Comparing the performance of calibration algorithms on a hierarchy of climate problems

Climate models rely on parameterizations to represent sub-grid scale dynamics and unresolved physics due to computational limitations. However, parameters within these codes are often poorly constrained by observations, leading to discrepancies between the model and real-world climate statistics. Currently, no standard methodology exists for calibrating these parameters effectively. Given the complexity of large climate models, traditional search methods like grid or Monte Carlo approaches are computationally infeasible. In this study, we explore advanced techniques, including Bayesian History Matching and Ensemble Kalman Inversion, which leverage information from previous model runs to guide parameter selection. We assess how these methods scale with an increasing number of parameters through idealized systems such as the Rosenbrock function and chaotic Lorenz63 and Lorenz96 models. Preliminary results have shown the two methods producing consistent posterior distributions of parameter values at low dimensionality. Furthermore, we apply these techniques to an intermediate complexity general circulation model (GCM), calibrating a pair of orographic and non-orographic atmospheric gravity wave parameterizations with a varying number of parameters.