A Deterministic Limit for Ocean Conveyor Collapse: Deriving the Critical AMOC Buoyancy Radius via Salinity Advection

The stability of the Atlantic Meridional Overturning Circulation (AMOC) is traditionally evaluated using probabilistic Global Circulation Models (GCMs) and classical Stommel box models, which treat thermohaline collapse as a statistical tipping point driven by gradual warming. While these models effectively simulate bulk density changes over time, they fail to deterministically define the exact spatial boundary where a localized freshwater anomaly irrevocably shuts down deep-water formation. This paper introduces a strict continuum framework for macroscopic thermohaline scaling. By modeling the subpolar downwelling zones as a dynamic balance between the macroscopic advection of ocean salinity and the localized suppression of density-driven sinking via freshwater flux, we derive a universal critical buoyancy radius (RAMOC). We demonstrate that the collapse of the global ocean conveyor is not a probabilistic climate event, but an exact deterministic limit where localized buoyancy strictly overpowers the advective thermal-salinity capacity of the global ocean. We contrast this geometric invariant with traditional climate probability matrices and propose a blueprint for Active Basin Monitoring (ABM) using real-time Argo float telemetry.