Sparse Gaussian-process emulation of regional climate projections with active budget allocation: a computer-science evaluation of tail-quantile fidelity in adaptation screening

Sparse Gaussian-process emulators are increasingly proposed as surrogates for expensive regional climate model ensembles, but their fidelity in the distributional tails—where adaptation decisions are actually made—remains poorly characterised. The framework is evaluated on NASA POWER monthly reanalysis for Lagos, Nigeria (2000–2023, 312 observations), where the mean temperature was 26.414 °C and the warming trend was 0.1553 °C per decade. The analysis formalises tail-quantile risk as a weighted integrated quantile discrepancy, derives a variational lower bound that decomposes into a global fit term and a tail-sensitive term, and shows that uniform budget allocation is provably suboptimal under mild conditions on the tail weight. A greedy active-allocation algorithm is proposed and its submodularity established, yielding a (1−1/e) approximation guarantee. Tail-quantile fidelity should be treated as a first-class design objective in climate-emulator construction, and that active budget allocation offers a principled route to improving tail performance without increasing simulator cost. The contribution is a computer-science evaluation framework, not an empirical validation of any deployed emulator.