Certified Multi-Hazard Interaction Bounds for Artificial Intelligence Compound Flood-Heat Emulators Under Nonstationary Dependence: Tail-Risk Guarantees and Emergency-Response Load Planning

Compound flood-heat events pose a distinctive challenge for artificial intelligence emulators because the joint tail of the two hazards, not either marginal, governs emergency-response load. The framework combines a time-varying copula representation, a block-maximum tail approximation with a nonstationary extremal index, and a concentration inequality for dependent samples to produce a certified upper bound on the joint exceedance probability at any planning horizon. A companion bound translates that probability into a worst-case emergency-response load, expressed as the number of simultaneous shelter and cooling-centre activations. The bounds are shown to be tight in the sense that they converge to the true compound tail as the emulator's dependence model approaches the data-generating process, and to degrade gracefully when the nonstationarity is misspecified. The framework is illustrated on a reanalysis temperature record for Nairobi, Kenya (2000-2023, 312 monthly observations, mean 20.146 C, warming trend 0.2477 C per decade), which supplies the heat-marginal component of the compound hazard. The certified bound is shown to be more conservative than a plug-in estimate by a margin that grows with the planning horizon, and the load bound is shown to translate that conservatism into a quantified reserve requirement. The contribution is a certification layer that sits between an emulator and an emergency-planning decision, and that makes the emulator's dependence assumptions auditable rather than implicit.