Optimizing Gaussian Process Emulation and Generalized Additive Model Fitting for Rapid, Reproducible Earth System Model Analysis

Abstract. Causes of model uncertainty in complex modeling systems can be identified using large perturbed-parameter ensembled (PPEs), combined with statistical emulators to increase sample size and enable variance-based sensitivity analyses and observational constraint. In global climate models such as the UK Earth System Model (UKESM), these approaches are typically applied at the global or regional mean scales for a limited set of variables. To accelerate progress in understanding the multi-faceted causes of climate model uncertainty, requires implementing such workflows at the model grid box scale, to enable analyses across variables that reveal how uncertainties propagate and interact spatially. However, this approach requires training millions of Gaussian process (GP) emulators and fitting an equal number of generalized additive models (GAMs) – a major computational bottleneck. We present a high-performance, open-source pipeline that introduces optimisations for this workflow. For GP emulation, we implement task-level parallelism and streamlined data handling on high-performance computing systems. For GAM fitting, we integrate a parallelized pyGAM interface with R's mgcv::bam() back end, using fast fREML estimation with discrete smoothing, memory-efficient batching, and improved input–output routines. These changes reduce GP training time by 97.5 % (6177 → 154 s) and GAM fitting time by 95.2 % (10623 → 511 s), yielding a ~ 25 times faster end-to-end workflow (96 % total runtime reduction) and cutting peak memory use by a factor of 12. Outputs are numerically identical to the baseline implementation (Pearson correlation = 1.00 for both GP and GAM predictions). We demonstrate the approach using a UKESM PPE comprising 221 members scaled up to 1 million using GP emulators, and GAM fits applied to output for a single target variable, to show that the improved performance enables multi-variable, higher-resolution, and potentially multi-model analyses that were previously impractical. These improvements pave the way for PPE studies to scale in scope without compromising statistical fidelity, enabling more comprehensive exploration of model parameter uncertainty within feasible HPC budgets.