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\authorrunninghead{MENVIEL ET AL.}
\titlerunninghead{Atmospheric $\delta^{13}$CO$_2$}
\authoraddr{L. Menviel, l.menviel@unsw.edu.au}


\begin{document}


\title{Supporting Information for ``Impact of oceanic circulation changes on atmospheric $\delta^{13}$CO$_2$''}

\authors{L. Menviel \altaffilmark{1,2}, A. Mouchet \altaffilmark{3,4}, K.J. Meissner \altaffilmark{1,2}, F. Joos \altaffilmark{5}, M.H. England \altaffilmark{1,2}}

\altaffiltext{1}{Climate Change Research Centre, University of New South Wales, Sydney, Australia}
\altaffiltext{2}{ARC Centre of Excellence for Climate System Science, Australia}
\altaffiltext{3}{Laboratoire des Sciences du Climat et de l'Environnement (LSCE), IPSL-CEA-CNRS-UVSQ, Gif-sur-Yvette, France}
\altaffiltext{4}{Astrophysics, Geophysics and Oceanography Department, Universit\'e de Li\`ege, Li\`ege, Belgium}
\altaffiltext{5}{Climate and Environmental Physics, Physics Institute and Oeschger Centre for Climate Change Research, University of Bern, CH-3012 Bern, Switzerland} 

\newpage
\begin{article}

\noindent\textbf{Contents of this file}
\begin{enumerate}
\item Text S1 
\item Figures S1 to S3
\end{enumerate}

\newpage
\noindent\textbf{Text S1: Attributing $\delta^{13}$C changes for changes in NADW} \\
Figures S1 and S2 show the attribution of $\delta^{13}$C anomalies to changes in remineralized versus preformed carbon
in response to a weakening and a shut-down in NADW formation using the method described in Section 2.5.  
Most of the simulated $\delta^{13}$C anomalies are due to changes in remineralized carbon in these experiments (Love-NA-W, Bern-NA-W, Love-NA-Off, and Bern-NA-Off):
weaker ventilation of the deep and intermediate Atlantic leads to an accumulation of remineralized carbon 
whereas less carbon accumulates in the intermediate North Pacific.

However, the relationships outlined in section 2.5 do not work well to attribute changes in surface $\delta^{13}$C.
Instead, we follow \citet{broecker92} who estimated that due to photosynthesis and remineralization of organic matter
in the ocean $\delta^{13}$C is usually correlated to phosphate (PO$_4$) by the following relation:
\begin{equation}
 \delta^{13}C - \overline{\delta^{13}C} = \frac{\epsilon_{om-d}}{\overline{DIC}} . R{c/p} . ([PO_4] - \overline{[PO_4]})
\end{equation}

Thus $\delta^{13}$C anomalies induced by surface PO$_4$ changes are:

\begin{equation}
\Delta\delta^{13}C_{BIOsurf} =  \frac{\epsilon_{om-d}}{\overline{DIC}} . R{c/p} .\Delta[PO_4]
\end{equation}

From that relation we estimate for LOVECLIM
\begin{equation}
\Delta\delta^{13}C_{BIOsurf} = -1.1182 * \Delta[PO_4]  \\
\end{equation}
For the Bern3D the relation is:
\begin{equation}
\Delta\delta^{13}C_{BIOsurf} = -1.1359 * \Delta[PO_4]  \\
\end{equation}

As the equilibrium fraction factor increases with decreasing ocean surface temperature ($\sim$-0.12$\permil$/$^\circ$C) \citep{mook74,charles93}, 
we can also estimate changes in surface $\delta^{13}$C due to SST changes at equilibrium.

\begin{equation}
\Delta\delta^{13}C_{SST} = -0.12 * \Delta SST  \\
\end{equation}


We can potentially estimate $\delta^{13}$C due to air-sea exchange by 
\begin{equation}
\Delta\delta^{13}C_{as} = \Delta\delta^{13}C - \Delta\delta^{13}C_{BIOsurf} - \Delta\delta^{13}C_{SST} 
\end{equation}

Figure \ref{figSurfDec} shows the attribution of surface $\delta^{13}$C changes during NADW shut down for experiments Love-NA-Off and 
Bern-NA-Off. This attribution shows the complex interplay between changes in SST, nutrient utilization and air-sea gas exchange. 
In the North Atlantic cooler conditions lead to positive surface $\delta^{13}$C anomalies. 
$\Delta\delta^{13}$C$_{SST}$ assumes that air-sea equilibrium is reached, which is rarely true. Large $\Delta\delta^{13}$C$_{as}$ 
are thus obtained in the areas covered by sea-ice, particularly north of 60$^\circ$N.
Enhanced  nutrient utilization 
in the Southern Ocean leads to significant positive surface $\delta^{13}$C anomalies in both models.



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\bibitem[Broecker and Maier-Reimer(1992)]{broecker92}
W.S. Broecker and E.~Maier-Reimer.
\newblock {The influence of air and sea exchange on the carbon isotope
  distribution in the sea}.
\newblock \emph{Global Biogeochem Cycles}, 6:\penalty0 315--320, 1992.

\bibitem[Charles et~al.(1993)Charles, Wright, and Fairbanks]{charles93}
C.D. Charles, J.D. Wright, and R.G. Fairbanks.
\newblock {Thermodynamics influences on the marine carbon isotope record}.
\newblock \emph{Paleoceanography}, 8:\penalty0 691--697, 1993.

\bibitem[Mook et~al.(1974)Mook, Bommerson, and Staverman]{mook74}
W.G. Mook, J.C. Bommerson, and W.H. Staverman.
\newblock {Carbon isotope fractionation between dissolved bicarbonate and
  gaseous carbon dioxide}.
\newblock \emph{Earth and Planet. Science Lett.}, 22:\penalty0 169--176, 1974.

\end{thebibliography}




\end{article}
\newpage
\begin{figure}
\setfigurenum{S1}
\centering
\includegraphics[width=16cm,angle=0]{2015GB005207-S1.eps}
\caption{\small{Attributing changes in zonally averaged $\delta^{13}$C over the Atlantic and the Pacific basin following a NADW weakening.
Experiment Love-NA-W is shown on the left and Bern-NA-W on the right.
a and d) $\Delta\delta^{13}$C ($\permil$); b and e) $\Delta\delta^{13}$C$_{BIO}$ ($\permil$);
 c and f) $\Delta\delta^{13}$C$_{TH}$ ($\permil$).}}
\label{figNAW}
\end{figure}



\begin{figure}
\setfigurenum{S2}
\centering
\includegraphics[width=16cm,angle=0]{2015GB005207-S2.eps}
\caption{\small{Attributing changes in zonally averaged $\delta^{13}$C over the Atlantic and the Pacific basin following a NADW shut down.
Experiment Love-NA-Off is shown on the left and Bern-NA-Off on the right.
a and d) $\Delta\delta^{13}$C ($\permil$); b and e) $\Delta\delta^{13}$C$_{BIO}$ ($\permil$);
 c and f) $\Delta\delta^{13}$C$_{TH}$ ($\permil$).}}
\label{figDec}
\end{figure}

\begin{figure}
\setfigurenum{S3}
\centering
\includegraphics[width=16cm,angle=0]{2015GB005207-S3.eps}
\caption{\small{Attributing changes in surface $\delta^{13}$C following a NADW shut down.
Experiment Love-NA-Off is shown on the left and Bern-NA-Off on the right.
a and b) Surface $\Delta\delta^{13}$C ($\permil$); c and d) $\Delta\delta^{13}$C$_{SST}$ ($\permil$);
 e and f) $\Delta\delta^{13}$C$_{BIOsurf}$ ($\permil$); g and h) $\Delta\delta^{13}$C$_{as}$ ($\permil$).}}
\label{figSurfDec}
\end{figure}



\clearpage
\end{document}
