QSER Decomposition for Forward and Inverse Modeling of Radon Transport in Lithosphere and Atmosphere

The Source–Environment–Response (SER) framework introduced a decomposition of radon transport into source-driven and environmental components, but treated the environment as a passive correction rather than an active memory accumulator. We present QSER (Generalized Source–Environment–Response), which extends the SER framework by making memory a central property of the radon transport phenomenon. The framework separates the governing transport operator into conservative (advective) and dissipative (diffusive and decay) parts, revealing the observed concentration as the difference between a conservative source field S and an environmental field E that accumulates the history of dissipative interactions. The continuity equation quantifies how the two fields interact to produce the observed concentration, and dissipation is the mechanism that writes history into E. For the forward case, the QSER steady plume is consistent with the Gaussian-plume structure of industry-standard atmospheric dispersion models (e.g., RESRAD-OFFSITE), exactly at the level of the Gaussian and sector structure and structurally at the level of the model-specific closures. For the inverse case, three routes are formulated and compared. The direct route exactly recovers the traditional fitting method, and the flexibility of QSER is demonstrated. QSER allows for hybridization with different methods and adds a physical layer to current forward and inverse approaches, giving additional insight into how radon transport processes evolve. The framework supports parameter estimation for radon monitoring applications in lithosphere–atmosphere coupling, earthquake precursor studies, uranium exploration, and atmospheric transport.