Model discrepancy can prevent a single calibration parameter from reproducing the physical response across the entire context domain. Uncertainties in observations and contexts also affect calibration and must be quantified. We construct a family of localized posteriors by weighting observation likelihoods according to their proximity to a target context. Gaussian localization weights incorporate context uncertainty via covariance inflation, reflect at domain boundaries, and optionally correct for uneven context sampling. A conditional normalizing flow approximates this family within an amortized variational inference framework. Integrating the localized posteriors under a prescribed context measure yields the marginalized parameter distribution. In a twin experiment with the Branin‑Hoo model we compare global and localized inference under uniform and skewed context distributions. Localization markedly reduces aggregate predictive errors relative to the global posterior. We then apply the method to the k‑ε turbulence closure in a single‑column ocean model, using atmospheric surface forcing as context. Localized posterior calibration further lowers temperature and zonal‑velocity errors compared with deterministic and global‑posterior calibration. Both twin experiments are designed to admit local compensation.
Review