Statistical Design for Adaptive Weather Observations

Suppose that one has 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 adaptive observations problem found in the literature are reviewed and interpreted from the optimal statistical design viewpoint. In addition, a numerical example, using the 40-variable model of Lorenz and Emanuel, suggests that some other proposed approaches may often be close to the optimal solution, at least in this highly idealized model.