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Wireless sensor networks enable monitoring of various physical phenomena. In this paper, we consider the monitoring of a phenomenon that is continuous and correlated both in space and time. The sensor nodes periodically sample the phenomenon and transmit their measurements to a sink node using a routing tree. The sink node reconstructs the phenomenon in time and space using the samples it gathers. Because the data is spatially and temporally continuous, perfect reconstruction is only possible if there is an infinite number of sensors continuously monitoring every point in the area of interest. A perfect reconstruction also requires that all measurements produced by the nodes are delivered to the sink. All these requirements are practically impossible. Hence, in this paper, we consider the practical situation where the phenomenon is discretized spatially and temporally, and samples might be lost while they traverse the network due to a variety of reasons including wireless-induced packet losses. These factors cause distortion between the actual phenomenon and the reconstructed phenomenon. We model the physical phenomenon as a Gaussian stochastic process and derive expressions for distortion in time (temporal distortion) and space (spatial distortion) for a fixed packet loss rate.