This project provides new tools for dynamic spatio-temporal 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. We make use of both the Box-Jenkins ARIMA models or the state space modeling framework, including continuous time. In addition, we combine optimal spatial sampling designs with geostatistical analysis of functional data. We develop methodologies and design criteria to find the set of spatial locations that minimizes the variance of the spatial functional prediction at unsampled sites for several functional predictors.