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\title{Bridging Local Decisions and Regional Forest Strategies under Climate Risks: A Flexibility-Based Optimization Framework} %% Article title


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\section{Tradeoffs between the number of available management options and carbon provisions}
%\label{app1}

\begin{figure}[!htbp]
    \centering
    \includegraphics[width=1\linewidth]{figures/FigureS1_3DPF}
    \caption{Comparison of tradeoffs between  management option availability  and carbon provision across different risk attitudes over the LdG Forest (RCP 4.5 A) RCP 8.5 B)). The carbon sequestered on site represents the biologic productivity of the forest, while the carbon exported highlights the operational productivity. We maximized the minimum provision of carbon sequestered, carbon exported and flexibility over the three periods (in a row) for three risk believes extreme-risk taker (100\%), high-risk taker (70\%), risk averse (30\%). The graphic represents via Pareto fronts maximum levels of provisions we can at least satisfy over the three periods.  The figure highlights the trade-off between the objectives emphasizing on the minimum level of provisions decision-maker can at least satisfy over the tree periods and the landscape. (1e7 is equivalent to $10^7$)}
    \label{fig:FigS1_3DPF}
\end{figure}




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\section{Treatment rules}
\textbf{Table S1:} Treatment rules describing the management regimens of maritime pine (sourced from Labarre et al., in prep and adapted from the \textit{forêts-21 platform}.

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        \begin{tabular}{|p{3cm}|p{3cm}|p{1.5cm}|p{2.2cm}|p{5cm}|p{4cm}|p{2cm}|}
            \hline
            \textbf{Management regime} & \textbf{Soil preparation} & \textbf{Stem density (ha$^{-1}$)} & \textbf{Stand age of understorey removal (disking)} & \textbf{Circumference threshold for treatment (cm)} & \textbf{Percentage of removed trees (\%)} & \textbf{Part harvested} \\
            \hline
            Classic & Full plowing & 1250 & 5, 10 years & 7 year, 50, 70, 85, 100, 120 & 50, 30, 30, 30, 30, 100 & Trunk \\
            \hline
            Short & Full plowing & 1250 & 5, 10 years & 50, 70, 85 & 30, 30, 100 & Trunk, branches, stump \\
            \hline
            Long & None & 1600 & None & 55, 75, 95, 115, 150 & 30, 30, 30, 30, 30 & Trunk \\
            \hline
            Adaptive & Row plowing & 1600 & 5,10 years & If cumulated stress index$^{(1)}$ $>$ 2.5 50, 70, 85, 100, 120 & 30, 30, 30, 30, 30, 100 & Trunk \\
            \hline
        \end{tabular}
        \caption{Management regimens and treatment rules for maritime pine.}
        \label{tab:TabS1}
    \end{table}
    \noindent $^{(1)}$ The stress index is given by Eq. 29 in Moreaux et al. (2020) as the complement to unity of the ratio of actual to potential annual tree stand transpiration.
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