  Computer model calibration involves using partial and imperfect observations
of the real world to learn which values of a model's input parameters lead to
outputs that are consistent with real-world observations. When calibrating
models with high-dimensional output (e.g. a spatial field), it is common to
represent the output as a linear combination of a small set of basis vectors.
Often, when trying to calibrate to such output, what is important to the
credibility of the model is that key emergent physical phenomena are
represented, even if not faithfully or in the right place. In these cases,
comparison of model output and data in a linear subspace is inappropriate and
will usually lead to poor model calibration. To overcome this, we present
kernel-based history matching (KHM), generalising the meaning of the technique
sufficiently to be able to project model outputs and observations into a
higher-dimensional feature space, where patterns can be compared without their
location necessarily being fixed. We develop the technical methodology, present
an expert-driven kernel selection algorithm, and then apply the techniques to
the calibration of boundary layer clouds for the French climate model IPSL-CM.
