This paper provides new tools for dynamic spatial sampling designs to find the optimal spatial mean estimation and the optimal spatial prediction, based on the temporal variation of the spatial dependence structure. We propose to model the time series formed by the sequence of the spatial covariance parameter estimators, taking into account the uncertainty associated with the estimations. A discussion of useful properties and techniques for estimation and forecasting under a variety of scenarios, including continuous time, is presented. An intensive simulation study is developed for a number of combinations of several time series lengths, spatial sample sizes, time series models, and covariance spatial functions. The methodology is applied to a network of air quality in Bogotá, Colombia, where we find the location of a mobile station that optimizes the spatial mean estimation. Copyright © 2016 John Wiley & Sons, Ltd.