To follow the path of sunlight through the Earth system, one needs consider attenuation, scattering, absorption, refraction and reflection throughout the atmosphere, ocean, cryosphere, and land surface, plus the wavelength dependence of these radiative transfer (RT) processes. This RT problem includes gases, surfaces, and aerosols (clouds). It is complex and thus rife with many approximations used to reduce the computational costs in global models. Here we identify and evaluate the errors caused by several of these approximations using a testbed reference model for solar heating and integrating over global atmospheric conditions taken from a weather forecast model. The testbed model (Solar-J) was built on a photochemistry model at short wavelengths augmented by the gas-phase absorption model from RRTMG-SW for wavelengths greater than 0.6 microns. It continues to be developed in order to evaluate errors in solar heating associated with the RT approximations used in RRTMG, CLIRAD, and similar codes. In this study, we assess separately the errors in each of the following approximations with the goal of identifying which improvements are highest priority for the next generation of solar heating modules in Earth system models:

1. Geometry, where incident solar rays see a spherical Earth vs. a flat disk;
2. Refraction, where the solar rays are bent and wrap past the terminator;
3. Scattering, where the cloud and aerosol scattering is multi-stream forward peaked vs. 2-stream isotropic with reduced cloud optical depth;
4. Cloud overlap, where vertical decorrelation length is used vs. maximum-random overlap;
5. Column atmosphere sampling, where different cloud structures and wavelengths are integrated independently (Cloud-J) vs. random sampling across both dimensions (MCICA);
6. Cloud wavelength binning, where spectral properties of water clouds are resolved vs. averaged across super-bins;
7. Ocean albedo, where the ocean surface albedo varies with incident angle, wavelength, wind speed and chlorophyll.

We evaluate the errors in total solar energy (W m^-2) reflected, absorbed in the atmosphere, and absorbed at the surface, in terms of mean and rms errors over a month, but do not assess the impact on climate. There remain errors beyond this scope of work, e.g., 3D RT and the interaction of neighboring grid cells.