Advancing the Predictability of the Earth System Processes: Insights from Optimal Mass Transport Theory

Abstract

The improvement in forecast lead time by operational forecasting centers is made possible through data assimilation (DA) in which the Earth system model outputs are optimally combined with the satellite observations. However, the presence of non-Gaussian state-space and systematic errors degrades the performance of classic Bayesian DA methodologies, which rely on affine Euclidean penalization of error. In the present thesis, inspired from the field of information geometry, modern DA paradigms over Riemannian manifolds equipped with the Wasserstein metric are proposed, whereby optimal mass transport theory promises to extend the geophysical forecast skills. The Wasserstein metric is a geodesic distance and enables assimilation in a space characterized by families of probability distributions with finite second-order moments leading to full recovery of non-Gaussian forecast probability distributions. Unlike Eulerian penalization of error in the Euclidean space, the Wasserstein metric is sensitive to the translation of probability measures, enabling to formally penalize geophysical biases. The presented frameworks are applied to dissipative and chaotic evolutionary dynamics as well as the high-dimensional quasi-geostrophic model of atmospheric circulation with a wide range of applications in the Earth system models. The results suggest that under systematic errors and non-Gaussian state-space, utilization of the Wasserstein metric in the DA framework can reduce the forecast uncertainty beyond what is possible through the classic DA methodologies. Preliminary evidence also suggests that the framework is more robust to the curse of dimensionality and requires fewer ensemble members than the dimension of the state-space.