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% AGUtmpl.tex: this template file is for articles formatted with LaTeX2e,
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% PLEASE USE THE DRAFT OPTION TO SUBMIT YOUR PAPERS.
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% Choose the journal abbreviation for the journal you are
% submitting to:

% jgrga JOURNAL OF GEOPHYSICAL RESEARCH (use for all of them)
% gbc GLOBAL BIOCHEMICAL CYCLES
% grl GEOPHYSICAL RESEARCH LETTERS
% pal PALEOCEANOGRAPHY
% ras RADIO SCIENCE
% rog REVIEWS OF GEOPHYSICS
% tec TECTONICS
% wrr WATER RESOURCES RESEARCH
% gc GEOCHEMISTRY, GEOPHYSICS, GEOSYSTEMS
% sw SPACE WEATHER
% ms JAMES
% ef EARTH'S FUTURE
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% (If you are submitting to a journal other than jgrga,
% substitute the initials of the journal for "jgrga" below.)

\documentclass[draft,grl]{agutexSI2019}

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% SUPPORTING INFORMATION TEMPLATE
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%Please use this template when formatting and submitting your Supporting Information.

%This template serves as both a “table of contents” for the supporting information for your article and as a summary of files.
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%OVERVIEW
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%Please note that all supporting information will be peer reviewed with your manuscript. It will not be copyedited if the paper is accepted.
%In general, the purpose of the supporting information is to enable authors to provide and archive auxiliary information such as data tables, method information, figures, video, or computer software, in digital formats so that other scientists can use it.
%The key criteria are that the data:
% 1. supplement the main scientific conclusions of the paper but are not essential to the conclusions (with the exception of
% including %data so the experiment can be reproducible);
% 2. are likely to be usable or used by other scientists working in the field;
% 3. are described with sufficient precision that other scientists can understand them, and
% 4. are not exe files.
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%USING THIS TEMPLATE
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%***All references should be included in the reference list of the main paper so that they can be indexed, linked, and counted as citations. The reference section does not count toward length limits.
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%All Supporting text and figures should be included in this document. Insert supporting information content into each appropriate section of the template. To add additional captions, simply copy and paste each sample as needed.

%Tables may be included, but can also be uploaded separately, especially if they are larger than 1 page, or if necessary for retaining table formatting. Data sets, large tables, movie files, and audio files should be uploaded separately. Include their captions in this document and list the file name with the caption. You will be prompted to upload these files on the Upload Files tab during the submission process, using file type “Supporting Information (SI)”

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% Placeholders for figures and tables appear after the \end{article} command, after references.
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\usepackage{graphicx}
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% You may need to use one of these options for graphicx depending on the driver program you are using.
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% [xdvi], [dvipdf], [dvipsone], [dviwindo], [emtex], [dviwin],
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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{Supporting Information for ``Poleward Shift of Northern Subtropics in winter: Time of Emergence of Zonal versus Regional Signals"}
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% e.g., \title{Supporting Information for "Terrestrial ring current:
% Origin, formation, and decay $\alpha\beta\Gamma\Delta$"}
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%DOI: 10.1002/%insert paper number here%

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% AUTHORS AND AFFILIATIONS
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% List authors by first name or initial followed by last name and
% separated by commas. Use \affil{} to number affiliations, and
% \thanks{} for author notes.
% Additional author notes should be indicated with \thanks{} (for
% example, for current addresses).

% Example: \authors{A. B. Author\affil{1}\thanks{Current address, Antartica}, B. C. Author\affil{2,3}, and D. E.
% Author\affil{3,4}\thanks{Also funded by Monsanto.}}

\authors{Roberta D'Agostino\affil{1}}

\authors{Ascanio Luigi Scambiati\affil{2}}
\authors{Johann Jungclaus\affil{1}}
\authors{Piero Lionello\affil{2,3}}

\affiliation{1}{Max Planck Institute for Meteorology, Hamburg, Germany.}
\affiliation{2}{University of Salento, DiSTBA, Lecce, Italy}
\affiliation{3}{Euro-Mediterranean Center on Climate Change, CMCC, Lecce, Italy}

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

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% TEXT
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\noindent\textbf{Contents of this file}
%%%Remove or add items as needed%%%
\begin{enumerate}
\item Text S1 and S2
\item Figure S1
%\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}

%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.
\newpage
\noindent\textbf{Text S1: Forced Response and Internal Variance}

The variance of the forced response is given by
\begin{equation}
FV = \frac{\sum_{i=i_1}^{i_2}(F_{fr}^i-F_{fr})^2}{i_2-i_1} \; , \; F_{fr}=\frac{\sum_{i=i_1}^{i_2}F_{fr}^i}{i_2-i_1+1} \; .
\end{equation}
The internal variance is computed following the procedure described by \citeA{maher2019max,bellomo2018historical} as:

\begin{equation}
IV = \frac{\sum_{i=i_1}^{i_2}\sum_{e=1}^{e=100}(f_e^i-F_{fr}^i)^2}{100*(i_2-i_1)} \; .
\end{equation}
The Total Variance, which is defined as
\begin{equation}
TV = \frac{\sum_{i=i_1}^{i_2}\sum_{e=1}^{e=100}(f_e^i-F_{fr})^2}{100*(i_2-i_1)} \; ,
\end{equation}
is then the sum of the forced and internal variances:

\begin{equation}
TV=FV+IV ;
\end{equation}

Here the time steps $i_1$ and $i_2$ delimit the period considered in the computation.

% \newpage
% \noindent\textbf{Text S2: Northern subtropical margins.}

% Subtropical margins are computed at each longitude within the 5$^\circ$ N - 45$^\circ$ N range for six different metrics:

% \begin{itemize}
% \item OLR (Outgoing Longwave Radiation): poleward-most latitudes where OLR falls below 250 W/m$^{2}$ \cite{hu2007observed,johanson2009hadley,davis2012multidiagnostic,chen2014orographic,davis2018reconciling,adam2018tropd}. It is associated with the absence of clouds in the subtropics.
% \item TP (Total Precipitation): latitudes of absolute precipitation minima in the subtropics \cite{hu2010decadal,chen2014orographic,chen2014regional}, describing the rainfall scarcity in the region.
% \item P-E (Precipitation - Evaporation): zero-crossing latitudes of P-E \cite{lu2007expansion,johanson2009hadley,davis2012multidiagnostic,davis2016climate,adam2018tropd,davis2018reconciling,staten2018re}, associated with dry conditions and negative surface water balance in the subtropics.
% \item MSLP (Mean Sea Level Pressure): latitudes of absolute maxima of the MSLP (i.e., high-pressure ridges in the subtropics), \cite{davis2018reconciling,adam2018tropd,hu2010decadal}.
% \item $\omega_\phi$ (vertical velocity associated with the meridional overturning circulation or, in other words, the vertical velocity associated with the meridional component of the divergent wind): latitudes of absolute maxima near the subsiding branches at 500 hPa \cite{schwendike2014local,schwendike2015trends}. It describes the subsidence in the subtropics.
% \item $\psi_\phi$ (streamfunction of the regional meridional overturning circulation): zero-crossing latitudes of $\psi_\phi$ at 500 hPa \cite{schwendike2014local,nguyen2018variability}, associated with the poleward limit of the HC in the subtropics.
% \end{itemize}

% Figure 1 in the manuscript shows the ensemble mean of wintertime Northern Hemisphere subtropical margins in the period 1971-2000 for the aforementioned six metrics.

\newpage
\noindent\textbf{Text S2: Time series of zonally-averaged Northern subtropical margins.}

Figure \ref{s1} shows time series evaluated by zonally averaging the Northern subtropical margins. Here most of the uncertainty on the shift is due to the internal climate variability for all metrics except OLR, which has a stronger sensitivity to the applied forcing than other metrics. In terms of total variance, the contribution of the forced response is smaller than that of the internal variability or even negligible with respect to it, ranging from a minimum 1\% for P-E and MSLP in the Historical to a maximum 30\% for OLR in the 1\%CO2 experiment. However, in spite of the large ensemble spread, the poleward shift of Northern subtropical margins is clear for all metrics and it is progressively increasing with time.
\\

\bibliography{references}

%Reference citation instructions and examples:
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% Please use ONLY \cite and \citeA for reference citations.
% \cite for parenthetical references
% ...as shown in recent studies (Simpson et al., 2019)
% \citeA for in-text citations
% ...Simpson et al (2019) have shown...
% DO NOT use other cite commands (e.g., \citet, \citep, \citeyear, \nocite, \citealp, etc.).
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%...as shown by \citeA{jskilby}.
%...as shown by \citeA{lewin76}, \citeA{carson86}, \citeA{bartoldy02}, and \citeA{rinaldi03}.
%...has been shown \cite<e.g.,>{jskilbye}.
%...has been shown \cite{lewin76,carson86,bartoldy02,rinaldi03}.
%...has been shown \cite{lewin76,carson86,bartoldy02,rinaldi03}.
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\begin{figure}
\setfigurenum{S1}
\centering
\noindent\includegraphics[width=30pc]{Figure_SI1.pdf}
\caption{Time series of the zonally averaged Northern subtropical margins (on the left) and its mean over the whole length of the simulation (on the right). Left panels show results for different metrics (top-left labels) for the Historical (blue), 1\%CO2 (purple) and RCP8.5 (red). Thick lines show the ensemble mean and the thin lines the ensemble members.}
\label{s1}
\end{figure}

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% EXAMPLE TABLE
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%\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) \\
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% $l1$ & 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}
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% 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}

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