Predictive error dependencies when using pilot points and singular value decomposition in groundwater model calibration

Advances in Water Resources

Volumn 31, Issue 4, 2008, Pages 674-700

  Christensen, Steen ^a   Doherty, John ^b  

^a AARHUS UNIVERSITY   (Denmark)

^b Watermark Numerical Computing   (Australia)

Author keywords

Calibration; Nonlinearity; Parameter estimation; Pilot point; Prediction error; Singular value decomposition; Tikhonov regularization

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; ERRORS; FORECASTING; MATRIX ALGEBRA; PARAMETERIZATION; REGRESSION ANALYSIS; SENSITIVITY ANALYSIS; SINGULAR VALUE DECOMPOSITION;

GROUNDWATER MODEL CALIBRATION; NONLINEAR REGRESSION; PREDICTIVE ERROR; TIKHONOV REGULARIZATION;

GROUNDWATER;

EIGENVALUES AND EIGENFUNCTIONS; ERRORS; FORECASTING; GROUNDWATER; MATRIX ALGEBRA; PARAMETERIZATION; REGRESSION ANALYSIS; SENSITIVITY ANALYSIS; SINGULAR VALUE DECOMPOSITION;

CALIBRATION; EIGENVALUE; FLOW MODELING; GROUNDWATER FLOW; NONLINEARITY; PARAMETERIZATION; TRANSMISSIVITY;

EID: 40649102862     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2008.01.003     Document Type: Article

References (28)

1. A. Alcolea J. Carrera A. Medina Pilot points method incorporating prior information for solving the groundwater flow inverse problem Adv Water Resour 29 2006 1678 1689
2. Anderman ER, Hill MC, MODFLOW-2000. The U.S. geological survey modular ground-water model – documentation of the advective-transport observation (ADV2) package, version 2: U.S. Geological Survey Open-File Report 01-54; 2001. p. 69.
3. Carrera J. State of the art of the inverse problem applied to the flow and solute transport equations, In Groundwater flow and quality modelling, Custodio E, Gurgui A, Ferreira JPL, editors. NATO ASI series C, vol. 122;1987. pp. 549–84.
4. C. Certes G. de Marsily Application of the pilot point method to the identification of aquifer transmissivities Adv Water Resour 14 5 1991 284 300
5. Christensen S, Cooley RL. Experiences gained in testing a theory for modelling groundwater flow in heterogeneous media. In: Kovar K, Hrkal Z, editors. Calibration and reliability in groundwater modelling: a few steps closer to reality. Proc. ModelCARE’2002 (Prague, June 2002). IAHS Publ. no. 277; 2003. p. 22–7.
6. Christensen S, Cooley RL. User guide to the UNC1NLI1 package and three utility programs for computation of nonlinear confidence and prediction intervals using MODFLOW-2000. U.S. Geological Survey, Techniques and Methods Report 2004-1349, ; 2004.
7. Christensen S., Doherty J. Using many pilot points and singular value decomposition in groundwater model calibration. In Pre-published proceedings of ModelCARE’2007, sixth int. conf. on calibration and reliability in groundwater modelling – credibility in modelling, Copenhagen, Denmark, September 9–13, 2007. p. 448–53.
8. Christensen S, Moore C, Doherty J. Comparison of stochastic and regression based methods for quantification of predictive uncertainty of model-simulated wellhead protection zones in heterogeneous aquifers. In: Bierkens MFP, Gehrels JC, Kovar K, editors. Calibration and reliability in groundwater modelling: from uncertainty to decision making, (Proceedings of ModelCARE’2005, The Hague, The Netherlands, June 2005), IAHS Publ. 304; 2006. p. 202–8.
9. R.L. Cooley Incorporation of prior information on parameters into nonlinear regression groundwater flow models – 1. Theory Water Resour Res 18 4 1982 965 976
10. R.L. Cooley An analysis of the pilot point methodology for automated calibration of an ensemble of conditionally simulated transmissivity fields Water Resour Res 36 4 2000 1159 1163
11. Cooley RL. A theory for modeling ground-water flow in heterogeneous media. U.S. Geological Survey Professional Paper 1679; 2004. p. 220.
12. R.L. Cooley S. Christensen Bias and uncertainty in regression-calibrated models of groundwater flow in heterogeneous media Adv Water Resour 29 5 2006 639 656
13. J. Doherty PEST user manual 5th ed. 2007 Watermark Numerical Computing Brisbane, Queensland, Australia
14. J. Doherty Ground water model calibration using pilot points and regularization Ground Water 41 2 2003 170 177
15. J.J. Gómez-Hernández A. Sahuquillo J.E. Capilla Stocahstic simulation of transmissivity fields conditional to both transmissivity and piezometric data – I. Theory J Hydrol 203 1997 162 174
16. Harbaugh AW, Banta ER, Hill MC, McDonald MC, MODFLOW-2000. The U.S. geological survey modular ground-water model – user guide to modularization concepts and the ground-water flow process, U.S. Geological Survey, Open-File Report 00-92, Reston, Virginia; 2000. p. 121.
17. P.K. Kitanidis Introduction to geostatistics vol. 249 1997 Cambridge University New York p. 1997
18. K.R. Koch Parameter estimation and hypothesis testing in linear models 1987 Springer-Verlag Berlin
19. A.M. Lavenue J.F. Pickens Application of a coupled adjoint sensitivity and kriging approach to calibrate a groundwater flow model Water Resour Res 28 6 1992 1543 1569
20. D. McLaughlin L.R. Townley A reassessment of the groundwater inverse problem Water Resour Res 32 5 1996 1131 1161
21. de Marsily G. De l’identification des systèmes hydrogéologiques. Thèse d’Etat, Université Paris VI; 1978. p. 900.
22. G. de Marsily Spatial variability of properties in porous media: a stochastic approach J. Bear M.Y. Corapcioglu Fundamentals of transport phenomena in porous media NATO ASI Series E vol. 82 1984 Martinus Nijhof Publishers Boston 719 769
23. G. de Marsily G. Lavedan M. Boucher G. Fasanino Interpretation of interference tests in a well field using geostatistical techniques to fit the permeability distribution in a reservoir model G. Verly M. David A.G. Journel A. Marechal Geostatistics for Natural Resources Characterization – Part 2 NATO ASI Series C vol. 122 1984 D. Reidel Publishing Company Boston 831 849
24. Moore C, Doherty J. Role of the calibration process in reducing model predictive error. Water Resour Res 2005; 41 (5):Art. No. W05020.
25. S.P. Neuman S. Yakowitz A statistical approach to the inverse problem of aquifer hydrology – 1 Theory Water Resour Res 15 4 1979 845 860
26. W.H. Press S.A. Teukolsky W.T. Vetterling B.P. Flannery Numerical recipes in C 2nd ed. 1992 Cambridge University Press Cambridge, USA
27. B.S. Ramarao A.M. Lavenue G. de Marsily 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 1995 475 493
28. Tonkin MJ, Doherty J. A hybrid regularized inversion methodology for highly parameterized environmental models. Water Resour Res 2005; 41 (10):Art. No. W10412.