This work presents an information-theoretic methodology for adaptive observation targeting within ensemble forecast frameworks. The mobile sensor targeting problem addresses decision making of assigning multiple sensor platforms (e.g. UAVs) to paths along which they will take additional measurements in order to reduce the forecast uncertainty in the verification region at the verification time. Employing entropy as a metric of uncertainty of the estimates, the targeting decision looks for a set of measurement points that reveals the largest mutual information related to the verification variables. In the ensemble forecast framework, entropy and mutual information are computed from the covariance information, as entropy is expressed as logarithm of the determinant of a covariance matrix under the Gaussian assumption. Also, constraints associated with the motion of the sensor platforms such as flight speed limitation of a UAV, are included in this decision.

A computationally efficient backward selection algorithm forms the backbone of the proposed targeting approach. To address the computational burden resulting from the expense of determining the impact of each measurement choice on the uncertainty reduction in the verification site, the backward selection algorithm exploits the commutativity of mutual information. This enables the contribution of each measurement choice to be computed by propagating information backwards from the verification space/time to the search space/time. This approach dramatically reduces the number of times of computationally expensive covariance updates -- equivalently, perturbation ensemble updates -- needed for finding the optimal targeting solution. Numerical experiments using an idealized chaos model verifies the effectiveness of the algorithm.

Due to limitation of available ensemble size for a realistic weather model, real implementation of the proposed targeting algorithm might suffer from performance degradation. This work performs sensitivity analysis to quantify the degree of impact that small ensemble size might have on the performance of the ensemble-based targeting. Two new concepts of range-to-noise ration (RNR) and probability of correct decision (PCD) are introduced in this quantification and their formulae are derived from statistical analysis of estimation error of mutual information. Theoretical prediction of the degree of impact of small ensemble size is verified to be consistent with the numerical results.