A continuous spatial model can be constructed by convolving a very simple, perhaps independent, process with a kernel or point spread function. This approach for constructing a spatial process offers a number of advantages over specification through a spatial covariogram. In particular, this process convolution specification leads to compuational simplifications and easily extends beyond simple stationary models. This paper uses process convolution models to build space and space-time models that are flexible and able to accomodate large amounts of data. Data from environmental monitoring is considered.

The manuscript is available in postscript and pdf formats.