Spatiotemporal Graph Neural Network Emulation of Regional Climate Models at Convection-Permitting Resolution: Spectral Fidelity Bounds and Downstream Flood-Exposure Equity Across West African River Basins

Emulating convection-permitting regional climate models with graph neural networks promises to make high-resolution climate projections tractable for adaptation planning, but the spectral fidelity of such emulators and the equity consequences of their errors remain unquantified. The framework defines a spectral fidelity bound as the supremum of the ratio between emulator and reference power spectral densities over resolvable wavenumbers, and it derives a propagation inequality linking spectral bias to bias in exceedance probabilities and to disparities in flood exposure across basins with differing hydrological and socioeconomic characteristics. The analysis is methodological and theoretical: no emulator is trained and no observational data are analysed. The derived bounds indicate that spectral fidelity at convective scales is constrained by the graph construction, the receptive field of the message-passing architecture, and the training loss weighting across scales. The propagation inequality shows that a given spectral bias produces larger equity disparities when basin exposure distributions are more heterogeneous and when the emulator's bias is concentrated at scales that coincide with the scales of extreme precipitation.