Even for a specific application, the design space of wireless sensor networks is enormous, and traditional disciplinary boundaries are disappearing in the search for efficient integrated network architectures and protocols. There is a strong need to develop objective frameworks for the evaluation of performance and energetic cost as a function of network control at multiple levels, including the signal/data processing application, network organization, routing, MAC, and physical layers. This paper, a step in this direction, addresses the efficiency of linear estimation of a second-order random spatial field at a central server-a snapshot - in terms of the precision of the estimate and the energetic cost of computing it. We present a model that is based on the tasks of taking samples at a specific resolution and reporting them over the network to the server where the estimate is computed. It provides insight into the joint design of sampling and routing, an explicit efficiency measure for finite networks, and a performance benchmark for precision. The model, with predefined sampling locations at each resolution, implicitly requires centralized control to obtain spatially uniform sampling. We describe a decentralized reporting protocol called PROSE (Protocol for Randomized Opportunistic Sampling and Estimation) that uses localized decisions for sampling, data aggregation, and routing that are random and opportunistic. Finally, we show that the performance of PROSE compares favorably with the benchmark, and that PROSE admits simpler nonopportunistic random behavior at the cost of lower performance.