Search for: All records

Radiative forcing by carbon dioxide depends on the difference between surface and stratospheric temperature scaled by the logarithm of its concentration (Wilson and Gea-Banacloche 2012; Jeevanjee et al. 2021). This relationship arises due to the cooling-to-space theory or theτ= 1 law, where all emission of infrared radiation originates from the atmospheric pressure level where the gas reaches sufficient optical thickness (in the case of CO₂, in the stratosphere). Here we develop theoretical understanding of forcing by other well-mixed greenhouse gases including methane (CH₄), nitrous oxide (N₂O), and chlorofluorocarbons (CFCs). Radiative forcing by an optically thin absorber (e.g., CFC-12) is governed by emission throughout the troposphere and scaled by the total change in gas concentration, such that a linear increase in gas abundance yields a linear increase in forcing. We examine the factors that control the magnitude of radiative forcing, demonstrating analytically that CFC-12 is a stronger per-molecule absorber than CO₂due to its larger average cross-section, rather than its band width or spectral position. Application in idealized atmospheres with simplified lapse rates illustrates how radiative forcing by optically thin gases depends almost linearly on lapse rate. Finally, gases that are both optically thin and optically thick across their absorption spectrum, such as N₂O and CH₄, can be understood as a combination of the two regimes, yielding a super-logarithmic relationship to concentration. Our theory is in excellent agreement with full-physics line-by-line calculations in atmospheres with and without spectral overlap by water vapor 

Abstract Broadband (spectrally‐integrated) radiation calculations are dominated by the expense of spectral integration, and many applications require fast parameterizations for computing radiative flux. Here we describe a novel approach using a linear weighted sum of monochromatic calculations at a small set of optimally‐chosen frequencies. The empirically‐optimized quadrature method is used to compute atmospheric boundary fluxes, net flux profiles throughout the atmosphere, heating rate profiles, and top‐of‐the‐atmosphere forcing by CO₂, in the longwave for clear skies. We evaluate the method against two modern correlatedk‐distribution models and find that we can achieve comparable errors with 32 spectral points. We also examine the effect of minimizing different cost functions, and find that in order to accurately represent heating rates and CO₂forcing, these quantities must be included in the cost function.