For shortwave radiation, surface solar irradiance ($S^{\downarrow}_s$) and net solar absorption by the atmospheric column ($S_t^{\downarrow}- S_t^{\uparrow}-S_s^{\downarrow}+S_s^{\uparrow}$) are the primary components of shortwave radiative fluxes for calculating the net heat flux in QTCM. The solar radiative fluxes mainly depend on solar zenith angle ($\theta$) and surface albedo ($A_s$). The impact of variations of aerosol and atmospheric gases, such as ozone and CO$_2$ on the solar radiative fluxes are relatively small compared to the dependence of $\theta$ and $A_s$. Therefore, the first order variation of the solar radiative fluxes can be approximated by simple formulas, \begin{eqnarray} S_t^{\downarrow}-S_t^{\uparrow}-S_s^{\downarrow}+S_s^{\uparrow}&=& S_{\bigodot}cos\theta\sum\limits_{n=0}^{N}\alpha_n f_{an}(\theta)g_{an} (A_s),\Label{SWa}\\ S^{\downarrow}_s&=&S_{\bigodot}cos\theta\sum\limits_{n=0}^{N}\alpha_n f_{sn}^{\downarrow}(\theta)g_{sn}^{\downarrow}(A_s), \Label{SWsd} \end{eqnarray} \noindent where $S_{\bigodot}$ is solar constant. To obtain the functions of $f_{an}(\theta)$, $g_{an}(A_s)$, $f_{sn}^{\downarrow}(\theta)$ and $g_{sn}^{\downarrow} (A_s)$, we use the Fu and Liou (1993) solar radiation scheme and input a typical vertical profile of water vapor, temperature, CO$_2$, ozone, and aerosol. Then, we use curve fitting to approximate these two functions for conditions with clear sky and with different cloud types. This stripped-down shortwave radiation scheme catches the first order effect of radiative processes in the Fu and Liou scheme implicitly, for instance multiple scattering between cloud base and the surface. The QTCM focuses mainly on the tropics, so functions $f_{an}(\theta)$, $g_{an}(A_s)$, $f_{sn}^{\downarrow}(\theta)$ and $g_{sn}^{\downarrow} (A_s)$ can be simply written as \begin{eqnarray} f_{an}(\theta)&=&a_{an}cos\theta+b_{an},\nonumber\\ f_{sn}^{\downarrow}(\theta)&=& a_{sn}^{\downarrow}cos\theta+b_{sn}^{\downarrow},\Label{fg}\\ g_{an}(A_s)&=&c_{an}A_s,\nonumber\\ g_{sn}^{\downarrow}(A_s)&=&c_{sn}^{\downarrow}A_s,\nonumber \end{eqnarray} \noindent where $a_{an}$, $b_{an}$, $c_{an}$, $a_{sn}^{\downarrow}$, $b_{sn}^{\downarrow}$ and $c_{sn}^{\downarrow}$ are constant and their values are given in Table \Ref{SWtb}. These approximations are accurate for low surface albedo ($A_s < 0.6$) and low solar zenith angle ($cos\theta > 0.4$). In the QTCM, the cloud prediction scheme is designed for longer time scale and larger spatial scale, so for consistency, the radiative fluxes are diurnally averaged before interacting with clouds in the standard version of radiation code (clrad1). This is done by analytically averaging of (\Ref{SWa})-(\Ref{SWsd}). A version with diurnal cycle also is included for examination of diurnal effects. Surface albedo in the current QTCM is monthly climatology derived from Darnell et al. (1992) which is consistent with the ERBE (the Earth Radiation budget Experiment) data. \begin{table} \caption{} \vspace{0.1in} \begin{center} \begin{tabular}{lcccccccc} \hline\hline Cloud type & $\epsilon^{\uparrow n}_{RT_1t}$ & $\epsilon^{\uparrow n}_{Rq_1t}$ & $\epsilon^{\uparrow n}_{RT_st}$ & $\epsilon^{\uparrow}_{R\alpha_nt}$ & $\epsilon^{\downarrow n}_{RT_1s}$ & $\epsilon^{\downarrow n}_{Rq_1s}$ & $\epsilon^{\downarrow}_{R\alpha_ns}$ & $\epsilon^{\uparrow}_{RT_ss}$ \vspace{0.1cm}\\ \hline n=0 & 0.926 & -1.477 & 0.533 & & 1.014 & 2.345 & & 6.283 \vspace{0.1cm} \\ \hline n=1 & 0.554 & -5.02$\times$10$^{-4}$ & 0.00 & -1.008$\times$10$^2$ & 1.398 & 0.508 & 24.892 & \vspace{0.1cm} \\ \hline n=2 & 0.698 & -0.575 & 0.207 & -61.635 & 1.200 & 1.508 & 8.383 & \vspace{0.1cm} \\ \hline n=3 & 0.998 & -1.079 & 1.0$\times$10$^{-3}$ & -12.258 & 1.476 & 0.039 & 36.126 & \vspace{0.1cm} \\ \hline\hline \end{tabular} \end{center} \Label{LWtb} \end{table} \begin{table} \caption{} \vspace{0.1in} \begin{center} \begin{tabular}{lcccccc} \hline\hline Cloud type & $a_n^{\downarrow}$ & $b_n^{\downarrow}$ & $c_n^{\downarrow}$ & $a_n^{net}$ & $b_n^{net}$ & $c_n^{net}$ \vspace{0.1cm}\\ \hline n=0 & -6.518$\times$10$^{-2}$ & 0.227 & 0.169 & 0.129 & 0.670 & 7.582$\times$10$^{-2}$ \vspace{0.1cm} \\ \hline n=1 & 3.519$\times$10$^{-2}$ & 0.146 & 7.853$\times$10$^{-2}$ & 0.161 & 9.089$\times$10$^{-2}$ & 0.728 \vspace{0.1cm} \\ \hline n=2 & -2.494$\times$10$^{-2}$ & 0.190 & 0.193 & 0.289 & 0.417 & 0.242 \vspace{0.1cm} \\ \hline n=3 & -1.172$\times$10$^{-2}$ & 0.217 & 9.177$\times$10$^{-2}$ & 0.306 & 0.169 & 0.540 \vspace{0.1cm} \\ \hline\hline \end{tabular} \end{center} \Label{SWtb} \end{table}