Bin Diffusion Model (BDM)

BDM couples the Bin Microphysics Model (BMM) to the moving-boundary radial diffusion model (MBD). BMM supplies the parcel thermodynamics, aerosol/droplet size distribution and condensational growth, while BDM resolves the radial water/solute concentration profile inside each representative liquid particle.

The bmm/ directory is a subtree. BDM deliberately supports only a restricted subset of BMM physics; BDM-specific coupling should therefore be implemented in the top-level BDM code rather than by modifying BMM itself.

Supported BMM configuration

The current BDM coupling is designed for:

• full-moving bins (bin_scheme_flag = 0);
• no stochastic collection / aggregation (sce_flag = 0);
• one soluble aerosol component (n_comps = 1);
• no semivolatile aerosol treatment (sv_flag = 0);
• molecular Koehler treatment (kappa_flag = 0), consistent with the radial water-activity calculation;
• homogeneous ice nucleation only, using Koop (ice_nucleation_mech = .true., .false., .false., .false.);
• no INP classes (n_inp_classes = 0);
• no entrainment or aerosol exchange;
• no secondary-ice or breakup mechanisms.

read_in_bdm_namelist checks these restrictions at startup. Unsupported combinations stop with an explanatory error rather than running with inconsistent BDM/BMM state.

These restrictions are physical as well as numerical. A BDM liquid bin has an associated internal radial concentration profile. Full-moving condensational growth preserves the identity of that representative particle. Aggregation, fixed-grid remapping and entrainment would require an additional rule for merging/remapping/diluting those internal radial profiles, which is not presently defined.

Coupling to the current BMM

The current BMM interface is

call bin_microphysics(func1, func2, func3, func4)

BDM calls it with

call bin_microphysics(fparcelwarmdiff, fparcelcold, icenucleation, &
                      noncollisional_iceformation_diff)

fparcelwarmdiff is the BDM warm-cloud callback. The active ice callback is noncollisional_iceformation_diff, which matches the current BMM func4 interface.

For homogeneous freezing, BDM retains its special radial calculation. In each radial shell it calculates water activity from the resolved water and soluble-material concentrations and evaluates the Koop homogeneous nucleation rate. The resulting frozen number concentration is then transferred to the ice population using the same full-moving number, mass and moment bookkeeping as the current BMM non-collisional ice-formation routine. Thus the nucleation physics remains BDM-specific, while the ice-state bookkeeping follows current BMM.

The BMM subtree itself is not modified for this coupling.

Diffusion coefficient

The top-level namelist.in selects the diffusion treatment:

diffusion_type = 0   ! constant diffusion coefficient from the MBD namelist
diffusion_type = 1   ! composition-dependent coefficient from DCC

For diffusion_type = 0, the constant coefficient is nmd%d_coeff in mbd/namelist.in.

For diffusion_type = 1, BDM uses diffusion_coeff_file (normally namelist.diff_coeffs) and the DCC parameterisation selected there.

Example simulations

The examples below show the evolution of the resolved radial water activity in selected BMM size bins. Radius is shown on a logarithmic scale and the colour field gives the water activity within the particle as a function of radius and time.

195 K — constant diffusion coefficient

This case uses a constant molecular diffusion coefficient of (D = 1\times10^{-17}\ \mathrm{m^2,s^{-1}}).

195 K — Lienhard2015 alpha-pinene

This case uses the composition-dependent Lienhard2015 diffusion-coefficient parameterisation for alpha-pinene.

243 K — constant diffusion coefficient

This case uses a constant molecular diffusion coefficient of (D = 1\times10^{-17}\ \mathrm{m^2,s^{-1}}) at the warmer initial temperature of 243 K.

These examples illustrate the sensitivity of the internal water distribution and particle growth to both temperature and the treatment of condensed-phase diffusion.

Scientific background and references

BDM follows the modelling approach developed by Fowler, Connolly and Topping (2020), who coupled size-resolved cloud-parcel microphysics to a condensed-phase diffusion model in order to investigate how restricted water transport within ultra-viscous aerosol particles affects particle growth and homogeneous ice nucleation. This is the primary scientific reference for the BDM approach described here.

The moving-boundary radial diffusion treatment is also closely related to Fowler et al. (2018), which describes a concentric-shell aerosol model in which the outer particle radius moves as water is taken up or lost and diffusion is solved through the particle interior.

References

• Fowler, K., Connolly, P., and Topping, D. (2020): Modelling the effect of condensed-phase diffusion on the homogeneous nucleation of ice in ultra-viscous particles, Atmospheric Chemistry and Physics, 20, 683–698. https://doi.org/10.5194/acp-20-683-2020
• Fowler, K., Connolly, P. J., Topping, D. O., and O'Meara, S. (2018): Maxwell–Stefan diffusion: a framework for predicting condensed phase diffusion and phase separation in atmospheric aerosol, Atmospheric Chemistry and Physics, 18, 1629–1642. https://doi.org/10.5194/acp-18-1629-2018

Repository layout

• bin_diffusion_model.f90 — BDM/BMM/MBD coupling, including the BDM-specific warm and ice callbacks.
• namelist.in — top-level BDM controls and paths to the component namelists.
• namelist.diffusion — BMM configuration used by BDM.
• namelist.diff_coeffs — DCC diffusion-coefficient configuration.
• bmm/ — Bin Microphysics Model subtree.
• mbd/ — moving-boundary radial diffusion subtree.
• dcc/ — diffusion-coefficient model subtree.

Compilation

A Fortran NetCDF installation is required. Set the NetCDF include/library variables used by the top-level Makefile for your system, then build with

make

The current BMM has dependencies in its sce/ and opt/ directories. The top-level BDM Makefile builds/links these because the BMM module references them, even though the supported BDM configuration sets sce_flag = 0 and does not use aggregation.

For a clean rebuild after updating a subtree or module interface, use

make cleanall
make

Running

Run BDM with a top-level namelist, for example

./main.exe namelist.in

The top-level namelist identifies the BMM, MBD and DCC namelists used for the run.

Validation of this BMM update

The BDM coupling was compiled against the supplied current BMM with explicit interfaces and bounds/runtime checking enabled. A short runtime-check integration also completed without callback or bounds errors. That test used a local NetCDF stub because the development environment did not contain the NetCDF Fortran module, so NetCDF I/O itself was not validated by that test.

Documentation

Doxygen documentation can be generated from the source with

doxygen fortran.dxg