A Simple Emulator That Enables Interpretation of Parameter-Output Relationships, Applied to Two Climate Model PPEs

We present a new additive method, referred to as sage for Simplified Additive Gaussian processes Emulator, for emulating climate model Perturbed Parameter Ensembles (PPEs). sage estimates the value of a climate model output as the sum of additive terms. Each additive term is the mean of a Gaussian Process, and corresponds to the impact of a parameter or parameter group on the variable of interest. This design caters to the sparsity of PPEs, which are characterized by limited ensemble members and high dimensionality of the parameter space and raise the issue of parameter sensitivity in the emulator design. sage quantifies the variability explained by different parameters and parameter groups, providing additional insights on the parameter-climate model output relationship. We apply sage to two climate model PPEs and compare it to a fully connected Neural Network. The two methods have comparable performance with both PPEs, but sage provides insights on parameter and parameter group importance as well as diagnostics useful for optimizing PPE design. Insights gained from applying the method and comparing its performance with Neural Network are pointed out which have not been previously addressed. Our work highlights that analyzing the PPE used to train an emulator is different from analyzing data generated from an emulator trained on the PPE, as the former provides more insights on the data structure in the PPE which could help inform the emulator design. Our work also proposes new questions on the optimal way of working with climate model PPEs.