Feature-Based Parameter Estimation of the Nonlinear Cloud and Rain Equation and Global Bayesian Optimization in Data Assimilation

Abstract

We introduce numerical methods for Bayesian estimation applications. The first chapter demonstrates the use of feature-based parameter estimation methods in atmospheric science. The nonlinear cloud and rain equation represents emergent behavior of stratocumulus clouds through a simplified predator-prey model with rain acting as a predator of the clouds. We use a large eddy simulation as the ``ground truth'' and extract cycles of cloud growth and decay from the simulation. Our method treats the cycles as features and subsequently performs a Bayesian inversion to estimate the model parameters. In the second chapter, we discuss the uses of global Bayesian optimization in data assimilation. Global Bayesian optimization is a derivative-free optimization technique designed for optimizing computationally expensive functions. We show how it can be coupled to an ensemble Kalman filter to estimate model parameters, model states, and simultaneously tune localization and inflation parameters. To illustrate these ideas, we present numerical experiments with the classical Lorenz models.