  We propose a new copula model for replicated multivariate spatial data.
Unlike classical models that assume multivariate normality of the data, the
proposed copula is based on the assumption that some factors exist that affect
the joint spatial dependence of all measurements of each variable as well as
the joint dependence among these variables. The model is parameterized in terms
of a cross-covariance function that may be chosen from the many models proposed
in the literature. In addition, there are additive factors in the model that
allow tail dependence and reflection asymmetry of each variable measured at
different locations and of different variables to be modeled. The proposed
approach can therefore be seen as an extension of the linear model of
coregionalization widely used for modeling multivariate spatial data. The
likelihood of the model can be obtained in a simple form and therefore the
likelihood estimation is quite fast. The model is not restricted to the set of
data locations, and using the estimated copula, spatial data can be
interpolated at locations where values of variables are unknown. We apply the
proposed model to temperature and pressure data and compare its performance
with the performance of a popular model from multivariate geostatistics.
