A separable covariance,A non−separable covariance

A separable covariance

Separable models

  

A spatial-temporal field Z(s, t), where s represent space and t time,

is separable if Cov{Z(s, t), Z(s , t )} = C1(s, s )C2(t, t ) for some

spatial covariance C1 and temporal covariance C2.

A class of nonseparable spatial-temporal models were proposed by

Cressie and Huang (JASA, 99), Gneiting (JASA, 02), Stein (2003)

  and Chen, Fuentes and Davis (2004).
http://www.stat.ncsu.edu/people/fuentes/courses/stwarwick/lectures/spacetime.pdf