System identification and validation for output prediction of a dynamic hydrologic process

The paper presents an identification procedure for a dynamic model of am hydrologic process. The process involves solute transport in streams subject to aquifer interaction and unsteady flows and the intended use of the model is prediction. Detailed assumptions and results are provided to illustrate...

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Veröffentlicht in:	Journal of forecasting Jg. 10; H. 3; S. 319 - 346
Hauptverfasser:	Jakeman, A. J., Thomas, G. A., Dietrich, C. R.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Chichester John Wiley & Sons, Ltd 01.05.1991 Wiley Wiley Periodicals Inc
Schlagworte:	Algorithms Forecasts Hydrology Identification Instrumental variables Monte Carlo simulation Predictions Recursion Specification Statistical analysis Stochastic models Studies System identification Theory Validation Validity Water resources
ISSN:	0277-6693, 1099-131X
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Abstract	The paper presents an identification procedure for a dynamic model of am hydrologic process. The process involves solute transport in streams subject to aquifer interaction and unsteady flows and the intended use of the model is prediction. Detailed assumptions and results are provided to illustrate the level of comprehensive analysis required to assess model adequacy. The assessment procedure easily generalizes to any dynamic model which is linear‐in‐the‐parameters. As a fundamental tool, instrumental variable algorithms can be adopted which have a number of attractive features. These algorithms make both model‐order identification and specification among alternatives a straightforward task. They are known to be consistent estimators in the presence of a wide class of errors. It is seen that they can be made stable and robust in the presence of data outliers. Instrumental variable algorithms can also be used which are asymptotically efficient and provide a covariance matrix of parameter estimates. The paper shows how they aid the quantification of predictive uncertainty and investigates the validity of the underlying assumptions. Further, it illustrates that, when instrumental variable algorithms are used in recursive mode, they can be used not only as an additional tool to access model inadequacy but also as an aid to model improvements.
AbstractList	The paper presents an identification procedure for a dynamic model of am hydrologic process. The process involves solute transport in streams subject to aquifer interaction and unsteady flows and the intended use of the model is prediction. Detailed assumptions and results are provided to illustrate the level of comprehensive analysis required to assess model adequacy. The assessment procedure easily generalizes to any dynamic model which is linear‐in‐the‐parameters. As a fundamental tool, instrumental variable algorithms can be adopted which have a number of attractive features. These algorithms make both model‐order identification and specification among alternatives a straightforward task. They are known to be consistent estimators in the presence of a wide class of errors. It is seen that they can be made stable and robust in the presence of data outliers. Instrumental variable algorithms can also be used which are asymptotically efficient and provide a covariance matrix of parameter estimates. The paper shows how they aid the quantification of predictive uncertainty and investigates the validity of the underlying assumptions. Further, it illustrates that, when instrumental variable algorithms are used in recursive mode, they can be used not only as an additional tool to access model inadequacy but also as an aid to model improvements. An identification procedure for a dynamic model of a hydrologic process is presented. The process involves solute transport in streams subject to aquifer interaction and unsteady flows. Detailed assumptions and results are provided to illustrate the level of comprehensive analysis required to assess model adequacy. The assessment procedure easily generalizes to any dynamic model that is linear-in-the-parameters. As a fundamental tool, instrumental variable algorithms that have a number of attractive features can be adopted. These algorithms make both model-order identification and specification among alternatives a straightforward task. The results show that, when instrumental variable algorithms are used in recursive mode, they can be used not only as an additional tool to asses model inadequacy but also as an aid to model improvements.
Author	Jakeman, A. J. Thomas, G. A. Dietrich, C. R.
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Cites_doi	10.1080/00207178108922540 10.1109/TSMC.1980.4308363 10.1080/00207177908922676 10.1016/0005-1098(78)90079-1 10.1016/0005-1098(80)90037-0 10.1007/BFb0009019 10.1080/00207178308933046 10.1080/00207177008905958 10.1029/WR025i010p02171 10.1080/00207177908922724 10.1016/0022-1694(86)90094-6 10.1007/978-3-642-82336-7 10.1016/0005-1098(71)90059-8 10.1093/biomet/59.1.73
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References	Dietrich, C. R., Jakeman, A. J. and Thomas, G. A., 'Statistical models for solute travel time', Journal of Hydrology, 88 (1986), 253-74. Jakeman, A. J. and Young, P. C., 'Refined instrumental variable methods of recursive time-series analysis. Part II: Multivariable systems', Int. J. Control, 29 (1979), 621-44. Jakeman, A. J. and Young, P. C., 'Advanced methods of recursive time series analysis', Int. J. Control, 37 (1983), 1291-1310. Pierce, D. A., 'Least squares estimation in dynamic disturbance time-series models', Biometrika, 59 (1972), 73-8. Dietrich, C. R., Jakeman, A. J. and Thomas, G. A., 'A dynamic model for solute transport in a stream-aquifer system, 1. Derivation of a dynamic model', Water Resources Research, 25 (1989), 2171-2176. Jakeman, A. J. and Young, P. C., 'On the decoupling of system and noise model parameter estimation in time series analysis', Int. J. Control, 34 (1981), 423-31. Box, G. E. P. and Jenkins, G. M., Time Series Analysis, Forecasting and Control, revised edition, San Francisco: Holden-Day, 1976. Astrom, K. J. and Eykhoff, P., 'System identificationa survey', Automatica, 7 (1971), 123-32. Young, P. C., Recursive Estimation and Time Series Analysis: an Introduction, Berlin: Springer-Verlag, 1984. Wellstead, P. E., 'An instrumental product model test for model order estimation', Automatica, 14 (1980), 89-91. Young, P. C. and Jakeman, A. J. 'Refined instrumental variable methods of recursive time-series analysis. Part 1: Single input, single output systems', Int. J. Control, 29 (1979), 1-30. Young, P. C., Jakeman, A. J. and McMurtrie, R. E. 'An instrumental variable method for model order identification'. Automatica, 16 (1980), 281-94. 1980; 16 1971; 7 1979; 29 1980; 14 1985; 1 1986; 88 1965 1976 1985 1984 1972 1979; 2 1983 1970 1980 1983; 37 1989; 25 1983; 57 1981; 34 1989 1988 1977 1972; 59 Box G. E. P. (e_1_2_1_5_1) 1976 Young P. C. (e_1_2_1_23_1) 1985 Jakeman A. J. (e_1_2_1_8_1) 1979 e_1_2_1_7_1 e_1_2_1_20_1 Akaike H. (e_1_2_1_2_1) 1972 e_1_2_1_6_1 Jakeman A. J. (e_1_2_1_9_1) 1985 e_1_2_1_12_1 e_1_2_1_4_1 e_1_2_1_13_1 e_1_2_1_24_1 e_1_2_1_10_1 e_1_2_1_21_1 e_1_2_1_11_1 e_1_2_1_22_1 e_1_2_1_16_1 e_1_2_1_17_1 e_1_2_1_14_1 e_1_2_1_25_1 e_1_2_1_15_1 Astrom K. J. (e_1_2_1_3_1) 1965 e_1_2_1_18_1 e_1_2_1_19_1
References_xml	– reference: Dietrich, C. R., Jakeman, A. J. and Thomas, G. A., 'Statistical models for solute travel time', Journal of Hydrology, 88 (1986), 253-74. – reference: Young, P. C., Jakeman, A. J. and McMurtrie, R. E. 'An instrumental variable method for model order identification'. Automatica, 16 (1980), 281-94. – reference: Young, P. C. and Jakeman, A. J. 'Refined instrumental variable methods of recursive time-series analysis. Part 1: Single input, single output systems', Int. J. Control, 29 (1979), 1-30. – reference: Pierce, D. A., 'Least squares estimation in dynamic disturbance time-series models', Biometrika, 59 (1972), 73-8. – reference: Young, P. C., Recursive Estimation and Time Series Analysis: an Introduction, Berlin: Springer-Verlag, 1984. – reference: Astrom, K. J. and Eykhoff, P., 'System identificationa survey', Automatica, 7 (1971), 123-32. – reference: Jakeman, A. J. and Young, P. C., 'Refined instrumental variable methods of recursive time-series analysis. Part II: Multivariable systems', Int. J. Control, 29 (1979), 621-44. – reference: Wellstead, P. E., 'An instrumental product model test for model order estimation', Automatica, 14 (1980), 89-91. – reference: Box, G. E. P. and Jenkins, G. M., Time Series Analysis, Forecasting and Control, revised edition, San Francisco: Holden-Day, 1976. – reference: Dietrich, C. R., Jakeman, A. J. and Thomas, G. A., 'A dynamic model for solute transport in a stream-aquifer system, 1. Derivation of a dynamic model', Water Resources Research, 25 (1989), 2171-2176. – reference: Jakeman, A. J. and Young, P. C., 'Advanced methods of recursive time series analysis', Int. J. Control, 37 (1983), 1291-1310. – reference: Jakeman, A. J. and Young, P. C., 'On the decoupling of system and noise model parameter estimation in time series analysis', Int. J. Control, 34 (1981), 423-31. – volume: 88 start-page: 253 year: 1986 end-page: 74 article-title: Statistical models for solute travel time publication-title: Journal of Hydrology – year: 1985 – year: 1983 – volume: 16 start-page: 281 year: 1980 end-page: 94 article-title: An instrumental variable method for model order identification publication-title: Automatica – start-page: 771 year: 1970 end-page: 8 – year: 1984 – volume: 2 start-page: 1219 year: 1979 end-page: 25 – volume: 59 start-page: 73 year: 1972 end-page: 8 article-title: Least squares estimation in dynamic disturbance time‐series models publication-title: Biometrika – volume: 34 start-page: 423 year: 1981 end-page: 31 article-title: On the decoupling of system and noise model parameter estimation in time series analysis publication-title: Int. J. Control – volume: 57 year: 1983 – year: 1965 – volume: 7 start-page: 123 year: 1971 end-page: 32 article-title: System identificationa survey publication-title: Automatica – volume: 29 start-page: 1 year: 1979 end-page: 30 article-title: Refined instrumental variable methods of recursive time‐series analysis. Part 1: Single input, single output systems publication-title: Int. J. Control – year: 1988 – year: 1989 – start-page: 593 year: 1980 end-page: 602 – volume: 25 start-page: 2171 year: 1989 end-page: 2176 article-title: A dynamic model for solute transport in a stream‐aquifer system, 1. Derivation of a dynamic model publication-title: Water Resources Research – volume: 37 start-page: 1291 year: 1983 end-page: 1310 article-title: Advanced methods of recursive time series analysis publication-title: Int. J. Control – volume: 14 start-page: 89 year: 1980 end-page: 91 article-title: An instrumental product model test for model order estimation publication-title: Automatica – year: 1977 – year: 1976 – volume: 1 start-page: 445 year: 1985 end-page: 50 – volume: 29 start-page: 621 year: 1979 end-page: 44 article-title: Refined instrumental variable methods of recursive time‐series analysis. Part II: Multivariable systems publication-title: Int. J. Control – start-page: 249 year: 1972 end-page: 50 – volume-title: Theory of Self Adaptive Systems year: 1965 ident: e_1_2_1_3_1 – ident: e_1_2_1_12_1 doi: 10.1080/00207178108922540 – ident: e_1_2_1_14_1 doi: 10.1109/TSMC.1980.4308363 – ident: e_1_2_1_24_1 doi: 10.1080/00207177908922676 – ident: e_1_2_1_17_1 – ident: e_1_2_1_21_1 doi: 10.1016/0005-1098(78)90079-1 – ident: e_1_2_1_25_1 doi: 10.1016/0005-1098(80)90037-0 – ident: e_1_2_1_19_1 doi: 10.1007/BFb0009019 – start-page: 249 volume-title: Proceedings of the Fifth Hawaii International Conference on Systems Science year: 1972 ident: e_1_2_1_2_1 – volume-title: Time Series Analysis, Forecasting and Control year: 1976 ident: e_1_2_1_5_1 – ident: e_1_2_1_13_1 doi: 10.1080/00207178308933046 – start-page: 445 volume-title: 7th IFAC Symposium on Identification and System Parameter Estimation, York year: 1985 ident: e_1_2_1_9_1 – start-page: 1219 volume-title: 5th IFAC Symposium on Identification and System Parameter Estimation, Darmstadt year: 1979 ident: e_1_2_1_8_1 – ident: e_1_2_1_16_1 – ident: e_1_2_1_20_1 doi: 10.1080/00207177008905958 – ident: e_1_2_1_7_1 doi: 10.1029/WR025i010p02171 – ident: e_1_2_1_11_1 doi: 10.1080/00207177908922724 – ident: e_1_2_1_6_1 doi: 10.1016/0022-1694(86)90094-6 – ident: e_1_2_1_22_1 doi: 10.1007/978-3-642-82336-7 – ident: e_1_2_1_4_1 doi: 10.1016/0005-1098(71)90059-8 – ident: e_1_2_1_10_1 – year: 1985 ident: e_1_2_1_23_1 – ident: e_1_2_1_18_1 doi: 10.1093/biomet/59.1.73 – ident: e_1_2_1_15_1
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Snippet	The paper presents an identification procedure for a dynamic model of am hydrologic process. The process involves solute transport in streams subject to... An identification procedure for a dynamic model of a hydrologic process is presented. The process involves solute transport in streams subject to aquifer...
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SubjectTerms	Algorithms Forecasts Hydrology Identification Instrumental variables Monte Carlo simulation Predictions Recursion Specification Statistical analysis Stochastic models Studies System identification Theory Validation Validity Water resources
Title	System identification and validation for output prediction of a dynamic hydrologic process
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