Sparse sensor placement for reducing forecast errors in ensemble Kalman filtering

Designing efficient observation networks for reducing forecast errors is a fundamental challenge in numerical weather prediction. Data‐driven sparse sensor placement (SSP), which selects observation locations based on optimal experimental design, has recently been proposed. However, it targets analysis error reduction and has not been explored for reducing forecast errors. In this study, we develop new SSP methods for reducing forecast errors in the ensemble Kalman filter (EnKF) by using a tangent linear model approximated by an ensemble forecast. We derive the Fisher information matrices in the ensemble and model spaces for the EnKF, and clarify the mathematical interpretations of A‐, D‐ and E‐optimality in terms of forecast error reduction. A‐optimality in the model space minimizes the mean forecast error variance; D‐optimality cannot be formulated for the forecast and is ill‐defined for the analysis in the model space, and is therefore formulated in the ensemble space; and E‐optimality in the model space minimizes the worst‐case forecast error variance. We further propose a fast greedy algorithm for selecting observation locations under A‐optimality in the model space, avoiding matrix inversion at each greedy step and substantially reducing computational cost. Numerical experiments using the Lorenz‐96 model support these theoretical findings. Among the three optimality criteria, A‐optimality in the model space most consistently reduces forecast spread and root‐mean‐squared error, and achieves the largest observation impact according to post‐assimilation observation impact diagnostics. These results indicate that, in the present idealized experiments, A‐optimality in the model space with the fast greedy algorithm is the most reliable and well‐balanced approach for observation network design in ensemble‐based data assimilation.