Title: Optimal Sensor Placement for Data Assimilations

Authors: LIANG XU (Marine Meteorology Division, Naval Research Laboratory, Monterey, CA, USA)
Wei Kang (Naval Postgraduate School, Monterey, CA, USA)

We explore the theoretical framework as well as the associated algorithms for the problem of optimally placing mobile observation platforms to maximize the improvement of forecasts. The current adjoint based observation monitor system can provide the observation impact only after the fact. A comprehensive solution to the planning of optimal sensor placement is still an open problem. The approach in this paper is based on the concept of observability, which is a quantitative measure of the information provided by sensor data and user-knowledge. The observability can be numerically computed based on the system's dynamic model. It provides the cost function for the optimization of sensor locations. The Burgers equation is used to verify this approach. In the computation, the system's observability is numerically approximated using empirical covariance matrix method. The observabiltiy is maximized using gradient projection method to find the optimal sensor location. To prove the optimality of the method, Monte Carlo simulations are carried out using standard 4DVAR algorithms based on two sets of data, one from equally spaced sensors and the other from the optimal sensor location. The results show that, relative to equally spaced sensors, the 4DVAR data assimilation achieves significantly improved estimation accuracy if the sensors are placed at the optimal location. Robustness study is also carried out in which the error covariance matrix is varied by 50% and the senor noise covariance matrix is varied by 100%. In both cases, the optimal sensor location results in improved estimation accuracy. To conclude, the optimal sensor placement is able to significantly improve the atmospheric analysis. The concept of observability is a fundamental property of the system that does not rely on the choice of the data assimilation system to be used. For future research, optimal sensor path planning will be developed using the same concept of observability.

GMAO Head: Michele Rienecker Global Modeling and Assimilation Office NASA Goddard Space Flight Center

Curator: Nikki Privé Last Updated: May 27 2011