Is the Lorenz reference state global or local and observable?

Abstract. Introduced over 70 years ago by Lorenz, the theory of available potential energy (APE) remains central to atmospheric and oceanic energetics. Yet the precise nature of its reference state is still debated and often misinterpreted. Because it is usually constructed from an energy-minimising adiabatic rearrangement of mass, the Lorenz reference state is commonly regarded as a global property of the fluid, requiring interactions between distant parcels. We argue instead that, analogously to the gravitational field, it should be viewed as a local and observable property of the environment. Gravity, though global in origin, functions in practice as a local property measurable from its effect on falling bodies. Likewise, the Lorenz reference density and pressure profiles, ρ₀(z) and p₀(z), can be inferred from observations of buoyancy oscillations near equilibrium. Farther from equilibrium, a structural analysis of the governing equations shows that only deviations from the reference state affect motion, regardless of amplitude, thereby recovering Lorenz's APE separation as a structural property of fluid mechanics. The Lorenz reference state is therefore best understood not as an arbitrary mathematical construct, but as an environmental constraint manifesting locally, reinforcing both the foundations of APE and its role in theories of ocean circulation and mixing.