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\def\ie{{\it i.~e.}}


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\begin{document}

\def\wpmc{W/m$^2$}
\def\fig#1{Fig.~S\ref{fg:#1}}
\def\tab#1{Tab.~S\ref{tb:#1}}



\def\CO{CO\textsubscript{2}}
\def\ACO{4$\times$\CO}
\def\abrupt{\texttt{abrupt\ACO}}
\def\picontrol{\texttt{piControl}}
\def\historical{\texttt{historical}}
\def\CTRL{CTRL}
\def\clim{\texttt{clim}}
\def\climp{\texttt{clim+4K}}
\def\wpmc{W/m$^2$}

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{SI1: Tuning}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\wbsrf{w_{B,\mbox{srf}}}
\def\wbmax{w_{B,\mbox{max}}}
\def\epmax{EP_{max}}
\def\ratqspz{{p_0}_r}
\def\ratqsdp{{\Delta p}_r}
\def\ratqspz{r_{P_0}}
\def\ratqsdp{r_{\Delta p}}
\def\ratqsmin{r_{\mbox{min}}}
\def\ratqsmax{r_{\mbox{max}}}
\def\alpblk{\gamma_{\mbox{Alp,th}}}
\def\alpwkk{\gamma_{\mbox{Alp,wk}}}
\def\fallv{\gamma_{\mbox{fall,v}}}
\def\fcldcon{\gamma_{\mbox{cld,cv}}}
\def\cldlc{\mbox{cld}_{l,conv}}
\def\sigdz{\sigma_{\mbox{cvpr}}}
\def\elcrit{q_{l,crit}}
\def\tlcrit{T_{l,crit}}
\def\eddz{\lambda_d}
\def\rei{\gamma_{\mbox{ice}}}

\begin{table}
	\centerline{\begin{tabular}{llclll}\hline
Name & code & range & 6A & unit & comment \\\hline
$wk_{dens,oce}$ & \texttt{WDENSO}  & $[10^{-11},10^{-8}]$ & 1.e-9 & m$^-2$ & (fixed) wake density over oceans \\\hline
$\alpblk$       & \texttt{ALPBLK}  & $[0.2,0.8]$ & 0.5 &  &   \multirow{2}{*}{$Alp=\alpblk\times ALP_{\mbox{thermals}} + \alpwkk\times ALP_{\mbox{wake}}$} \\
$\alpwkk$       & \texttt{ALPWKK}  & $[0.01,0.5]$ & 0.25 & & \\\hline
$\cldlc$        & \texttt{CLDLC }  & $[0.1,1]$ & 0.65 & g/kg & threshold for conversion of cloud liquid water to rainfall \\\hline
$\fcldcon$      & \texttt{CLDCV }  & $[0.5,10]$ & 1 &  & scaling factor on the convective cloud water for computation of cloud cover \\\hline
$\fallv$        & \texttt{FALLV }  & $[0.3,2.]$ & 0.8 &  & scaling factor on the fall velocity of ice crystals \\\hline
$\ratqspz$      & \texttt{RQSP0 }  & $[300,600]$ & 450 & hPa & width of the subgrid scale distribution of total water $q_t$ is  $\sigma_{q_t}= r\times q_t$\\
$\ratqsdp$      & \texttt{RQSDP }  & $[50,300]$ & 100 & hPa &   where $r$ varies between $\ratqsmin$ (=0.002) and $r_{max}$ with decreasing \\
$\ratqsmax$     & \texttt{RQSTOP}  & $[0.05,0.6]$ & 0.4   &  &  pressure $p$ as  $r=r_{min}+(r_{max}-r_{min}) \ \{ \mbox{tanh} [ (\ratqspz - P) / \ratqsdp] +1 \} /2$\\\hline
$b_0$           & \texttt{AERIE }  & $[0.5,2]$ & 1.3 & & droplet number concentration CDNC=10$^{b_0+b_1\mbox{log}(q_{aer})}$, $b_1=0.02$\\
                &                  &           &     & & $q_{aer}$ being the concentration of soluble aerosols in $\mu$g/m$^3$  \\\hline
$\sigdz$        & \texttt{SIGDZ }  & $[0.001,0.02]$ & 0.003 &  & Grid cell fraction covered by unsaturated precipitating downdrafts \\\hline
$\wbsrf$        & \texttt{WBSRF }  & $[0.05,2.]$ & 0.5 & m/s & Deep convection vertical velocity at cloud base (m/s)\\
$\wbmax$        & \texttt{WBMAX }  & $[1.5,6]$ & 2.8 & m/s & $w_B=\wbsrf+\wbmax/[1.+500/(P_s-P_{LFC})]$, where $P_s$ and $P_{LFC}$ \\
                &                  &           &     &     &  are the surface and "Level of Free Convection" pressure in hPa. \\\hline
$\epmax$        & \texttt{1-OMEPMX}& $[0.9,0.9999]$ & 0.999 & & Rainfall efficiency for deep convection is \\
$\elcrit$       & \texttt{ELCV  }  & $[0.1,2]$ & 0.3 & g/kg & $ EP=\mbox{min} \{ \mbox{max}  [ 1.-  \elcrit*(1.0-T/\tlcrit)/q_{\mbox{liq}} , 0 ] , \epmax \}$ \\
$\tlcrit$       & \texttt{TLCV  }  & $[-65,-35]$ & -55 & $^{\mbox{o}}$C & where $q_{\mbox{liq}}$ is the incloud liquid water (in g/kg).   \\\hline
$\rei$          & \texttt{REI}     & $[0.5,1.3]$ &  1. &   & Scaling factor on an imposed vertical profile of ice particle size \\\hline
$\eddz$         & \texttt{DZTH  }  & $[0.05,0.15]$ & 0.07 & & $z^*=z+\eddz z$ for plume detrainment \\\hline
\end{tabular}}
\caption{List of parameters varied during the history matching procedure. For each parameter, the minimum and maximum values authorized during the tuning process are given, as well as the value used in the 6A configuration (not used in the tuning procedure). The authorized range arises from the expertise of the parametrization developers. The table is essentially reproduced from
(37) %\cite{Hour:20LMDZ6A} REFERENCE
and additional explanations on the meaning of the various parameters are given there. The second column gives the name of the parameter used in the tuning procedure. WDENSO
CLDCV and
OMEPMX are explored with a logarithmic rather than linear sampling.
\label{tb:param}}
\end{table}


\end{document}
