Copula-driven construction for the joint distribution of spatial-temporal variables

In this work an equivalent stochastic representation is provided for generic mixture distributions using standard uniform distribution． Based on this result, driving spatially with Copula and assuming temporally Markovian, a general modelling framework is established for spatial-temporal joint distribution． This work is inspired by an attempt to understand the rationale of Wilks’s stochastic precipitation generator, and will be useful for more general context concerning spatial-temporal joint modelling．