Inverse Adjoint Estimation of Eddy Viscosity for Coastal Flow Models
Publication: Journal of Hydraulic Engineering
Volume 119, Issue 4
Abstract
Tuning a three‐dimensional (3‐D) coastal circulation model for vertical eddy viscosities can be a laborious task. An efficient alternative is to use adjoint inverse estimation methods, and one such method is developed here. A cost functional that consists of two terms is formulated: The first describes the lack of fit between model results and available data, and the second measures the variance of the eddy viscosity with depth. This latter term has been introduced with a view to eliminate the instabilities commonly associated with inverse methods. Weights are used to vary the relative influence of each term. The “optimized” eddy viscosity estimate is obtained by a variational minimization of the functional. The procedure is tested using velocity data at the center of a rectangular sea domain. Wind and tidal forcing are considered along with known eddy viscosity profiles. The inverse model retrieves extremely good estimates of the eddy viscosities in all cases, even when data are sparse. The estimates are all smooth, and the method and the solutions exhibit no sign of instability.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Carrera, J., and Neuman, S. P. (1986). “Estimation of aquifer parameters under transient and steady state conditions: II. Uniqueness, stability, and solution algorithms.” Water Resour. Res., 22(2), 211–227.
2.
Cushman‐Roisin, M. (1986). “The hydrological inverse problem: reconsideration and application to the microcomputer,” PhD dissertation, Florida State Univ., Tallahassee, Fl.
3.
Das, S., and Lardner, R. W. (1991). “On the estimation of parameters of hydraulic models by assimilation of periodic tidal data.” J. of Geophysical Res., 96(8), 15,187–15,196.
4.
Davies, A. M. (1987). “On extracting current profiles from vertically integrated numerical models.” Coastal Engrg., 11, 445–447.
5.
Ghil, M., and Malanotte‐Rizzoli, P. (1991). “Data assimilation in meteorology and oceanography.” Advances in Geophysics, 33, 141–266.
6.
Hasselmann, K. (1991). “Summary of open meeting of the wave model development group,” Westerland, 5 (June).
7.
Heaps, N. S. (1972). “On the numerical solution of the three‐dimensional hydrodynamical equations for tides and storm surges.” Mem. Soc. R. Sci. Liege, 6, 143—180.
8.
Lardner, R. W., and Cekirge, H. M. (1988). “A new algorithm for three‐dimensional tidal storm surge computations.” Applied Math. Modeling, 12, 471–481.
9.
Liggett, J. A. (1990). “Computation (Investigation, Education, and Application).” J. Hydr. Engrg., ASCE, 116(12), 1436–1453.
10.
Panchang, V. G., and O'Brien, J. J. (1990). “On the determination of hydraulic model parameters using the adjoint state formulation.” Modeling Marine Syst., I, 5–18.
11.
Smedstad, O. M., and O'Brien, J. J. (1991). “Variational data assimilation and parameter estimation in an equatorial Pacific Ocean model.” Progress in Oceanography, 26, 179–241.
12.
Tee, K. T. (1982). “The structure of three‐dimensional tide‐generating currents: experimental verification of a theoretical model.” Estuarine, Coastal and Shelf Sci., 14, 27–48.
13.
Tziperman, E., and Thacker, W. C. (1989). “An optimal‐control/adjoint‐equations approach to studying the oceanic general circulation.” J. Phys. Oceanogr., 19, 1471–1485.
14.
Yeh, W. W. G. (1986). “Review of parameter identification in groundwater hydrology: the inverse problem.” Water Resour. Res., 22(2), 95–108.
15.
Yu, L., and O'Brien, J. J. (1991). “Variational estimation of the wind stress drag coefficient and the oceanic eddy viscosity profile.” J. Phys. Oceanogr., 21, 709–719.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 119 • Issue 4 • April 1993
Pages: 506 - 524
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: Feb 21, 1992
Published online: Apr 1, 1993
Published in print: Apr 1993
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.