  Stochastic process models for spatiotemporal data underlying random fields
find substantial utility in a range of scientific disciplines. Subsequent to
predictive inference on the values of the random field (or spatial surface
indexed continuously over time) at arbitrary space-time coordinates, scientific
interest often turns to gleaning information regarding zones of rapid
spatial-temporal change. We develop Bayesian modeling and inference for
directional rates of change along a given surface. These surfaces, which
demarcate regions of rapid change, are referred to as ``wombling'' surface
boundaries. Existing methods for studying such changes have often been
associated with curves and are not easily extendable to surfaces resulting from
curves evolving over time. Our current contribution devises a fully model-based
inferential framework for analyzing differential behavior in spatiotemporal
responses by formalizing the notion of a ``wombling'' surface boundary using
conventional multi-linear vector analytic frameworks and geometry followed by
posterior predictive computations using triangulated surface approximations. We
illustrate our methodology with comprehensive simulation experiments followed
by multiple applications in environmental and climate science; pollutant
analysis in environmental health; and brain imaging.
