Radiative flux and forcing parameterization error in aerosol-free clear skies

This article reports on the accuracy in aerosol- and cloud-free conditions of the radiation parameterizations used in climate models. Accuracy is assessed relative to observationally validated reference models for fluxes under present-day conditions and forcing (flux changes) from quadrupled concentrations of carbon dioxide. Agreement among reference models is typically within 1 W/m2 , while parameterized calculations are roughly half as accurate in the longwave and even less accurate, and more variable, in the shortwave. Absorption of shortwave radiation is underestimated by most parameterizations in the present day and has relatively large errors in forcing. Error in present-day conditions is essentially unrelated to error in forcing calculations. Recent revisions to parameterizations have reduced error in most cases. A dependence on atmospheric conditions, including integrated water vapor, means that global estimates of parameterization error relevant for the radiative forcing of climate change will require much more ambitious calculations. 1. Assessing the Accuracy of Radiation Parameterizations in Climate Models Radiative transfer is unique among parameterization problems for global atmospheric models because the governing equations are deeply grounded in fundamental physics, the approximations (e.g., of one-dimensional radiative transfer) applicable across many relevant scales, and the result entirely deterministic. In aerosol-free clear skies, where scattering is small relative to absorption and emission, the problem is defined by the profile of extinction of the gaseous atmosphere, which is itself determined by the profiles of temperature, pressure, and the concentrations of radiatively active gases. Fluxes of longwave or terrestrial radiation also depend on how the extinction profile is related to the profile of local emission (which also depends on temperature), while for fluxes of shortwave or solar radiation local emission can be neglected, but Rayleigh scattering, which increases extinction and single-scattering albedo, changes the problem slightly. For monochromatic problems these calculations are straightforward so that the main challenge for atmospheric models is treating the spectral dependence of radiative fluxes. The best available information for the spectral variation of radiation in the atmosphere comes from so-called line-by-line models with full spectral detail. When the state of the atmosphere is well characterized, such models are now able to match carefully calibrated observations to within fractions of percent at full spectral resolution [see, for example, Turner et al., 2004; Alvarado et al., 2013]. This is sufficiently accurate, for example, that the very small spectrally dependent signal from a decade’s increase in CO2 concentrations can be teased from surface measurements of spectral intensity that are dominated by secular changes in temperature and water vapor [Feldman et al., 2015]. The absolute accuracy of these models in individual cases is difficult to judge because it is quite difficult to separate errors in the characterization of the atmosphere from errors in the