\chapter{Aerosol Processes}
\labelchapter{processes}

Haero offers implementations for each of the important stages in the aerosol
life cycle. Here we describe the physics of each stage, the approximations
made by the associated parametrizations, and the implementations of the
underlying prognostic and diagnostic processes.

In each of the processes, we assume the state of an aerosol system is specified
by the following prognostic variables:

\begin{itemize}
  \item $ n_m(x_i, y_i, z_k, t)$ [\# /m$^3$]: the {\em number density} of mode $m$,
        defined within the cell in column $i$ at vertical level $k$
  \item $ q_{m,s}(x_i, y_i, z_k, t)$ [kg aerosol species $s$/kg air]: the
        {\em mass mix fraction} of aerosol species $s$ within mode $m$, defined
        within the cell in column $i$ at vertical level $k$
  \item $ q_g(x_i, y_i, z_k, t)$ [kmol gas species $g$/mkol air]: the {\em mole
        fraction} of gas species $g$, defined within the cell in column $i$ at
        vertical level $k$
\end{itemize}

Further, each process is independent of all other processes. In other words,
state variables are taken directly from the prognostics and diagostics passed
to the process, and no assumptions are made about how these state variables
were computed.

\begin{defn}[Aerosol process]
  Aerosol processes are \emph{prognostic} in the sense that they update a tendency, which provides the right-hand-side for a differential equation solved either by Haero or its model.
\end{defn}


  Processes may need intermediate quantities using the available state data and metadata to evaluate their tendencies.  
  These intermediate quantities are \emph{diagnostic} in the sense they they can be computed, or diagnosed, from the current state variables; they are not evolved in time by either Haero or its host model.
  They are computed by diagnostic functions; storage of these quantities depends on their use in various aerosol processes and/or the host model.
\begin{defn}[Diagnostic function]
  A diagnostic function updates any relevant diagnostic variables in place at simulation time $t$.
  
  Diagnostic functions are therefore associated with the design of Kokkos kernel \emph{functors}.
  In Haero, we apply the design priniciple that each diagnostic function updates exactly 1 diagnostic quantity.
  In software, therefore, diagnostic functions are launched as separate kernels.
\end{defn}

\begin{assume}[Independent aerosol processes]
  Every aerosol process is independent of other aerosol processes. Specifically:
  a process takes a set of state variables and diagnostics, and {\em using only
  these variables}, it computes a set of tendencies for the prognostic state variables at simulation time $t$.
\end{assume}

This process independence is a dramatic departure from prior implementations of
aerosol physics in MAM. Any sequential coupling of processes must be performed
by a host model.

With this assumption, it's possible to recover the legacy MAM algorithms by
constructing a coupling procedure that follows the relevant assumptions. But
it's also possible to construct more sophisticated coupling processes that take
advantage of advances in numerical analysis.

The following sections list the available aerosol processes provided by Haero.

\input{processes/nucleation.tex}