Inference for spatial processes using imperfect data from measurements and numerical simulations

We present a framework for inference for spatial processes that have actual values imperfectly represented by data. Environmental processes represented as spatial fields, either at fixed time points, or aggregated over fixed time periods, are studied. Data from both measurements and simulations performed by complex computer models are used to infer actual values of the spatial fields. Methods from geostatistics and statistical emulation are used to explicitly capture discrepancies between a spatial field's actual and simulated values. A geostatistical model captures spatial discrepancy: the difference in spatial structure between simulated and actual values. An emulator represents the intensity discrepancy: the bias in simulated values of given intensity. Measurement error is also represented. Gaussian process priors represent each source of error, which gives an analytical expression for the posterior distribution for the actual spatial field. Actual footprints for 50 European windstorms, which represent maximum wind gust speeds on a grid over a 72-hour period, are derived from wind gust speed measurements taken at stations across Europe and output simulated from a downscaled version of the Met Office Unified Model. The derived footprints have realistic spatial structure, and gust speeds closer to the measurements than originally simulated.