Uncertainty-Aware Spatial Mixture Classification of Imbalanced CO₂ Plume States: Application to the Sleipner 2019 Benchmark

Reliable plume-state classification is essential for monitoring geological carbon dioxide storage, but benchmark reservoir data are often spatially heterogeneous, severely imbalanced, and affected by collinearity among geological and petrophysical predictors. We develop a spatially informed, expectation-maximization-type cluster-weighted multinomial logit mixture for classifying binned plume states. Spatial coordinates enter the component-specific covariate distributions, while plume-state probabilities are represented by component-specific multinomial logit models. A two-parameter shrinkage update stabilizes local estimates under collinearity and small effective component sizes, and class-weighted estimation addresses class imbalance. The method is evaluated on a 200-metre binned table from the Sleipner 2019 carbon dioxide storage benchmark, containing 3,409 bins and three plume-state classes, with 87% of observations outside the plume. Performance is assessed using spatial-block cross-validation, leave-one-layer-out transfer, and an ablation analysis. The model identifies three interpretable, depth-organized latent regimes and provides posterior uncertainty for each bin. It achieves a cross-validated balanced accuracy of 0.561, compared with 0.343 for an unweighted global multinomial logit model and 0.333 for a majority-class baseline. The ablation analysis shows that class weighting and spatial covariates drive most of the improvement. The latent mixture and shrinkage update provide smaller, statistically indistinguishable gains. Overall, the framework offers an interpretable and uncertainty-aware approach to minority plume-state recovery under severe imbalance, while the shrinkage update primarily stabilizes ill-conditioned local fits.