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Summary form only given. Information processing, communication and routing are intimately coupled in sensor networks and the sensor signal characteristics in space and time directly impact these vital network functions. In this paper, we propose a signal modeling framework for sensor measurements that exposes the interaction between space-time signal sampling, distributed signal processing, and communication and routing of information through the network. We assume that the signal in a region of interest is a bandlimited stationary Gaussian field in spatial and temporal dimensions. The proposed model is based on the notion of spatial coherence regions that are dictated by Nyquist sampling in the spatial dimensions: the signals remain strongly correlated within each coherence region and vary approximately independently between different coherence regions. This simple approximate model has several implications for the design of sensor networks. First, it imposes a structure on distributed signal processing algorithms that is naturally suited to the communication constraints: high-bandwidth (feature-level) information exchange is limited to spatially local nodes within each coherence region, whereas low-bandwidth (decision-level) information exchange is sufficient between farther nodes in different coherence regions. Second, it enables simple bounds on the rate at which information is generated by any sub-region in the network. Third, it suggests natural communication strategies for transporting information from the coherence regions to a destination node or region and enables estimates of the corresponding link capacities.