The heat from sunlight drives the weather and climate system, the energy in solar photons drives atmospheric chemistry, and the photosynthetically active radiation drives life. For Earth system models (ESMs), one needs to calculate the scattering, absorption, and reflection of solar radiation throughout the atmosphere, ocean, cryosphere, and land surface. The idealized radiative transfer (RT) problem is well known and in many cases has near-exact, but costly solutions; whereas the atmospheric physics of the problem involving gases, clouds, aerosols and surface properties includes unknowns that cause a fundamental uncertainty in the solution. One motivation for this study is to evaluate the potential improvements in solar heating rates if more accurate physics or RT codes are used, but the overriding motivation is to assess a wide range of approximations and uncertainties within a single climate-relevant framework. Where more accurate physics or numerical solutions are known, we can estimate the error in current RT codes, and where there is fundamental uncertainty, we can estimate the potential for error using different methods for framing the problem. The solar heating module Solar-J (Hsu et al., 2017; hence H2017) is embedded in our chemistry-transport model (CTM) and used to integrate climate-relevant heating rates using the European Center's Integrated