Determination of Structheral Dependence of Spatial Data with Copula Functions

Copula functions are powerful tools for construction the multivariate distribution of dependent variables in terms of their marginal distributions. Each of these functions provide a model which represents all properties of the variables dependency. For spatial data analysis، the dependence structure of the data should be determined by using the multivariate distribution of the random field. In analysis of Spatio-temporal data it is also necessary to identify the relations between spatial and temporal structure of the data in terms of Spatio-temporal covariance function. Sometimes a separable Spatio-temporal covariance function is used for the ease of application، but in some applications this property is not realistic. In these cases it is required to use a non-separable Spatio-temporal covariance function. In this paper the role of copula functions in determination of joint distribution of a random field is considered and the properties of a valid spatial copula function are determined. Then a new valid spatial copula family is introduced. Next some spatial and nonseparable Spatio-temporal covariance functions are constructed by using these copula functions