Uncertainty Quantification in Earth System Models Using Polynomial Chaos Expansions

This work explores stochastic responses of various earth system models to different random sources, using polynomial chaos (PC) approaches. The following earth systems are considered, namely the HYbrid Coordinate Ocean Model (HYCOM, an ocean general circulation model (OGCM)) for the study of ocean circulation in the Gulf of Mexico (GoM); the Unified Wave INterface - Coupled Model (UWIN-CM, a dynamically coupled atmosphere-wave-ocean system) for Hurricane Earl (2010) modeling; and the earthquake seismology model for Bayesian inference of fault plane configurations.

In the OGCM study, we aim at analyzing the combined impact of uncertainties in initial conditions and wind forcing fields on ocean circulation using PC expansions. Empirical Orthogonal Functions (EOF) are used to represent both spatial perturbations of initial condition and space-time wind forcing fields, namely in the form of a superposition of modal components with uniformly distributed random amplitudes. The forward deterministic HYCOM simulations are used to propagate input uncertainties in ocean circulation in the GoM during the 2010 Deepwater Horizon (DWH) oil spill, and to generate a realization ensemble based on which PC surrogate models are constructed for both localized and field quantities of interest (QoIs), focusing specifically on Sea Surface Height (SSH) and Mixed Layer Depth (MLD). These PC surrogate models are constructed using Basis Pursuit DeNoising (BPDN) methodology, and their performance is assessed through various statistical measures. A global sensitivity analysis is then performed to quantify the impact of individual random sources as well as their interactions on ocean circulation. At the basin scale, SSH in the deep GoM is mostly sensitive to initial condition perturbations, while over the shelf it is sensitive to wind forcing perturbations. On the other hand, the basin MLD is almost exclusively sensitive to wind perturbations. For both quantities, the two random sources (initial condition and wind forcing) of uncertainties have limited interactions. Finally, computations indicate that whereas local quantities can exhibit complex behavior that necessitates a large number of realizations to build PC surrogate models, the modal analysis of field sensitivities can be suitably achieved with a moderate size ensemble.

It is noted that HYCOM simulations in the aforementioned OGCM study only focus on the ocean circulation, and ignore the oceanic feedback (e.g. momentum, energy, humidity etc) to the atmosphere. A more elaborated analysis is consequently performed to understand the atmosphere dynamics in a fully-coupled atmosphere-wave-ocean system. In particular, we explore the stochastic evolution of Hurricane Earl (2010) in response to uncertainties stemming from random perturbations in the storm's initial size, strength and rotational stretch. To this end, the UWIN-CM framework is employed as the forecasting system, which is used to propagate input uncertainties and generate a realization ensemble. PC surrogate models for time evolutions of both maximum wind speed and minimum sea level pressure (SLP) are constructed. These PC surrogates provide statistical insights on probability distributions of model responses throughout the simulation time span. Statistical analysis of rapid intensification (RI) process suggests that storms with enhanced initial intensity and counter-clockwise rotation perturbations are more likely to undergo a RI process. In addition, the RI process seems mostly sensitive to the mean wind strength and rotational stretch, rather than storm size and asymmetric wind amplitude perturbations. This is consistent with global sensitivity analysis of PC surrogate models. Finally we combine parametric storm perturbations with global stochastic kinetic energy backscatter (SKEBS) forcing in UWIN-CM simulations, and conclude that whereas the storm track is substantially influenced by global perturbations, it is weakly influenced by the properties of the initial storm.

The PC framework not only provides easy access to traditional statistical insights and global sensitivity indices, but also reduces the computational burden of sampling the system response, as performed for instance in Bayesian inference. These two advantages of PC approaches are well demonstrated in the study of earthquake seismology model response to random fault plane configurations. The PC statistical analysis suggests that the hypocenter location plays a dominant role in earthquake ground motion responses (in terms of peak ground velocities, PGVs), while elliptical patch properties only show secondary influence. In addition, Our PC based Bayesian analysis successfully identified the most `likely' fault plane configuration with respect to the chosen ground motion prediction equation (GMPE) curve, i.e. the hypocenter is more likely to be in the bottom right quadrant of the fault plane and the elliptical patch centers at the bottom left quadrant. To incorporate additional physical restrictions on fault plane configurations, a novel restricted sampling methodology is introduced. The results indicate that the restricted inference is more physically sensible, while retaining plausible consistency with findings from unrestricted inference.