A comparison of Latin hypercube and grid ensemble designs for the multivariate emulation of an Earth system model

A statistical emulator is a fast proxy for a complex computer model which predicts model output at arbitrary parameter settings from a limited ensemble of training data. Regular grid designs for the training set are commonly used for their simplicity. However, Latin hypercube designs have well known theoretical advantages in the design of computer experiments, especially as the dimension of the parameter space grows. Here we use time series output from a simple Earth system model to compare the influence of these two design choices on the cross-validation prediction skill of a statistical emulator. We find that an emulator trained on a Latin hypercube design shows a small but clear improvement in prediction quality relative to an emulator trained on a grid design. We also find that the Latin hypercube emulator is more accurate than the grid emulator in single-parameter model sensitivity studies. We conclude with a discussion of ensemble design choices for emulator computer experiments.