A proposed stepwise regression method for model structure identification

Water Resources Research

Volumn 34, Issue 10, 1998, Pages 2561-2572

  Sun, Ne Zheng ^a,b   Yang, Shu Li ^a,b   Yeh, William W G ^a,b  

^a Los Angeles   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GROUNDWATER; METHODOLOGY; MODELING; REGRESSION ANALYSIS; REMEDIATION;

AQUIFERS; ERRORS; GROUNDWATER; GROUNDWATER RESOURCES; ITERATIVE METHODS; MODEL STRUCTURES; PROBLEM SOLVING; REGRESSION ANALYSIS; WATER QUALITY;

APPROPRIATE MODELS; GROUNDWATER MODELS; HOMOGENEOUS MODELS; MANAGEMENT PROBLEMS; OBSERVATION ERRORS; QUALITY CONSTRAINTS; STEPWISE REGRESSION METHOD; STRUCTURE IDENTIFICATION;

INVERSE PROBLEMS;

EID: 0031690045     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/98WR01860     Document Type: Article

References (41)

1. Akaike, H., Information theory and an extension of the maximum likelihood principle, in Proceedings of the 2nd International Symposium on Information Theory, edited by B. N. Petrov and F. Csaki, pp. 267-281, Akad. Kiado, Budapest, 1972.
2. Bollout, H., Stability result for the inverse transmissivity problem, J. Math. Anal. Appl., 168, 13-27, 1992.
3. Carrera, J., and S. P. Neuman, Estimation of aquifer parameters under transient and steady state conditions, 3, Application to synthetic and field data, Water Resour. Res., 22(2), 228-242, 1986.
4. Chapman, M. J., and K. R. Godfrey, On structural equivalence and identifiability constraint ordering, in Identifiability of Parametric Models, edited by E. Walter, chap. 3, pp. 32-39, Pergamon, Tarrytown, N. Y., 1987.
5. Chavent, G., M. Dupuy, and P. Lemonnier, History matching by use of optimal theory, Soc. Pet. Eng. J., 15(1), 74-86, 1975.
6. Coleman, T. F., A note on new algorithms for constrained minmax optimization, Math. Programming, 15, 239-242, 1978.
7. Cooley, R. L., Incorporation of prior information on parameters into nonlinear regression groundwater flow models, 1, Theory, Water Resour. Res., 18(4), 965-976, 1982.
8. Dagan, G., Stochastic modeling of groundwater flow by unconditional and conditional probabilities: The inverse problem, Water Resour. Res., 21(1), 65-72, 1985.
9. Emsellem, Y., and G. de Marsily, An automatic solution for the inverse problem, Water Resour. Res., 7(5), 1264-1283, 1971.
10. Eppstein, M. J., and D. E. Dougherty, Simultaneous estimation of transmissivity values and zonation, Water Resour. Res., 32(11), 3321-3336, 1996.
11. Ezzedine, S., and Y. Rubin, A geostatistical approach to conditional estimation of spatially distributed solute concentration and notes on the use of tracer data in the inverse problem, Water Resour. Res., 32(4), 853-862, 1996.
12. Haber, R., and H. Unbehauen, Structure identification of nonlinear dynamic systems - A survey on input/output approaches, Automatica, 26(4), 651-677, 1990.
13. Haest, M., G. Bastin, M. Gevers, and V. Wertz, A branch-and-bound approach to the identification problem, in Identification and System Parameter Estimation 1991, vol. 2, IFAC Symp. Ser., vol. 3, edited by C. Banyasz and L. Keviczky, pp. 1061-1066, Pergamon, Tarrytown, N. Y., 1992.
14. Hoeksema, R. J., and P. K. Kitanidis, Comparison of Gaussian conditional mean and Kriging estimation in the geostatistical solution of the inverse problem, Water Resour. Res., 21(6), 825-836, 1985.
15. Hyndman, D. W., and S. M. Gorelick, Estimating lithologie and transport properties in three dimensions using seismic and tracer data: The Kesterson aquifer, Water Resour. Res., 32(9), 2659-2670, 1996.
16. Kitanidis, P., Quasi-linear geostatistical theory for inversing, Water Resour. Res., 31(10), 2411-2420, 1995.
17. Kitanidis, P. K., and E. G. Vomvoris, A geostatistical approach to the inverse problem in groundwater modeling (steady state) and one-dimensional simulations, Water Resour. Res., 19(3), 677-690, 1983.
18. Koltermann, C. E., and S. M. Gorelick, Heterogeneity in sedimentary: A review of structure-imitating, process-imitating, and descriptive approaches, Water Resour. Res., 32(9), 2617-2658, 1996.
19. Loaiciga, H. A., and M. A. Marino, The inverse problem for confined flow: Identification and estimation with extension, Water Resour. Res., 23(1), 92-104, 1987.
20. Loaiciga, H. A., R. B. Laipnik, P. K. Herdak, and M. A. Marino, Effective hydraulic conductivity of nonstationary aquifers, Stochastic Hydrol. Hydraulics, 8(1), 1-17, 1994.
21. McLaughlin, D., and L. R. Townley, A reassessment of the groundwater inverse problem, Water Resour. Res., 32(5), 1131-1162, 1996.
22. Neuman, S. P., Calibration of distributed parameter groundwater flow models viewed as a multiple-objective decision process under uncertainty, Water Resour. Res., 9(4), 1006-1021, 1973.
23. Poeter, E. P., and M. C. Hill, Inverse models: A necessary next step in ground-water modeling, Ground Water, 35(2), 250-260, 1997.
24. RamaRoa, B. S., M. A. LaVenue, G. de Marsily, and M. G. Marietta, Pilot point methodology for automated calibration of an ensemble of conditionally simulated transmissivity fields, 1, Theory and computational experiments, Water Resour. Res., 31(3), 475-493, 1995.
25. Rubin, Y., and G. Dagan, Stochastic identification of transmissivity and effective recharge in steady groundwater flow, 1, Theory, Water Resour. Res., 23(7), 1185-1192, 1992.
26. Rubin, Y., G. Mavko, and J. Harris, Mapping permeability in heterogeneous aquifers using hydrologie and seismic data, Water Resour. Res., 28(7), 1809-1816, 1992.
27. Rustem, B., A constrained min-max algorithm for rival models of the same economic system, Mathematical Programming, 53, 279-295, 1992.
28. Shah, P. C., G. R. Gavalas, and J. H. Seinfeld, Error analysis in history matching: The optimum level of parameterization, Soc. Pet. Eng. J., 18(3), 219-228, 1978.
29. Sun, N.-Z., Inverse Problems in Groundwater Modeling, Kluwer Acad., Norwell, Mass., 1994.
30. Sun, N.-Z., Identification and reduction of model structure for modeling distributed parameter systems, in Parameter Identification and Inverse Problems in Hydrology, Geology and Ecology, edited by J. Gottlieb and P. DuChateau, Kluwer Acad., Norwell, Mass., 1996.
31. Sun, N.-Z., and W. W-G. Yeh, Identification of parameter structure in groundwater inverse problem, Water Resour. Res., 21(6), 869-883, 1985.
32. Sun, N.-Z., and W. W-G. Yeh, Coupled inverse problem in groundwater modeling, 1, Sensitivity analysis and parameter identification, Water Resour. Res., 26(10), 2507-2525, 1990.
33. Sun, N.-Z., and W. W-G. Yeh, A stochastic inverse solution for transient groundwater flow: Parameter identification and reliability analysis, Water Resour. Res., 28(12), 3269-3280, 1992.
34. Sun, N.-Z., M-C. Jeng, and W. W-G. Yeh, A proposed geological parameterization method for parameter identification in three-dimensional groundwater modeling, Water Resour. Res., 31(1), 89-102, 1995.
35. Xiang, Y., J. F. Sykes, and N. R. Thomson, A composite L, parameter estimator for model fitting in groundwater flow and solute transport simulation, Water Resour. Res., 29(6), 1661-1674, 1993.
36. Yeh, J. T.-C., and J. Zhang, A geostatistical inverse method for variably saturated flow in the vadose zone, Water Resour. Res., 32(9), 2757-2766, 1996.
37. Yeh, W. W-G., Review of parameter identification procedures in groundwater hydrology: The inverse problem, Water Resour. Res., 22(2), 95-108, 1986.
38. Yeh, W. W-G., and Y. S. Yoon, A systematic optimization procedure for the identification of inhomogeneous aquifer parameters, Advances in Groundwater Hydrology, edited by Z. A. Saleen, American Water Resources Association, 72-82, 1976.
39. Yeh, W. W-G., and Y. S. Yoon, Aquifer parameter identification with optimum dimension in parameterization, Water Resour. Res., 17(3), 664-672, 1981.
40. Yeh, W. W-G., Y. S. Yoon, and K. S. Lee, Aquifer parameter identification with Kriging and optimum parameterization, Water Resour. Res., 19(1), 225-233, 1983.
41. Zheng, C., and P. Wang, Parameter structure identification using tabu search and simulated annealing, Adv. Water Resour., 19(4), 215-224, 1996.