Long-Term Climate Reconstruction Using a Statistical Emulator Based on Gaussian Process and Multivariate Principal Component Analysis

In order to reconstruct long-term global climate variability, climate simulations using Global Climate Models (GCMs) are essential. However, long-term GCM simulations that incorporate complex physical processes require substantial computational resources, often prompting studies to adopt a time-slice simulation approach or use GCMs with intermediate complexity. To address issues arising from limited computational resources, statistical climate emulators constructed from GCM ensemble simulations have been proposed as a mean of quickly producing GCM’s climate responses to any changes in input parameters that were not explicitly simulated by the GCM. In this study, we built a Gaussian Process (GP)–based emulator to approximate key climate variables simulated by the intermediate-complexity climate model LOVECLIM, including surface air temperature, precipitation, surface pressure and zonal and meridional winds. Following future the CO₂ emission scenarios employed by Lord et al., we constructed 80 LOVECLIM ensemble equilibrium climate simulations covering both the near-future high-CO₂ state and the long-term low-CO₂ state. Each simulation was distinguished by four external forcing variables (ecosω, esinω, ε and CO₂). Multivariate (five climate variables) principal component analysis (PCA) was applied to extract the principal components (PCs) of inter-ensemble variability. GP emulations were conducted using the leading five PCs, thereby setting up a GP-PCA-based emulator. The performance of this emulator was evaluated using Leave-One-Out Cross Validation (LOOCV). Comparisons with LOVECLIM simulations revealed stable overall predictive performance, as indicated by scatter plots and RMSE values. Reconstructed climate time series over the past one million years exhibit differences in scale and variability specific to each variable, leading to variations in the magnitude and representation of prediction errors. Nevertheless, the multivariate emulator consistently reproduces the evolution of the climate time series over the past one million years, as well as the corresponding global spatial patterns. Its evaluation through comparisons with regional sea surface temperature (SST) proxy records. Future projections exhibited scenario-dependent differences in the early stages, followed by gradual convergence across CO₂ scenarios. Future work will extend to the ensemble emulator by incorporating additional GCMs, such as CESM, and will compare their predictive performance.