Detecting Climate Tipping Points via Online Predictive-Regime Monitoring
Climate tipping points—abrupt, potentially irreversible transitions in Earth subsystems such as the Atlantic Meridional Overturning Circulation (AMOC)— represent one of the most consequential risks in climate science. Existing early-warning indicators based on critical slowing down (rising variance and autocorrelation) have shown inconsistent reliability across model classes and parameter regimes. We present and evaluate a predictive-regime monitoring framework that continuously compares linear and nonlinear (Volterra-kernel) predictive models over a sliding window, using the Bayesian Information Criterion (δBIC) to detect the emergence of nonlinear predictive structure—the mathematical signature of an approaching tipping point. Unlike statistical precursors based on variance or autocorrelation, the proposed approach detects regime change through shifts in predictive model structure. Multi-channel coherence aggregation across climate observables suppresses false alarms through channel-group voting. All results are obtained in controlled tipping simulations designed to isolate regime transitions under known onset conditions. In ensemble validation, the framework provides multi-year lead time prior to tipping onset while maintaining zero false positives at actionable alert levels in control scenarios. Specifically, detection achieves 100% success rate with a mean early warning lead time of 38 months (3.2 years) across five onset positions, zero false positives across 20 control simulations, and robust detection through 4×baseline noise amplification. The coherence gate correctly suppresses single-channel anomalies while detecting system-wide transitions. No domain-specific training data is required, and the framework operates in a streaming fashion suitable for deployment on ocean sensor networks.Version 2 (2026-03-18) Added ERA5 reanalysis validation. The framework was applied to 75 years of North Atlantic SST data (1950–2025) under a blind-run protocol. Result: persistent linear dominance across the full observational record, zero false positives (including Pinatubo and the global warming trend), and a post-2000 δBIC drift of 11 points toward nonlinearity — consistent with AMOC weakening that has not yet crossed the nonlinear-dominance threshold. Sensitivity analysis across seven parameter configurations confirms robustness. New Section 5; abstract, discussion, and limitations revised accordingly. 10pp → 12pp.Version 3 (2026-03-18) Extended to 4-channel ERA5/ORAS5 analysis (SST ×2, surface salinity, mixed layer depth; 1958–2024) and CMIP6-like collapse validation. The 2-channel SST-only result from V2 is superseded by the full 4-channel analysis. Key finding: per-channel divergence — Labrador Sea mixed layer depth crosses from linear to nonlinear dominance around 2014 (100% nonlinear-dominant from 2020), while SST and salinity remain firmly linear. The coherence gate (3-of-4 channels) correctly suppresses system-level alarms. This is consistent with a possible subsurface-led precursor pattern in Labrador Sea convective dynamics, though the signal may be partly influenced by Argo observing-system changes. CMIP6 validation (5-member collapse ensemble, 5 controls) confirms MLD is the first and only channel to cross zero in all collapse runs, with zero false positives. ERA5 MLD already shows stronger nonlinearity (δBIC = +38) than the synthetic model produces during active collapse. Discussion, conclusion, and limitations rewritten to reflect the full synthetic → reanalysis → CMIP6 validation chain. 12pp → 16pp. Version 4 (2026-03-19) Added empirical comparison with classical critical-slowing-down (CSD) indicators. Rolling variance and lag-1 autocorrelation computed on the same 4-channel ERA5/ORAS5 data with a matched 20-year window, side-by-side with δBIC. Key finding: CSD and δBIC agree on only 1 of 4 channels. On the two most diagnostic channels, the methods give opposite assessments — CSD dismisses the MLD channel (autocorrelation falling, τ = −0.64) while flagging SST Warming Hole as a weak tipping precursor (autocorrelation rising, τ = +0.27). δBIC correctly identifies MLD as the structurally changing channel (τ = +0.79) and SST Warming Hole as a linear trend effect (τ = −0.18). This demonstrates that δBIC detects nonlinear regime change that classical EWS miss, while rejecting linear persistence changes that classical EWS flag. New Section 8 (Empirical CSD Comparison) with Kendall trend statistics and epoch-mean tables; Discussion subsection rewritten to incorporate empirical evidence; abstracts updated. 16pp → 17pp.Version 5 (2026-03-19) Update conclusions section to reflect only the remaining planned work.Version 6 (2026-03-19) Resolved the ORAS5 MLD confound definitively. Epoch-split analysis (pre-Argo 1958–2000 vs Argo-era 2004–2024) showed the MLD nonlinear signal is entirely confined to the Argo era (0% positive months pre-Argo). Independent validation against 15,933 direct Argo float profiles (Holte et al. 2017) confirmed the signal is a reanalysis artifact: direct profiles yield δBIC = −81 (0% positive) where ORAS5 shows −16, with 11× variance amplification. The coherence gate's suppression of this single-channel signal was retrospectively vindicated. Extended to a 5-channel observation-derived configuration replacing reanalysis subsurface fields with direct measurements: ERA5 SST (×2), Denmark Strait overflow transport (ICDC Hamburg ADCP moorings), RAPID AMOC transport at 26.5°N (mooring array), and Argo MLD (direct float profiles). Result across 2004–2021 overlap: all 5 channels show linear dominance with 0% positive months. Denmark Strait overflow trends away from nonlinearity (τ = −0.60). The AMOC system is unanimously linearly predictable across all direct observations. The V3 "subsurface-led precursor" interpretation is superseded — the finding is now that the multi-channel coherence architecture correctly protected the system-level assessment from a compelling reanalysis artifact. New sections on Argo validation and observation-derived channel analysis; abstract, discussion, limitations, and conclusion rewritten throughout. 17pp → 20pp. Version 7 (2026-03-19) Recompiled PDF to incorporate all V6 edits. No content changes; V6 PDF was generated from a stale intermediate build.Version 8 (2026-07-03) Cross-channel white-box robustness test. Adds a new section (White-Box Coupling Attribution: A Cross-Channel Robustness Test) that independently corroborates the paper's central finding via a richer, cross-channel method. A sparse Fast-Orthogonal-Search white-box network was applied to the same channels to (a) attempt nonlinear coupling attribution ahead of the CMIP6-like collapse, and (b) extract a directed linear influence graph. Two results: nonlinear coupling attribution is a null once significance is computed on the correct independent unit (run-level exact permutation, p = 0.33–0.93) rather than on autocorrelation-inflated per-window statistics; and an apparent linear MLD→salinity edge in ERA5/ORAS5 — which survives differencing, phase-randomized surrogates, and Bonferroni — is unmasked by independent Argo-float validation and temporal localization as the same pre-Argo ORAS5 model-infill artifact identified elsewhere in the paper. The section contributes two transferable methodological cautions (per-window significance in overlapping-window monitoring is inflated ~10×; reanalysis subsurface structure must be validated against independent products) and a reusable artifact-detection recipe. No prior results are altered; the additions are corroborative. Three references added (Korenberg 1988; Theiler et al. 1992; Ebisuzaki 1997).Version 9 (2026-09-04)Surrogate testing of the observational verdicts, and reinterpretation of the synthetic validation. Two substantive changes, neither of which alters an observational number. First, every per-channel verdict is re-tested. All nine channel records — four ERA5/ORAS5 and five observation-derived — were compared against 999 IAAFT surrogates (Schreiber & Schmitz 1996), fitted once on the whole record at fixed lag 6, with a Holm correction across the family. One rejects the linear null: Labrador Sea mixed layer depth in ORAS5 (δBIC = +13.77, uncorrected p ≤ 0.001 at the add-one floor and reported as an upper bound, Holm-adjusted p = 0.009); on non-overlapping 240-month windows it rejects in 1998–2017 alone and in neither earlier window. Direct Argo mixed layer depth is the most linear of the nine records (p = 0.97). The five observation-derived channels reject in none of five, so the paper's unanimous observational verdict is retained and now rests on a test of significance rather than on the sign of δBIC alone. The single rejection falls on the channel the coherence gate had already suppressed, which supports rather than weakens that design. The sliding-window δBIC remains the monitoring statistic throughout: no trace, no regime classification and no percent-positive table was re-scored. What crossing zero requires is now stated at each configuration — reductions in residual sum of squares of 38.7%, 58.2%, 16.1% and 42.3% — together with the caution that whole-record and windowed δBIC are not comparable, since the complexity penalty grows as ln n while the evidence term grows as n, so a longer record is a weaker bar rather than a stronger one. Second, the synthetic validation is reinterpreted. The data generator applies its cubic restoring term to a deviation expressed in physical units, so the threshold beyond which the cubic overwhelms the linear restoring force falls at 0.075σ, 0.8σ and 1.2σ for three of the five channels and at 5.3σ and 21.1σ for the other two. The first three diverge on every run, and a clamp present to prevent numerical overflow converts the divergence into a bounded oscillation rather than an error — which is why the defect produced no warning. The regression is consequently ill-conditioned on those channels (median maximum con