Zehrung et al. (2025) Standardising the “Gregory method” for calculating equilibrium climate sensitivity

Identification

• Journal: Geoscientific model development
• Year: 2025
• Date: 2025-12-03
• Authors: Anna Zehrung, Andrew D. King, Zebedee Nicholls, Mark D. Zelinka, Malte Meinshausen
• DOI: 10.5194/gmd-18-9433-2025

Research Groups

• School of Geography, Earth and Atmospheric Sciences, The University of Melbourne, Melbourne, Australia
• Australian Research Council Centre of Excellence for Weather of the 21st Century, Clayton, Australia
• International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria
• Climate Resource, Melbourne, Australia
• Lawrence Livermore National Laboratory, Livermore, CA, USA

Short Summary

This study systematically assesses 32 data processing pathways for the "Gregory method" to estimate Equilibrium Climate Sensitivity (ECS) using 44 CMIP6 models, revealing that while the multi-model ECS range is robust, individual model estimates can vary significantly based on processing choices, leading to a recommended standardized method for improved reproducibility.

Objective

• To systematically assess how different data processing choices (global mean weighting, net radiative flux variable, anomaly calculation method) and linear regression methods (Ordinary Least Squares vs. Total Least Squares) influence Equilibrium Climate Sensitivity (ECS) estimates derived from the Gregory method across 44 CMIP6 models.
• To establish a standardized Gregory method analysis approach to promote transparency and reproducibility in future climate sensitivity research, especially for upcoming CMIP7 data.

Study Configuration

• Spatial Scale: Global mean, individual CMIP6 model grid cells (spacing between 100 km and 500 km), Top of Atmosphere (TOA), Top of Model (TOM).
• Temporal Scale: 150-year abrupt-4xCO2 and piControl experiments; monthly and annual mean data; 21-year rolling averages for anomaly calculation (window sizes of 3, 5, 11, 21, 31, 41, 71 years tested); linear regression performed over years 1–150 and 21–150.

Methodology and Data

• Models used: 44 CMIP6 Earth System Models (ESMs).
• Data sources: CMIP6 abrupt-4xCO2 and piControl experiments.
  • Variables: 2 m surface air temperature (tas), top of model (TOM) net radiative flux (rtmt), top of the atmosphere (TOA) reflected shortwave radiation (rsut), TOA outgoing longwave radiation (rlut), TOA downward shortwave radiation (rsdt), atmospheric cell area spatial variable (areacella).
  • Data processing pathways: 32 alternatives based on:
    • Global mean weighting: grid-cell area or cosine of latitude.
    • Net radiative flux variable: TOA net radiative flux (rndt = rsdt - rsut - rlut) or explicit TOM radiative flux (rtmt).
    • Anomaly calculation method: Baseline (raw piControl subtraction), Rolling (21-year rolling average of piControl), Linear (linear trend of piControl), Long-term (climatological mean of piControl).
  • Linear regression methods: Ordinary Least Squares (OLS) and Total Least Squares (TLS).
  • Uncertainty calculation: Standard bootstrap and moving block bootstrap (with a block size of 4 years) for 95% confidence intervals, repeated 10,000 times.

Main Results

• The multi-model ECS range (median 3.88 K [1.84 K, 5.67 K]) is statistically insensitive to the 32 data processing pathways or the choice between OLS and TLS regression.
• Individual model ECS estimates show notable differences based on processing choices:
  • Global mean weighting: Using cosine of latitude instead of native grid cell area can decrease ECS by up to 11% (e.g., MPI-ESM-1-2-HAM).
  • Net radiative flux variable: The choice between rndt and rtmt can change ECS by up to 6% (e.g., INM-CM4-8).
  • Anomaly calculation method: Differences are generally small (up to 3.4% for NorESM2-MM), but methods applying a rolling average or linear trend to the piControl improve correlation and reduce variance compared to raw subtraction.
• TLS regression systematically yields lower ECS values compared to OLS, with individual model differences ranging from 1.4% to 24% (e.g., NorESM2-LM).
• Uncertainty ranges for individual ECS estimates can be highly biased when bootstrapping over the full 150 years due to sensitivity to early experiment years; restricting the analysis to years 21–150 yields more consistent confidence intervals.
• A standardized Gregory method is recommended: weight global mean by cell area, use TOA (rndt) as the N-variable, and calculate anomalies by applying a 21-year rolling average to the piControl timeseries before subtracting from the abrupt-4xCO2 experiment.

Contributions

• Provides the first systematic assessment of the impact of various data preparation choices on Equilibrium Climate Sensitivity (ECS) estimates derived from the Gregory method across a large ensemble of CMIP6 models.
• Quantifies the uncertainty introduced by different data processing pathways and linear regression methods, highlighting their influence on individual model ECS estimates.
• Offers a comprehensive set of recommendations for standardizing the Gregory method, enhancing transparency and reproducibility in future climate sensitivity research, particularly in anticipation of CMIP7.
• Challenges the traditional assumption of arbitrary dependent variable choice in OLS regression for the Gregory method, advocating for further exploration of statistically robust alternatives like TLS.
• Emphasizes the importance of reporting uncertainty ranges and considering interannual dependence in time series for robust ECS assessments.

Funding

• U.S. Department of Energy (DOE) Regional and Global Model Analysis program area (Contract DE-AC52-07NA27344)
• Australian Research Council (CE230100012 and FT240100306)
• Australian Government through the National Environmental Science Program
• Australian National Environmental Science Program – Climate Systems Hub
• European Union’s Horizon 2020 research and innovation programmes (grant agreement no. 101003536) (ESM2025)

Citation

@article{Zehrung2025Standardising,
  author = {Zehrung, Anna and King, Andrew D. and Nicholls, Zebedee and Zelinka, Mark D. and Meinshausen, Malte},
  title = {Standardising the “Gregory method” for calculating equilibrium climate sensitivity},
  journal = {Geoscientific model development},
  year = {2025},
  doi = {10.5194/gmd-18-9433-2025},
  url = {https://doi.org/10.5194/gmd-18-9433-2025}
}