Hierarchical statistical modeling of rates and variability of sea level
Creators: name: Ashe, Erica L.
Publisher: name: No Publisher Supplied
Year: 2018

description: Climate change is driving sea-level change around the world today. Understanding the physical mechanisms behind global and regional sea-level variations requires historical reconstructions. Prior to the instrumental period [when tide gauges, about 2-3 centuries ago, and satellites, over the last three decades, began to record relative sea level (RSL)], the sea-level record depends upon proxy- based reconstructions that contain vertical and temporal uncertainty, which creates challenges to modeling paleo-sea levels. One specific problem in interpreting these proxy data is parsing the complex spatial and temporal patterns of RSL and its rate of change from sparse data of different resolutions from distinct locations and sources. Another challenge is accounting for known uncertainties in a consistent and realistic manner. Making use of data that does not adhere to normality assumptions poses additional challenges to models of RSL.  Within this dissertation, we employ several methods to handle these challenges in order to quantify past rates of RSL change probabilistically. Hierarchical models are central to model clarity. They explicitly distinguish between a process level, which characterizes the spatio-temporal field, and a data level, which characterizes the way in which sparse proxy data and noise are recorded. A parameter level depicts prior expectations about the structure of variability in the spatio-temporal field. Many past statistical models have not included a spatial component; here, we demonstrate methods for incorporating sparse data from disparate locations that share information over space and time through covariance functions, describing Gaussian process (GP) priors in spatio-temporal empirical hierarchical models (STEHMs). An analysis of several techniques recently implemented in the literature with both instrumental and proxy data illustrates the transparency and flexibility of hierarchical statistical modeling frameworks for sea-level analysis. Non-parametric methods, such as the Kalman smoother and hierarchical models with GP priors, incorporate physical prior information into the process levels and provide flexible and robust ways to model the spatio- temporal RSL field and GMSL. Empirical Bayesian analyses provide a good approximation for large datasets and require fewer computing resources than fully Bayesian analyses; conversely, fully Bayesian analyses include parameter uncertainties to more thoroughly characterize known uncertainty in sea-level models.    While past models frequently assumed Gaussian uncertainties in RSL proxy data, or excluded data that cannot be approximated with a normal distribution, we present new techniques within a Bayesian hierarchical framework with GP priors that incorporate non-Gaussian uncertainties through Markov Chain Monte Carlo (MCMC) sampling. The framework readily accommodates parametric and non-parametric likelihood distributions; however, we find that the non-parametric likelihoods are more robust to geographical changes in our case study of south Florida coral and sedimentary archives. Incorporating non-Gaussian likelihoods allows the inclusion of a variety of coral taxa, as illustrated here, as well as many other new RSL proxy data.    We also introduce new methods of modeling high-resolution proxy data, optimizing age shifts with complex temporal constraints to model RSL over the mid-Holocene at sites in Indonesia. We detect ∼0.6 m mid-Holocene fluctuations in RSL in Southeast Asia due to dynamic, steric, or eustatic effects through the implementation of new techniques that incorporate high-frequency process modeling and methods for optimizing temporal shifts due to age uncertainties. We are able to separate secular trends in a robust manner to detect peak rates in RSL rise of 9.6±4.2 mm/yr and RSL fall of 12.6±4.2 mm/yr. Although each dataset has unique characteristics, these methods would accommodate other high-resolution proxy records of RSL around the globe.