Decoupling Stratospheric Wave Geometry and Eurasian Blocking: The SDI–BI–CI–EI Suite and 86-Year ERA5 Master Database (1940–2026)

Classical univariate teleconnection metrics (e.g., NAO, AO, NAM) frequently fail to capture the non-linear, vertically decoupled dynamics governing the Euro-Mediterranean winter and sub-seasonal weather extremes. By artificially projecting complex atmospheric states onto single-level scalars, traditional indices obscure the critical physical distinction between stratospheric wave bifurcations and boundary-layer thermodynamic advection. To resolve these structural limitations, this paper introduces the SDI–BI–CI–EI Suite, a novel four-index diagnostic framework physically calibrated across 1,041 consecutive months using the ECMWF ERA5 global reanalysis (1940–2026). The suite systematically decouples the middle-stratospheric kinetic trigger from the lower-tropospheric thermal engine. The Split-Displacement Index (SDI) at 10 hPa isolates Wave-1 off-pole displacements from Wave-2 resonant splits, while the Buran Index (BI) at 850 hPa quantifies the retrograde advection capacity driven by the Voejkov Bridge and Mediterranean cyclogenesis. High-resolution phenological metrics, the Christmas Index (CI) and Easter Index (EI), incorporate astronomical insolation corrections to capture sub-seasonal wave-preconditioning. Empirical validation against historical benchmarks demonstrates the framework's superior diagnostic fidelity. By tracking atmospheric evolution within a four-dimensional phase space, the SDI-BI-CI-EI Suite resolves longstanding dynamic paradoxes, providing the scientific community with a deterministic-probabilistic roadmap for anticipating high-impact continental freezes. Data Availability: This repository contains both the full theoretical manuscript (PDF) and the complete master empirical database (CSV) comprising 1,041 continuous months of atmospheric, oceanic, and teleconnective parameters extracted from ECMWF ERA5 and global observational archives.