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In this paper we study the problem of efficient data dissemination over one- and two-dimensional multi-hop wireless sensor grids with spatially correlated sample measurements. In particular, we investigate the trade-offs of exploiting correlations via cooperatively compressing the sensor data as it hops around the network. We focus on two performance metrics, namely transport traffic and scheduling latency. More specifically, we investigate using basic information theory the feasibility of sublinear scaling laws , with the number of nodes, under a variety of cooperation strategies ranging from naive non-cooperative forwarding to sophisticated hierarchical cooperation. First, we show that a simple cooperation scheme, namely forward/reverse cooperation, achieves a logarithmic growth rate for the transport traffic and a linear growth rate for the schedule length with the number of nodes. Thus, we shift our focus to multi-phase cooperation to show that: i) O(radicN) schedule length is achievable using two-phase cooperation which is a combination of noncooperative and forward/reverse cooperation schemes and ii) Logarithmic schedule length and transport traffic are both achievable using hierarchical cooperation, yet at the expense of more complexity in coordinating nodes' cooperation. This also opens room for optimizing these performance measures for a given network size. Finally, we analyze the impact of fixed bit rate and derive upper bounds on the scheduling latency.