Sunlight's interaction with the atmosphere drives the Earth's weather, climate, chemistry and biosphere. Our image of the atmosphere from space is that of a thin layer wrapped around the Earth: we see it as curved, but thin enough to be treated as flat. In most all climate models, the 3D grid comprising the atmosphere is tied to a 2D flat-Earth surface grid whose fixed shape and area extends through the atmospheric layers to a subjective top-of-atmosphere height. We present here results from a solar heating module (Solar-J) that had been modified to include accurate spherical ray tracing of the direct solar beam, including refraction. It also includes the geometric expansion of the atmosphere with altitude as occurs in a spherical hydrostatic atmosphere (see Trenberth and Guillemot, JGR 1994). For these results, Solar-J is run offline using meteorological data from the European Centre (~1º, 60 layers).

We find that flat-atmosphere errors are >2 W m^-2 over the sunlit globe and exceed 4 W m^-2 in two bands about 66ºS and 66ºN in January. Climate models shut off solar heating when the unrefracted solar zenith angle reaches 90º, and thus they miss the twilight atmospheric heating for angles out to 96º. With spherical atmospheres, we find the unusual, but seemingly obvious, result that the amount of total solar energy incident on the climate system depends on the atmospheric constituents, not just the surface area of the Earth. For example, anthropogenic aerosols are found to increase the amount of reflected sunlight by about 1.5 W m^-2, but they also capture 0.2 W m^-2 more sunlight. an hence their climate impact is related to the reduction in total heating, -1.3 W m^-2. The flat-Earth errors, ~1%, are unlikely to affect a model's climate sensitivity, but the latitudinal errors are relatively larger, and they will probably shift the current climate state. After all, 2-3 W m^-2 is the radiative forcing that has driven current climate change, and it is typical of the model-to-model differences in atmospheric heating. Calculation of the direct solar beam in this model can be readily adapted to use 3D cloud and elevation data, but the scattering code is limited to horizontally homogeneous atmospheres.