A Self-Evolving AI Agent System for Climate Science

1 Introduction

• Vast, fragmented Earth-system data exceed human analytical capacity and limit scientific discovery.Climate science faces this challenge across cross-disciplinary datasets used to inform mitigation and adaptation.Source: §1 · p. 2
• CMIP6 combines petabytes of data from thousands of simulations and more than 50 modeling centers, challenging traditional analysis.Source: §1 · p. 2
• Manual workflows make even model-observation comparisons labor-intensive and error-prone, with ECS estimates requiring analysis of hundreds of simulations.These inefficiencies also affect large assessment efforts such as the IPCC.Source: §1 · pp. 2–3
• Diagnostic toolkits standardize and support reproducible model evaluation, but extending them requires programming expertise and architectural familiarity.This can hinder rapid exploration of new ideas and adaptation to emerging datasets.Source: §1 · p. 3
• EarthLink is presented as the first self-evolving Earth-science agent to automate research workflows, with expert assessments and an Atlantic Ni case demonstrating its capabilities.Across 36 large-scale tasks, it performed core climate work comparably to an early-career researcher and identified physically consistent precursors at an eight-month lead.Source: §1 · p. 3

2.1 Confronting model simulations and observational data

• EarthLink reproduced standard reasoning across basic statistics, ECS and TCR estimation, and ENSO diagnosis, including identifying ENSO's 23-year periodicity.Its ECS and TCR estimates fell within IPCC AR6 ranges; an instructed non-regression ECS estimate was less accurate.Source: §2.1 · p. 4

2.2 Exploring scientific scenario in climate change

• EarthLink replicated climate detection and attribution workflows, identified greenhouse gases as the dominant warming contributor, and processed projections across four SSP scenarios.The projection scenarios included SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5.Source: §2.2 · p. 5
• For regional projections, EarthLink applied spatial aggregation and hierarchical emergent constraints, while user-guided analysis identified seven effective constraints for future African temperatures.The autonomously generated HEC code closely matched expert-developed scripts.Source: §2.2 · p. 5
• Across 36 benchmark tasks, expert reviews found practically useful performance in multiple cases, with strategic planning stronger than code generation and visualization.EarthLink also replicated key conclusions from several high-impact climate studies.Source: §2.2 · pp. 5–6

2.3 Investigating adaptive capabilities and self-evolving mechanisms

• GPT-5 showed the most balanced performance across task complexities, while Llama-4-Maverick was efficient but struggled with accuracy on complex tasks.Source: §2.3 · p. 6
• After one evolution cycle, debug rounds shifted toward lower values and average task time decreased as EarthLink used knowledge and tools from prior successful runs.Source: §2.3 · p. 6

2.4 Discovering precursors and mechanisms to understand Atlantic Ni

• TCC 0.46 fell short of the 0.5 target but improved on the 0.39 state-of-the-art benchmark in the Atlantic Ni forecast task.EarthLink screened candidate precursors and tested them using regression models and automated parameter tuning.Source: §2.4 · p. 7
• The proposed Atlantic Ni pathway links late-autumn westerly anomalies to a downwelling Kelvin wave, subsurface heat storage, spring Bjerknes feedback, and summer ATL3 warming.The AI-generated hypothesis requires further validation.Source: §2.4 · p. 7

3 Discussion

• EarthLink’s evaluations support climate analyses comparable to junior-researcher work, while the discussion envisions shifting scientists toward higher-level judgment.The authors report that complex analysis cycles could be shortened from months to days.Source: §3 · p. 7
• EarthLink treats community-vetted tool functions as callable components that can be dynamically combined with generated code and applied to new questions.The authors describe this as a flexible, composable alternative to rigid tool frameworks, not a replacement for established tools.Source: §3 · pp. 7–8
• In the Atlantic Ni case, EarthLink proposed a novel, testable mechanism from observational evidence and existing knowledge, while human scientists retain validation and critical judgment.Source: §3 · p. 8
• EarthLink’s reasoning is interpolative, depends on knowledge-base quality and prompt clarity, and can produce scientifically incorrect code that runs without error.The authors emphasize transparent workflows and partnership with a human expert.Source: §3 · p. 8
• The long-term vision is a continuously learning global resource that locates, accesses, and harmonizes heterogeneous Earth data while building an internal semantic map.The authors propose that this architecture could address data fragmentation and lower barriers to advanced analysis.Source: §3 · p. 8

4.1.1 Core modules

• EarthLink’s three modules plan experiments, execute and validate workflows, then synthesize results into interpretable reports for varied decision contexts.The system also stores expert-verified plans and scripts in its libraries for knowledge accumulation and continual improvement.Source: §4.1 · p. 18, §4.1.1 · p. 19
• The Planning Module converts natural-language requests into candidate analysis plans, which are ranked and aggregated for feasibility, data availability, and methodological coherence.Optional human oversight can support interpretability and validity before a plan becomes an executable pipeline.Source: §4.1.1 · p. 18
• The Scientific Diagnosis Module turns finalized plans into code, runs analyses on climate simulations and observations, and checks outputs through iterative diagnostics and recovery.Validated plans and scripts are returned to the Knowledge and Tool Libraries.Source: §4.1.1 · pp. 18–19

4.1.2 Foundation LLMs

• GPT-5 achieved the highest success rates across four task-complexity levels and required the fewest debug rounds, despite slightly higher API cost.The authors selected it as the foundation model for all framework modules.Source: §4.1.2 · p. 19

4.1.3 Resource library

• The Knowledge, Data, and Tool Libraries combine expert-validated methods, climate datasets, and analysis software in an extensible infrastructure for reproducible workflows.The Data Library spans over 100 models and observational datasets totaling more than 3 PB; the libraries support transparency, reproducibility, and adaptability.Source: §4.1.3 · pp. 19–20

4.2.1 Task design

• The evaluation framework organizes climate research tasks into four described levels, progressing from statistical analysis to mechanistic diagnosis, complex reasoning, and a semi-open problem.The semi-open task includes human guidance and tests dataset choice, adaptive workflows, constraint methods, uncertainty quantification, and decision-oriented recommendations.Source: §4.2.1 · p. 21

4.2.2 Basic evaluation and scoring criteria

• Three independent domain experts score each task on planning, coding, and result synthesis using a five-point rubric, with reviewer scores averaged.Composite averages above 4 are categorized as expert-level, while scores from 2.5 to 4 indicate research-ready performance with minor oversight.Source: §4.2.2 · p. 22

Extended Data

• Extended Data Figures 1–3 illustrate EarthLink workflows for precipitation seasonal cycles, cloud radiative effects, and ocean heat content, from task setup through analysis outputs.The figures include generated plans and code, visualized model or observation comparisons, and automated interpretations.Source: Figure 1 · p. 24, Figure 2 · p. 25, Figure 3 · p. 26
• The evaluation tables cover tasks from simple statistical analysis through complex ENSO reasoning and semi-open climate projection constraints.Examples include ECS and TCR estimation, ENSO diversity analysis, and constraining African temperature trends over the next 20 years.Source: Extended Data · p. 28

A.1.1 Knowledge Library

• The Knowledge Library retrieves plans for similar requests using embedding-based cosine similarity and provides agents with package documentation and real-time web search.API-documentation queries return the three most similar text chunks.Source: §A.1.1 · p. 34

A.1.2 Data Library

• The Data Library contains over 3 PB of climate data, including CMIP6 data from over 70 models and observational datasets spanning the atmosphere, ocean, land, and cryosphere.Only a subset of some datasets has been downloaded in the current version, and the library is expanding.Source: §A.1.2 · p. 34, Table A1 · p. 35
• Dataset metadata and query APIs let agents check variables, ensemble members, and time coverage when planning analyses and configuring data access.Source: §A.1.2 · p. 34

A.1.3 Tool Library

• The Tool Library combines diagnostic software and scientific Python packages with expert-vetted scripts that provide reusable workflow examples for code generation.Scripts are retrieved by matching task descriptions to embedded functional descriptions.Source: §A.1.3 · p. 35

A.2 Literature parsing

• Literature parsing structures uploaded text, tables, and figures for retrieval, then supplies retrieved evidence to query enrichment and experiment planning.Text and figure summaries are embedded in a shared retrieval space for cross-modal alignment.Source: §A.2 · pp. 35–36

A.3.1 Model configuration

• Agent settings balance reproducible code generation with exploratory planning by using a coding temperature of 0.3 and a planning temperature of 1.0.Planning uses low reasoning effort to generate candidate plans quickly, while aggregation uses medium effort to finalize a plan.Source: §A.3.1 · pp. 36–37

A.3.2 Running configuration

• Running limits bound retrieval, retries, and resource use, including ten result-checking rounds, five image-feedback rounds, and up to 30 debug rounds per execution attempt.Scripts have a one-hour limit, and diagnostic tasks are capped at 20 images.Source: §A.3.2 · p. 37

A.4 Emergent constraint methods

• The emergent-constraint methods progress from native-grid projections to 3°×3° spatial aggregation and then a hierarchical Bayesian-style constraint using observed HadCRUT5 warming.The observed trend is 0.20 °C per decade ± 0.03 °C; quantile mapping adjusts future projections while retaining model ranking.Source: §A.4 · pp. 37–38

B.1 Climate impact estimation across scenarios

• For climate-impact assessments, a chair agent assigns domain-specific sub-experts and synthesizes their textual and quantitative reports, including disagreements and uncertainties.For plan aggregation, candidate plans are selectively combined; the ENSO example retains detrending and a sustained event definition from one plan and a stronger threshold and weighted ranking metric from another.Source: §B.1 · p. 39, §B.2 · pp. 39–40

B.3.1 Result checking loop

• The Result Checking Agent rejects empty files or NaN-filled arrays with descriptive feedback, prompting the Coding Agent to revise its script before outputs proceed.Valid, well-formed data objects pass the check and move to the next workflow stage.Source: §B.3.1 · p. 42, Figure B4 · p. 42
• Intermediate validation is intended to improve final-analysis integrity and reduce the need for manual oversight.The loop checks both whether outputs are valid and whether data objects are well formed.Source: §B.3.1 · p. 42

B.3.2 Image feedback loop

• Image feedback revises plot presentation, including color-bar range, whitespace, and title placement, and can add a labeled color bar and clearer color scheme to a model-performance heatmap.The heatmap’s revised colors clarify “green = better, magenta = worse.”Source: §B.3.2 · p. 43

C Case study of evaluation tasks

• The evaluation section shows only a subset of visualization results and omits the generated code scripts.Source: C Case study of evaluation tasks · p. 43

C.1.1 Annual mean and seasonal cycle of precipitation

• The evaluation compared 21 CMIP6 models with ERA5 over 1985–2014 using annual-mean bias, seasonal-cycle RMSE and correlation, and composite skill scores across eleven regions.The plan harmonized units, regridded datasets to a common 1.0° × 1.0° grid, and applied land-ocean masks.Source: §C.1.1 · pp. 45–46
• The multi-model mean captured primary global precipitation characteristics, but showed a +3–6% wet bias across the Tropics and a −13–16% dry bias in the Amazon.ERA5 consistently fell near the upper quartile of the model ensemble in the Amazon.Source: §C.1.1 · p. 46
• Seasonal-cycle deficiencies included an underestimated Sahel monsoon peak, an overly dry European summer, and a slight lag in the Northern Hemisphere summer precipitation maximum.Source: §C.1.1 · p. 46
• E3SM-2-0, IPSL-CM6A-LR, and CMCC-ESM2 ranked highest for balanced performance across regions and metrics, while newer model versions generally outperformed predecessors.EarthLink recommended top-ranked models for seasonal-precipitation-sensitive applications and bias correction for regions with large systematic errors, including the Amazon and Sahel.Source: §C.1.1 · p. 46

Annual mean and interannual variability

• The multi-model mean tracks ERA5 at global and extratropical scales but damps interannual variability; regional patterns include tropical wet bias, Amazon dry bias, and large Sahel and East Asia spread.The Amazon and Sahel show strong damping of variability and underrepresented prominent wet years; Europe has a modest dry bias, while Sahel and East Asia have weaker modeled variability.Source: §C.1.1 · p. 52

Seasonal cycle

• Seasonal-cycle phase and shape are generally captured, but wet biases range from slight year-round excess to persistent tropical excess, sometimes with an oversized amplitude.Reported biases include about 0.05–0.1 mm day−1 year-round and 0.15–0.3 mm day−1, largest in November–December.Source: §C.1.1 · p. 53
• Regional seasonal cycles include a Northern extratropical summer peak about a month late and weak, Southern extratropical wet bias in March–July, and Amazon summer dryness.The Amazon summer dry bias is about 0.4–0.5 mm day−1; the Sahel cycle timing is broadly right, but peak monsoon intensity is underestimated by about 0.8–1.1 mm day−1 with very large spread.Source: §C.1.1 · p. 53

Model ranking

• Most models score near 69–70, newer configurations generally outperform predecessors, and the listed ranks include TaiESM1 (4th, 71.4), CanESM5 (7th, 70.4), and MIROC6 (12th, 68.5).The composite score integrates annual-mean bias, seasonal-cycle RMSE and correlation, and interannual variability across regions; higher scores are better.Source: §C.1.1 · pp. 53–54

Regional priorities and practical use

• East Asia timing, the Southern extratropics, and the global region show the strongest performance, while the Amazon, Sahel, Europe, and Tropics have notable issues.For applications sensitive to seasonal timing and amplitude, the analysis recommends top-ranked models such as E3SM-2-0, IPSL-CM6A-LR, CMCC-ESM2, and TaiESM1, with bias correction for the Amazon, Sahel, and European summer.Source: §C.1.1 · p. 54

C.1.2 Climatology and variability of cloud radiative effect

• The task compared 21 CMIP6 models with ISCCP-FH for 1985–2014, assessing SW, LW, and net CRE climatology and variability and producing a composite model ranking.EarthLink planned and executed statistical comparisons using spatial patterns, mean biases, and interannual variability.Source: §C.1.2 · p. 54
• GFDL-ESM4 ranked as the top-performing model, while the analysis found SWCRE overestimation over subtropical stratocumulus decks and LWCRE underestimation in deep convective regions.The analysis included zonal-mean visualizations of shortwave, longwave, and net CRE across models and observations.Source: §C.1.2 · pp. 54–55
• The analysis linked SWCRE errors to deficiencies in low-cloud representation and LWCRE weaknesses to problems simulating high, cold clouds.Net CRE performance in many models resulted from a complex compensation of errors between the shortwave and longwave components.Source: §C.1.2 · pp. 54–55

Climatology biases

• SWCRE biases dominate CRE errors: models are 5–10 W m−2 too weak over subtropical stratocumulus decks and 5–10 W m−2 too strong over the Southern Ocean storm belt.The subtropical errors reflect deficient low-cloud amount or optical depth; SWCRE errors are the dominant source of CRE biases and intermodel spread.Source: §C.1.2 · pp. 60–62
• LWCRE is too weak in convective tropics and high latitudes in many models, while net CRE is commonly too positive in the tropics and subtropics and too negative over the Southern Ocean.Weak LWCRE implies cloud tops that are too warm or low, or insufficient high/ice cloud; Arctic net CRE sign errors are also common.Source: §C.1.2 · pp. 60–61

Interannual variability

• SWCRE variability is strongest in subtropical cloud belts and storm tracks at 12–19 W m−2, while LWCRE reaches 10–13 W m−2 in convective tropics and storm tracks.Models commonly underestimate SWCRE variability in extratropical storm tracks and the Southern Ocean but overestimate it in convective tropics and monsoon regions, typically by ±3–6 W m−2.Source: §C.1.2 · p. 61

Composite skill ranking

• 0.87 for GFDL-ESM4 leads the overall skill ranking, followed by CESM2-WACCM at 0.82.SWCRE has the widest component-skill spread, while NETCRE can benefit from SW–LW error compensation.Source: §C.1.2 · pp. 61–62

Model skill characteristics

• NETCRE realism often results from SW–LW compensation, but the highest fidelity requires balanced improvement in both components.GFDL-ESM4 has high, balanced skill; IPSL-CM6A-LR improves markedly over IPSL-CM5A2-INCA, and ACCESS-CM2 outperforms ACCESS-ESM1-5 primarily through better NET skill.Source: §C.1.2 · p. 62

C.1.3 Change and trend of ocean heat content

• The evaluation compared six CMIP6 models with IAP for 1970–2010, calculating OHC from potential temperature alone across 0–300 m, 0–700 m, and 0–2000 m.The planned workflow included bathymetry-aware vertical integration, anomalies relative to 1991–2010, decadal changes, and spatial trends.Source: §C.1.3 · pp. 62–63
• Across all depth layers, CMIP6 models—especially the multi-model mean—captured OHC increase’s sign and decadal phasing, but the 0–300 m mean change had a +40.0% bias versus IAP.The analysis also identified high-end warmers and noted GFDL-CM4 aligned more closely with observations for the 0–700 m change.Source: §C.1.3 · p. 63
• Trend maps showed shared regional biases: underestimated warming in the subpolar North Atlantic and overestimated warming in the Southern Ocean and along western boundary currents.Source: §C.1.3 · p. 63
• EarthLink flagged the 0–2000 m bar chart as not physically credible because of internal inconsistencies, likely reflecting a processing error, and advised against inference.Source: §C.1.3 · p. 63
• All datasets show sustained upper-ocean warming, while MMM tracks IAP’s phase with muted interannual variability; most models and MMM overestimate the 1991−2010 minus 1970−1990 change.A Pinatubo-related dip around 1991−1993 is captured by most models, and CMCC-ESM2 is closest while FIO-ESM-2-0 is highest on the change metric.Source: §C.1.3 · p. 69
• Model proximity to IAP varies by metric: CMCC-ESM2 is closest on the upper-ocean change, GFDL-CM4 on the decadal-change metric, and MMM overall for time series.CIESM and FIO-ESM-2-0 are high-end warmers, while FGOALS-f3-L tends to under-warm at 0−700 m.Source: §C.1.3 · pp. 69–71
• At 0−2000 m, all datasets show near-monotonic deep-ocean warming with major dips captured; MMM is close to IAP after the mid-1990s, though CIESM warms too strongly.IAP and MMM show widespread deep warming, strongest in the Southern Ocean and western boundary current regions.Source: §C.1.3 · p. 70
• The 0−2000 m ΔOHC bar chart contains processing errors and physically implausible values, so it should not support decadal-change inferences.The figure is flagged for recomputation; the corresponding time series and trend maps are considered plausible.Source: §C.1.3 · pp. 70–71
• Across depth ranges, the MMM reproduces OHC anomaly signs, decadal phasing, and major transient cooling, but overestimates upper-ocean increases and shows regional positive biases at 0−2000 m.Intermodel spread narrows after about 1995; 0−2000 m time series and trend maps are internally consistent and physically plausible.Source: §C.1.3 · p. 71
• MMM trend maps are overly smooth, with too-weak warming in the subpolar North Atlantic and equatorial Pacific, and too-strong warming in western boundary-current extensions and broad Southern Hemisphere mid-latitudes.This pattern is common across depths; regional biases can reach ~±1 W m−2.Source: §C.1.3 · pp. 70–71

C.2.1 Equilibrium climate sensitivity

• The task assessed EarthLink’s ability to plan and carry out multi-step climate analysis, including model ranking, ensemble statistics, and visualizations for 22 CMIP6 models.The requested outputs included per-model regression visualizations, a ranked ECS list, and an ensemble mean and probability density function.Source: §C.2.1 · pp. 71–72
• EarthLink’s plan calculated ECS from the Gregory regression ∆N = a + b∆T, with α = −b, F4× = a, and ECS = −a/(2b).It specified annual anomalies for 150 years of abrupt-4xCO2 relative to a stable piControl baseline, with area-weighting and native-calendar handling.Source: §C.2.1 · p. 71
• The 22-model multi-model mean ECS was 3.82 ± 1.05 K, ranging from 1.90 K (INM-CM5-0) to 5.65 K (CIESM).EarthLink also generated per-model regressions, a ranked ECS chart, and an ensemble probability density function.Source: §C.2.1 · p. 72
• Inter-model differences in climate feedback parameter α primarily drove the ECS spread, while forcing F4× was more consistent across models.In many models, earlier-period regressions showed stronger feedback and therefore lower ECS estimates than regressions over the full 150 years, indicating time-dependent feedbacks (pattern effects).Source: §C.2.1 · p. 72

Equilibrium climate sensitivity

• Many models showed curvature, with early-year fits typically steeper than late-year fits, implying weakening feedback with warming and higher long-term ECS than early-year estimates.This pattern effect is especially evident in high-ECS models, where early-year estimates tend to fall below all-years estimates.Source: §C.2.1 · pp. 76–77
• Median ECS was ≈3.58 K (IQR ≈3.01−4.69 K; IQR ≈1.68 K), with a 1.90−5.65 K range and a right-skewed high-ECS tail.The high-ECS tail (≥5 K) lifts the mean above the median, while a smaller low-ECS cluster sits near 2−3 K.Source: §C.2.1 · p. 77
• The ensemble included 6/22 models at ≤3 K and 9/22 at 3−4.5 K, alongside a sizable high-ECS group at ≥4.5 K.Source: §C.2.1 · p. 77
• Across 22 models, mean effective ECS from all-years Gregory fits was 3.82 ± 1.05 K.The ensemble standard deviation was 1.05 K, with CV ≈27%.Source: §C.2.1 · p. 77
• Inter-model ECS differences were driven chiefly by feedback strength (α = −b), while forcing magnitudes were comparatively tightly clustered.All models had physically consistent negative slopes (b < 0), indicating that TOA imbalance decreases as the system warms.Source: §C.2.1 · pp. 76–77

C.2.2 Future projection of surface temperature

• EarthLink’s analysis used eight CMIP6 models to calculate global temperature anomalies against 1985–2014 and produce time-series and 2050–2099 warming comparisons for four SSPs.Its plan called for area-weighted annual global means, consistent model realizations across historical and scenario runs, and multi-model means and standard deviations.Source: §C.2.2 · p. 78
• 1.06°C for SSP1-2.6, 1.74°C for SSP2-4.5, 2.40°C for SSP3-7.0, and 2.88°C for SSP5-8.5 are the projected mean warmings for 2050–2099.By 2100, multi-model mean anomalies reach approximately 1.1°C under SSP1-2.6, over 2.0°C under SSP2-4.5, 3.3°C under SSP3-7.0, and 4.2°C under SSP5-8.5; inter-model spread grows with forcing and is widest under SSP5-8.5.Source: §C.2.2 · p. 78
• The scenario time series diverge around the mid-2030s, and SSP1-2.6’s late-century warming is roughly half that under SSP5-8.5.All pathways continue warming in the near term; SSP1-2.6 stabilizes near 1.1°C above baseline by mid-century before slightly declining, while higher-emissions pathways continue rising.Source: §C.2.2 · p. 78
• By ~2035−2040, scenario trajectories separate clearly, and inter-model spread grows with forcing, becoming smallest for SSP1-2.6 and largest for SSP5-8.5 by 2100.The ±1σ bands widen with forcing, yet mean differences remain substantial.Source: §C.2.2 · pp. 82–83
• By 2100, MMM anomalies reach ~1.0−1.1 °C for SSP1-2.6, ~2.0−2.2 °C for SSP2-4.5, ~3.1−3.4 °C for SSP3-7.0, and ~4.1−4.3 °C for SSP5-8.5.The scenario ordering is robust: SSP1-2.6 < SSP2-4.5 < SSP3-7.0 < SSP5-8.5.Source: §C.2.2 · pp. 82–83
• From 2015−2050, MMM warming rates are ~0.15−0.20 °C per decade for SSP1-2.6, ~0.30−0.35 °C for SSP2-4.5, ~0.35−0.40 °C for SSP3-7.0, and ~0.40−0.50 °C for SSP5-8.5.The SSP1-2.6 rate slows after ~2050.Source: §C.2.2 · p. 82
• For 2050−2099, individual model ranges are ~0.7 to ~1.8 °C for SSP1-2.6, ~1.3 to ~2.7 °C for SSP2-4.5, ~1.7 to ~3.9 °C for SSP3-7.0, and ~1.9 to ~4.6 °C for SSP5-8.5.The SSP5-8.5 range includes one high outlier.Source: §C.2.2 · p. 83
• Following SSP1-2.6 roughly halves late-century warming relative to SSP5-8.5 for this model set.The anomalies are relative to 1985−2014.Source: §C.2.2 · p. 83

• EarthLink planned an optimal fingerprinting analysis using generalized least squares to estimate GHG, aerosol, and natural-forcing contributions against HadCRUT5 observations.The plan used multi-model-mean CMIP6 DAMIP fingerprints and estimated internal-variability covariance from long pre-industrial control simulations, with uncertainty quantification and diagnostic tests.Source: §C.3.1 · pp. 83–84
• To make model–observation comparisons like-for-like, EarthLink planned to blend land tas and ocean tos, regrid model data, and apply HadCRUT5’s time-varying coverage mask.It would estimate variability covariance from piControl simulations to weight the regression.Source: §C.3.1 · p. 83
• Greenhouse gases were the dominant driver of observed warming from 1901 to 2015, while aerosols offset warming and natural forcings explained short-term variability.GHG-attributable warming was approximately +1.42 K versus ≈+1.30 K total observed warming; aerosols contributed approximately −0.12 K and natural forcings +0.07 K. The three scaled contributions reconstructed the historical record, and β_GHG was approximately 0.95.Source: §C.3.1 · p. 84

Time-evolving contributions

• GHG warming strengthened after ~1975, reaching about +0.95 to +1.0 K by 2015 relative to the 1961−1990 baseline.Its contribution rose monotonically, with weaker warming early in the century.Source: §C.3.1 · p. 89
• AER was positive early in the century, declined through mid-century, and was near zero to slightly negative by 2015, offsetting GHG warming during the mid-century slowdown.Its century-scale net cooling is small and not robustly detected in the global mean.Source: §C.3.1 · pp. 89–90
• NAT contributions were small and near zero, with episodic volcanic cooling and a slightly positive 2015 value; they mainly modulated short-term variability rather than sustained warming.There was little sustained natural-forcing trend over the period.Source: §C.3.1 · pp. 89–90

Observed vs reconstructed warming (closure)

• The reconstructed contributions sum to ≈+1.37 K (≈±0.15 K, 5−95%), closely track HadCRUT5, and reproduce early warming, the mid-century slowdown, and late-century acceleration.Reconstruction uncertainty is of order a few tenths of a kelvin.Source: §C.3.1 · pp. 89–90

Scaling factors and detection

• β_GHG ≈0.95 (95% CI ~0.85−1.05) and β_NAT ≈1.0 (95% CI ~0.6−1.4) were detected; β_AER ≈0.25 was not robustly detected because its 95% CI overlaps zero.The weak AER separability reflects partial collinearity with GHG over time.Source: §C.3.1 · p. 90

Main drivers of the observed 1901−2015 warming

• Well-mixed greenhouse gases are the dominant driver, with their scaled contribution accounting for essentially all of the long-term warming and exceeding the observed increase, with offsets from other factors.Source: §C.3.1 · p. 90

C.3.2 ENSO period

• EarthLink planned a Morlet continuous wavelet analysis of HadISST and 29 CMIP6 models’ Niñ o3.4 series for 1870–2014, using 1981–2010 anomalies, detrending, standardization, and AR(1) significance testing.Source: §C.3.2 · p. 91
• HadISST showed a statistically significant 2–7-year ENSO peak, strongest in the late-19th and late-20th centuries, while the multi-model median captured a 4-year periodicity but understated extreme-event intensity.Source: §C.3.2 · p. 91
• CESM2, CanESM5, ACCESS-CM2, and GFDL-ESM4 reproduced observed spectral shape and intermittency, while other models showed overly regular, weak, or decadal-biased ENSO behavior.Source: §C.3.2 · p. 91
• The ensemble median peaks near 4 years, matching HadISST, but has lower 3–6-year power and generally less relative decadal energy; spread is largest beyond about 7–8 years.Source: §C.3.2 · pp. 97–98
• Observed ENSO-band power is intermittent, with strong HadISST epochs around 1880–1905 and 1965–1995; model strong and weak phases occur commonly but are not synchronized with observations.Source: §C.3.2 · p. 98
• CESM2, CanESM5, ACCESS-CM2/ESM1-5, CMCC-CM2-HR4/SR5, GFDL-CM4/ESM4, MIROC6, and several other models align more closely with HadISST in spectral shape and intermittency.Source: §C.3.2 · pp. 97–98
• Interpret decadal power beyond about 8–10 years cautiously because limited record length and proximity to the cone of influence complicate its assessment.Features near record ends are also partly outside the cone of influence.Source: §C.3.2 · p. 98
• HadISST shows a broad significant ENSO maximum at 3–5 years, and CMIP6 models broadly reproduce this primary periodicity and its nonstationary amplitude.Source: §C.3.2 · pp. 98–99
• Model deficiencies include short, overly regular ENSO near 2–3 years, underpowered ENSO-band activity, and excess low-frequency or decadal variance.Short-biased examples include FGOALS*, KIOST-ESM, FIO-ESM-2-0, and BCC-ESM1; long-leaning examples include CMCC-ESM2, BCC-CSM2-MR, and CanESM5.Source: §C.3.2 · pp. 98–99
• CESM2, CanESM5, ACCESS-CM2/ESM1-5, CMCC-CM2-HR4/SR5, GFDL-CM4/ESM4, and MIROC6 best match observations, while INM-CM5-0, MCM-UA-1-0, and MPI-ESM1-2-LR are weak and FGOALS* is overly regular.Source: §C.3.2 · p. 99

C.4.1 Constrained future projection

• EarthLink proposed ten historical constraint factors and regressed each against projected 2015–2035 warming across 20 CMIP6 models, using ERA5 as the observational reference.Factors included African and seasonal temperature trends, regional trends, and cross-variable relationships such as African precipitation.Source: §C.4.1 · p. 99
• The African mean tas trend was the strongest historical predictor of future warming trends at |R| = 0.66, and no factor met the |R| ≥0.7 selection threshold.The JJA mean tas trend followed at 0.63.Source: §C.4.1 · pp. 101, 103
• The final constrained trend provides a robust, observation-informed estimate of ~0.35–0.4 °C/decade, reducing uncertainty from the raw model ensemble’s projected 0.1–0.6 °C/decade range.Source: §C.4.1 · p. 103
• Historical constraints narrowed the model-ensemble range, with most factor-based predictions clustering around 0.3–0.4 °C/decade.The analysis says this reduction in projection uncertainty supports impact assessment.Source: §C.4.1 · p. 103
• All models and the constrained projection showed warming through 2035, with anomalies exceeding 1 °C; the constraint slightly moderated warming after 2025 and lowered the projected upper bound.Anomalies are relative to the 1981–2010 baseline.Source: §C.4.1 · p. 103
• The analysis linked projected warming to African agricultural risks and recommended heat-tolerant crops, improved irrigation, and adjusted planting dates.The reported reduction in projection uncertainty was said to support more confident, targeted adaptation measures.Source: §C.4.1 · p. 103

D Application in research reproduction

• The reproduction request followed [28]’s process, but EarthLink selected 37 CMIP experiments itself because the available database was insufficient.The supplied plan specified observational and model data, model screening, event identification, composites, and future-frequency analysis.Source: D Application in research reproduction · pp. 104, 106
• EarthLink reconstructed the original study’s full workflow, from data preparation and model screening through event detection, composite analysis, and statistical evaluation.The plan made input variables, time ranges, and ensemble selection explicit, supporting reproducibility and transparency.Source: D Application in research reproduction · p. 104
• EarthLink reproduced ’s finding of more frequent consecutive La Niña events under anthropogenic warming, alongside stronger, more persistent second-year cooling.Its analysis also found spatial and temporal patterns consistent with intensified off-equatorial trades and subtropical–tropical coupling, while incorporating inter-model spread and control-run benchmarks.Source: D Application in research reproduction · p. 104
• The case shows EarthLink translating natural-language hypotheses into executable multi-model experiments while extending the analysis through standardized data handling and uncertainty quantification.The authors characterize this as a potential for verifiable, interpretable, and extensible agent-driven research.Source: D Application in research reproduction · p. 104
• The observational benchmark averages three SST datasets that agree closely after about 1950, captures ENSO asymmetry, and supports model screening despite greater pre-1950 uncertainty.Across 37 CMIP6 models, skewness ranges roughly −0.5 to +0.64; screening retains positive-skewness models, while the observational benchmark skewness is about 0.23.Source: D Application in research reproduction · pp. 111–112
• Many screened models show more multi-year La Niña sequences in 2000−2099 than in 1900−1999, although some show little increase, reflecting model spread.Because the threshold is fixed to each model’s 1900−1999 σ, the future increase reflects altered event occurrence or persistence, not a looser threshold.Source: D Application in research reproduction · p. 112
• Models reproduce observed single-year event cooling and decay, while multi-year composites capture pre-onset warming and second-winter persistence but slightly underestimate both.Observed composites include only 10−11 single-year and 8 multi-year events, making fine-scale features more uncertain.Source: D Application in research reproduction · pp. 112–113
• Future single-year composites remain essentially unchanged, while multi-year events show modestly deeper, more persistent second-year cooling and slower decay.Onset and first-winter growth are similar between periods; the future second-year minima are slightly stronger.Source: D Application in research reproduction · p. 112
• Multi-year events account for approximately 50% of future versus 33% of past composite samples, indicating a marked increase in their share under warming.The samples contain about 161 multi-year and 159 single-year future events, compared with 131 multi-year and 261 single-year past events.Source: D Application in research reproduction · p. 112
• For single-year events, the MME captures equatorial cooling and easterlies but mutes observed subtropical warm anomalies and wind signals, likely underplaying subtropical coupling.Observed composites show a central-eastern Pacific cold tongue, subtropical warm horseshoe, and strengthened trades.Source: D Application in research reproduction · p. 113
• Multi-year events have a broader first-winter fingerprint, with trades extending into 10–25° latitude; off-equatorial WES and entrainment feedback slows equatorial recharge and favors second-year persistence.Observed and MME wind structures agree directionally, though observations are patchier and the MME smoother.Source: D Application in research reproduction · p. 113
• Multi-year La Niña frequency rises under warming, emerging above internal variability in the early 21st century and strengthening toward 2100; ensemble estimates show a ~43% rise, from ~6.8 to ~12 events per century.Most screened models show increases, although inter-model spread and early-century observational uncertainty remain.Source: D Application in research reproduction · pp. 113–114
• Reproducing study [29], EarthLink reconstructed its CMIP6 workflow and recovered the projected increase in ENSO SST variability and its linkage to strengthened air–sea coupling and nonlinear feedbacks.It also standardized outputs, added robustness checks, and generated interpretable visual summaries and statistical evaluations.Source: §D.2 · p. 115
• A positive relationship between ΔSD(Niño3.4) and Niño3 skewness supports enhanced nonlinear Bjerknes feedback as a variability amplifier, with observed skewness values on the positive side of the relationship.The observational reference indicates a modest positive ΔSD under ssp370–585.Source: §D.2 · p. 121
• Despite greater sensitivity to internal variability on 50-year windows, most models still show enhanced late-century variability, especially under strong forcing.Source: §D.2 · p. 121
• ENSO SST variability increases from the 20th to 21st century across CMIP6, most consistently in Niño3.4, while MME increases are significant only under ssp370 and ssp585 and robust to normalization.The analysis notes a discrepancy with reported lower-forcing significance: ssp126 and ssp245 were not significant under its bootstrap criterion, potentially reflecting model sets, sample sizes, or the criterion used.Source: §D.2 · p. 122
• The reproduction target was Song et al., which links delayed tropical rainy-season onset to amplified pre-monsoon hot-season warming through increased solar radiation and reduced evaporative cooling.EarthLink was not given the target paper; it was primed with four preceding studies documenting rainfall delay and its drivers, to test whether it could formulate and test hypotheses from established knowledge.Source: §D.3 · p. 122
• EarthLink began the Song et al. reproduction by defining a rigorous plan to quantify later rainy-season onset effects, diagnose mechanisms, and synthesize findings into a process-based framework.The supplied passage begins describing the plan's scope but is truncated after “global.”Source: §D.3 · p. 122
• EarthLink’s analysis found that later rainy-season onset follows hotter, drier land conditions, is linked to remote SST forcing such as ENSO, and produces shorter, drier wet seasons.Its unified framework identified ocean-forced circulation, thermodynamic thresholds for convection, and local land-atmosphere feedbacks as interacting controls on onset timing and impacts.Source: §D.3 · p. 123
• EarthLink decomposed a broad question about rainfall delay into five testable hypotheses spanning land-surface, atmospheric, and ocean-driven processes.The hypotheses covered pre-onset heat and evaporative stress, wet-season length and precipitation, remote SST and circulation, ecosystem water stress, and thermodynamic preconditioning.Source: §D.3 · p. 123
• EarthLink specified datasets, variables, a quantitative rainy-season-onset definition, and statistical analyses from preprocessing and regridding to significance testing and multi-model projections.The plan was described as a viable, actionable research design rather than plausible-sounding text.Source: §D.3 · p. 123
• By integrating land-atmosphere coupling with thermodynamic preconditioning, EarthLink independently rediscovered the target paper’s “hot-season-gets-hotter” thesis.It connected delayed rainfall to amplified heating without prior knowledge of the thesis.Source: §D.3 · p. 123
• The plan tests whether basin-scale SST patterns and circulation delay land rainfall onset, using lagged regressions, circulation diagnostics, and early-versus-late onset composites.It also relates onset anomalies to land–sea thermal contrast and separates basin influences with multiple regression.Source: §D.3 · p. 127
• The plan examines whether later onset increases ecosystem water stress by extending the dry season, using soil-moisture and leaf-area-index regressions and early-versus-late onset composites.It proposes interpreting regression slopes as ecosystem water-stress sensitivity to onset timing.Source: §D.3 · p. 127
• The plan tests whether stability and mid-level moisture alter convective triggering thresholds and onset timing, and whether pre-onset conditions modulate early-wet-season intensity.It defines stability and humidity proxies, lagged regressions, and a monthly precipitation intensity proxy, with daily-extreme measures reserved for sensitivity analysis.Source: §D.3 · pp. 127–128
• Moisture- and surface-energy-budget diagnostics are combined with onset-centered composites to trace the seasonal sequence of conditions associated with onset timing differences.The plan uses P − E ≈ −∇·Q − dW/dt for the column moisture budget and EF = hfls /(hfls+hfss) for surface energy partitioning.Source: §D.3 · p. 128
• The plan compares observed and CMIP6 historical onset trends, contextualizes them with piControl variability, and analyzes future onset changes and their drivers under SSP scenarios.It proposes mid- and late-century changes, cross-model attribution to physical drivers, and scaling regional onset change per °C of global-mean warming.Source: §D.3 · p. 128
• Statistical and robustness procedures include area weighting, autocorrelation-adjusted trend intervals, resampling and false-discovery control, plus tests of onset thresholds and persistence criteria.Where daily precipitation is available, monthly onset is cross-validated against pentad-based onset without changing the primary monthly analysis.Source: §D.3 · pp. 128–129
• Under warming, many tropical regions are projected to have later onset, shorter seasons, and lower rainfall, with robust hotspots in the Amazon-Cerrado, Central America, northern Australia, and southern Africa.Mid-century onset delays are about +0.5 to +1.5 months; affected regions show wet-season shortening of roughly 1–2 months and rainfall declines up to about 100–300 mm.Source: §D.3 · pp. 132, 134
• Onset is early after the driest month in humid equatorial cores but later along semi-arid margins, where variability reaches 1.5–2.8 months.Interannual variability is generally under one month in humid cores; 2000–2016 anomalies include ENSO-linked delays over the Maritime Continent and Amazon in 2014–2016.Source: §D.3 · p. 132
• Delayed onset extends the dry season, depleting soil moisture and increasing plant water stress, heat stress, and fire risk in seasonally dry forests and savannas.The analysis reports pre-onset warming of about +0.5 to +2 K per month of delay and soil-moisture declines of about −1 to −5 mm per month of delay across much of tropical land.Source: §D.3 · p. 133
• Drier mid-levels and greater stability delay convection, while land drying raises heat and evaporative stress; onset sensitivity is −0.2 to −0.4 months per +10% RH700.The proposed land feedback prolongs soil drying, lowers evaporative fraction, and increases sensible heating and vapor-pressure deficit; convective thresholds also depend on sufficient ascent and moisture import.Source: §D.3 · pp. 133–135
• CMIP6 reproduces observed mean and variability patterns, but 36-year piControl segments show 1–3-month variability hotspots without coherent trends, limiting detection of forced delays.The analysis calls for regional aggregation, longer records or ensembles, and mechanistic attribution; bimodal rainfall regions require daily or pentad onset validation, and model spread in land hydrology remains a concern.Source: §D.3 · pp. 134–135
• Lagged SST controls provide 3–6-month onset predictability for the Maritime Continent, Amazon, and Sahel, while RH700 and stability add month-ahead predictors.ENSO correlations reach r ≈ 0.8–0.9 for the Maritime Continent and r ≈ 0.65–0.75 for the Amazon; South Asian lagged SST correlations are weak or inconsistent.Source: §D.3 · pp. 133–134
• A one-month onset delay typically shortens the wet season by about 12 days and reduces seasonal rainfall by about 100 mm, although pan-tropical averages can obscure local relationships.Grid-cell sensitivities are broadly negative, but spatial compensation and asynchronous phasing can weaken or reverse pan-tropical regressions; regional analysis reveals the local drying and shortening signal.Source: §D.3 · pp. 133, 135
• Later tropical onset couples weaker moisture convergence, drier mid-levels and greater stability, and hotter, drier land; warming is projected to amplify the resulting seasonal delays and stress.The analysis identifies ocean-forced circulation, thermodynamic preconditioning, and land feedbacks as connected controls on onset.Source: §D.3 · pp. 132, 136

E.2 Causal link between pantropical climate variability and sea ice changes

• Pantropical SST gradients link to sea-ice changes through a fast atmospheric bridge and a slow oceanic and stratospheric branch.The fast branch operates over weeks to months; the slow branch unfolds over 6 to 18 months through Ekman heat transport and descending stratospheric effects.Source: §E.2 · pp. 146–147
• The pathway is asymmetric: Atlantic-Pacific gradients drive rapid Amundsen-Bellingshausen Sea responses, while Indian-Pacific gradients drive delayed Barents-Kara sea-ice decline and Weddell Sea growth.The delayed changes occur a year later.Source: §E.2 · p. 147
• The teleconnection may enable forecasts of Barents-Kara and Weddell Sea ice anomalies 12 to 20 months ahead and explain asynchronous variability across polar regions.The two-branch hypothesis attributes these patterns to distinct timescales and pathways of pantropical forcing.Source: §E.2 · p. 147
• PTV correlates with westward equatorial Pacific wind stress at r ≈0.30 (p ≈1e−11; N ≈504 months, 1980–2021), and its sea-ice signals largely persist after controlling for Niño3.4.The PTV–trade correlation varies by epoch, with 20-year sliding correlations of approximately 0.18–0.38 that peaked around 1999–2003 and weakened near 2007–09.Source: §E.2 · pp. 153, 155
• Per +1σ predictor, Barents–Kara SIC falls 2–3% at 12–20-month leads, Weddell SIC rises 1.5–2% at 12–18 months, and Amundsen–Bellingshausen SIC falls 0.5–1% at 0–6 months.The strongest delayed Barents–Kara losses are associated with PTV and TBV_IND; TBV_ATL peaks at zero months for the immediate Amundsen–Bellingshausen loss.Source: §E.2 · p. 153
• Seasonal stratospheric wind changes and wind-driven Ekman heat convergence provide delayed links to sea ice: positive HEk implies ice loss, while negative HEk implies ice gain.Southern Hemisphere spring PTV is associated with vortex strengthening, and the analysis describes a rapid AO/SAM-like surface response to stratospheric winds.Source: §E.2 · p. 154
• Positive pantropical SST gradients trigger fast PNA−/PSA and SAM+-like atmospheric forcing that reduces Amundsen–Bellingshausen ice and increases North Pacific ice, followed by delayed Barents–Kara loss and Weddell gains.The fast response is strongest for TBV_ATL; the delayed responses are strongest for TBV_IND and PTV.Source: §E.2 · pp. 153–155

E.3 Teleconnection mechanism among the Pacific, Indian, and Atlantic basins

• Atlantic Niño warming in boreal summer initiates an atmospheric Kelvin-wave response that strengthens Pacific trades and favors an EP-leaning La Niña, with observed cooling of approximately −0.2 to −0.3 K by the following winter.A positive IOD then enhances Indonesian Throughflow export from the western Pacific warm pool, sustaining or amplifying La Niña cooling about 6–12 months after the IOD event.Source: §E.3 · pp. 155–156
• Positive JJA ATL3 warming is proposed to promote an EP-leaning La Niña by the following DJF and raise the likelihood of WIO warming and a positive SON IOD.The proposed pathway involves an atmospheric Kelvin response, stronger equatorial Pacific easterlies, and eastern-Pacific thermocline shoaling.Source: §E.3 · p. 156
• DJF ENSO is proposed to drive MAM Indian Ocean basin and tropical North Atlantic warming, which can precondition ATL3 by the next JJA.The proposed closure is qualified as occurring in some years.Source: §E.3 · p. 156
• Positive SON IOD may affect Pacific and Atlantic conditions through distinct oceanic pathways: enhanced Indonesian Throughflow heat export and stronger Agulhas leakage eddy activity.The proposed lags are about 6–12 months for increased Pacific cooling likelihood, absent offsetting westerly wind bursts, and 6–18 months for South/Tropical Atlantic warming that can precondition ATL3.Source: §E.3 · p. 156
• On decadal scales, positive AMV is proposed to strengthen subtropical Pacific WES feedback, favor CP-type El Niño, and modulate PDO/IPO, while tropical Atlantic warming favors Indo-western Pacific warming and EP cooling.The AMV signal is defined as variability longer than 10 years.Source: §E.3 · p. 156
• An Atlantic–Indian–Pacific chain links interannual to decadal variability through an Atlantic-forced atmospheric bridge, a delayed IOD-related oceanic tunnel, and ENSO feedback toward the Atlantic.The proposed sequence includes Atlantic Niño warming the western Indian Ocean and raising positive-IOD odds; positive IOD enhances ITF heat export and conditions further Pacific cooling, while ENSO warms the spring Indian Ocean basin and tropical North Atlantic and can precondition the next Atlantic Niño.Source: §E.3 · pp. 162–163
• ≈−0.15 to −0.3 K equatorial Pacific cooling develops by the following MAM−JJA after a 1σ SON DMI lead, consistent with a delayed oceanic pathway.Lead–lag maps and wavelet coherence support the IOD-to-Pacific link, but the proposed causal DMI-to-ITF and ITF-to-ENSO links were not retained by FDR, likely reflecting proxy and seasonal-node limitations.Source: §E.3 · pp. 163–165
• The teleconnections are intermittent and strongest in the mid-to-late 1990s, while strict FDR masking leaves precipitation and wind regressions spatially patchy.Seasonal targeting matters (ATL3 in JJA and DMI in SON); the Agulhas-leakage pathway was not evaluated, and decadal AMV/PDO modulation was not addressed in these interannual diagnostics.Source: §E.3 · pp. 164–165
• Most CMIP6 models capture western Indian Ocean warming but miss or reverse the observed eastern-Pacific cooling at +6/+9 months, indicating systematic teleconnection bias.Only a minority show the observed sequence; the observed lag patterns include Atlantic Niño-associated WIO warming and a positive-IOD-like pattern.Source: §E.3 · p. 164
• ≈−0.2 to −0.3 K equatorial Pacific SST cooling follows a 1σ ATL3 lead by DJF, alongside ≈−2 to −3 cm sea-level anomalies and 0.5−1.5 m s−1 easterlies.The ATL3-forced easterlies launch an eastward-propagating upwelling Kelvin wave, shoaling the eastern-Pacific thermocline; the reported PCMCI ATL3(JJA) → Niño3.4(DJF) semi-partial r is ≈−0.53 at ~6-month lag, stronger for EP than CP.Source: §E.3 · pp. 163–164
• Years with JJA ATL3+ followed by SON DMI+ have the highest probability of an EP−leaning La Niña peaking in DJF and persisting into the following spring–summer.Source: §E.3 · p. 165
• Observations verify the interannual Atlantic→Indian→Pacific chain, but most CMIP6 models miss the Pacific response to ATL3, limiting three-ocean predictive skill.The passage recommends prioritizing models that capture ATL3→EP cooling and the IOD dipole, and improving tropical Atlantic convection, atmospheric Kelvin response, ITCZ biases, and Pacific thermocline feedbacks.Source: §E.3 · p. 165

E.4 Emergent constraints on subtropical eastern Pacific low-cloud shortwave feedbacks under global warming

• Among ten tested predictors, “Regime-slope” most reliably constrains the combined Northeast and Southeast Pacific feedback trend to 0 to +0.1 W m−2 K−1 decade−1.The constrained trend is expected to be small and slightly positive, suggesting the positive low-cloud feedback is unlikely to keep strengthening and may weaken or stabilize.Source: §E.4 · pp. 165–166
• Regime-slope measures how SWCRE responds to EIS across stability regimes, offering a process-based diagnostic of models’ state-dependent cloud-inversion relationships.EIS controls the inversion capping the marine boundary layer and thus turbulent entrainment of dry air; reproducing this present-climate relationship is linked to simulating cloud evolution as the background climate changes.Source: §E.4 · p. 166
• The NEP posterior shifts toward a slightly positive trend, whereas the SEP converges near zero or slightly negative.Both regional posteriors narrow, with moderate narrowing in the NEP and significant narrowing in the SEP.Source: §E.4 · p. 174
• Posterior PDFs significantly constrain the future trend, with the combined region concentrated near a weakly positive, limited-magnitude trend.Most predictors narrow the combined-region posterior, whose peak is near 0 to +0.1.Source: §E.4 · p. 174
• Regime_slope has the highest combined-region correlation (r ≈0.5+), while CRE_EIS_beta converges significantly across regions and LCF_SST_beta independently supports these predictors.Cov(CRE, LCF) converges in all regions and helps reduce extreme distribution tails.Source: §E.4 · p. 175
• LCF_tau is among the most significant constraints across regions, while W500_mean constrains more strongly in the NEP and LCF_amp shows region-dependent convergence.LCF_tau represents cloud persistence or memory; W500_mean is relatively weak in the combined region.Source: §E.4 · p. 175
• LCF_mean provides limited convergence, EIS_mean is the weakest constraint, and SST’-glob provides almost no constraint on its own.The mean-state stability represented by EIS_mean alone is insufficient to explain the rate of change of the trend.Source: §E.4 · p. 175

E.2 Causal link between pantropical climate variability and sea ice changes

• Regime_slope is the most reliable combined-region constraint, with the highest reported correlation (r ≈0.53), stable leave-one-out predictive skill, and directional consistency with other process metrics.ODR agrees with OLS, and performance is robust in SEP and the combined region.Source: §E.4 · p. 176
• Regime_slope links stability-regime-dependent CRE sensitivity to future SWCRE trends, while stronger SEP subsidence supports a more robust EIS-to-CRE process chain.EIS affects inversion strength and entrainment, which shape low-cloud fraction and liquid water path; the resulting CRE sensitivity maps long-term EIS and subsidence changes onto SWCRE evolution.Source: §E.4 · p. 176
• Although LCF_tau and LCF_amp narrow the distribution, their weaker mechanistic robustness and transferability place them below Regime_slope and CRE_EIS_beta in composite reliability.The trend in λ_SW,cld has only weak-to-moderate correlation with global warming magnitude and varies regionally, so ΔTglob was not used as a primary constraint.Source: §E.4 · pp. 176–177
• The combined-region trend is most likely close to zero and slightly positive, implying a weaker positive shortwave low-cloud feedback or a less extreme one later this century.The constrained trend also reduces uncertainty in future warming associated with low clouds.Source: §E.4 · p. 177
• The NEP posterior shifts toward more positive values, whereas the SEP is closer to zero or slightly negative, yielding partial cancellation in the combined estimate.This indicates slight anti-phase behavior between the northern and southern regions.Source: §E.4 · p. 177