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% jgrga JOURNAL OF GEOPHYSICAL RESEARCH
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\documentclass[draft,jgrga]{agutexSI}



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% Author names in capital letters:
%\authorrunninghead{BALES ET AL.}

% Shorter version of title entered in capital letters:
%\titlerunninghead{SHORT TITLE}

%Corresponding author mailing address and e-mail address:
%\authoraddr{Corresponding author: A. B. Smith,
%Department of Hydrology and Water Resources, University of
%Arizona, Harshbarger Building 11, Tucson, AZ 85721, USA.
%(a.b.smith@hwr.arizona.edu)}

\begin{document}

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%  TITLE
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%\includegraphics{agu_pubart-white_reduced.eps}


\title{Supporting Information for "Comparison of the SAWNUC model with CLOUD measurements of sulphuric acid-water nucleation"}
%
% e.g., \title{Supporting Information for "Terrestrial ring current:
% Origin, formation, and decay $\alpha\beta\Gamma\Delta$"}
%
%DOI: 10.1002/%insert paper number here%

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%  AUTHORS AND AFFILIATIONS
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\authors{Sebastian Ehrhart,\altaffilmark{1,2}
         Luisa Ickes, \altaffilmark{1,*}
         Joao Almeida, \altaffilmark{1,2}
         Antonio Amorim, \altaffilmark{3}
         Peter Barmet, \altaffilmark{4} 
         Federico Bianchi, \altaffilmark{4,*} 
         Josef Dommen, \altaffilmark{4} 
         Eimear M. Dunne, \altaffilmark{5,6} 
         Jonathan Duplissy, \altaffilmark{7,8}
         Alessandro Franchin, \altaffilmark{7}
         Juha Kangasluoma, \altaffilmark{7}
         Jasper Kirkby, \altaffilmark{1,2}
         Andreas K\"urten, \altaffilmark{1}
         Agnieszka Kupc, \altaffilmark{9}
         Katrianne Lehtipalo, \altaffilmark{4,7}
         Tuomo Nieminen, \altaffilmark{7,8}
         Francesco Riccobono, \altaffilmark{4} 
         Linda Rondo, \altaffilmark{2}
         Siegfried Schobesberger, \altaffilmark{7,+}
         Gerhard Steiner, \altaffilmark{7,9,10}
         Ant\'{o}nio Tom\'{e},\altaffilmark{3}
         Daniela Wimmer, \altaffilmark{1,7} 
         % PI list
         Urs Baltensperger, \altaffilmark{4}
         Paul E. Wagner, \altaffilmark{9}
         Joachim Curtius\altaffilmark{1}}



\affil{1}{Goethe-University Frankfurt am Main, Institute for Atmospheric and Environmental Sciences, Altenhoeferallee 1, 60438 Frankfurt am Main, Germany}
\affil{2}{CERN, 1211 Geneva, Switzerland }
\affil{3}{SIM, University of Lisbon and University of Beira Interior, 1749-016 Lisbon, Portugal} 
\affil{4}{Paul Scherrer Institute, 5232 Villigen, Switzerland}
\affil{5}{School of Earth and Environment, University of Leeds, LS2 9JT, UK}
\affil{6}{Finnish Meteorological Institute, Atmospheric Research Centre of Eastern Finland, PL 1627, 70211 Kuopio, Finland}
\affil{7}{Department of Physics, P.O. Box 64, FI-00014 University of Helsinki, Finland}
\affil{8}{Helsinki Institute of Physics, P.O.Box 64, FI-00014 University of Helsinki, Finland}
\affil{9}{Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria}
\affil{10}{Institute of Ion Physics and Applied Physics, Leopold-Franzens University, Innsbruck Technikerstra\ss{}e 25, 6020 Innsbruck, Austria}
\affil{*}{Now at: Institute for Atmospheric and Climate Science, ETH Zurich, Switzerland}
\affil{+}{Now at: Department of Atmospheric Sciences, University of Washington, Seattle, WA 98195, USA}


%Use \author{\altaffilmark{}} and \altaffiltext{}

% \altaffilmark will produce footnote;
% matching \altaffiltext will appear at bottom of page.

% \authors{A. B. Smith,\altaffilmark{1}
% Eric Brown,\altaffilmark{1,2} Rick Williams,\altaffilmark{3}
% John B. McDougall\altaffilmark{4}, and S. Visconti\altaffilmark{5}}

%\altaffiltext{1}{Department of Hydrology and Water Resources,
%University of Arizona, Tucson, Arizona, USA.}

%\altaffiltext{2}{Department of Geography, Ohio State University,
%Columbus, Ohio, USA.}

%\altaffiltext{3}{Department of Space Sciences, University of
%Michigan, Ann Arbor, Michigan, USA.}

%\altaffiltext{4}{Division of Hydrologic Sciences, Desert Research
%Institute, Reno, Nevada, USA.}

%\altaffiltext{5}{Dipartimento di Idraulica, Trasporti ed
%Infrastrutture Civili, Politecnico di Torino, Turin, Italy.}



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%
%  BEGIN ARTICLE
%
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% The body of the article must start with a \begin{article} command
%
% \end{article} must follow the references section, before the figures
%  and tables.

\begin{article}

%% ------------------------------------------------------------------------ %%
%
%  TEXT
%
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\noindent\textbf{Contents of this file}
%%%Remove or add items as needed%%%
\begin{enumerate}
% \item Text S1 to Sx
\item Figures S1 to S4
% \item Tables S1 to Sx
%if Tables are larger than 1 page, upload as separate excel file
\end{enumerate}
% \noindent\textbf{Additional Supporting Information (Files uploaded separately)}
% \begin{enumerate}
% \item Captions for Datasets S1 to Sx
% \item Captions for large Tables S1 to Sx (if larger than 1 page, upload as separate excel file)
% \item Captions for Movies S1 to Sx
% \item Captions for Audio S1 to Sx
% \end{enumerate}

% \noindent\textbf{Introduction}
% Text S1 gives additional information on the changes made to SAWNUC.
%Type or paste your text here. The introduction gives a brief overview of the supporting information. You should include information %about as many of the following as possible (when appropriate):
% 1. a general overview of the kind of data files;
% 2. information about when and how the data were collected or created;
% 3. a general description of processing steps used;
% 4. any known imperfections or anomalies in the data.

%\clearpage

%Delete all unused file types below. Copy/paste for multiples of each file type as needed.
\noindent\textbf{Text S1.}
The SAWNUC model was originally described in \cite{Lovejoy2004}. 
Table S4 summarises the current state of SAWNUC and provides the literature sources containing further details. 
The reaction schemes, forward reaction rate constants and evaporation rate constants presented there are still used, with the following exceptions: 
\begin{itemize}
 \item The evaporation rates of neutral particles was adjusted in \cite{kazil_parnuc_2007}. 
 \item Instead of calculating a diurnal cycle of H$_2$SO$_4$ the measured sulphuric acid concentrations are used. 
 \item The ion-ion recombination rate constant for small ions from \cite{brasseur_chatel_1983} was used.
 \item A wall loss term was added as first order loss term
\end{itemize}

% Therefore we will summarise only changes that were done to the original code. 

% 
% As mentioned in the text SAWNUC was used to calculated particle formation rates in two ways, strictly speaking only one way was calculating particle formation rates. 
% The first way is a direct calculation of the particle formation rates from the steady state cluster distribution based on the approach given by \cite{kazil_parnuc_2007}. 
% The details of this approach are given in \cite{kazil_parnuc_2007} and the main difference is that here we use the thermodynamics from SAWNUC to calculate the forward and backward reaction rate constants. 
% SAWNUC includes in the calculation of cluster Free Energies the water and sulfuric acid content and the temperature. 
% % Each cluster is assumed to be in equilibrium with the surrounding water vapour and the cluster with the most probable water content is used for the calculation of effect uptake and evaporation rate constants.
% PARNUC uses parameterised forward and backward reaction rates which were derived from the thermodynamics included in SAWNUC. 
% For the calculations in this paper we determine the uptake, evaporation and all other loss rate constants with SAWNUC for clusters up to the diameter for which we want to determine the formation rate. 
% The steady state cluster distribution is then solved for the steady state case where, $\partial_t N_{i} = 0$, is true for all clusters $i$, with $N_i$ being the cluster concentration. 
% Once the steady state cluster distribution is calculated the rate of particles exceeding a certain diameter is calculated based on equation X in \cite{kazil_parnuc_2007}. 
% 
% 
% The second way does not calculate the particle formation rate directly from particle distributions but simulates an actual experiment in the CLOUD chamber time resoled. 
% SAWNUC originally treated clusters up to 20 monomers (typically around 2~nm) in bins with linear increase in monomer content, i.e. increasing the index number of a bin by one added one H$_2$SO$_4$ molecule to the cluster.  
% Clusters with higher monomer content were in bins that increase the monomer content geometrically by a factor 1.5. 
% This allowed to have aerosol particles over the full range of atmospherically relevant sizes. 
% 
% However the focus for the CLOUD experiments is a different one. 
% There are no large pre-existing aerosols and typical time scales of nucleation experiments are too short for aerosols to grow to large diameters and typically stay below 50~nm.
% The focus in this study is to compare with the particle counters, and the counting efficiency curves of the CPCs with high D$_{50}$ flattens out beyond 3~nm. 
% As explained in the main text we kept the linear increase in size bins up to 3.3~nm to ensure a good resolution in that critical region. 

 
%Type or paste text here. This should be additional explanatory text, such as: extended descriptions of results, full details of models, extended lists of acknowledgements etc.  It should not be additional discussion, analysis, interpretation or critique. It should not be an additional scientific experiment or paper.
%
%Repeat for any additional Supporting Text

%%Enter Data Set, Movie, and Audio captions here
%%EXAMPLE CAPTIONS

% \noindent\textbf{Data Set S1.} %Type or paste caption here.
% %upload your dataset(s) to AGU's journal submission site and select "Supporting Information (SI)" as the file type. Following naming %convention: ds01.
% 
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% %upload your movie(s) to AGU's journal submission site and select, "Supporting Information %(SI)" as the file type. Following naming convention: ms01.
% 
% %Repeat any additional Supporting movies
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%upload your audio file(s) to AGU's journal submission site and select "Supporting Information %(SI)" as the file type. Following naming convention: auds01.

%Repeat for any additional Supporting audio files

%%% End of body of article:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Optional Notation section goes here
%
% Notation -- End each entry with a period.
% \begin{notation}
% Term & definition.\\
% Second term & second definition.\\
% \end{notation}
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%% ------------------------------------------------------------------------ %%
%%  REFERENCE LIST AND TEXT CITATIONS
%
% Either type in your references using
% \begin{thebibliography}{}
% % % \bibitem{}
% % % Text
% % \bibitem[{\textit{Lovejoy et~al.}(2004)\textit{Lovejoy, Curtius, and
% %   Froyd}}]{Lovejoy2004}
% % Lovejoy, E.~R., J.~Curtius, and K.~D. Froyd (2004), Atmospheric ion-induced
% %   nucleation of sulfuric acid and water, \textit{J. Geophys. Res. -
% %   Atmospheres}, \textit{109}, D08,204.
% %   
% %   \bibitem[{\textit{Kazil and Lovejoy}(2007)}]{kazil_parnuc_2007}
% % Kazil, J., and E.~R. Lovejoy (2007), A semi-analytical method for calculating
% %   rates of new sulfate aerosol formation from the gas phase,
% %   \textit{Atmospheric Chemistry and Physics}, \textit{7}(13), 3447--3459,
% % %   \doi{10.5194/acp-7-3447-2007}.
%   
% \end{thebibliography}
%
% Or,
%
% If you use BiBTeX for your references, please use the agufull08.bst file (available at % ftp://ftp.agu.org/journals/latex/journals/Manuscript-Preparation/) to produce your .bbl
% file and copy the contents into your paper here.
%
% Follow these steps:
% 1. Run LaTeX on your LaTeX file.
%
% 2. Make sure the bibliography style appears as \bibliographystyle{agufull08}. Run BiBTeX on your LaTeX
% file.
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% 3. Open the new .bbl file containing the reference list and
%   copy all the contents into your LaTeX file here.
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% 4. Comment out the old \bibliographystyle and \bibliography commands.
%
% 5. Run LaTeX on your new file before submitting.
%
% AGU does not want a .bib or a .bbl file. Please copy in the contents of your .bbl file here.

% \begin{thebibliography}{}

%\providecommand{\natexlab}[1]{#1}
%\expandafter\ifx\csname urlstyle\endcsname\relax
%  \providecommand{\doi}[1]{doi:\discretionary{}{}{}#1}\else
%  \providecommand{\doi}{doi:\discretionary{}{}{}\begingroup
%  \urlstyle{rm}\Url}\fi
%
%\bibitem[{\textit{Atkinson and Sloan}(1991)}]{AtkinsonSloan}
%Atkinson, K., and I.~Sloan (1991), The numerical solution of first-kind
%  logarithmic-kernel integral equations on smooth open arcs, \textit{Math.
%  Comp.}, \textit{56}(193), 119--139.
%
%\bibitem[{\textit{Colton and Kress}(1983)}]{ColtonKress1}
%Colton, D., and R.~Kress (1983), \textit{Integral Equation Methods in
%  Scattering Theory}, John Wiley, New York.
%
%\bibitem[{\textit{Hsiao et~al.}(1991)\textit{Hsiao, Stephan, and
%  Wendland}}]{StephanHsiao}
%Hsiao, G.~C., E.~P. Stephan, and W.~L. Wendland (1991), On the {D}irichlet
%  problem in elasticity for a domain exterior to an arc, \textit{J. Comput.
%  Appl. Math.}, \textit{34}(1), 1--19.
%
%\bibitem[{\textit{Lu and Ando}(2012)}]{LuAndo}
%Lu, P., and M.~Ando (2012), Difference of scattering geometrical optics
%  components and line integrals of currents in modified edge representation,
%  \textit{Radio Sci.}, \textit{47},  RS3007, \doi{10.1029/2011RS004899}.

%\end{thebibliography}

%Reference citation examples:

%...as shown by \textit{Kilby} [2008].
%...as shown by {\textit  {Lewin}} [1976], {\textit  {Carson}} [1986], {\textit  {Bartholdy and Billi}} [2002], and {\textit  {Rinaldi}} [2003].
%...has been shown [\textit{Kilby et al.}, 2008].
%...has been shown [{\textit  {Lewin}}, 1976; {\textit  {Carson}}, 1986; {\textit  {Bartholdy and Billi}}, 2002; {\textit  {Rinaldi}}, 2003].
%...has been shown [e.g., {\textit  {Lewin}}, 1976; {\textit  {Carson}}, 1986; {\textit  {Bartholdy and Billi}}, 2002; {\textit  {Rinaldi}}, 2003].

%...as shown by \citet{jskilby}.
%...as shown by \citet{lewin76}, \citet{carson86}, \citet{bartoldy02}, and \citet{rinaldi03}.
%...has been shown \citep{jskilbye}.
%...has been shown \citep{lewin76,carson86,bartoldy02,rinaldi03}.
%...has been shown \citep [e.g.,][]{lewin76,carson86,bartoldy02,rinaldi03}.
%
% Please use ONLY \citet and \citep for reference citations.
% DO NOT use other cite commands (e.g., \cite, \citeyear, \nocite, \citealp, etc.).

%% ------------------------------------------------------------------------ %%
%
%  END ARTICLE
%
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\end{article}
\clearpage

% Delete all unused file types below. Copy/paste for multiples of each file type as needed.

% enter figures and tables here:


\begin{figure}
\setfigurenum{S2} %%Change number for each figure
\noindent\includegraphics[width=20pc]{J_vs_RH.pdf}
\caption{Modelled particle formation rate as function of relative humidity under GCR conditions in CLOUD (4~ion~pairs~cm$^{-3}$~s$^{-1}$). The solid line gives results for temperatures below 273~K while the dashed lines give results for warmer temperatures. The temperature is also given in the colour scale. For the colder temperatures the sulphuric acid concentration was $5\cdot10^{6}$~cm$^{3}$ and for the warmer temperatures $1\cdot10^{8}$~cm$^{-3}$. }
 \label{figure_label}
\end{figure}



\begin{figure}
\setfigurenum{S3} %%Change number for each figure
\noindent\includegraphics[width=20pc]{/home/sebastian/work/simulation_CLOUD5/full_campaign_uvstart_extended/cluster_distribution/H2SO4_and_water_vs_diameter.pdf}
\caption{Number of sulphuric acid and water molecules in the particles as function of diameter for neutral particles (solid lines) and charged particles (solid lines) at 278~K and 40\% relative humidity.}
 \label{figure_label}
\end{figure}


\begin{table}
\settablenum{S4} %%Change number for each table
\caption{Summary of SAWNUC:}
\centering
\begin{tabular}{l | l}
\hline
\parbox[t]{5cm}{Max. cluster diameter \\for steady state calculation} & 1.7~nm \\
 & \\
\hline
\parbox[t]{5cm}{Max. diameter \\linear size bin} & 3.3~nm\\
 & \\
\hline
\parbox[t]{5cm}{Geometric scaling factor} & 1.15\\
 & \\
\hline
Diameter of a particle & \parbox[t]{5cm}{fixed H$_2$SO$_4$ and most probable water content} \\
\hline
Most recent description of : & \\
neutral thermodynamics & \cite{kazil_parnuc_2007}\\
charged thermodynamics & \cite{Lovejoy2004}\\
H$_2$SO$_4$ uptake & \cite{Lovejoy2004, kazil_parnuc_2007}\\
recombination & \cite{brasseur_chatel_1983, Franchin-acp-2015}\\
\hline
Ions : &  \\
Negative& (H$_2$SO$_4$)$_i \cdot$HSO$_4^-$ \\
Positive & (H$_2$O)$_5 \cdot$H$_3$O$^{+}$\\
\end{tabular}

\end{table}


\clearpage

\begin{thebibliography}{}
\providecommand{\natexlab}[1]{#1}
\expandafter\ifx\csname urlstyle\endcsname\relax
 \providecommand{\doi}[1]{doi:\discretionary{}{}{}#1}\else
 \providecommand{\doi}{doi:\discretionary{}{}{}\begingroup
 \urlstyle{rm}\Url}\fi

   \bibitem[{\textit{Brasseur and Chatel}(1983)}]{brasseur_chatel_1983}
Brasseur, G., and A.~Chatel (1983), Modeling of stratospheric ions: a first
  attempt,, \textit{Annales Geophysicae}, \textit{1}, 173--185,
  \doi{doi:10.1016/0032-0633(82)90101-5}.
  
\bibitem[{\textit{Franchin et~al.}(2015)\textit{Franchin, Ehrhart, Lepp\"a,
  Nieminen, Gagn\'e, Schobesberger, Wimmer, Duplissy, Riccobono, Dunne, Rondo,
  Downard, Bianchi, Kupc, Tsagkogeorgas, Lehtipalo, Manninen, Almeida, Amorim,
  Wagner, Hansel, Kirkby, K\"urten, Donahue, Makhmutov, Mathot, Metzger,
  Pet\"aj\"a, Schnitzhofer, Sipil\"a, Stozhkov, Tom\'e, Kerminen, Carslaw,
  Curtius, Baltensperger, and Kulmala}}]{Franchin-acp-2015}
Franchin, A., S.~Ehrhart, J.~Lepp\"a, T.~Nieminen, S.~Gagn\'e,
  S.~Schobesberger, D.~Wimmer, J.~Duplissy, F.~Riccobono, E.~M. Dunne,
  L.~Rondo, A.~Downard, F.~Bianchi, A.~Kupc, G.~Tsagkogeorgas, K.~Lehtipalo,
  H.~E. Manninen, J.~Almeida, A.~Amorim, P.~E. Wagner, A.~Hansel, J.~Kirkby,
  A.~K\"urten, N.~M. Donahue, V.~Makhmutov, S.~Mathot, A.~Metzger,
  T.~Pet\"aj\"a, R.~Schnitzhofer, M.~Sipil\"a, Y.~Stozhkov, A.~Tom\'e, V.-M.
  Kerminen, K.~Carslaw, J.~Curtius, U.~Baltensperger, and M.~Kulmala (2015),
  Experimental investigation of ion–ion recombination under atmospheric
  conditions, \textit{Atmospheric Chemistry and Physics}, \textit{15}(13),
  7203--7216, \doi{10.5194/acp-15-7203-2015}.

\bibitem[{\textit{Kazil and Lovejoy}(2007)}]{kazil_parnuc_2007}
Kazil, J., and E.~R. Lovejoy (2007), A semi-analytical method for calculating
  rates of new sulfate aerosol formation from the gas phase,
  \textit{Atmospheric Chemistry and Physics}, \textit{7}(13), 3447--3459,
  \doi{10.5194/acp-7-3447-2007}.

\bibitem[{\textit{Lovejoy et~al.}(2004)\textit{Lovejoy, Curtius, and
  Froyd}}]{Lovejoy2004}
Lovejoy, E.~R., J.~Curtius, and K.~D. Froyd (2004), Atmospheric ion-induced
  nucleation of sulfuric acid and water, \textit{J. Geophys. Res. -
  Atmospheres}, \textit{109}, D08,204.

\end{thebibliography}

% 
% \begin{figure}
% \setfigurenum{S2} %%Change number for each figure
% \noindent\includegraphics[width=20pc]{nucme_vs_apitof_292K_revised_log.pdf}
% \caption{Steady state cluster distribution as measured by the APi-TOF (black) and simulated with SAWNUC (red circles) at 292~K (same as Figure 8, but with logarithmic scale on the y-axis). The red triangles show the result of an $\pm$0.5~kcal~mol$^{-1}$ shift in the free energies of the clusters. The open circles give the total number concentration of clusters containing at least one ammonia molecule.}
%  \label{figure_label}
% \end{figure}
% 
%  
% 
% \begin{figure}
% \setfigurenum{S3} %%Change number for each figure
% \noindent\includegraphics[width=20pc]{nucme_vs_apitof_278K_revised_log.pdf}
% \caption{Steady state cluster distribution as measured by the APi-TOF (black) and simulated with SAWNUC (red circles) at 278~K (same as Figure 9, but with logarithmic scale on the y-axis). The red triangles show the result of an $\pm$0.5~kcal~mol$^{-1}$ shift in the free energies of the clusters. The open circles give the total number concentration of clusters containing at least one ammonia molecule.}
%  \label{figure_label}
% \end{figure} 
%  
% 
% \begin{figure}
% \setfigurenum{S4} %%Change number for each figure
% \noindent\includegraphics[width=20pc]{nucme_vs_apitof_248K_revised_log.pdf}
% \caption{Steady state cluster distribution as measured by the APi-TOF (black) and simulated with SAWNUC (red circles) at 248~K (same as Figure 10, but with logarithmic scale on the y-axis). The red triangles show the result of an $\pm$0.5~kcal~mol$^{-1}$ shift in the free energies of the clusters. The open circles give the total number concentration of clusters containing at least one ammonia molecule.}
%  \label{figure_label}
%  \end{figure} 

%
% EXAMPLE FIGURE
% ---------------
% \begin{figure}
%\setfigurenum{S1} %%Change number for each figure
% \noindent\includegraphics[width=20pc]{samplefigure.eps}
%\caption{Caption text here}
 %\label{figure_label}
 %\end{figure}

% ---------------
% EXAMPLE TABLE
%
%\begin{table}
%\settablenum{S1} %%Change number for each table
%\caption{Time of the Transition Between Phase 1 and Phase 2\tablenotemark{a}}
%\centering
%\begin{tabular}{l c}
%\hline
% Run  & Time (min)  \\
%\hline
%  $l1$  & 260   \\
%  $l2$  & 300   \\
%  $l3$  & 340   \\
%  $h1$  & 270   \\
%  $h2$  & 250   \\
%  $h3$  & 380   \\
%  $r1$  & 370   \\
%  $r2$  & 390   \\
%\hline
%\end{tabular}
%\tablenotetext{a}{Footnote text here.}
%\end{table}
% ---------------
%
% EXAMPLE LARGE TABLE (UPLOADED SEPARATELY)
%\begin{table}
%\settablenum{S1} %%Change number for each table
%\caption{Time of the Transition Between Phase 1 and Phase 2\tablenotemark{a}}
%\end{table}


\end{document}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

More Information and Advice:

%% ------------------------------------------------------------------------ %%
%
%  SECTION HEADS
%
%% ------------------------------------------------------------------------ %%

% Capitalize the first letter of each word (except for
% prepositions, conjunctions, and articles that are
% three or fewer letters).

% AGU follows standard outline style; therefore, there cannot be a section 1 without
% a section 2, or a section 2.3.1 without a section 2.3.2.
% Please make sure your section numbers are balanced.
% ---------------
% Level 1 head
%
% Use the \section{} command to identify level 1 heads;
% type the appropriate head wording between the curly
% brackets, as shown below.
%
%An example:
%\section{Level 1 Head: Introduction}
%
% ---------------
% Level 2 head
%
% Use the \subsection{} command to identify level 2 heads.
%An example:
%\subsection{Level 2 Head}
%
% ---------------
% Level 3 head
%
% Use the \subsubsection{} command to identify level 3 heads
%An example:
%\subsubsection{Level 3 Head}
%
%---------------
% Level 4 head
%
% Use the \subsubsubsection{} command to identify level 3 heads
% An example:
%\subsubsubsection{Level 4 Head} An example.
%
%% ------------------------------------------------------------------------ %%
%
%  IN-TEXT LISTS
%
%% ------------------------------------------------------------------------ %%
%
% Do not use bulleted lists; enumerated lists are okay.
% \begin{enumerate}
% \item
% \item
% \item
% \end{enumerate}
%
%% ------------------------------------------------------------------------ %%
%
%  EQUATIONS
%
%% ------------------------------------------------------------------------ %%

% Single-line equations are centered.
% Equation arrays will appear left-aligned.

Math coded inside display math mode \[ ...\]
 will not be numbered, e.g.,:
 \[ x^2=y^2 + z^2\]

 Math coded inside \begin{equation} and \end{equation} will
 be automatically numbered, e.g.,:
 \begin{equation}
 x^2=y^2 + z^2
 \end{equation}

% IF YOU HAVE MULTI-LINE EQUATIONS, PLEASE
% BREAK THE EQUATIONS INTO TWO OR MORE LINES
% OF SINGLE COLUMN WIDTH (20 pc, 8.3 cm)
% using double backslashes (\\).

% To create multiline equations, use the
% \begin{eqnarray} and \end{eqnarray} environment
% as demonstrated below.
\begin{eqnarray}
  x_{1} & = & (x - x_{0}) \cos \Theta \nonumber \\
        && + (y - y_{0}) \sin \Theta  \nonumber \\
  y_{1} & = & -(x - x_{0}) \sin \Theta \nonumber \\
        && + (y - y_{0}) \cos \Theta.
\end{eqnarray}

%If you don't want an equation number, use the star form:
%\begin{eqnarray*}...\end{eqnarray*}

% Break each line at a sign of operation
% (+, -, etc.) if possible, with the sign of operation
% on the new line.

% Indent second and subsequent lines to align with
% the first character following the equal sign on the
% first line.

% Use an \hspace{} command to insert horizontal space
% into your equation if necessary. Place an appropriate
% unit of measure between the curly braces, e.g.
% \hspace{1in}; you may have to experiment to achieve
% the correct amount of space.


%% ------------------------------------------------------------------------ %%
%
%  EQUATION NUMBERING: COUNTER
%
%% ------------------------------------------------------------------------ %%

% You may change equation numbering by resetting
% the equation counter or by explicitly numbering
% an equation.

% To explicitly number an equation, type \eqnum{}
% (with the desired number between the brackets)
% after the \begin{equation} or \begin{eqnarray}
% command.  The \eqnum{} command will affect only
% the equation it appears with; LaTeX will number
% any equations appearing later in the manuscript
% according to the equation counter.
%

% If you have a multiline equation that needs only
% one equation number, use a \nonumber command in
% front of the double backslashes (\\) as shown in
% the multiline equation above.

%% ------------------------------------------------------------------------ %%
%
%  SIDEWAYS FIGURE AND TABLE EXAMPLES
%
%% ------------------------------------------------------------------------ %%
%
% For tables and figures, add \usepackage{rotating} to the paper and add the rotating.sty file to the folder.
% AGU prefers the use of {sidewaystable} over {landscapetable} as it causes fewer problems.
%
% \begin{sidewaysfigure}
% \includegraphics[width=20pc]{samplefigure.eps}
% \caption{caption here}
% \label{label_here}
% \end{sidewaysfigure}
%
%
%
% \begin{sidewaystable}
% \caption{}
% \begin{tabular}
% Table layout here.
% \end{tabular}
% \end{sidewaystable}
%
%

