Aerosol Properties

Aerosol Properties#

Aerosol properties bridge representations and processes. Processes declare which properties they need; the Model builds providers by querying the representations.

AerosolProperty Enum#

MIAM defines three aerosol properties:

Property	Units	Description
`EffectiveRadius`	m	The effective radius of particles in the mode or section
`NumberConcentration`	# m⁻³	The total number concentration of particles
`PhaseVolumeFraction`	dimensionless	Fraction of total particle volume belonging to a specific phase

Provider Pattern#

An AerosolPropertyProvider is a lightweight callable object created at setup time by a representation. It captures all necessary column indices so that runtime calls are free of string lookups or map searches.

Each provider exposes:

dependent_variable_indices: A vector of state variable indices that the property depends on. Used for Jacobian sparsity analysis and partial derivative mapping.
ComputeValue(params, vars, result): Computes the property value for all grid cells. Called inside the forcing function loop.
ComputeValueAndDerivatives(params, vars, result, partials): Computes the property value and partial derivatives with respect to each dependent variable. Called inside the Jacobian function loop. The partials matrix has one column per dependent variable, in the same order as dependent_variable_indices.

How Providers Are Built#

When you register processes and representations with a Model, the Model’s BuildProviders method:

Collects RequiredAerosolProperties() from each process.
De-duplicates properties per phase.
Finds the representation that owns each phase prefix.
Calls GetPropertyProvider(property, param_indices, var_indices, phase_name) on the representation.
Stores the resulting providers in a map keyed by phase prefix.

This happens once at solver setup time. The providers are then passed to the process ForcingFunction and JacobianFunction closures.

Derivative Chain#

For the Jacobian, MIAM implements a chain rule through aerosol properties. When a process depends on an aerosol property that itself depends on state variables, the total Jacobian contribution is:

\[\frac{\partial f_i}{\partial x_j} = \underbrace{\frac{\partial f_i}{\partial P}}_{\text{process}} \cdot \underbrace{\frac{\partial P}{\partial x_j}}_{\text{provider}}\]

where \(P\) is an aerosol property (e.g., effective radius) and \(x_j\) is a state variable (e.g., species concentration).

The process computes \(\partial f_i / \partial P\) (e.g., how forcing depends on effective radius), and the provider supplies \(\partial P / \partial x_j\) via the partials matrix. The process then assembles the complete Jacobian entries by multiplying these factors.

Per-Representation Derivatives#

The partial derivatives \(\partial P / \partial x_j\) vary by representation type. For details, see Henry’s Law Phase Transfer § Aerosol property derivatives.

Representation	\(\partial r_\text{eff} / \partial x_j\)	Notes
SingleMomentMode	0	Radius is fixed by GMD/GSD parameters
TwoMomentMode	Non-zero (depends on V, N)	Chain rule through total volume and number concentration
UniformSection	0	Radius is fixed by section bounds