  We propose a new copula model that can be used with replicated spatial data.
Unlike the multivariate normal copula, the proposed copula is based on the
assumption that a common factor exists and affects the joint dependence of all
measurements of the process. Moreover, the proposed copula can model tail
dependence and tail asymmetry. The model is parameterized in terms of a
covariance function that may be chosen from the many models proposed in the
literature, such as the Matern model. For some choice of common factors, the
joint copula density is given in closed form and therefore likelihood
estimation is very fast. In the general case, one-dimensional numerical
integration is needed to calculate the likelihood, but estimation is still
reasonably fast even with large data sets. We use simulation studies to show
the wide range of dependence structures that can be generated by the proposed
model with different choices of common factors. We apply the proposed model to
spatial temperature data and compare its performance with some popular
geostatistics models.
