Abstract
The “hot model” problem is a widely recognized concern, highlighting the need to assess whether a climate model exhibits a warm bias before utilizing its simulations. Traditionally, climate sensitivity indicators such as the Transient Climate Response or the Equilibrium Climate Sensitivity have been used for the assessment, which, however, requires substantial computational resources and suffers from high uncertainty. Here we propose a novel method based on the scaling behavior of the climate system to objectively evaluate warm biases in climate models. The method relies on two indices, \(a\) and \(H\), which measure the fast responses of global mean surface temperatures to external forcings and their cumulative effects, respectively. By comparing the (\(a,H\)) values from climate models with those derived from observations, one can readily identify whether a model tends to be too warm or too cold. Detailed analysis indicates that the overestimated cumulative effects of temperature responses to external forcings are a primary driver of warming biases in CMIP6 models. Since the two indices can be derived directly from historical observations and simulations, they together provide an efficient framework for model evaluation, improvement, and calibration.
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Data availability
Climate model data is available from the CMIP6 official website: https://esgf-node.llnl.gov/projects/cmip6/. HadCRUT5.0.1 data can be downloaded from the following website: https://www.metoffice.gov.uk/hadobs/hadcrut5/data/HadCRUT.5.0.1.0/download.html#gridded_fields. The historical anthropogenic effective radiative forcings (ERF) are obtained from the KNMI Climate Explorer: https://climexp.knmi.nl/getindices.cgi?WMO=LeedsData/Anthropogenic_total_ERF.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (No. 42475057, No. 42261144687, and No. 42175068). N.Y. thanks also the support from the Guangdong Basic and Applied Basic Research Foundation (2023B1515020084). C.L.E.F. was supported by the Institute for Basic Science (IBS), Republic of Korea, under IBS-R028-D1 and by the National Research Foundation of Korea (NRF-2022M3K3A1097082 and RS-2024-00416848).
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N.Y. and J.Y. conceptualized the study and developed the methodology. J.Y., N.Y., and C.F. conducted the investigation. J.Y. carried out the visualization. J.Y. and N.Y. wrote the original draft. J.Y., N.Y., and C.F. reviewed and edited the manuscript.
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Yan, J., Yuan, N. & Franzke, C.L.E. Assessing the warming biases in CMIP6 models: the roles of fast response and cumulative effects to external forcings. npj Clim Atmos Sci (2026). https://doi.org/10.1038/s41612-026-01390-z
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DOI: https://doi.org/10.1038/s41612-026-01390-z
