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The need for efficient monitoring of spatio-temporal dynamics in large environmental surveillance applications motivates the use of robotic sensors to achieve sufficient spatial and temporal coverage. A common approach in machine learning to model spatial dynamics is to use the nonparametric Bayesian framework known as Gaussian Processes (GPs) (c.f., ) which are fully specified by a mean and a covariance function. However, defining suitable covariance functions that are able to appropriately model complex space-time dependencies in the environment is a challenging task. In this paper, we develop a generic approach for constructing several classes of covariance functions for spatio-temporal GP modeling. The GP models are then extended to perform efficient path planning in continuous space while maximizing the information gain. Extensive empirical evaluation for the different classes of covariance functions using real world sensing datasets is discussed, including experiments on a tethered robotic system - Networked Info Mechanical System (NIMS).