\begin{table}%T1
\caption{\label{param}Parameter values for the evolution model for mantle temperature  and water.}  
     \small  
%\centering
\par
\begin{tabular}{l l l l l l}         
\hline\hline                 
Parameter & \multicolumn{3}{c}{Value}   & Unit & Description \\     
     & $1~M_\oplus$ & $5~M_\oplus$ & $8~M_\oplus$ &   &         \\
\hline   \noalign{\smallskip}                  
$d_{{\rm bas}}$    & $5\times 10^3$ & $5\times 10^3$ & $5\times 10^3$ & m & average thickness of the basalt layer \\
$f_{{\rm bas}}$    & $0.03$ & $0.03$ & $0.03$ & ... & mass fraction of water in the basalt layer \\
$f_{\rm w}$                 & $0.194$ & $0.194$ & $0.194$ & ... & degassing fraction of water \\
$d_{\rm m}$                 & $40\times 10^3$ & $40\times 10^3$ & $40\times 10^3$ & m & melting depth \\
$k$                   & $4.2$ & $4.2$ & $4.2$ & J s$^{-1}$ m$^{-1}$ K$^{-1}$ & thermal conductivity \\
$M_{\rm w}(0)$              & $4.2\times 10^{21}$ & $2.1\times 10^{22}$ & $5.36\times 10^{22}$ & kg & initial amount of mantle water \\
$R_{\rm c}$                 & $3471\times 10^3$ & $5360\times 10^3$ & $6085\times 10^3$ & m & inner radius of the mantle \\
$R_{\rm m}$                 & $6271\times 10^3$ & $9684\times 10^3$ & $10~994\times 10^3$ & m & outer radius of the mantle \\
$T_{\rm m}(0)$              & $3000$ & $3000$ & 3000 & K & initial mantle temperature \\
$\kappa$              & $10^{-6}$ & $10^{-6}$ & $10^{-6}$ & m$^2$ s$^{-1}$ & thermal diffusivity \\
$\rho_{{\rm bas}}$ & $2950$ & $4005$ & 4,379 & kg m$^{-3}$ & density of the basalt \\
$\rho c$              & $4.2\times 10^6$ & $4.2\times 10^{6}$ & $4.2\times 10^6$ & J m$^{-3}$ K$^{-1}$ & density $\times$ specific heat \\
$R_{\rm T}$                 &  $29.8\times 10^{-5}$ & $29.8\times 10^{-5}$ &  $29.8 \times 10^{-5}$ & K$^{-1}$ & temperature dependence of regassing ratio \\
$\alpha$              & $3\times 10^{-5}$ & $3\times 10^{-5}$ &$3\times 10^{-5}$ & K$^{-1}$ & coefficient of thermal expansion \\
$\beta$               & $0.3$ & $0.3$ &$0.3$ & ... & empirical constant in Eq. (\ref{eqheat}) \\
${\rm Ra}_{{\rm crit}}$ & $1,100$  &$1,100$ &$1,100$ & ... & critical Rayleigh number \\
$\lambda$             & $0.34$ & $0.34$& $0.34$ &~Gyr$^{-1}$ & decay constant of radiogenic heat \\
$E_0$                 &  $1.46\times 10^{-7}$ & $1.46\times 10^{-7}$ & $1.46\times 10^{-7}$ & J s$^{-1}$ m$^{-3}$ & initial heat generation per time and volume \\
$g$                   & 9.81 & 20.6 & 25.5 & m s$^{-2}$ & gravitational acceleration \\
\hline                                    
\end{tabular}
\end{table}