On the Use of Emulators with Extreme and Highly Nonlinear Geophysical Simulators

Gaussian process emulators are a powerful tool for understanding complex geophysical simulators, including oceanic and atmospheric general circulation models. Concern has been raised about their ability to emulate complex nonlinear systems. For the first time, using the simple Stommel model, the way in which emulators can reasonably represent the full sampling space of an extreme nonlinear, bimodal system is illustrated. This simple example also shows how an emulator can help to elucidate interactions between parameters. The ideas are further illustrated with a second, more realistic, intermediate complex climate simulator. The paper describes what is meant by an emulator, the methodology of emulators, how emulators can be assessed, and why they are useful. It is shown how simple emulators can be useful to explore the parameter space (initial conditions, process parameters, and boundary conditions) of complex computer simulators, such as ocean and climate general circulation models, even when simulator outcomes contain steps in the response.