  Surrogate models are often used to replace costly-to-evaluate complex coastal
codes to achieve substantial computational savings. In many of those models,
the hydrometeorological forcing conditions (inputs) or flood events (outputs)
are conveniently parameterized by scalar representations, neglecting that the
inputs are actually time series and that floods propagate spatially inland.
Both facts are crucial in flood prediction for complex coastal systems. Our aim
is to establish a surrogate model that accounts for time-varying inputs and
provides information on spatially varying inland flooding. We introduce a
multioutput Gaussian process model based on a separable kernel that correlates
both functional inputs and spatial locations. Efficient implementations
consider tensor-structured computations or sparse-variational approximations.
In several experiments, we demonstrate the versatility of the model for both
learning maps and inferring unobserved maps, numerically showing the
convergence of predictions as the number of learning maps increases. We assess
our framework in a coastal flood prediction application. Predictions are
obtained with small error values within computation time highly compatible with
short-term forecast requirements (on the order of minutes compared to the days
required by hydrodynamic simulators). We conclude that our framework is a
promising approach for forecast and early-warning systems.
