UC San Diego

Uncertainties in global climate projections are largely due to the uncertain representation of subgrid-scale processes in global simulations (e.g., clouds and convection). There are multiple approaches to improve the physics parameterizations within global climate models (GCMs). One approach is to improve our physical understanding of specific subgrid-scale processes (e.g., clouds and cloud microphysics). Another approach is to calibrate GCM parameterizations using observed climate statistics. I leverage simplified numerical models and optimization to contribute to both approaches. Simplified numerical models provide insights into how physical processes behave and are good for testing numerical methods. Optimization is a powerful calibration tool for solving high-dimensional inverse problems. First, I connect two very different stratocumulus cloud models to understand how simplified cloud models adapt to varying meteorological conditions. I calibrate a scalar delay differential equation (DDE) which represents precipitation and clouds as predator-prey dynamics to a suite of large eddy simulations (LES) to track how the DDE parameters change under different meteorology. Our results highlight the robustness of the scalar DDE and the limitations of using a simplified numerical model to represent realistic cloud processes. Next, I contribute to the greater GCM calibration effort by determining which optimization methods are promising for learning GCM parameters from observed climate statistics. I “race” several ensemble-based optimization methods with potential to scale to GCM calibration on several idealized test problems using Lorenz-type dynamics. Our results establish guidelines for using ensemble-based optimization and determine the most promising ensemble method for GCM calibration. Lastly, I make use of new developments in auto-differentiable modeling to calibrate an intermediate complexity atmospheric model against reanalysis data. I explore under what calibration timescales parameters can reproduce realistic long-term atmospheric variability and uncover the limitations of calibrating simplified atmospheric models to realistic dynamics. Overall, I show that the development and implementation of mathematical tools can answer pressing questions in the climate sciences.