  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.
