  We seek statistical methods to study the occurrence of multiple rain types
observed by satellite on a global scale. The main scientific interests are to
relate rainfall occurrence with various atmospheric state variables and to
study the dependence between the occurrences of multiple types of rainfall
(e.g. short-lived and intense versus long-lived and weak; the heights of the
rain clouds are also considered). Commonly in point process model literature,
the spatial domain is assumed to be a small, and thus planar domain. We
consider the log-Gaussian Cox Process (LGCP) models on the surface of a sphere
and take advantage of cross-covariance models for spatial processes on a global
scale to model the stochastic intensity function of the LGCP models. We present
analysis results for rainfall observations from the TRMM satellite and
atmospheric state variables from MERRA-2 reanalysis data over the tropical
Eastern and Western Pacific Ocean, as well as over the entire tropical and
subtropical ocean regions. Statistical inference is done through Monte Carlo
likelihood approximation for LGCP models. We employ covariance approximation to
deal with massive data.
