/rh_w/qsat_i/rh_i/xl, see saturation.esm; and the applied rain evaporation prevp_raw of the warm-rain block), the expected values the rates the kernel dumps right after evaluating them (`<rate>_raw`, after the sequential vapor-budget limiters, before the mass-conservation rescaling) and the mp_wsm6_init coefficients, from the real64 replay. No small-dt replay because WSM6's increments are not rate x dt (EqWeFiC FORTRAN_BUGS.md N3). Real64 replay vs real32 dump: <= 1e-5 relative in these rates (pidep 1.0 relative only in the near-zero threshold layer 33/34 where a branch flips). Residual esm-vs-real64 mismatch from the kernel's default-real literals and real32 WRF constants (EqWeFiC FORTRAN_BUGS.md N2), measured with zero tolerances: pidep 4.8e-8, psdep 1.1e-7, pgdep 0, pgaut 7e-8 of the column maximum; pigen 7.7e-7 because it is the small difference of the nucleation target and the ice content, each carrying the 1e-7 rounding of 4.92e-11, 1.33 and 0.1 (hence rel 5e-6 on its spot checks and Linf 3e-6 of column maximum); psaut up to 1.4e-5 relative on its spot checks because it is the small difference of qi and qimax = roqimax/rho, and roqimax = 2.08e22 dimax^8 carries a 4.3e-7 rounding from the real32 dimax (hence rel 5e-5 on the psaut spot checks; its Linf bound is unaffected). Tolerances otherwise 1e-6 relative on coefficients, absolute Linf bounds on the limited whole columns at 1e-6 of each column's maximum, relative 2e-6 spot checks of the UNLIMITED rates at layers where the dumped rate lies strictly inside every limiter bound (below 0.8 of min(|satdt/2|, |supice|, q/dtcld)). Regime: supercell step 250 (t = 50 min), row j = 23, column i = 24: freezing level at layer 9; ice 9-39, snow 6-33, graupel 1-33; supersaturated over ice (satdt > 0) in layers 3-29, subsaturated above, so pidep/psdep/pgdep change sign near layer 30 and sublimate above; nucleation active 9-29, ice-to-snow aggregation 21-24 (where qi > qimax), snow-to-graupel aggregation 16-28; the vapor budget never closes (ifsat = 0 everywhere); above 0 C the column is saturated over water, so psevp = pgevp = 0.",
      "parameter_overrides": {
        "dtcld": 12.0
      },
      "expression_template_imports": [
        {
          "ref": "./tests/qss_step250_row23_col24_mixed_phase_deposition_inputs.esm"
        }
      ],
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "roqimax",
          "time": 0.0,
          "expected": 8.125003470069448e-05,
          "tolerance": {
            "rel": 1e-06
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        },
        {
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          "time": 0.0,
          "reduce": "Linf_error",
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          "tolerance": {
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        {
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    {
      "id": "qss_step250_row22_col25_mixed_phase_deposition",
      "description": "Same reference chain and tolerance reasoning as qss_step250_row23_col24_mixed_phase_deposition, tile row j = 22 (call 9982), column i = 25: the strongest nucleation column of the run (pigen 21 layers, up to 1.3e-5 kg/kg/s) with ice-to-snow aggregation in layers 21-24 and snow-to-graupel aggregation 15-29; the vapor budget never closes. Measured residuals: pidep 4.8e-8, psdep 1.1e-7, pigen 7.2e-7, pgaut 6.9e-8 of column maximum.",
      "parameter_overrides": {
        "dtcld": 12.0
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    {
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      "expression_template_imports": [
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    {
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        "dtcld": 60.0
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      "expression_template_imports": [
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        "end": 1.0
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}