Stratosphere Model Verification with Manufactured Geometry

We propose an exact solution for a stratosphere dynamical core formulated in geopotential/pressure coordinates with a time-evolving lower boundary supplied by the troposphere. Rather than constraining the stratospheric circulation via specified dynamics (``nudging'') to a reanalysis, we treat the tropopause as a moving geometric boundary. The stratospheric domain thus expands, contracts, and undulates in response to tropospheric variability while preserving familiar hybrid $σ$--$p$ structure and pressure-gradient calculations. The approach integrates naturally with arbitrary Lagrangian--Eulerian (ALE) updates and conservative remap to maintain positive layer thickness and tracer monotonicity. We outline the formulation, highlight analytical properties (well-posedness, energetics, wave propagation), and sketch a verification/validation path based on modified standard test cases and reanalysis-driven experiments.