## Abstract

To estimate the earth's radiation budget at the top of the atmosphere (TOA) from satellite-measured radiances, it is necessary to account for the finite geometry of the earth and recognize that the earth is a solid body surrounded by a translucent atmosphere of finite thickness that attenuates solar radiation differently at different heights. As a result, in order to account for all of the reflected solar and emitted thermal radiation from the planet by direct integration of satellite-measured radiances, the measurement viewing geometry must be defined at a reference level well above the earth's surface (e.g., 100 km). This ensures that all radiation contributions, including radiation escaping the planet along slant paths above the earth's tangent point, are accounted for. By using a field-of-view (FOV) reference level that is too low (such as the surface reference level), TOA fluxes for most scene types are systematically underestimated by 1–2 W m^{−2}. In addition, since TOA flux represents a flow of radiant energy per unit area, and varies with distance from the earth according to the inverse-square law, a reference level is also needed to define satellite-based TOA fluxes. From theoretical radiative transfer calculations using a model that accounts for spherical geometry, the optimal reference level for defining TOA fluxes in radiation budget studies for the earth is estimated to be approximately 20 km. At this reference level, there is no need to explicitly account for horizontal transmission of solar radiation through the atmosphere in the earth radiation budget calculation. In this context, therefore, the 20-km reference level corresponds to the effective radiative “top of atmosphere” for the planet. Although the optimal flux reference level depends slightly on scene type due to differences in effective transmission of solar radiation with cloud height, the difference in flux caused by neglecting the scene-type dependence is less than 0.1%. If an inappropriate TOA flux reference level is used to define satellite TOA fluxes, and horizontal transmission of solar radiation through the planet is not accounted for in the radiation budget equation, systematic errors in net flux of up to 8 W m^{−2} can result. Since climate models generally use a plane-parallel model approximation to estimate TOA fluxes and the earth radiation budget, they implicitly assume zero horizontal transmission of solar radiation in the radiation budget equation, and do not need to specify a flux reference level. By defining satellite-based TOA flux estimates at a 20-km flux reference level, comparisons with plane-parallel climate model calculations are simplified since there is no need to explicitly correct plane-parallel climate model fluxes for horizontal transmission of solar radiation through a finite earth.

*Corresponding author address:* Dr. Norman G. Loeb, NASA Langley Research Center, Mail Stop 420, Hampton, VA 23681-2199. Email: n.g.loeb@larc.nasa.gov