A Priori Identifiability of Unsaturated Soil Parameters
Publication: Journal of Irrigation and Drainage Engineering
Volume 126, Issue 3
Abstract
A priori identifiability (i.e., identifiability under perfect data) is a necessary condition for posteriori identifiability (i.e., identifiability under real data), and by implication a priori nonidentifiability is a sufficient condition for posteriori nonidentifiability. Therefore, it is important to prove a priori identifiability before attempting to estimate model parameters through nonlinear regression with real noisy data. This paper investigates the a priori (also called classical, structural, or deterministic) identifiability of soil parameters using Richards's equation with perfect distributed pressure data and prescribed initial and boundary conditions. The study of a priori identifiability is made possible through the concept of linear independence of vectors. As expected, it is shown that the unsaturated soil parameters are not a priori identifiable, and thus not posteriori identifiable, with either zero flow pressure data or steady-state flow pressure data. In addition, it is shown that models with more than two parameters are not a priori identifiable with transient pressure data. Therefore, models with more than two parameters are not posteriori identifiable with real pressure data regardless of the quantity and quality of this data. However, it is found that two parameter models are a priori identifiable with transient pressure data. Hence, the necessary condition for the posteriori identifiability of two parameter models is proven.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Abeliuk, R., and Wheater, H. S. (1990). “Parameter identification of solute transport models for unsaturated soils.” J. Hydro., Amsterdam, 117, 199–224.
2.
Brooks, R. H., and Corey, A. T. ( 1964). “Hydraulic properties of porous media.” Hydro. Paper 3, Colorado State University, Fort Collins, Colo.
3.
Celia, M. A., Bouloutas, E. T., and Zarba, R. L. (1990). “A general mass conservative numerical solution for the unsaturated flow equation.” Water Resour. Res., 26(7), 1483–1496.
4.
Chavent, G. ( 1979). “Identification of distributed parameter system: About the output least square method, its implementation, and identifiability.” Identification and system parameter estimation. I. Isermann, ed., Pergamon, New York, 85–97.
5.
Chavent, G. ( 1987). “Identifiability of parameters in the output least square formulation.” Identifiability of parametric models, E. Walter, ed., Pergamon, New York, 67–74.
6.
Dane, J. H., and Hruska, S. (1983). “In situ determination of soil hydraulic properties during drainage.” Soil Sci. Soc. Am. J., 47, 619–624.
7.
Gardner, W. R. (1958). “Some steady state solutions of unsaturated moisture flow equations with applications to evaporation from a water table.” Soil Sci., 85, 228–232.
8.
Godfrey, K. R., and DiStefano, J. J. ( 1987). “Identifiability of model parameters.” Identifiability of parametric models, E. Walter, ed., Pergamon, New York, 1–20.
9.
Hornung, U. (1983). “Identification of nonlinear soil physical parameters from an input-output experiment.” Proc., Workshop on Numer. Treatment of Inverse Problems in Differential and Integral Equations, 227–237.
10.
Karney, B. W., and Seneviratne, A. (1991). “Application of energy concepts to groundwater flow: Time step control and integrated sensitivity analysis.” Water Resour. Res., 27(12), 3225–3235.
11.
Kitamura, S., and Nakagiri, S. (1977). “Identifiability of spatially-varying and constant parameters in distributed systems of parabolic type.” SIAM J., 15(2), 785–802.
12.
Kool, J. B., and Parker, J. C. (1988). “Analysis of the inverse problem for transient unsaturated flow.” Water Resour. Res., 24(6), 817–830.
13.
Kool, J. B., Parker, J. C., and Van Genuchten, M. Th. (1985). “Determining soil hydraulic properties from one-step outflow experiments by parameter estimation. I. Theory and numerical studies.” Soil Sci. Soc. Am. J., 49, 1348–1354.
14.
Kool, J. B., Parker, J. C., and Van Genuchten, M. Th. (1987). “Parameter estimation for unsaturated flow and transport models—A review.” J. Hydro., Amsterdam, 91, 255–293.
15.
McCarthy, J. M., and Yeh, W. W.-G. (1990). “Optimal pumping test design for parameter estimation and prediction in groundwater hydrology.” Water Resour. Res., 26(4), 779–791.
16.
Mous, S. L. J. (1993). “Identification of the movement of water in unsaturated soils: The problem of identifiability of the model.” J. Hydro., Amsterdam, 143, 153–167.
17.
Mualem, Y. (1976). “A new model for predicting the hydraulic conductivity of porous media.” Water Resour. Res., 12, 513–522.
18.
Richards, L. A. (1931). “Capillary conduction of liquids through porous medium.” Physics, 1, 318–333.
19.
Russo, D. (1988). “Determining soil hydraulic properties by parameter estimation: On the selection of a model for the hydraulic properties.” Water Resour. Res., 24, 453–459.
20.
Russo, D., Bresler, E., Shani, U., and Parker, J. C. (1991). “Analyses of infiltration events in relation to determining soil hydraulic properties by inverse problem methodology.” Water Resour. Res., 27(6), 1361–1373.
21.
Vajda, S. ( 1987). “Identifiability of polynomial systems: Structural and numerical aspects.” Identifiability of parametric models, E. Walter, ed., Pergamon, New York, 42–49.
22.
Van Genuchten, M. Th. (1980). “A closed form equation for predicting the hydraulic conductivity of unsaturated soils.” Soil Sci. Soc. Am. Proc., 44, 892–898.
23.
Walter, E. (1982). Identifiability of state space models. Springer, New York.
24.
Walter, E. (1987). Identifiability of parametric models. Pergamon, New York.
25.
Wise, W. R., Clement, T. P., and Molz, F. J. (1994). “Variably saturated modeling of transient drainage: Sensitivity to soil properties.” J. Hydro., Amsterdam, 161, 91–108.
26.
Yeh, W. W.-G. (1986). “Review of parameter identification procedures in groundwater hydrology: The inverse problem.” Water Resour. Res., 22(2), 95–108.
27.
Yeh, W. W.-G., and Sun, N.-Z. (1984). “An extended identifiability in aquifer parameter identification and optimal pumping test design.” Water Resour. Res., 20(12), 1837–1847.
28.
Zachmann, D. W., Duchateau, P. C., and Klute, A. (1982). “Simultaneous approximation of water capacity and soil hydraulic conductivity by parameter identification.” Soil Sci., 134, 157–163.
29.
Zijlstra, J., and Dane, J. H. (1996). “Identification of hydraulic parameters in layered soils based on quasi-Newton method.” J. Hydro., Amsterdam, 181, 233–250.
Information & Authors
Information
Published In
Journal of Irrigation and Drainage Engineering
Volume 126 • Issue 3 • May 2000
Pages: 163 - 171
History
Received: May 21, 1998
Published online: May 1, 2000
Published in print: May 2000
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.