A Computational Framework for Assessing and Optimizing the Performance of Observational Networks in 4D-Var Data Assimilation

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Virginia Tech

A deep scientific understanding of complex physical systems, such as the atmosphere, can be achieved neither by direct measurements nor by numerical simulations alone. Data assimilation is a rigorous procedure to fuse information from a priori knowledge of the system state, the physical laws governing the evolution of the system, and real measurements, all with associated error statistics. Data assimilation produces best (a posteriori) estimates of model states and parameter values, and results in considerably improved computer simulations.

The acquisition and use of observations in data assimilation raises several important scientific questions related to optimal sensor network design, quantification of data impact, pruning redundant data, and identifying the most beneficial additional observations. These questions originate in operational data assimilation practice, and have started to attract considerable interest in the recent past.

This dissertation advances the state of knowledge in four dimensional variational (4D-Var) - data assimilation by developing, implementing, and validating a novel computational framework for estimating observation impact and for optimizing sensor networks. The framework builds on the powerful methodologies of second-order adjoint modeling and the 4D-Var sensitivity equations. Efficient computational approaches for quantifying the observation impact include matrix free linear algebra algorithms and low-rank approximations of the sensitivities to observations. The sensor network configuration problem is formulated as a meta-optimization problem. Best values for parameters such as sensor location are obtained by optimizing a performance criterion, subject to the constraint posed by the 4D-Var optimization. Tractable computational solutions to this "optimization-constrained" optimization problem are provided.

The results of this work can be directly applied to the deployment of intelligent sensors and adaptive observations, as well as to reducing the operating costs of measuring networks, while preserving their ability to capture the essential features of the system under consideration.

data assimilation, dynamic data-driven problem, second-order adjoints, adaptive observations, sensor placement, intelligent sensors, sensitivity analysis, uncertainty quantification, nonlinear optimization, inverse problems, parameter estimation, matrix-free linear solvers, truncated singular value decomposition