Finding spatial locations of physical sensors is critical to reliably estimating and monitoring spatiotemporal systems, such as weather, traffic, or social networks. Existing sensor placement approaches that leverage mutual information or coverage do not take into account the spatiotemporal dynamics of the underlying phenomena. Leveraging recent work in modeling evolving Gaussian processes, we show that a sensor placement method can be constructed by applying observability theory on linear models of the spatiotemporal phenomena in a higher dimensional feature space. We show that this approach outperforms traditional mutual information based approaches by taking into account the invariant subspaces induced by the spatiotemporal dynamics. Furthermore, fundamental results relating the observability of spatiotemporal phenomena with deterministic and stochastic sensors placement are proven.