Doctor of Philosophy / Department of Statistics / Juan Du / It is common to assume the spatial or spatio-temporal data are realizations of underlying random elds or stochastic processes. E ective approaches to modelling of the underlying autocorrelation structure of the same random eld and the association among multiple processes are of great demand in many areas including atmospheric sciences, meteorology and agriculture. To this end, this dissertation studies methods and application of the spatial modeling of large-scale dependence structure and spatio-temporal regression modelling. First, variogram and variogram matrix functions play important roles in modeling dependence structure among processes at di erent locations in spatial statistics. With more and more data collected on a global scale in environmental science, geophysics, and related elds, we focus on the characterizations of the variogram models on spheres of all dimensions for both stationary and intrinsic stationary, univariate and multivariate random elds. Some e cient approaches are proposed to construct a variety of variograms including simple polynomial structures. In particular, the series representation and spherical behavior of intrinsic stationary random elds are explored in both theoretical and simulation study. The applications of the proposed model and related theoretical results are demonstrated using simulation and real data analysis. Second, knowledge of the influential factors on the number of days suitable for fieldwork (DSFW) has important implications on timing of agricultural eld operations, machinery decision, and risk management. To assess how some global climate phenomena such as El Nino Southern Oscillation (ENSO) a ects DSFW and capture their complex associations in space and time, we propose various spatio-temporal dynamic models under hierarchical Bayesian framework. The Integrated Nested Laplace Approximation (INLA) is used and adapted to reduce the computational burden experienced when a large number of geo-locations and time points is considered in the data set. A comparison study between dynamics models with INLA viewing spatial domain as discrete and continuous is conducted and their pros and cons are evaluated based on multiple criteria. Finally a model with time- varying coefficients is shown to reflect the dynamic nature of the impact and lagged effect of ENSO on DSFW in US with spatio-temporal correlations accounted.

Dolphinfish (Coryphaena hippurus) is a pelagic species that is ecologically and commercially important in the western Atlantic region. This species has been linked to dominant oceanographic features such as sea surface temperature (SST) frontal regions. This work first explored the linkages between the catch rates of dolphinfish and the oceanography (satellite-derived SST, distance to front calculations, bottom depth and hook depth) using Principal Components Analysis (PCA). It was demonstrated that higher catch rates are found in relation to warmer SST and nearer to frontal regions. This environmental information was then included in standardizations of catch-per-unit-effort (CPUE) indices. It was found that including the satellite-derived SST and distance to front increases the confidence in the index. The second part of this work focused on addressing spatial variability in the catch rate data for a subsection of the sampling area: the Gulf of Mexico region. This study used geostatistical techniques to model and predict spatial abundances of two pelagic species with different habitat utilization patterns: dolphinfish (Coryphaena hippurus) and swordfish (Xiphias gladius). We partitioned catch rates into two components, the probability of encounter, and the abundance, given a positive encounter. We obtained separate variograms and kriged predictions for each component and combined them to give a single density estimate with corresponding variance. By using this two stage approach we were able to detect patterns of spatial autocorrelation that had distinct differences between the two species, likely due to differences in vertical habitat utilization. The patchy distribution of many living resources necessitates a two-stage variogram modeling and prediction process where the probability of encounter and the positive observations are modeled and predicted separately. Such a "geostatistical delta-lognormal" approach to modeling spatial autocorrelation has distinct advantages in allowing the probability of encounter and the abundance, given an encounter to possess separate patterns of autocorrelation and in modeling of severely non-normally distributed data that is plagued by zeros.