Yan et al. (2026) Assessing the warming biases in CMIP6 models: the roles of fast response and cumulative effects to external forcings

Identification

• Journal: npj Climate and Atmospheric Science
• Year: 2026
• Date: 2026-03-27
• Authors: Jiaxin Yan, Naiming Yuan, Christian L. E. Franzke
• DOI: 10.1038/s41612-026-01390-z

Research Groups

• School of Atmospheric Sciences, Sun Yat-sen University, Zhuhai, China
• Key Laboratory of Tropical Atmosphere-Ocean System, Ministry of Education, Zhuhai, China
• Center for Climate Physics, Institute for Basic Science, Busan, Republic of Korea
• Department of Carbon Neutrality and Climate Change, Pusan National University, Busan, Republic of Korea

Short Summary

This study introduces a novel method to assess warming biases in CMIP6 climate models using two indices, 𝑎 (fast response sensitivity) and 𝐻 (cumulative effects/long-term memory), derived from the climate system's scaling behavior. It finds that overestimated cumulative effects are a primary driver of warming biases in these models, offering an efficient framework for model evaluation and improvement.

Objective

• To propose a novel method, based on the scaling behavior of the climate system and two indices (𝑎 and 𝐻), to objectively evaluate warm biases in climate models.
• To assess whether a climate model exhibits a warm bias before utilizing its simulations, addressing the "hot model" problem.
• To identify the roles of fast response (𝑎) and cumulative effects (𝐻) in contributing to warming biases in CMIP6 models.

Study Configuration

• Spatial Scale: Global (Global Mean Surface Temperature - GMST), with an illustrative example for regional scale (Mean Surface Temperatures - MST over China).
• Temporal Scale: Historical period (1850-2014 for HadCRUT5.0.1 data; 1900-2000 for index 𝑎 calculation; 1970-2000 for GMST trend analysis; 1995-2014 for warming level indicator). Monthly data were used for analysis.

Methodology and Data

• Models used: 21 CMIP6 models (ACCESS-CM2, BCC-CSM2-MR, BCC-ESM1, CanESM5, CESM2-WACCM, CMCC-CM2-SR5, E3SM-1-0, EC-Earth3-Veg, FGOALS-g3, FIO-ESM-2-0, IITM-ESM, INM-CM4-8, INM-CM5-0, IPSL-CM6A-LR, KACE-1-0-G, MCM-UA-1-0, MPI-ESM1-2-HR, MRI-ESM2-0, NorCPM1, NorESM2-LM, TaiESM1).
• Data sources:
  • Observation: Met Office Hadley Centre (HadCRUT5.0.1 ensemble, 200 members, monthly anomaly data from 1850-2014).
  • Model simulations: Historical simulations from 21 CMIP6 models (single ensemble member for main analysis, CanESM5 with 62 ensemble members for illustration).
  • Forcing data: Anthropogenic Effective Radiative Forcing (ERF) data from KNMI Climate Explorer.
• Key Analytical Techniques:
  • Detrended Fluctuation Analysis of second order (DFA2) for quantifying the Hurst index (𝐻).
  • Fractional Integral Statistical Model (FISM) for extracting the fast response signal (𝜀(𝑡)) and calculating the fast-response sensitivity index (𝑎).
  • Ensemble Empirical Mode Decomposition (EEMD) for estimating long-term trends in time series.
  • Sensitivity analysis to assess the impacts of 𝐻 and 𝑎 on simulated temperatures.
  • Euclidean distance for quantifying deviations of model (𝐻, 𝑎) points from observational curves.

Main Results

• CMIP6 models generally overestimate the long-term memory strength (𝐻) and underestimate the fast-response sensitivity (𝑎) compared to HadCRUT5.0.1 observations.
• A negative correlation was observed between simulated 𝐻 and 𝑎 in CMIP6 models, indicating an intrinsic balance within models to reproduce observed temperature trends.
• The proposed diagnostic method, based on the (𝐻, 𝑎) values, effectively categorizes CMIP6 models into "warmer" or "colder" bias groups, showing a strong linear relationship (R² = 0.911) between the deviation of model (𝐻, 𝑎) points from observational curves and their GMST warming biases (1970-2000).
• Models identified with "warmer" biases (red group) exhibited higher GMST trends (average 0.139 °C/decade) and generally higher Transient Climate Response (TCR) and Equilibrium Climate Sensitivity (ECS) values compared to "colder" bias models (blue group, average 0.077 °C/decade).
• The nonlinear response of warming levels to variations in 𝐻 and 𝑎 is primarily driven by changes in 𝐻, suggesting that the overestimation of 𝐻 in CMIP6 models is a key factor contributing to their warming biases.
• The 𝐻-𝑎 based method was successfully extended to regional scales, demonstrating its feasibility for assessing regional warming biases (e.g., Mean Surface Temperatures over China).

Contributions

• Proposes a novel, efficient, and objective method to assess warming biases in climate models using two indices (𝐻 for cumulative effects/long-term memory and 𝑎 for fast response sensitivity) derived from the scaling behavior of the climate system.
• Identifies that overestimated cumulative effects (higher 𝐻) are a primary driver of warming biases in CMIP6 models, providing guidance for model improvement.
• Offers an alternative framework for model evaluation, improvement, and calibration that relies solely on historical simulations and observations, avoiding the high computational cost and inherent uncertainty of traditional climate sensitivity metrics (TCR, ECS).
• Demonstrates the applicability and effectiveness of the method at regional scales, addressing a limitation of traditional climate sensitivity metrics.

Funding

• National Natural Science Foundation of China (No. 42475057, No. 42261144687, and No. 42175068)
• Guangdong Basic and Applied Basic Research Foundation (2023B1515020084)
• Institute for Basic Science (IBS), Republic of Korea (IBS-R028-D1)
• National Research Foundation of Korea (NRF-2022M3K3A1097082 and RS-2024-00416848)

Citation

@article{Yan2026Assessing,
  author = {Yan, Jiaxin and Yuan, Naiming and Franzke, Christian L. E.},
  title = {Assessing the warming biases in CMIP6 models: the roles of fast response and cumulative effects to external forcings},
  journal = {npj Climate and Atmospheric Science},
  year = {2026},
  doi = {10.1038/s41612-026-01390-z},
  url = {https://doi.org/10.1038/s41612-026-01390-z}
}