Suppose that we have the freedom to adapt the observational network by choosing the times and locations of observations. Which choices would yield the best analysis of the atmospheric state or the best subsequent forecast? Here, this problem of "adaptive observations" is formulated as a problem in statistical design. The statistical framework provides a rigorous mathematical statement of the adaptive observations problem and indicates where the uncertainty of the current analysis, the dynamics of error evolution, the form and errors of observations, and data assimilation each enter the calculation. The statistical formulation of the problem also makes clear the importance of the optimality criteria (for instance, one might choose to minimize the total error variance in a given forecast) and identifies approximations that make calculation of optimal solutions feasible in principle. Optimal solutions are discussed and interpreted for a variety of cases. Selected approaches to the adaptiv...

The main objective of the paper is to describe and develop model oriented methods and algorithms for the design of spatial experiments. Unlike many other publications in this area, the approach proposed here is essentially based on the ideas of convex design theory. 1.

We examine the problem of optimal design in the context of filtering multiple random walks. Specifically, we define the steady state E-optimal design criterion and show that the underlying optimization problem leads to a second order cone program. The developed methodology is applied to tracking network flow volumes using sampled data, where the design variable corresponds to controlling the sampling rate. The optimal design is numerically compared to a myopic and a naive strategy. Finally, we relate our work to the general problem of steady state optimal design for state space models.