Eqweather

Sedimentation (fallout) of the precipitating hydrometeors of the WRF single-moment 6-class microphysics scheme (WSM6; Hong and Lim 2006), written as the flux-form continuity law of each falling category, dq/dt = -(1/rho) d/dz(rho v_t q), with the mass-weighted terminal fall speeds v_t of hydrometeor_slopes.esm (mounted as subsystem sd) and lowered on the column_nonuniform_1d grid by EarthSciDiscretizations sedimentation_jh2010_flux_D_lev (PR #42), the dt -> 0 limit of WSM6's own forward semi-Lagrangian fallout (nislfv_rain_plm, Juang and Hong 2010): the flux through a layer's lower face is a third-order interpolated interface fall speed times the monotone average-slope face value of the layer above (FORTRAN_BUGS N77), nothing enters through the model top, and the outflow through the lowest face is the surface precipitation rate. Rain falls at its own speed v_r; snow and graupel fall TOGETHER at the mixing-ratio-weighted speed v_sg (WSM6 sediments the two categories jointly since V3.0, nislfv_rain_plm6 with the combined worka), so the snow and graupel fluxes both use W_sg; cloud ice falls at v_i (Heymsfield-Donner power law of the mean crystal diameter); cloud water does not fall. Negative input mixing ratios (round-off in the kernel inputs) are advected as zero mass; WSM6 advects den*q with the negatives in it, which in these tests changes the tendencies by <= 1.1e-9 of the column maximum. THIS IS THE METHOD-OF-LINES (INSTANTANEOUS DERIVATIVE) FORM: WSM6 integrates fallout with that semi-Lagrangian scheme, whose increment over one WRF step is not dt times this derivative, but as dt -> 0 its tendency converges to exactly the operator written here (measured against the verbatim Fortran routine in every test, to <= 1.14e-7 of the column maximum for rain, snow and graupel and 6.4e-6 for ice; the ice gap is the one branch the rule omits, the upwind side of a face whose interpolated speed overshoots below zero). The fall speeds are set to zero where WSM6 zeroes them (rain where q_r <= 0, ice where q_i <= 0, the joint snow/graupel speed where q_s + q_g <= 1e-15): with donor-cell that was immaterial, because the flux of an empty layer is zero either way, but the jh2010 interface speed reads the NEIGHBOURS' speeds and switches to the layer above wherever a speed is exactly zero, and without the zero the early-storm rain tendency was 16 % off. The kernel's `fall` flux DIAGNOSTIC converges (linearly in dt) to the layer-centred fluxes rho v_t q, which is what the FLUX assertions pin; they do not depend on the rule. Until 2026-09-22 this component imported the first-order donor-cell rule sedimentation_upwind1_flux_D_lev, which differs from WRF's converged fallout by 16-112 % of the column maximum in these tests. Transcribed from the fallout block of mp_wsm6_run in phys/physics_mmm/mp_wsm6.F90 (WRF 4.8, NCAR/MMM-physics fork ctessum-claude/MMM-physics@52cfbd7): slope_wsm6 -> workr/worka -> nislfv_rain_plm/plm6 -> fall, and the ice fallout work1c -> nislfv_rain_plm -> fallc. 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.