Super-Droplets

The super-droplet method represents the condensed phase with Lagrangian particles rather than with bulk mixing ratios. Each particle carries a multiplicity – the number of real droplets it stands for – together with the mass of each condensate species and of each aerosol it contains. The method is selected with erf.moisture_model = SuperDroplets; see Microphysics model for where it sits among the other moisture models, and 3D plotfile variable reference for the per-species plotfile names it provides.

All of the inputs below use the prefix super_droplets_moisture, which is the name of the particle container (ERF_SuperDropletsMoist.H). Inputs that the container inherits from the generic ERF particle container use the same prefix; they are listed under Particles for tracer particles and behave the same way here.

Note

These entries were reconstructed from the source rather than from a specification, so the descriptions state what each input controls and where it is read. The physical guidance – which kernel or which time integrator to prefer for a given problem – is not covered here.

Anelastic compatibility

Warning

SuperDroplets cannot currently be used in a simulation in which any AMR level has erf.anelastic = 1. ERF detects this combination during input validation and exits with an error.

Use SuperDroplets with compressible dynamics, or choose a supported Eulerian microphysics scheme for an anelastic simulation.

The current Super-Droplet thermodynamic coupling uses the compressible equation of state and does not consume the hydrostatic base-state pressure used by anelastic Eulerian microphysics.

Model configuration

These inputs select which processes the model includes and what it carries. They are read by the moisture model itself (ERF_SuperDropletsMoistInit.cpp) rather than by the particle container, but use the same prefix.

Parameter	Definition	Acceptable Values	Default
species	additional condensate species carried besides water, and ice when cold processes are on. Naming a species that is already modelled aborts the run, and at most five extra species may be given	List of species names	none
aerosols	aerosol materials carried by the super-droplets	List of species names	none
include_phase_change	include condensation and evaporation	Boolean	true
include_advection	advect the super-droplets	Boolean	true
include_coalescence	include coalescence	Boolean	true
include_cold_processes	include ice; adds ice to the species list	Boolean	true
distribution_type	how the initial condensate is distributed over the particles	uniform, condensate_density	uniform
radius_raindrop	radius [m] above which a drop is counted as rain rather than cloud water	Real > 0	4.0e-5
rime_mass_ratio	rime mass fraction above which a particle is treated as rimed	Real	0.3
kinematic_mode	run with a prescribed flow field rather than a coupled one	Boolean	false
dimensionality	dimensionality of the super-droplet dynamics	one_d_z, two_d_xz, two_d_yz, three_d	three_d
recycle_particles	return deactivated particles to the domain instead of dropping them	Boolean	false
num_substeps_phase_change	sub-steps taken per time step for the phase-change update	Integer > 0	1
initial_phase_change_relaxation	relax the particles to an equilibrium size at initialization	Boolean	false
initial_phase_change_relaxation_time	duration [s] of that relaxation	Real > 0	10.0
diagnostics_interval	number of steps between writes of the distribution diagnostics	Integer > 0	1

The species and aerosol names given here determine the per-material keys used by the initialization and injection blocks below, and the qv_<species> and qc_<species> plotfile names.

Solver and time integration

The condensational growth of each particle is an ODE in the droplet mass, solved per particle per step.

Parameter	Definition	Acceptable Values	Default
mass_change_ti_method	time integrator for the mass-change ODE. An unrecognized value aborts the run	backward_euler, crank_nicolson, dirk2, rk3bs, rk4	backward_euler
mass_change_cfl	CFL-like limit on the mass-change sub-step	Real > 0	1000.0
newton_solver_rtol	relative tolerance of the Newton solve for the implicit integrators	Real > 0	1.0e-6
newton_solver_atol	absolute tolerance of that solve	Real >= 0	1.0e-99 (0.0 in single precision)
newton_solver_stol	step tolerance of that solve	Real > 0	1.0e-12
newton_solver_maxits	maximum Newton iterations per particle	Integer > 0	10
mass_change_unconverged_log	write a log entry for every particle whose mass-change solve fails to converge	Boolean	false
mass_change_unconverged_log_filename	name of that log file	String	unconverged_superdroplets.log

Ventilation

The ventilation factor enhances the mass-change rate of a falling drop. It follows Bayley et al. (2025), Eq. 3, and is off by default.

Parameter	Definition	Acceptable Values	Default
mass_change_ventilation	include the ventilation factor in the phase change	Boolean	false
ventilation_alpha1	fit coefficient alpha_1	Real	6.954e7
ventilation_beta1	fit exponent beta_1	Real	1.963
ventilation_alpha2	fit coefficient alpha_2	Real	1.069e3
ventilation_beta2	fit exponent beta_2	Real	0.702
ventilation_fcap	upper bound applied to the ventilation factor	Real > 0	20.0

Coalescence

Parameter	Definition	Acceptable Values	Default
coalescence_kernel	collision kernel used for coalescence. An unrecognized value aborts the run. Note that Longs and Halls are matched case-sensitively	sedimentation, golovin, Longs, Halls	sedimentation
kernel_relative_velocity	which relative velocity enters the kernel	terminal_velocity, absolute_velocity, radial_velocity	terminal_velocity
include_brownian_coalescence	add the Brownian contribution to the kernel	Boolean	false
ice_aggregation_efficiency	collection efficiency prefactor for ice-ice aggregation	Real	0.1
coalescence_bin_size	size, in cells, of the bins within which candidate collision pairs are drawn	3 Integers > 0	1 1 1
terminal_velocity_model	terminal-velocity model. One value sets the water model; a second, if given, sets the ice model. Giving more than two values aborts the run	RogersYau, AtlasUlbrich, CloudRainShima, IceBohm	CloudRainShima IceBohm

Particle population and motion

Parameter	Definition	Acceptable Values	Default
nucleate_particles	create new super-droplets from the vapour field	Boolean	false
density_scaling	scale the initial number density with the local air density	Boolean	false
place_randomly_in_cells	place new particles at random positions within each cell	Boolean	true
prescribed_advection	move the particles with a prescribed vertical velocity instead of the resolved flow	Boolean	false
prescribed_w	the prescribed updraft [m/s] used in that mode; a value of zero selects a sinusoidal pulse instead of a constant	Real	0.0
split_merge_amr	split and merge particles as they cross AMR level boundaries	Boolean	false
sigma0	width parameter of the assumed mass distribution	Real > 0	0.62

Deactivation and recycling

A particle whose multiplicity falls below a threshold is deactivated and may be returned to the domain at a new position.

Parameter	Definition	Acceptable Values	Default
inactive_threshold	multiplicity below which a particle is deactivated	Real > 0	0.01
write_inactive_plt	include deactivated particles in the particle plotfiles	Boolean	false
recycle_xmin, recycle_xmax	x-bounds of the region into which recycled particles are returned	Real	domain bounds
recycle_ymin, recycle_ymax	y-bounds of that region	Real	domain bounds
recycle_zmin, recycle_zmax	z-bounds of that region	Real	domain bounds

Diagnostics

Parameter	Definition	Acceptable Values	Default
distribution_grid_size	number of points in the one-dimensional radius grid on which size distributions are accumulated	Integer > 0	100
distribution_rmin	smallest radius [m] of that grid. Read only when built with ERF_USE_ML_UPHYS_DIAGNOSTICS	Real > 0	1.0e-6
distribution_rmax	largest radius [m] of that grid. Read only when built with ERF_USE_ML_UPHYS_DIAGNOSTICS	Real > 0	5.0e-3

Initialization blocks

The initial particle population is described by one or more numbered blocks. super_droplets_moisture.num_initializations sets how many there are, and block i is read under the prefix super_droplets_moisture.<i> for i = 0 ... num_initializations-1 (ERF_SuperDropletPCInitializations.cpp).

Parameter	Definition	Acceptable Values	Default
num_initializations	how many initialization blocks are read	Integer > 0	1
<i>.distribution_type	shape of the seeded region	box, bubble	box
<i>.particles_per_cell	super-droplets created per cell in that region	Integer > 0	set from the number density
particle_box_lo, particle_box_hi	corners of the seeded box; read when distribution_type = box	3 Reals	domain corners
particle_bubble_center, particle_bubble_radius	centre and radii of the seeded bubble; read when distribution_type = bubble	3 Reals	none
initial_number_density	number density of real droplets represented	Real > 0	none
initial_super_droplet_density	number density of super-droplets used to represent them	Real > 0	none
maximum_multiplicity	cap on the multiplicity assigned to a super-droplet	Real > 0	none
multiplicity_type	how multiplicity is distributed across the population	see ERF_SDInitialization.cpp	none
ice_apparent_density	apparent density [kg/m^3] used for ice particles	Real > 0	none

Within a block, each condensate species and each aerosol is given its own initial size or mass distribution, using keys named after that material – <species>_init_type, and then the subset of <species>_mass_min, <species>_mass_mean, <species>_mass_max, <species>_radius_min, <species>_radius_mean, <species>_radius_max and a standard deviation (_std) or geometric standard deviation (_gstd) that the chosen type requires. Aerosol materials use the same pattern. The exact key names depend on the configured species and aerosol names; see ERF_SDInitialization.cpp.

Injection blocks

Particles may also be injected during the run. super_droplets_moisture.num_injections sets how many injection blocks are read, and block i uses the prefix super_droplets_moisture.injection.<i>.

Parameter	Definition	Acceptable Values	Default
num_injections	how many injection blocks are read	Integer >= 0	0
rate	injection rate of real droplets	Real > 0	none
sd_rate	injection rate of super-droplets; an alternative to deriving it from rate	Real > 0	derived from rate
min_multiplicity	lower bound on the multiplicity of injected particles	Real > 0	none
t_start, t_stop	simulation times [s] between which injection is active	Real	whole run
domain_velocity	velocity [m/s] imposed on the injected particles	3 Reals	0.0 0.0 0.0
fractional_tol	tolerance used when converting a fractional injection count into whole particles	Real > 0	none

An injection block also accepts the same per-species and per-aerosol distribution keys as an initialization block.