Representations

Representations describe how particle populations are distributed in size space. Each representation owns one or more phases, manages the corresponding state variables and parameters, and provides aerosol property calculations.

SingleMomentMode

A log-normal size distribution with fixed geometric mean diameter (GMD) and geometric standard deviation (GSD). The number concentration is diagnosed from the total species volume.

auto cloud = SingleMomentMode{
  "CLOUD",                // mode name
  { aqueous_phase },      // phases
  1.0e-6,                 // geometric mean radius [m]
  1.4                     // geometric standard deviation
};

State variables: species concentrations for each phase (no number concentration variable).

State parameters (2): geometric_mean_radius, geometric_standard_deviation.

Aerosol properties:

Property	Formula	State dependencies
Effective radius	\(r_\text{eff} = \text{GMD} \cdot \exp(2.5 \ln^2 \text{GSD})\)	None (parameterized)
Number concentration	\(N = V_\text{total} / V_\text{single}\)	All species (all phases)
Phase volume fraction	\(\varphi_p = V_\text{phase} / V_\text{total}\)	All species (all phases)

TwoMomentMode

A log-normal distribution with prognostic number concentration and fixed GSD. Effective radius is derived from the total volume and number concentration.

auto aitken = TwoMomentMode{
  "AITKEN",               // mode name
  { aqueous_phase },      // phases
  1.2                     // geometric standard deviation
};

// Set the number concentration in the solver state:
state[aitken.NumberConcentration()] = 1.0e8;  // m-3

State variables: species concentrations + one number_concentration variable per mode.

State parameters (1): geometric_standard_deviation.

Aerosol properties:

Property	Formula	State dependencies
Effective radius	\(r_\text{eff} = (3 V / 4\pi N)^{1/3} \cdot \exp(2.5 \ln^2 \text{GSD})\)	All species + N
Number concentration	\(N = [\text{N\_var}]\)	Number concentration variable
Phase volume fraction	\(\varphi_p = V_\text{phase} / V_\text{total}\)	All species (all phases)

UniformSection

A sectional bin with fixed minimum and maximum radius bounds. Number concentration is diagnosed from total species volume and average particle size.

auto dust = UniformSection{
  "DUST",                 // section name
  { organic_phase },      // phases
  1.0e-7,                 // min radius [m]
  1.0e-6                  // max radius [m]
};

State variables: species concentrations for each phase.

State parameters (2): min_radius, max_radius.

Aerosol properties:

Property	Formula	State dependencies
Effective radius	\(r_\text{eff} = (r_\min + r_\max) / 2\)	None (parameterized)
Number concentration	\(N = V_\text{total} / V_\text{single}\)	All species (all phases)
Phase volume fraction	\(\varphi_p = V_\text{phase} / V_\text{total}\)	All species (all phases)

Multi-Phase Modes

A representation can host multiple phases. For example, an accumulation mode with both aqueous and organic phases:

auto accumulation = TwoMomentMode{
  "ACCUMULATION",
  { aqueous_phase, organic_phase },  // two phases
  1.4
};

All species across all phases contribute to the total particle volume used for size calculations. The phase volume fraction φ_p partitions the particle surface area among phases (see Henry’s Law Phase Transfer § Phase volume fraction).

Species Property Requirements

Species used in representations must carry physical properties for volume calculations:

auto nacl = Species{ "NaCl",
    { { "molecular weight [kg mol-1]", 0.058 },
      { "density [kg m-3]", 2165.0 } } };

These are accessed at provider creation time (once, not on the hot path).

Accessing State Variables

Representations provide helper methods for constructing fully qualified state variable names:

// Returns "DROPLET.AQUEOUS.CO2"
std::string name = droplet.Species(aqueous_phase, co2);

// For TwoMomentMode: returns "AITKEN.number_concentration"
std::string nc_name = aitken.NumberConcentration();

Use these with the MICM State object to set initial conditions:

state[droplet.Species(aqueous_phase, co2)] = 1.0e-5;  // mol m-3