Mathematical Geology, Vol. 31, No. 6, 1999 Geostatistical Space–Time Models: A Review 1 Phaedon C. Kyriakidis 2 and Andre ´ G. Journel 3 Geostatistical space–time models are used increasingly for addressing environmental problems, such as monitoring acid deposition or global warming, and forecasting precipitation or stream flow. Each discipline approaches the problem of joint space–time modeling from its own perspective, a fact leading to a significant amount of overlapping models and, possibly, confusion. This paper attempts an annotated survey of models proposed in the literature, stating contribu- tions and pinpointing shortcomings. Stochastic models that extend spatial statistics (geostatistics) to include the additional time dimension are presented with a common notation to facilitate comparison. Two conceptual viewpoints are distinguished: (1) approaches involving a single spatiotemporal random function model, and (2) approaches involving vectors of space random functions or vectors of time series. Links between these two viewpoints are then revealed; advantages and shortcomings are highlighted. Inference from space–time data is revisited, and assessment of joint space–time uncertainty via stochastic imaging is suggested. KEY WORDS: space–time models, geostatistics, time series, trend models, stochastic simu- lation. INTRODUCTION The modeling of spatiotemporal distributions resulting from dynamic pro- cesses evolving in both space and time is critical in many scientific and engineering fields: environmental sciences, climate prediction and meteo- rology, hydrology and reservoir engineering, to name but a few. Geostatisti- cal space–time models have been applied for modeling spatiotemporal distributions in several scientific disciplines. Examples of such applications include determination of space–time trends in the deposition of atmo- spheric pollutants (Eynon and Switzer, 1983; Bilonick, 1985; Rouhani and others, 1992; Oehlert, 1993; Vyas and Christakos, 1997), characterization 1 Received 1 September 1997; accepted 18 August 1998. 2 Department of Geological and Environmental Sciences, Stanford University, Stanford, California 94305-2115. e-mail: phaedon@pangea.stanford.edu 3 Department of Petroleum Engineering, Stanford University, Stanford, California 94305-2220. e-mail: journel@pangea.stanford.edu 651 0882-8121/99/0800-0651$16.00/1  1999 International Association for Mathematical Geology