## 2 Material and Methods
### TOA SW Reflectances
#### 2.1.2 Broadband Radiative Transfer Simulations  
To supplement observations, we simulated TOA SW reflectances using the radiative transfer code MOMO Matrix-Operator Model [20]. Simulations covered the solar spectrum between 0.25 and \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**No. of CERES Footprints**} \\ \hline
**Year** & **Terra** & **Aqua** & **Mode** \\ \hline  & **(FM1 and FM2)** & **(FM3 and FM4)** & \\ \hline
2000 & 192,604 & / & RAPS \\
2001 & 259,810 & / & RAPS \\
2002 & 278,305 & 85,745 & RAPS \\
2003 & 266,966 & 223,979 & RAPS \\
2004 & 274,189 & 27,6981 & RAPS \\
2005 & 4730 & 62,213 & RAPS \\
2006 & / & / & / \\
2007 & 273,343 & 271,234 & cross-track \\ \hline \hline \end{tabular}
\end{table} 
Table 1: A list of CERES footprints, obtained after screening for low-level and single-layer clouds, overcast conditions, a cloud optical depth of 10, and cases free of horizontal inhomogeneity: in total, 2,470,099 footprints. 4.00 um through 53 spectral subintervals, chosen such that water spectral refractive indices changed near-linearly with wavelength. For each subinterval, non-correlated k-binning [21] produced--based on HITRAN-2008 database [22]--\(\mathcal{O}\)(10\({}^{1}\)-10\({}^{3}\)) k-terms to represent gaseous absorption. We chose about 80 vertical layers between 0 and 120 km, vertically resolving the lowest 2 km of atmosphere at 25-100 m (except for cloud-top and cloud-topped inversion, resolved at 5 m), 2-5 km altitude at 500 m, and 5-20 km at 2.5 km intervals. The choice of 70 Fourier terms allowed for an azimuthal resolution of 6\({}^{\circ}\). \(\theta_{s}\) (and likewise \(\theta_{v}\)) were resolved at 35 angles, most of them listed in Table 2, Column 1. We used an isotropic ocean surface and Mie-calculated phase functions to represent scattering and absorption by clouds droplets in each vertical layer, and assumed a Gamma-Hansen droplet size distribution [23]. To cover realistic ranges of cloud-topped water vapor in simulations, we extracted four representative temperature and moisture profiles from radiosonde observations (Figure 2), covering 3.2-20.1 kg m\({}^{-2}\) of cloud-topped water vapor. We found St. Helena often exposed to the South-East Atlantic stratocumulus deck and therefore believe that vertical radiosonde profiles represent moisture conditions of the mid to upper troposphere in the larger subsidence area well. The shape of the moisture profiles had minor impact on simulated TOA SW reflectances as variation of pressure and temperature broadened water vapor absorption lines was small compared to the variation in mass absorption. Concentrations of other gases (i.e., CO\({}_{2}\), O\({}_{3}\), N\({}_{2}\)O, CO, CH\({}_{4}\), O\({}_{2}\), and NO) correspond to the AFGL (Air Force Geophysics Laboratory) midlatitude summer atmospheric profile [24]. To explore potential scenarios of cloud vertical profiles which resemble stratocumulus clouds of optical thickness 10 and were subject to weaker or stronger cloud-aerosol interaction, we used the adiabatic theory (e.g., [25]). Adiabatic clouds increase linearly in liquid water content (LWC) from cloud base to top and have a vertically constant cloud droplet number concentration. Sub-adiabatic conditions (i.e., an adiabaticity of \(<\)1) capture the intrusion of dry air from aloft and this reduces the linear slope of LWC accordingly. Figure 3 shows the resulting 13 scenarios of adiabatic clouds, assuming an adiabaticity of 0.6. All cloud scenarios had a cloud top-pressure of 875 hPa. Figure 2: Four main clusters of vertical moisture profiles as observed during cloudy days (ascertained  
through MODIS imagery from Aqua and Terra satellites) over 12 months (August 2016 to July 2017) of radiosonde observations on St. Helena ([[http://catalogue.ceda.ac.uk/uuid/c6](http://catalogue.ceda.ac.uk/uuid/c6) fccd62a8 ad4d49 ea35 fb825c3968910]([http://catalogue.ceda.ac.uk/uuid/c6](http://catalogue.ceda.ac.uk/uuid/c6) fccd62a8 ad4d49 ea35 fb825c3968910)).