This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
This project studies classes of spatial-temporal covariance functions for nonstationary, multivariate processes on a globe. Many processes in geophysical and environmental problems these days take large portion of the Earth as their spatial domain and exhibit strong spatial nonstationarity (particularly with respect to latitude). Moreover, it is common to have multiple variables of interest, such as relationship between precipitation and temperature. However, there are not many spatial-temporal covariance functions that can deal with nonstationary processes on a globe and there are almost none developed so far for multivariate problems. In this regard, the investigator develops a flexible class of spatial-temporal covariance functions for univariate as well as multivariate processes on a globe. The idea of applying differential operators with respect to latitude, longitude, and time to an isotropic process on a globe is explored. The coefficients of the operators, varying over latitude, allow flexible nonstationary covariance models for univariate process. It also helps to create a rich class of cross covariance models suitable for real physical processes. The ultimate goal of this project is to build a joint statistical model for multiple climate model outputs. It has been demonstrated that these numerical climate models have correlated errors and it is critical to have flexible cross covariance models to accurately model the dependence structure among different climate model errors. There are several interesting computational issues that arise from this application. In particular, the investigator studies algorithms for fast computation of inverse of covariance matrix with special structures, covariance tapering, likelihood approximation, and missing data imputation method.
This study is motivated by the scientific problem of evaluation and integration of multiple climate model outputs. Under the coordination of the Intergovernmental Panel on Climate Change (IPCC), various organizations over the world are developing numerical climate models and the cost to develop and run these models are enormous. However, it is common to simply take averages of these models and assume they are independent. In addition to the contribution to the field of statistics, the proposed study will provide a useful tool for climate scientists for inter-comparison of multiple climate models. Moreover, it will help climate scientists to improve their understanding of past, current, and future climate by accurately integrating multiple climate models beyond simple averages and allow them to achieve more precise uncertainty in their predictions. The results of the proposed research will be formed as multidisciplinary courses for students of both statistics and atmospheric scientists. The investigator anticipates that this type of effort will boost future collaboration between statisticians and atmospheric scientists.
