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The data gathering problem in wireless sensor networks for environmental monitoring, where the physical phenomena can be modeled by partial differential equations (PDEs), is investigated. In this context, it suffices for the sensor network to update the base station with estimates of model parameters rather than transmitting raw sensor measurements. In-network processing techniques to estimate the PDE coefficients are presented. A scheme that provides a hybrid combination of decision and data fusion is proposed to find a tradeoff between performance and energy efficiency. The role that the assumptions of PDE models can play in designing such methods is investigated.