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We consider a mobile sensor network monitoring a spatio-temporal field. Given limited caches at the sensor nodes, the goal is to develop a distributed cache management algorithm to efficiently answer queries with a known probability distribution over the spatial dimension. First, we propose a novel distributed information theoretic approach assuming knowledge of the distribution of the monitored phenomenon. Under this scheme, nodes minimize an entropic utility function that captures the average amount of uncertainty in queries given the probability distribution of query locations. Second, we propose a correlation-based technique, which only requires knowledge of the second-order statistics, relaxing the stringent constraint of a priori knowledge of the query distribution, while significantly reducing the computational overhead. We show that the proposed approaches considerably improve the average field estimation error. Further, we show that the correlation-based technique is robust to model mismatch in case of imperfect knowledge of the underlying generative correlation structure. [ABSTRACT FROM AUTHOR]