Paleoclimate Sampling as a Sensor Placement Problem

We treat paleoclimatic sampling as a sensor placement problem, attempting to find the locations where observations would optimally characterize the variability of climate fields of interest. Starting from a set of realistically-constrained, predefined potential sampling locations and observational uncertainties, we formulate optimized observing networks as the solution to a data-assimilation problem: given a stochastic representation of the Gaussian-distributed climate states of interest, which are linked to direct climate observations via a proxy system model, we may update the distribution and quantify the information gain from each possible sensor network. Furthermore, using submodular cost functions considerably reduces the size of the numerical optimization problem, as it enables iterative addition of sensors to the network. We illustrate this process with the design of an optimal network of coral δ¹⁸O used to jointly infer sea surface temperature and sea surface salinity fields. For example, given the current coral network, we show that an additional 25 to 75 observations would greatly improve the SST field reconstruction with the resampling rate being the highest in the central Pacific region.
We analyze the impact of various design choices on the resulting optimal sensor network, such as the cost function formulation, the quantification of uncertainty within the proxy system model and the targeted fields. We conclude with a discussion of applications to other proxy classes.