Practical and theoretical aspects of adjoint parameter estimation and identifiability in meteorology and oceanography

Dynamics of Atmospheres and Oceans

Volumn 27, Issue 1-4, 1998, Pages 55-79

  Navon, I M ^a  

^a FLORIDA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADJOINT METHOD; METEOROLOGY; OCEANOGRAPHY; PARAMETER ESTIMATION;

EID: 0031944948     PISSN: 03770265     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0377-0265(97)00032-8     Document Type: Article

References (120)

1. Acar, R., Vogel, C.R., 1994. Analysis of bounded variation penalty method for ill-posed problems. Inverse Problems 10 (6), 1217-1229.
2. Alvarez, L., Lions, P.L., Morel, J.-M., 1992. Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal. 29 (3), 845-866.
3. Banks, H.T., 1992a. Control and estimation in distributed parameter systems. In: Frontiers in Applied Mathematics, vol. 11. SIAM, Philadelphia, 227 pp. edited by H.T. Banks.
4. Banks, H.T., 1992b. Computational issues in parameter estimation and feedback control problems for partial differential equation systems. Physica D 60, 226-238.
5. Banks, H.T., Kunish, K., 1989. Estimation Techniques for Distributed Parameter Systems. Birkhauser, Boston, 315 pp.
6. Banks, H.T., Rosen, I.G., 1987. Numerical schemes for the estimation of functional parameters in distributed models for mixing mechanisms in lake and sea sediment cores. Inverse Problems 3, 1-23.
7. Bellman, R., Jaquez, J., Kalaba, R., Schwimmer, S., 1965a. Quasi-linearization and the estimation of chemical rate constants from raw kinetic data. The Rand Corporation, RM-4721-NIH.
8. Bellman, R., Kagiwada, H., Kalaba, R., Ueno, S., 1965b. Inverse problems in radiative transfer: layered media. Icarus 4, 119.
9. Bennett, A.F., 1992. Inverse Methods in Physical Oceanography. Cambridge University Press, Cambridge, 346 pp.
10. Bennett, A.F., McIntosh, P.C., 1982. Open ocean modeling as an inverse problem: tidal theory. J. Phys. Occeanogr. 12, 1004-1018.
11. Cacuci, D.G., 1981. Sensitivity theory for nonlinear systems: II. Extensions to additional classes of responses. J. Math. Phys. 22, 2803-2812.
12. Cacuci, D.G., 1988. The forward and adjoint methods of sensitivity analysis. In: Ronen, Y. (Ed.), Uncertainty Analysis. CRC Press, Inc., 282 pp.
13. Carrera, J., Neuman, S.P., 1986a. Estimation of aquifer parameters under transient and steady state conditions: 1. Maximum likelihood method incorporating prior information. Water Resour. Res. 22 (2), 199-210.
14. Carrera, J., Neuman, S.P., 1986b. Estimation of aquifer parameters under transient and steady state conditions: 2. Uniqueness, stability and solution algorithms. Water Resour. Res. 22 (2), 211-227.
15. Carrera, J., Neuman, S.P., 1986c. Estimation of aquifer parameters under transient and steady state conditions: 3. Application to synthetic and field data. Water Resour. Res. 22 (2), 228-242.
16. Chavent, G., 1974. Identification of functional parameters in partial differential equations. In: Goodson R.E., Polis, M. (Eds.), Identification of Parameters in Distributed Systems, ASME Conference on Automatic Control, 17-21 June 1974, Austin, TX. pp. 31-48. American Society of Mechanical Engineers, New York, NY 10017.
17. Chavent, G., 1979. Identification of Distributed Parameter Systems: About the Output Least Squares Methods, Its Implementation and Identifiability, Proc. 5th IFAC Symp. on Identification and System Parameter Estimation, Darmstadt. Pergamon Press, Oxford, pp. 85-97.
18. Chavent, G., 1983. Local stability of the output least square parameter estimation technique. Mat. Appl. Comp. 2, 3-22.
19. Chavent, G., 1991. On the theory and practice of non-linear least-squares. Adv. Water Resour. 14 (2), 55-63.
20. Chavent, G., Lemonnier, P., 1974. Identification de la non-linearite d'une equation parabolique quasi-lineaire. Appl. Math. Opt. 1, 121-162.
21. Chavent, G., Dupuy, M., Lemonnier, F., 1975. History matching by use of optimal theory. Soc. Pet. Eng. J. 15, 74-86.
22. Chertok, D.L., Lardner, R.W., 1996. Variational data assimilation for a nonlinear hydraulic model. Appl. Math. Modeling 20, 675-682.
23. Courtier, P., 1986. Le modele adjoint, outil pour des experiences de sensibility. Note de travail no 166, EERM, Paris, France, 36 pp. (available from Meteo-France).
24. Courtier, P., 1987. Application du contrôle optimal á le prévision numérique en Météorologie. These de Doctorat de l'Universite Paris 6.
25. Cushman-Roisin, M., 1986. The hydrological inverse problem: reconsideration and application to the micro-compute. Ph.D. Dissertation, Florida State University, Tallahassee, FL, USA.
26. Daley, R., 1991. Atmospheric Data Analysis. Cambridge University Press, 497 pp.
27. Das, S.K., Lardner, R.W., 1990. On the estimation of parameters of hydraulic models by assimilation of periodic tidal data. J. Geophys. Res. (Oceans) 96, 15187-15196.
28. Das, S.K., Lardner, R.W., 1992. Variational parameter estimation for a two dimensional numerical tidal model. Int. J. Numer. Meth. Fluids 15, 313-327.
29. Dee, D.P., 1995. On-line estimation of error covariance parameter for atmospheric data assimilation. Mon. Weather Rev. 123, 1128-1145.
30. Dobson, D.C., Santosa, F., 1994. An image enhancement technique for electrical impedance tomography. Inverse Problems 10, 317-334.
31. Dobson, D.C., Santosa, F., 1995. Recovery of blocky images from noisy and blurred data. SIAM J. Appl. Math. Vol. 56 (4), 1996, p. 1181-1198.
32. Errico, R.M., Vukićević, T., Raeder, K., 1993a. Examination of the accuracy of a tangent linear model. Tellus 45A, 462-477.
33. Errico, R.M., Vukićević, T., Raeder, K., 1993b. Comparison of initial and lateral boundary condition sensitivity for a limited area model. Tellus 45A, 539-557.
34. Ewing, R.E., Lin, T., 1989. Parameter identification problems in single phase and two-phase flow. In: F. Kappel, W. Kunish and W. Shappacher (Eds.), Control and Estimation of Distributed Parameter Systems. Birkhauser Verlag, Boston, 434 pp. Full Series On Numerical Maturities, Vol. 91.
35. Fukumori, I., Benveniste, J., Wunsch, C., Haidvogel, D.B., 1993. Assimilation of sea surface topography into an ocean circulation model using a steady state smoother. J. Phys. Ocean. 23, 1831-1855.
36. Ghil, M., 1996. Advances in sequential estimation for atmospheric and oceanic flows. J. Meteor. Jpn. Vol. 75, No. 1B, pp. 289-304, (Special issue "Data Assimilation in Meteorology and Oceanography: Theory and Practice, Ghil, M., Ike, K., H. Bennett, P. Courtier, M. Kimoto, H. Nagata, M. Saiki and N. Sato (Eds.).
37. Ghil, M., 1996. Advances in sequential estimation for atmospheric and oceanic flows. J. Meteor. Jpn. Vol. 75, No. 1B, pp. 289-304, (Special issue "Data Assimilation in Meteorology and Oceanography: Theory and Practice, Ghil, M., Ike, K., H. Bennett, P. Courtier, M. Kimoto, H. Nagata, M. Saiki and N. Sato (Eds.).
38. Ghil, M., Malanotte-Rizzoli, P., 1991. Data assimilation in meteorology and oceanography. In: Saltzman, B. (Ed.), Advances in Geophysics, vol. 33. Academic Press, pp. 141-266.
39. Gong, J., Wahba, G., Johnson, D.R., Tribbia, J., 1996. Adaptive tuning of numerical weather prediction models: simultaneous estimation of weighting, smoothing and physical parameters. Mon. Weather Rev. (submitted).
40. Goodson, R.E., Polis, M.P., 1979. Parameter identification in distributed systems: a synthesizing overview in identification of parameters in distributed systems. In: Symposium of Annual Aut. Control. Am. Soc. Mech. Eng., New York. pp. 1-31.
41. Goodwin, G.C., Sin, K.S., 1984. Adaptive Filtering Prediction and Control. Prentice-Hall, Englewood Cliffs, NJ, 540 pp.
42. Gunson, J.G., 1995. Estimating open ocean boundary conditions: sensitivity studies. Doctoral Thesis, MIT and Woods Hole Oceanographic Institution, Joint Program in Physical Oceanography, 149 pp.
43. Gutman, S., 1990. Identification of discontinuous parameters in flow equations. SIAM J. Control Optim. 28, 1049-1060.
44. Haidvogel, D.B., Robinson, A.R. (Eds.), 1989. Data Assimilation. Special Issue. Dyn. Atmos. Oceans 13 (3-4).
45. Hao, Z., 1994. Data assimilation for interannual climate-change prediction. Ph.D. Thesis, Dept of Atmospheric Sciences, UCLA, 224 pp.
46. Hao, Z., Ghil, M., 1994. Data assimilation in a simple tropical ocean model with wind stress errors. J. Phys. Oceanogr. 24 (10), 2111-2128.
47. Hao, Z., Ghil, M., 1995. Sequential parameter estimation for a coupled ocean - atmosphere model. In: WMO/TD No. 651, Second Int. Symposium on Assimilation of Observations in Meteorology and Oceanography, 13-17 March 1995, Tokyo, Japan, vol. 1. pp. 181-186. World Meteorological Organization, Geneva, Switzerland.
48. Hao, Z., Ghil, M., Neelin, J.D., 1996. Data assimilation for a coupled ocean atmosphere model, Part I: Sequential state estimation. J. Phys. Oceanogr. (submitted).
49. Haykin, S., 1986. Adaptive Filter Theory. Prentice-Hall, Englewood Cliffs, NJ, 590 pp.
50. Heemink, A.W., 1987. Two-dimensional shallow water flow identification. Appl. Math. Model. 12, 109-118.
51. Hogg, N.G., 1996: Oceanographic data for parameter estimation. In Modern Approaches to data Association in Ocean Modeling. Vol. 61. Elsevier Oceanography Series 53-77, 455 pp.
52. Kitamura, S., Nakarigi, S., 1977. Identifiability of spatially-varying and constant parameters in distributed systems of parabolic type. SIAM J. Control Optim. 15, 785-802.
53. Kravaris, C., Seinfeld, J.H., 1985. Identification of parameters in distributed parameters systems by regularization. SIAM J. Control Optim. 23, 217-241.
54. Kravaris, C., Seinfeld, J.H., 1986. Identification of spatially varying parameters in distributed parameters systems by discrete regularization. J. Math. Anal. Appl. 119, 128-152.
55. Kubrusly, C.S., 1977. Distributed parameter system identification: a survey. Int. J. Control 26 (4), 509-535.
56. Kunish, K., Sachs, E.W., 1992. Reduced SQP methods for parameter estimation problems. SIAM J. Numer Anal. 29 (6), 1793-1820.
57. Lardner, R.W., 1993. Optimal control of open boundary conditions for a numerical tidal model. Comput. Methods Appl. Mech. Eng. 102 (3), 367-387.
58. Lardner, R.W., Das, K.S., 1994. Optimal estimation of eddy viscosity for a quasi-three dimensional numerical tidal and storm surge model. Int. J. Num. Methods Fluids 18, 295-312.
59. Lardner, R.W., Song, Y., 1995. Optimal estimation of eddy viscosity and friction coefficients for a quasi-3-dimensional numerical tidal model. Atmos.-Ocean 33, 581-611.
60. Lardner, R.W., Al-Rabeh, A.H., Gunay, N., 1993. Optimal estimation of parameters in a two dimensional hydrodynamical model of the Arabian Gulf. JGR Oceans 98, C10, 18, 229-18, 242.
61. Le Dimet, F.X., Navon, I.M., 1988. Variational and optimization methods in meteorology: a review. Technical Report SCRI 144, Supercomputer Computations Research Institute, Florida State University, Tallahassee, FL, 83 pp.
62. Ljung, L., 1987. System Identification. Theory for the User. Prentice-Hall, Englewood Cliffs, NJ, 519 pp.
63. Louis, J.-F., Živković, M., 1994. Optimizing a local weather forecast system. AER, Inc., Final Report, Cambridge, MA.
64. Malanotte-Rizzoli, P. (Ed.), 1996. Modem Approaches to Data Assimilation in Ocean Modeling, vol. 61. Elsevier Oceanography Series, 455 pp.
65. Malanotte-Rizzoli and E. Tziperman, 1996. The Oceanographic data Assimilation Problem: Overview, Motivation and Purposes. In Modern Approaches to data assimilation in Ocean Modeling. Vol. 61. Elsevier Oceanography Series. 3-17, 455 pp.
66. Marotzke, J., 1992. The role of integration time in determining a steady state through data assimilation. J. Phys. Oceanogr. 22, 1556-1567.
67. Marotzke, J., Wunsch, C., 1993. Finding the steady state of a general circulation model trough data assimilation. J. Geophys. Res. 98, 20149-20167.
68. Menke, W., 1984. Geophysical Data Analysis: Discrete Inverse Theory. Academic Press, 289 pp.
69. Miller, R.N., 1987. Theory and practice of data assimilation for oceanography. Harvard Tech. Rep. 26, 59 pp.
70. Morozov, V.A., 1968. The error principle in the solution of operator equations by the regularization method. USSR Comput. Math. Math. Phys. 892, 63-87.
71. Morozov, V.A., Stessin, M., 1993. Regularization Methods for Ill-Posed Problems. CRC Press, Boca Raton, FL, 257 pp.
72. Nakarigi, S., 1983. Identifiability of linear systems in Hilbert spaces. SIAM J. Control Optim. 21, 501-530.
73. Nash, S.G., Sofer, A., 1996. Linear and Nonlinear Programming. McGraw-Hill Companies Inc., 692 pp.
74. Navon, I.M., Legler, D.M., 1987. Conjugate-gradient methods for large-scale minimization in meteorology. Mon. Weather Rev. 115, 1479-1502.
75. Navon, I.M., Zou, X., Berger, M., Phua, P.K.H., Schlick, T., Le Dimet, F.X., 1992a. Numerical experience with limited memory quasi-Newton and truncated Newton methods. In: K.H. Phua, C.M. Wang, W.Y. Yeong, T.Y.Y. Leong (Eds.), Optimization Techniques and Applications, vol. 1. World Scientific Publishing Co., 1232 pp.
76. Navon, I.M., Zou, X., Berger, M., Phua, P.K.H., Schlick, T., Le Dimet, F.X., 1992b. Testing for reliability and robustness of optimization codes for large scale optimization problems. In: K.H. Phua, H.T. Loh, K.C. Tau and F.S. Chou (Eds.), Optimization Techniques and Applications, vol. 1. World Scientific Publishing Co., 1232 pp.
77. Nocedal, J., 1991. Theory of algorithms for unconstrained minimization. Acta Numerica 1, 199-247.
78. Omatu, S., Seinfeld, J.H., 1989. Distributed Parameter Systems: Theory and Applications. Oxford Mathematical Monographs, Oxford University Press, 430 pp.
79. Osher, S., Rudin, L.I., 1990. Feature oriented image enhancement using shock filters. SIAM J. Numer. Anal. 27 (4), 919-940.
80. Panchang, V.G., O'Brien, J.J., 1989. On the determination of hydraulic model parameters using the strong constraint formulation. In: Davies, A.M. (Ed.), Modeling Marine Systems, I. CRC Press, Inc., pp. 5-18.
81. Prevost, C., Salmon, R., 1986. A variational method for inverting hydrographic data. J. Mar. Sci. 44, 1-34.
82. Rabier, F., Courtier, P., Talagrand, O., 1992. An application of adjoint models to sensitivity. Beitr. Phys. Atmos. 65 (3), 177-192.
83. Rabier, F., Courtier, P., Hervou, M., Strauss, B., Persson, A., 1993. Sensitivity of forecast error to initial conditions using the adjoint model. ECMWF Tech. Memo. 197, 29 pp.
84. Richardson, J.E., Panchang, V.G., 1992. A modified adjoint method for inverse eddy viscosity estimation in coastal circulation models. In: Malcolm L. Spaulding, Keith Bedford, Alan Blumberg, Ralph Cheng and Craig Swanson (Eds.), Estuarine and Coastal Modeling, Proc. 2nd Int. Conf. Am. Soc. Civil Eng., New York, pp. 733-745.
85. Rudin, L.I., 1987. Images, numerical analysis of singularities and shock filters. Ph.D. Thesis, Computer Sci. Dept. Caltech, Pasadena, CA, Tech. Rep 5250: TR-87.
86. Rudin, L.I., Osher, S., 1994. Total variation based image restoration with free local constraints. In: IEEE International Conference on Image Processing, vol. 1. IEEE Signal Processing Society (Eds.), Los Alamitos, CA, USA, pp. 31-35.
87. Rudin, L.I., Osher, S., Fatemi, E., 1992. Nonlinear total variation based noise removal algorithm. Physica D. 60, 259-268.
88. Rudin, L.I., Osher, S., Fu, C., 1994. Total variation based restoration of noisy blurred images. SIAM J. Numer. Anal. (in press).
89. Santosa, F., Symes, W., 1988. Reconstruction of blocky impedance profiles from normal incidence reflection seismograms which are band-limited and miscalibrated. Wave Motion 10, 209-230.
90. Seinfeld, J.H., Kravaris, C., 1982. Distributed parameter identification in geophysics-petroleum reservoirs and aquifers. In: Tzafestas, S.G. (Ed.), Distributed Parameter Control Systems. Pergamon Press, Oxford, pp. 367-390.
91. Smedstad, O.M., O'Brien, J.J., 1991. Variational data assimilation and parameter estimation in an equatorial Pacific Ocean model. Progr. Oceanogr. 26, 179-241.
92. Stauffer, D.R., Bao, J., 1993. Optimal determination of nudging coefficients using the adjoint equations. Tellus 45A, 358-369.
93. Sun, N.-Z., Yeh, W.W.-G., 1990a. Coupled inverse problem in groundwater modeling, 1, Sensitivity and parameter identification. Water Resour. Res. 26 (10), 2507-2525.
94. Sun, N.-Z., Yeh, W.W.-G., 1990b. Coupled inverse problem in groundwater modeling, 2, Identifiability and experimental design. Water Resour. Res. 26 (10), 2527-2540.
95. Sun, N.-Z., Yeh, W.W.-G., 1992. A stochastic inverse solution for transient groundwater flow: parameter identification and reliability analysis. Water Resour. Res. 28, 3269-3280.
96. Tarantola, A., 1987. Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation. Elsevier Science, 613 pp.
97. ten Brummelhuis, P.C.J., Heemink, A.W., 1990. Parameter identification in tidal models with uncertain boundary conditions. Stochastic Hydrol. Hydraul. 4, 193-208.
98. ten Brummelhuis, P.C.J., Heemink, A.W., van den Boogaard, H.P.F., 1993. Identification of shallow-sea models. Int. J. Numer. Meth. Fluids 17, 637-665.
99. Tichonov, A.N., 1963. Regularization of ill-posed problems. Dokd. Akad. Nauk, USSR 153, 49-52.
100. Tichonov, A.N., Arsenin, V.Y., 1977. Solutions of Ill-Posed Problems. Halsted Press, New York, 258 pp.
101. Tziperman, E., Thacker, W.C., 1989. An optimal control/adjoint equations approach to studying the oceanic general circulation. J. Phys. Oceanogr. 19, 1471-1485.
102. Tziperman, E., Thacker, W.C., Long, R.B., Hwang, S.-M., 1992. Oceanic data analysis using a general circulation model. Part 1: Simulations. J. Phys. Ocean. 22, 1434-1485.
103. Vogel, C.R., 1994. Non-convergence of the L-curve regularization parameter selection method. Inverse Problems, Vol. 12, 1996, 535-547.
104. Vogel, C.R., Oman, M.E., 1995. Fast numerical methods for total variation minimization in image reconstruction. In: SPIE Proceedings Vol. 2563, "Advanced Signal Processing Algorithms", July 1995. Society of Photo Optical Instrumentation Engineers, Franklin Luk (Ed.).
105. Vogel, C.R., Oman, M.E., 1996. Iterative methods for total variation denoising. SIAM J. Sci. Comput. 17 (1), 227-238.
106. Vogel, C.R., Wade, J.G., 1995. Analysis of costate discretizations in parameter-estimation for linear evolution-equations. SIAM J. Control Optim. 33 (1), 227-254.
107. Wahba, G., 1990. Spline models for observational data. In: CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 59. Society for Industrial and Applied Mathematics, 169 pp., SIAM eds., Philadelphia, PA.
108. Wahba, G., Johnson, D.R., Gao, F., Gong, J., 1994. Adaptive tuning of numerical weather prediction models: Part I: randomized GCV and related methods in three and four dimensional data assimilation. Tech. Rep. 920, Dept of Statistics, University of Wisconsin, Madison, WI, 34 pp.
109. Wahba, G., Johnson, D.R., Gao, F., Gong, J., 1995. Adaptive tuning of numerical weather prediction models, randomized GCV in three and four dimensional data assimilation. Mon. Weather Rev. 123, 3358-3369.
110. Wang, Z., 1993. Variational data assimilation with 2-D shallow water equations and 3-D FSU global spectral models. Ph.D. Thesis, Dept. of Mathematics, Florida State University, Tallahassee, FL, 235 pp.
111. Wang, Z., Navon, I.M., Zou, X., Le Dimet, F.X., 1995. A truncated Newton optimization algorithm in meteorology applications with analytic Hessian/vector products. Comput. Optim. Appl. 4, 241-262.
112. Wergen, W., 1992. The effect of model errors in variational assimilation. Tellus 44A, 297-313.
113. Wunsch, C., 1996. The Ocean Circulation Inverse Problem. Cambridge University Press, 442 pp.
114. Yakowitz, S., Duckstein, L., 1980. Instability in aquifer identification: theory and case studies. Water Resour. Res. 16, 1045-1064.
115. Yeh, W.W.-G., 1986. Review of parameter estimation procedures in groundwater hydrology. Water Res. Rev. 22, 95-108.
116. Yu, L., 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.
117. Yu, L., O'Brien, J.J., 1992. On the initial condition in parameter estimation. J. Phys. Oceangr. 22, 1361-1364.
118. Zou, X., Navon, I.M., Le Dimet, F.X., 1992. An optimal nudging data assimilation scheme using parameter estimation. Q. J. R. Met. Soc. 118, 1163-1186.
119. Zou, X., Navon, I.M., Barcilon, A., Whittaker, J., Cacuci, D., 1993a. An adjoint sensitivity study of blocking in a two-layer isentropic model. Mon. Weather Rev. 121 (10), 2833-2857.
120. Zou, X., Navon, I.M., Berger, M., Phua, M.K., Schlick, T., Le Dimet, F.X., 1993b. Numerical experience with limited-memory, quasi-Newton methods for large-scale un-constrained nonlinear minimization. SIAM J. Optim. 3 (3), 582-608.