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update in parcel documentation (chemistry) [ci skip]
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% misc
\usepackage{amsmath}

% chemistry!
\usepackage[version=4]{mhchem}

% refrerences, url
\usepackage[colorlinks=true,allcolors=blue]{hyperref}

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\section{Introduction}\label{sec:intro}

The parcel model represents an idealised scenario of a 0-dimensional air parcel rising adiabatically with a~constant vertical velocity.
Because of its simplicity, the parcel approach provides computationally efficient testbed for cloud microphysics schemes.\\
The parcel model represents an idealized scenario of a 0-dimensional air parcel
rising adiabatically with a~constant vertical velocity.
Because of its simplicity, the parcel approach provides
computationally efficient testbed for cloud microphysics schemes.\\

Representation of microphysical and chemical processes in the parcel model is done using the particle-based scheme.
Representation of microphysical and chemical processes in the parcel model
is done using the particle-based scheme.
The particle-based scheme (aka Lagrangian scheme) allows to track the properties of both
aerosol particles and cloud droplets throughout the entire simulation.
The processes resolved by the particle-based scheme cover:
Expand All @@ -109,21 +115,35 @@ \section{Introduction}\label{sec:intro}
(iv) aqueous phase chemical reactions.
All the processes can be easily switched on/off by the user.

We are using the particle-based scheme from the \emph{libcloudph++} library. This is a library of algorithms for representing cloud microphysics in numerical models.
The introduction to the \emph{libcloudph++} containing description of the particle-based scheme used in the parcel model,
We are using the particle-based scheme from the \emph{libcloudph++} library.
This is a library of algorithms for representing cloud microphysics in numerical models.
The introduction to the \emph{libcloudph++} containing description
of the particle-based scheme used in the parcel model,
complete description of the programming interface of the library and a performance analysis
is available online at \cite{Arabas_et_al_2015}.
The aqueous phase chemistry module of \emph{libcloudph++} is focused on the
oxidation of \ce{SO2} dissolved inside water drops to sulfate.
Two reaction paths are included - oxidation by \ce{O3} and \ce{H2O2}.
A description of the representation of aqueous phase chemistry in \emph{libcloudph++} is
available in the PhD thesis of Jaruga.

\section{Solved equations}\label{sec:eqs}

The particle-based microphysics scheme used within the parcel model expects dry air density $\rho_d$ as one of the input arguments.
To evaluate $\rho_d$, the profile of pressure within the parcel model is predicted by integrating the hydrostatic equation:
The particle-based microphysics scheme used within the parcel model
expects dry air density $\rho_d$ as one of the input arguments.
To evaluate $\rho_d$, the profile of pressure within the parcel model
is predicted by integrating the hydrostatic equation:
\begin{equation}
\frac{dp}{dz} = -\rho g,
\label{hydro}
\end{equation}
\noindent{where p - pressure, z - vertical displacement, $\rho$ - density of air, g - gravitational acceleration.}
A method used in the parcel model to integrate eq.~\ref{hydro} is to assume a piecewise constant profile of $\rho$.
\noindent
where $p$ represents pressure,
$z$ is the vertical displacement,
$\rho$ is the density of air and
$g$ is the gravitational acceleration.
To integrate Eq.~(\ref{hydro}) it is assumed that $\rho$ is constant
at each height level (i.e. piecewise constant profile).
As a result, at a given time level $n$ the pressure used to predict $\rho_d$ is defined as
\begin{equation*}
p^n = p^{n-1} - \rho^{n-1} g z^n .
Expand All @@ -135,56 +155,91 @@ \section{Solved equations}\label{sec:eqs}
\label{rho}
\end{equation}
\noindent
where $p_v(p, r_v)$ represents partial pressure of water vapour,
$p_{1000}$ stands for pressure equal 1000 $hPa$ that comes from the definition of potential temperature,
$R_d$ is the gas constant for dry air and
$c_{pd}$ is the specific heat at constant pressure for dry air.
where
$p_v(p, r_v)$ represents partial pressure of water vapor,
$p_{1000}$ stands for pressure equal 1000 $hPa$ that comes from the definition of potential temperature,
$R_d$ is the gas constant for dry air and
$c_{pd}$ is the specific heat at constant pressure for dry air.
The dry air density at a given time level $n$ is calculated as $\rho_d(p^n, \theta^n, r_v^n)$.
The pressure outputted by the parcel model is the same as the one used to calculate dry air density for the microphysics scheme.
The pressure outputted by the parcel model is the same
as the one used to calculate dry air density for the microphysics scheme.

At each timestep the microphysics scheme changes the temperature and moisture fields.
The parcel model uses water vapor mixing ratio and dry air potential temperature
as model variables, see \citet{Arabas_et_al_2015} for definition.
Both variables can only be changed due to the microphysical processes
(the model is adiabatic and includes only microphysics and aqueous phase chemistry).
The derivation of source terms of heat and moisture due to microphysical processes
is available in Appendix A of \citep{Arabas_et_al_2015}.

For simulations with aqueous phase chemistry six additional model variables are needed
that specify the mixing ratio of \ce{SO2}, \ce{O3}, \ce{H2O2}, \ce{CO2}, \ce{NH3} and \ce{HNO3}
trace gases in the model.
The aqueous phase chemistry module of \emph{libcloudph++} changes the
trace gas mixing ratios as described in Chapter 3.3 of the PhD thesis of Jaruga.

\section{Initial condition}

The user needs to specify the initial temperature $T_0$, pressure $p_0$ and water vapor mixing ratio $r_0$.
The initial thermodynamic condition must be set below supersaturation, i.e.
\begin{equation}
r_0 < \epsilon \frac{e_s(T_0)}{p_0 - e_s(T_0)},
\end{equation}
\noindent
where $r_0$ is initial water vapour mass mixing ratio, $e_s(T_0)$ is water vapour saturation pressure at initial temperature $T_0$, $p_0$ is initial pressure and $\epsilon = 0.622$.

where
$e_s(T_0)$ is water vapor saturation pressure at initial temperature
and $\epsilon = 0.622$.
The initial lognormal monomodal size distribution of dry aerosol is assumed:
\begin{equation}
n(r) = \frac{n_{tot}}{r\sqrt{2\pi}ln(\sigma_g)}exp(-\frac{(ln(r)-ln(\overline{r}))^2}{2ln^2(\sigma_g)})
n(r) = \frac{n_{tot}}{r\sqrt{2\pi}ln(\sigma_g)}exp\left(-\frac{(ln(r)-ln(\overline{r}))^2}{2ln^2(\sigma_g)}\right)
\label{lognormalny}
\end{equation}
\noindent
where $n(r)$ is spectral density function for particles radius $r$, $n_{tot}$ is total aerosol concentration, $\overline{r}$ is mode radius and $\sigma_g$ is geometric standard deviation.
The parametres of the size distribution can be specified by the user.

If chemical reactions are enabled, the model assumes that the initial aerosol is ammonium bisulfate aerosol.
where
$n(r)$ is spectral density function for particles radius $r$,
$n_{tot}$ is total aerosol concentration,
$\overline{r}$ is mode radius and
$\sigma_g$ is geometric standard deviation.
The parameters of the size distribution can be specified by the user.

For simulations with aqueous phase chemistry the initial trace gas mixing ratios
need to be additionally specified.
If chemical reactions are enabled, the model assumes that
the initial aerosol is ammonium bisulfate aerosol (\ce{NH4HSO4}).
The initial mass of chemical compounds is then calculated using the initial
dry aerosol size distribution and assumed dry particle density of 1.8 $g/cm^3$.

The dry particle density can be changed by the user.

\section{Arguments}

The arguments of the parcel model are divided into 4 groups:
The arguments of the parcel model are divided into 5 groups:

\subsection{thermodynamic variables}

\begin{itemize}

\item \textbf{T\_0} : float (default = 300);\\ initial temperature [K]
\item \textbf{p\_0} : float (default = 101300);\\ initial pressure [Pa]
\item \textbf{r\_0} : float (default = 0.022);\\ initial water vapour mass mixing ratio [kg/kg].
\item \textbf{r\_0} : float (default = 0.022);\\ initial water vapor mass mixing ratio [kg/kg].
\item \textbf{w} : float (default = 1);\\ Updraft velocity [m/s]

\end{itemize}

\subsection{chemistry module variables}

\begin{itemize}

\item \textbf{SO2\_g} : float (default = 0); \\ initial \ce{SO2} trace gas mixing ratio [kg/kg]
\item \textbf{O3\_g} : float (default = 0); \\ initial \ce{O3} trace gas mixing ratio [kg/kg]
\item \textbf{H2O2\_g} : float (default = 0); \\ initial \ce{H2O2} trace gas mixing ratio [kg/kg]
\item \textbf{CO2\_g} : float (default = 0); \\ initial \ce{CO2} trace gas mixing ratio [kg/kg]
\item \textbf{NH3\_g} : float (default = 0); \\ initial \ce{NH3} trace gas mixing ratio [kg/kg]
\item \textbf{HNO3\_g} : float (default = 0); \\ initial \ce{HNO3} trace gas mixing ratio [kg/kg]
\item \textbf{chem\_rho} : float (default = 1800); \\ assumed dry particulate density [kg/m3]
\item \textbf{chem\_dsl} : bool (default = false); \\ switch for dissolving trace gases into droplets
\item \textbf{chem\_dsc} : bool (default = false); \\ switch for dissociation of chemical compounds in droplets
\item \textbf{chem\_rct} : bool (default = false); \\ switch for aqueous phase reactions in droplets

\end{itemize}

\subsection{aerosol attributes}

\begin{itemize}
Expand All @@ -194,7 +249,6 @@ \subsection{aerosol attributes}
\item \textbf{n\_tot} : float (default = 60e6);\\ total concentration of lognormal distribution in standard conditions
(T=20C, p=1013.25 hPa, r=0) [m\textsuperscript{-3}]
\item \textbf{kappa} : float (default = 0.5);\\ $\kappa$ hygroscopicity parameter (see \citep{Petters_et_al_2007} for more details)
\item{TODO - mole fractions of trace gases}

\end{itemize}

Expand All @@ -208,10 +262,9 @@ \subsection{simulation parameters}\label{sec:simpar}
\item \textbf{pprof} : string (default = "pprof\_piecewise\_const\_rhod"); \\
method to calculate pressure profile used to calculate
dry air density that is used by the super-droplet scheme. The parcel model uses method described in sec. \ref{sec:eqs}. It is possible to switch on another option: "pprof\_const\_th\_rv" (see Appendix A for details).
\item TODO - open/closed chem system
\end{itemize}

\subsection{output parametres}\label{sec:output}
\subsection{output parameters}\label{sec:output}

\begin{itemize}
\item \textbf{outfile} : string (default = "test.nc"); \\ output file name; the output file is in NetCDF format
Expand Down Expand Up @@ -254,46 +307,50 @@ \subsection{output parametres}\label{sec:output}

\vspace{0.35cm}
It will generate five output spectra:
0-th spectrum moment for 26 bins spaced logaritmically between $10^{-9}$ and $10^{-4}$ m for wet radius for variable 'A' and
0, 1, 2 and 3-rd moments for 49 bins spaced linearly between $5\cdot10^{-7}$ and $2.5\cdot10^{-5}$ m for wet radius for variable 'B'.

TODO - chem output
0-th spectrum moment for 26 bins spaced logaritmically
between $10^{-9}$ and $10^{-4}$ m for wet radius for variable 'A' and
0, 1, 2 and 3-rd moments for 49 bins spaced linearly
between $5\cdot10^{-7}$ and $2.5\cdot10^{-5}$ m for wet radius for variable 'B'.

\vspace{1.5em}
For simulations with aqueous phase chemistry the ``moms'' key can also be used
for outputting the total mass of chemical compounds dissolved in droplets.
The allowed values for moms are "SO2\_a", "CO2\_a", "NH3\_a", "HNO3\_a", "O3\_a", "H2O2\_a", "S\_VI" and "H".
The first six output the total dissolved mass of the corresponding trace gases.
The "S\_VI" outputs the mass of created \ce{H2SO4} and the "H" outputs the mass of \ce{H^+} ions.
The number of bins and the size range of droplets selected for output
is defined in the same way as for the previously described output of size distribution moments.

\end{itemize}

\section{Output}

The parcel model uses NetCDF file format\footnote{see unidata.ucar.edu/software/netcdf/ for details} for output.
The content of the output file can be be viewed in terminal by using the \prog{ncdump} command.
Output variables describing time-dependent ambient conditions in the parcel are:

All the initial parameters of the parcel model are saved as global attributes of the output file.
Additionally the maximum relative humidity reached during simulation
\textbf{RH\_{max}} is also saved as a global attribute.
Output variables describing time-dependent ambient conditions in the parcel are saved as:
\begin{itemize}
\item \textbf{t} - time [s],
\item \textbf{z} - height above the starting point[m],
\item \textbf{p} - pressure [Pa],
\item \textbf{r\_v} - water vapour mixing ratio [kg/kg],
\item \textbf{r\_v} - water vapor mixing ratio [kg/kg],
\item \textbf{RH} - relative humidity [1],
\item \textbf{T} - temperature [K],
\item \textbf{th\_d} - dry potential temperature [K],
\item TODO - chem trace gases.

There is also one value for the entire simulation:

\item \textbf{RH\_{max}} - maximum relative humidity reached during the simulation [1].

\item \textbf{SO2\_g, O3\_g, H2O2\_g, CO2\_g, NH3\_g, HNO3\_g} - trace gas mixing ratios [kg/kg of dry air]
\item \textbf{SO2\_a, O3\_a, H2O2\_a, CO2\_a, NH3\_a, HNO3\_a} - total number of moles dissolved in droplets [moles/kg of dry air]
\end{itemize}

\noindent
Output variables describing size distribution of particles from microphysics scheme depend
on the user-defined "out\_bin" parameter.
Output variables describing size distribution of particles or mass of the dissolved chemical compounds
from the particle tracking scheme depend on the user-defined "out\_bin" parameter.
For example, for the default setting of "out\_bin" parameter there are two output variables
describing placing and spacing of size distribution bins:

\begin{itemize}
\item \textbf{radii\_r\_wet} - left edges of the bins of the spectrum histogram [m],
\item \textbf{radii\_dr\_wet} - bins width [m]
\end{itemize}

and one output variable containing the time-dependent chosen moment of size distribution:
\begin{itemize}
\item \textbf{radii\_m0} - 0th moment of spectrum.
Expand All @@ -302,7 +359,7 @@ \section{Output}
\section{Installation}

The parcel model requires the \emph{libcloudph++} library to be installed.
The \emph{libcloudph++} library can be obtained from the project github repository
The \emph{libcloudph++} library can be obtained from the project Github repository
at \url{https://github.com/igfuw/libcloudphxx}.
The library dependencies and installation guidelines are available there in a Readme file.

Expand Down Expand Up @@ -333,8 +390,8 @@ \subsection{bash}

\subsection{py.test}

The parcel model is shipped with a set of tests designed for checking the particle-based microphysics scheme
from the \emph{libcloudph++} library.
The parcel model is shipped with a set of tests designed for checking the particle-based microphysics
and aqueous phase chemistry schemes from the \emph{libcloudph++} library.
The tests may serve as usage examples for the parcel model and \emph{libcloudph++} library.
The tests are located in the {\bf unit\_test} and {\bf long\_test} folders.
The tests use the py.test Python package for test automation and can be run by typing from terminal:\\
Expand Down Expand Up @@ -370,7 +427,8 @@ \subsection{Gdl/Idl}
\newpage
\subsection{Python}

The following example shows how to use the parcel model from Python programming language and plot vertical profiles for pressure, temperature and relative humidity from NetCDF file.
The following example shows how to use the parcel model from Python programming language
and plot vertical profiles for pressure, temperature and relative humidity from NetCDF file.

% first column
\begin{minipage}[t]{0.65\textwidth}
Expand All @@ -382,11 +440,10 @@ \subsection{Python}

\appendix


\section*{\\Appendix A} \label{App:AppendixA}

Another method for integrating equation (\ref{hydro}) and retrieving pressure profile is to
assume constant potential temperature, $\theta = \theta^0$, and constant water vapour mixing ratio, $r_v = r_v^0$ (option "pprof\_const\_th\_rv", see sec. \ref{sec:simpar}).
assume constant potential temperature, $\theta = \theta^0$, and constant water vapor mixing ratio, $r_v = r_v^0$ (option "pprof\_const\_th\_rv", see sec. \ref{sec:simpar}).

As a result at a given time level $n$ the pressure used to predict $\rho_d$ is defined as
\begin{equation*}
Expand All @@ -405,11 +462,6 @@ \section*{\\Appendix A} \label{App:AppendixA}
described in \citep{Arabas_et_al_2015} and was added to the parcel model to allow better comparison
between the two setups.



\section*{Acknowledgements}
\footnotesize

\bibliography{doc}

\end{document}

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