Paleoclimate data provide constraints on climate models’ large-scale response to past CO₂ changes

Climate models are often used to project climates under CO₂ levels outside those observed in the instrumental era. Paleoclimate proxies offer an opportunity to evaluate models under large CO₂ perturbations relevant to future warming. This study aims to assess climate models using proxy-derived metrics across three past climates characterized by distinct CO₂ levels and boundary conditions: the Last Glacial Maximum (LGM, ~21 ka, ~180 ppm CO₂, expanded ice sheets), an interglacial slice KM5c within the mid-Pliocene Warm Period (MPWP, ~3.2 Ma, ~400 ppm CO₂, reduced Greenland and Antarctic ice), and the early Eocene Climatic Optimum (EECO, ~53.3–49.1 Ma, ~1500 ppm CO₂, ice-free). The focus is on large-scale, integrative metrics pertinent to future projections: global mean surface temperature (GMST), polar amplification, and land–sea warming contrast (LSWC). Because paleo proxies are sparse and uncertain, the study develops site-specific metrics aligned with proxy locations, alongside ‘true’ global metrics, to enable robust model–data comparisons and to benchmark improvements from PMIP3/CMIP5 to PMIP4/CMIP6.

The paper situates its work within efforts to expand model evaluation beyond the historical period to include paleoclimate states across a wide range of forcings. It highlights prior understanding of polar amplification mechanisms (heat transport, sea-ice/snow and lapse-rate feedbacks) and land–sea warming contrast links to hydrology and circulation. It notes challenges in deriving robust metrics from sparse proxies and that earlier studies did not always find clear correlations between equilibrium climate sensitivity (ECS) and paleo GMST. It also references uncertainties in historical aerosol forcing and transient pattern effects that can obscure ECS inference from the instrumental period. Recent advances in PMIP protocols and boundary conditions (e.g., updated LGM ice sheets, Pliocene gateways such as Bering Strait closure, and new EECO palaeogeography) and model physics (notably cloud microphysics) provide a context for reassessing model performance with updated simulations and datasets.

- Time periods: LGM (~21 ka, ~180 ppm CO₂, large NH ice sheets), MPWP KM5c (~3.2 Ma, ~400 ppm CO₂, reduced Greenland/Antarctic ice), and EECO (~53.3–49.1 Ma, ~1500 ppm CO₂, no ice sheets). Older periods have fewer proxy sites and larger uncertainties. - Model ensembles: PMIP4/CMIP6 simulations for each period following standardized experimental designs (LGM: Kageyama et al. 2017; MPWP PlioMIP2: Haywood et al. 2016; EECO DeepMIP: Lunt et al. 2017). For comparison, PMIP3/CMIP5 simulations are also analyzed. Some models ran multiple paleo periods; CESM2 ran all five periods including two historical windows. - Boundary conditions: Updated ice sheets (LGM), Pliocene paleogeography and ocean gateways (notably Bering Strait closure), consistent EECO experimental design with new paleogeography. EECO model inclusion limited to 4×–8× preindustrial CO₂ (except CESM2.1 slab at 3× for context). NorESM1_F EECO included only for GMST due to a different reference frame affecting spatial metrics. - Metrics: Two types per variable: • True (global) metrics computed over complete gridded fields: SST (ocean-only), LAT (land-only SAT), SAT (global SAT) to derive GMST change (ΔT), polar amplification (ΔAP), and land–sea warming contrast (ΔAL). • Site-specific metrics computed using model values sampled at proxy site locations to mirror proxy coverage and enable direct comparison with site-based proxies. - Observational constraints: GMST ‘true’ values use IPCC AR6 assessments for LGM, MPWP, EECO (plus an alternative LGM estimate from Annan et al. 2022). Site-based datasets: LGM SST (Tierney et al. 2020), LGM LAT aligned with assimilated proxy locations; MPWP SST (McClymont et al. 2020) and LAT (Salzmann et al. 2013); EECO SST and LAT (Inglis et al. 2020). Uncertainties and data screening procedures are described in Online Methods. - Comparative periods: Historical (1850–2014) and post-1975 (1975–2014) periods analyzed for context. ECS categories used to flag models with very high (>5–6 °C) or very low (<2 °C) sensitivity where available. - Analysis: Compute anomalies relative to preindustrial for paleo runs and relative to 1850–1900 or 1975–1984 for modern periods. Compare ensemble means and spreads against proxy metrics; assess site-specific vs true metric consistency; examine relationships between ΔT, ΔAP, and ΔAL across time periods; evaluate improvements from PMIP3/CMIP5 to PMIP4/CMIP6.

- GMST agreement: For all three paleo periods (LGM, MPWP, EECO), the multi-model ensemble mean GMST lies within the proxy-assessed ranges despite spanning ~20 °C from LGM to EECO. Many individual models fall outside proxy ranges: 78% (LGM), 65% (MPWP), 29% (EECO). - Improvement over generations: PMIP4/CMIP6 ensemble means show improved GMST agreement relative to PMIP3/CMIP5 for all paleo periods, reflecting both updated boundary conditions and model physics (e.g., cloud microphysics). - LGM as stringent target: LGM has the largest GMST signal-to-noise ratio among the five evaluated periods and better-constrained forcings (e.g., CO₂ from ice cores), making it a strong discriminator for model evaluation. Alternative LGM GMST estimate centers at ~4.5 °C cooling vs IPCC’s 5–7 °C range. - ECS discrimination: Models with very high ECS tend to over-warm paleo periods; models with very low ECS under-warm them. Both high and low ECS models can still match historical warming, implying paleoclimate states provide stronger constraints on ECS than the modern record. - Polar amplification (site-specific SST metric): • LGM: Proxies ≈ −0.4 °C; PMIP4 ensemble mean ≈ −0.7 °C; model spread from +0.1 °C (IPSLCM5A2) to −1.4 °C (CESM2). • MPWP: Proxy amplification (~1.7 °C) exceeds model ensemble means; PMIP4 improved over PMIP3 (≈0.8 °C vs 0.25 °C) but remains lower than proxies; Bering Strait closure contributes to improvement. • EECO: Proxy amplification ≈ 12 °C vs maximum model ≈ 7 °C (CESM2). Excluding southwest Pacific SST sites reduces proxy amplification to ≈ 4 °C, bringing models and proxies closer. - SAT high-latitude changes: LGM Northern Hemisphere SAT polar amplification is well matched by PMIP4 ensemble mean (−4.1 °C) vs proxies (−4.2 °C). Pliocene NH high latitudes: models colder than proxies; EECO SH high latitudes match well, supporting that SW Pacific SST proxies are likely biased warm. - Land–sea warming contrast (LSWC, site-specific): LGM and MPWP proxies indicate negative (cooling) and positive (warming) contrasts respectively; PMIP4/CMIP6 underestimates magnitude relative to proxies for both periods. EECO proxies indicate negative LSWC driven by SW Pacific SSTs; excluding those sites yields positive LSWC, aligning better with models. True vs site-specific LSWC metrics differ markedly, with true metrics lower by ~70% (LGM), ~50% (MPWP), and ~40% (EECO). - Cross-metric relationships: A near-linear relationship between ΔT and ΔAP across periods in both models and proxies (more robust when excluding EECO SW Pacific) suggests compensating mechanisms (e.g., cloud feedbacks) maintain linearity even with reduced sea ice in warm climates. ΔT vs ΔAL shows nonlinear, saturating behavior: LSWC increases at lower ΔT, then flattens at EECO-level warmth, consistent with theory on humidity/lapse-rate contrasts.

Findings demonstrate that paleoclimate metrics provide powerful constraints on model behavior across a wide range of CO₂ and climate states. Ensemble mean GMSTs align with proxies and have improved from PMIP3/CMIP5 to PMIP4/CMIP6, increasing confidence in model climate sensitivity near the central assessed range. However, individual models with very high or low ECS produce paleo GMSTs outside proxy uncertainty, indicating paleoclimate tests can better discriminate sensitivity extremes than the historical record, which is confounded by transient effects and aerosol forcing uncertainties. The approximately linear ΔT–ΔAP relationship across LGM, Pliocene, and EECO suggests robust and compensating feedback processes (beyond sea ice) dominate polar amplification across climate states. The ΔT–ΔAL relationship shows saturation at high warmth, consistent with theoretical expectations of land–ocean thermodynamic constraints. Remaining model–data mismatches are linked in part to regional proxy issues (e.g., very warm EECO southwest Pacific SSTs, possible seasonal biases, proxy calibration uncertainties, and paleoelevation uncertainties) and to mid-latitude NH terrestrial Pliocene proxies. These insights reinforce the value of coordinated paleo–model comparisons for constraining ECS and for guiding model development.

The study establishes a practical framework using proxy-informed metrics (GMST, polar amplification, LSWC) to evaluate CMIP6/PMIP4 and CMIP5/PMIP3 paleoclimate simulations of the LGM, MPWP, and EECO. Key contributions include: (i) ensemble mean GMSTs consistent with proxies across all three periods and improved agreement in PMIP4/CMIP6; (ii) evidence that paleoclimate states better constrain models with extreme ECS than historical observations; (iii) robust relationships between GMST and both polar amplification (linear) and LSWC (nonlinear, saturating), consistent with theory. The work supports using paleoclimate metrics to screen and refine models across a range of CO₂ concentrations and informs future development cycles (e.g., CMIP7). Future research should prioritize: running more paleo experiments with the same models used for historical CMIP simulations; conducting standardized 4×CO₂ experiments to derive ECS alongside paleo runs; improving proxy coverage and calibrations, especially in the Pliocene NH interiors and EECO southwest Pacific; resolving paleogeographic and paleoelevation uncertainties; and narrowing temporal windows (e.g., within the EECO) to limit orbital and CO₂ variability.

- Proxy data limitations: Sparse spatial coverage, larger uncertainties for older periods, potential seasonal biases (e.g., EECO high-latitude SSTs), and calibration uncertainties (e.g., TEX86 at high temperatures). Some terrestrial proxies lack precise paleoelevation, especially in the EECO, affecting SAT estimates. - Boundary condition uncertainties: For MPWP and EECO (e.g., CO₂ estimates rely on indirect proxies; paleogeography choices). LGM forcings are better constrained, but uncertainties remain in ice-sheet reconstructions. - Temporal window mismatch: EECO proxies span a relatively wide interval (~4.1 Myr), introducing orbital and CO₂ variability that complicates single-time-slice comparisons; marine vs terrestrial windows also differ. - Metric representativeness: Differences between site-specific and true metrics (notably for LSWC) can be substantial; site distribution biases can skew comparisons (e.g., EECO southwest Pacific dominance). Reference frame inconsistencies (e.g., NorESM1_F in EECO) preclude inclusion in spatial metrics. - Model ensemble limitations: Not all models provide ECS estimates or run all paleo periods; long integrations required for equilibrium limit participation. Historical simulations are transient and affected by pattern effects and aerosol forcing, complicating direct ECS inference.