GoKawiilLine-by-line calculations
The Geophysical Fluid Dynamics Laboratory’s GPU-compatible radiation code (GRTcode) is a line-by-line radiative transfer code using HITRAN2016 (ref. 50) and MT_CKD 2.5 (ref. 51). It has been benchmarked in ref. 16, showing excellent agreement with other line-by-line radiative transfer models, including LBLRTM v12.8 (ref. 52) provided by Atmospheric and Environmental Research, RFM53 calculation conducted by the Geophysical Fluid Dynamics Laboratory, 4AOP54 provided by the Laboratoire de Météorologie Dynamique and ARTS 2.3 (ref. 55) provided by the University of Hamburg. We also note that although GRTcode does not include CO 2 line mixing, it agrees well with models (such as RFM and LBLRTM) that include the mechanism, which is consistent with the understanding that the line mixing induces negligible (within 1%) effects on the LW radiative forcing14. Details of this comparison are listed in Extended Data Table 1. Inter-model discrepancies are estimated as the standard deviations and are multiplied by 1.96 to infer 95% confidence interval in IRF caused by gas spectroscopy.
For clouds, the GRTcode uses a high-spectral-resolution cloud optics parameterization developed in ref. 37, which has been validated to achieve reasonable radiative closure with hyperspectral-resolution remote sensing instruments in the mid-infrared56,57. The cloud optics parameterization37 is built on Mie-scattering calculations for liquid clouds and an optics library for severely roughened solid columns developed in ref. 58. On the basis of grid-cell-mean cloud fraction and cloud water content, subgrid cloud water content is stochastically generated at every wavenumber following ref. 25 and cloud optical depth is assumed to be uniform within each 1 cm−1 bin.
The all-sky calculations of GRTcode, with broadband cloud optics parameterizations, have shown good agreement in long-term global mean trend with spaceborne hyperspectral infrared sounders59. Sensitivity experiments have been conducted, using different configurations for the stochastic cloud generation and effective radius, and alternatively building the cloud optics parameterization on a state-of-the-art, irregularly shaped Voronoi ice model60,61. Although the maximum deviations could exceed 10% in the simulated all-sky IRF, these deviations do not affect the regression coefficients, which are derived from clear-sky conditions, nor the all-sky residual (r; Tables 1 and 2). The insensitivity of the IRF–OLR linearity to cloud parameterizations is consistent with the idealized simulations shown in Extended Data Fig. 4a–d and supports the robustness of the observationally constrained IRF presented in this study.
Using monthly mean surface temperature, humidity, ozone concentration and cloud conditions from the ERA5 (refs. 32,62) reanalysis dataset, a set of global-scale line-by-line experiments perturbing the concentrations of WMGHGs was conducted for the period 2001–2024 (ref. 47). These experiments include:
Control: a control experiment using a time series of global mean, annual mean concentrations of WMGHGs 13 .
x PI: Identical to control except that an individual WMGHG species, x , is held fixed at its 1850 concentration (CO 2 : 284.297 ppmv; CH 4 : 0.7988 ppmv; N 2 O: 0.2716 ppmv; 8.2 × 10 −6 ppmv for CFC12-eq and 2.02 × 10 −5 ppmv HFC134a-eq).
x2×PI, x3×PI, x4×PI, x4×: similar to xPI except that x is two to four times the 1850 concentration (PI) or four times its annual mean concentration.
To minimize computational costs, we conduct radiative transfer calculations at a resolution of 2.5° for the year 2010, which is used to construct the regression model, and at a coarser resolution of 7.5° for other years that are used to evaluate the model. The resolution differences cause small (<0.5%) differences in the IRF. These experiments generate TOA OLR (W m−2). For the period from 2001 to 2022, the time series of WMGHG concentrations is based on the CMIP7 greenhouse input dataset13. For the years 2023 and 2024, global mean concentrations of CO 2 , CH 4 and N 2 O are taken from NOAA’s Global Monitoring Laboratory33,63, with a bias correction applied to ensure continuity with ref. 13. Concentrations of CFC12-eq and HFC134a-eq gases after 2022 are held fixed at their 2022 levels. Radiative transfer calculations are conducted at 0.1 cm−1 resolution; we have performed tests to demonstrate that increasing the resolution does not alter the broadband IRF. Extended Data Table 1 lists the clear-sky LW IRF estimated from GRTcode–ERA5 calculations for the year 2014. The difference between the GRTcode results submitted to ref. 16 is small and arises from differences in gas concentrations that have been updated since CMIP6.
The linear OLR–regression method
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