With the advancement of science and technology, many geophysical problems involve data sets on a global scale with multiple variables of interest. As a consequence, there is a pressing need for flexible nonstationary covariance models for multivariate processes defined on a sphere. On the other hand, the development of covariance models for geostatistical data should accompany methodologies for thorough goodness-of-fit diagnostics of the proposed models. The goal of this project is to provide in-depth development of multivariate spatial (-temporal) covariance models on a spherical domain that address certain nonstationary properties of the covariance structures, in small and large scale, paired with thorough goodness-of-fit diagnostics of the proposed models. Proposed covariance models are flexible to capture complex nonstationarity, such as varying smoothness and geometric anisotropy. The investigator develops Bayesian and non-Bayesian methods for goodness-of-fit diagnostics and studies the effect of plug-in estimators of covariance models. The investigator applies the models developed in this project to the problem of validating multiple climate model outputs from the CMIP5 archive with thorough diagnostics of the model fits. Different covariance structures over land and the ocean, as well as their dependence on latitude, are thoroughly investigated. The investigator also explores efficient computation methods for large data sets.
The motivation of this project is the scientific problem of combining multiple climate model outputs and studying the relationships between different climate variables. A great deal of effort is being invested in developing state-of-the-art climate models by climate scientists worldwide, and a new set of climate model outputs (CMIP5-Coupled Model Intercomparison Project Phase 5), that are the basis of the results in the fifth assessment report of the Intergovernmental Panel on Climate Change (IPCC), are becoming available. This project will provide climate scientists and climate modelers with useful tools to intercompare and combine climate models and test the improvement of the CMIP5 results over the previous CMIP3 results. Statistical models developed in this project will enable more accurate assessments of the relationships between multiple climate variables such as temperature and precipitation, and future climate change.