Universal Dynamic Convergence Formula for the Probabilistic Prediction of the AMOC Tipping Point (UCD-AMOC)

Universal Dynamic Convergence Formula for the Probabilistic Prediction of the AMOC Tipping Point (UCD-AMOC) DescriptionThis document introduces the Universal Dynamic Convergence Formula for the Probabilistic Prediction of the Atlantic Meridional Overturning Circulation (AMOC) tipping point (UCD-AMOC). The framework proposes a unified probabilistic model to describe convergence toward collapse in a bistable, noisy climate system, addressing a long-standing limitation of deterministic AMOC modeling. Adapted from Stommel’s two-regime model, UCD-AMOC integrates thresholds (S), resistances (R), volumes (V), divergences and convergences (D/C), temporal cycles (T), dynamic memory (M), energy density (E), observables O(t), and external drivers D(t) into a single convergence function ϕ governing the probabilistic state C(t). Dynamic memory introduces non-Markovian effects, allowing cumulative saturation and delayed regime transitions to be explicitly modeled. The document presents the full theoretical formulation, differential equations, normalization scheme, and algorithmic implementation, together with Monte Carlo simulations and numerical experiments. Results show probabilistic convergence toward tipping (C(t) → 0) under increasing forcing (γ > 1.5), with low RMSE ( 0.92) relative to reference models (Stommel, Lorenz, ECMWF, CMIP6). Multiple application cases (cyclones, heatwaves, circulation, bioclimate extensions) illustrate robustness, sensitivity, and stability properties, including Lyapunov analysis. This work is intended as a theoretical and computational framework. While simulations are compatible with ERA5, NOAA, and RAPID-like data, full empirical validation is identified as future work. The document is suitable for use as a conceptual, methodological, and exploratory reference for climate tipping-point analysis.