Abstract
Abstract Assimilating hydrographic observations into a planetary geostrophic model is posed as a problem in control theory. The cost functional is the sum of weighted model and data residuals. Model errors are assumed to be spatially correlated, and hydrographic station data are assimilated directly. Searches in state space and data space, for minimizing the cost functional, are compared to a direct matrix inversion algorithm in the data space. State-space methods seek the minimizer of the cost functional by performing a preconditioned search in an N-dimensional space of state or control variables, where N is approximately 650 000 in the present calculations. Data-space methods solve the Euler–Lagrange equations for the extremum of the cost functional by working in an M-dimensional dual space, where M is the number of measurements. The following four solvers are compared: (i) an iterative state-space solver, with a naive diagonal matrix preconditioner; (ii) an iterative state-space solver, with a sophisticated preconditioner based on the inverse of the model’s dynamical operators; (iii) an iterative data-space solver, with no preconditioning; and (iv) a direct, M × M matrix inversion, data-space solver. The best solver is the iterative data-space solver, (iii), which is approximately 10 times faster than the sophisticated preconditioned state-space solver, (ii), and 100 times faster than the direct data-space solver, (iv).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.