Portmann et al. (2025) ClimLoco1.0: CLimate variable confidence Interval of Multivariate Linear Observational COnstraint

Identification

• Journal: Geoscientific model development
• Year: 2025
• Date: 2025-11-25
• Authors: Valentin Portmann, Marie Chavent, Didier Swingedouw
• DOI: 10.5194/gmd-18-9015-2025

Research Groups

• Environnements et Paléoenvironnements Océaniques et Continentaux (EPOC), Univ. Bordeaux, CNRS, Pessac, France
• Univ. Bordeaux, CNRS, INRIA, Bordeaux INP, IMB, UMR 5251, Talence, France

Short Summary

This paper introduces ClimLoco1.0, a new statistical model that rigorously describes the confidence interval of a projected climate variable obtained using multivariate linear observational constraints, explicitly accounting for observational noise and estimator quality. It demonstrates that observational constraints correct the best guess and reduce uncertainty, with observational noise weakening this effect, and highlights the underestimation of uncertainty in existing methods that neglect estimator quality.

Objective

• To develop a new statistical model, ClimLoco1.0, that provides a rigorous confidence interval for a projected climate variable, incorporating multivariate linear observational constraints and accounting for observational noise and the quality of estimators (e.g., due to limited climate model sample size).

Study Configuration

• Spatial Scale: Global (e.g., global mean surface air temperature).
• Temporal Scale: Future climate projections (e.g., 2081–2100 mean), historical periods for observable variables (e.g., 2015–2024 mean, 1970–2014 trend).

Methodology and Data

• Models used: ClimLoco1.0 (a new statistical model based on multivariate linear regression and measurement error models theory). Comparisons are made with statistical approaches (Bowman et al., 2018; Ribes et al., 2021) and linear regression methods (Cox et al., 2018).
• Data sources:
  • Synthetic data for illustrative examples.
  • Ensembles of climate model projections (e.g., CMIP6, HighResMIP).
  • Case study: 32 CMIP6 climate models (SSP2-4.5 scenario) and 200 members of HadCRUT5 reanalysis for real-world observations.

Main Results

• ClimLoco1.0 provides a statistically rigorous confidence interval for projected climate variables, accounting for both multivariate observational constraints and observational noise.
• Observational constraints (OCs) have two main effects: they correct the best guess (center of the interval) of the projected variable based on the multi-model bias (difference between multi-model mean and observation) and reduce the associated uncertainty (width of the interval).
• Neglecting the quality of estimators (e.g., due to a limited number of climate models, M) leads to an underestimation of uncertainty, with relative errors ranging from 3 % to 30 % for typical climate model ensemble sizes (M between 5 and 50).
• Observational noise weakens the constraint, resulting in less uncertainty reduction and a smaller correction of the best guess. This effect is quantified by an attenuation coefficient (1/(1 + 1/SNR²)).
• The multivariate approach in ClimLoco1.0 can lead to stronger uncertainty reduction (e.g., 44 % in a case study using two variables) compared to univariate constraints (e.g., 37 % or 26 % for individual variables).
• ClimLoco1.0 demonstrates an equivalence between its approach and the statistical methods of Bowman et al. (2018) and Ribes et al. (2021) but highlights their neglect of estimator quality, leading to underestimated uncertainty.
• The paper identifies mathematical issues in the widely used linear regression OC approach by Cox et al. (2018), particularly concerning the inconsistent treatment of variable distributions and conditioning.

Contributions

• Introduction of ClimLoco1.0, a novel statistical model that provides a rigorous, multivariate linear observational constraint framework for climate projections, explicitly incorporating confidence intervals and observational noise.
• Rigorous quantification of uncertainty by accounting for the quality of estimators, which depends on the number of climate models, addressing a common oversight in existing literature.
• A clear mathematical and graphical interpretation of the impact of observational noise on observational constraints, showing how it attenuates the constraint's effectiveness.
• A didactic, step-by-step construction of the statistical model, enhancing clarity and reproducibility.
• Critical comparison and clarification of the mathematical foundations and limitations of prominent existing observational constraint methods (Bowman et al., Ribes et al., Cox et al.).
• Provision of open-source Python code and data, including a user-friendly example and a real-world case study, to facilitate replication and adaptation.

Funding

• Institut national de recherche en informatique et en automatique (INRIA)
• TipESM (grant no. 101137673)
• Blue-Action (grant no. 727852)
• European Union’s Horizon 2020 research and innovation programme

Citation

@article{Portmann2025ClimLoco10,
  author = {Portmann, Valentin and Chavent, Marie and Swingedouw, Didier},
  title = {ClimLoco1.0: CLimate variable confidence Interval of Multivariate Linear Observational COnstraint},
  journal = {Geoscientific model development},
  year = {2025},
  doi = {10.5194/gmd-18-9015-2025},
  url = {https://doi.org/10.5194/gmd-18-9015-2025}
}