Predictive error analysis for a water resource management model

In calibrating a model, a set of parameters is assigned to the model which will be employed for the making of all future predictions. If these parameters are estimated through solution of an inverse problem, formulated to be property posed through either pre-calibration or mathematical regularisation, then solution of this inverse problem will, of necessity, lead to a simplified parameter set that omits the details of reality, while still fitting historical data acceptably well Furthermore, estimates of parameters so obtained will be contaminated by measurement noise. Both of these phenomena will lead to errors in predictions made by the model, with the potential for error increasing with the hydraulic property detail on which the prediction depends. Integrity of model usage demands that model predictions be accompanied by some estimate of the possible errors associated with them. The present paper applies theory developed in a previous work to the analysis of predictive error associated with a real world, water resource management model. The analysis offers many challenges, including the fact that the model is a complex one that was partly calibrated by hand. Nevertheless, it is typical of models which are commonly employed as the basis for the making of important decisions, and for which such an analysis must be made. The potential errors associated with point-based and averaged water level and creek inflow predictions are examined, together with the dependence of these errors on the amount of averaging involved. Error variances associated with predictions made by the existing model are compared with "optimized error variances" that could have been obtained had calibration been undertaken in such a way as to minimize predictive error variance. The contributions by different parameter types to the overall error variance of selected predictions are also examined. (c) 2006 Elsevier B.V. All rights reserved.

[1]  S. Constable,et al.  Occam's inversion to generate smooth, two-dimensional models from magnetotelluric data , 1990 .

[2]  T.-C. Jim Yeh,et al.  Stochastic modelling of groundwater flow and solute transport in aquifers , 1992 .

[3]  Arlen W. Harbaugh,et al.  MODFLOW-2000, The U.S. Geological Survey Modular Ground-Water Model - User Guide to Modularization Concepts and the Ground-Water Flow Process , 2000 .

[4]  J. Doherty,et al.  Role of the calibration process in reducing model predictive error , 2005 .

[5]  Mary C. Hill,et al.  Analysis of accuracy of approximate, simultaneous, nonlinear confidence intervals on hydraulic heads in analytical and numerical test cases , 1989 .

[6]  Catherine Moore.  The use of regularized inversion in groundwater model calibration and prediction uncertainty analysis , 2006 .

[7]  J. Doherty,et al.  A hybrid regularized inversion methodology for highly parameterized environmental models , 2005 .

[8]  Andres Alcolea,et al.  Inverse problem in hydrogeology , 2005 .

[9]  R. L. Cooley.  A theory for modeling ground-water flow in heterogeneous media , 2004 .

[10]  J. Gómez-Hernández,et al.  Stochastic conditional inverse modeling of subsurface mass transport: A brief review and the self-calibrating method , 2003 .

[11]  D. A. Zimmerman,et al.  A comparison of seven geostatistically based inverse approaches to estimate transmissivities for modeling advective transport by groundwater flow , 1998 .

[12]  Peter K. Kitanidis,et al.  Recent advances in geostatistical inference on hydrogeological variables (95RG00183) , 1995 .

[13]  J. Carrera,et al.  On geostatistical formulations of the groundwater flow inverse problem , 1991 .

[14]  Richard L. Cooley,et al.  Simultaneous confidence and prediction intervals for nonlinear regression models with application to a groundwater flow model , 1987 .

[15]  Catherine Certes,et al.  Application of the pilot point method to the identification of aquifer transmissivities , 1991 .

[16]  Allan L. Gutjahr,et al.  Spatial variability in subsurface flow and transport: a review , 1993 .

[17]  K. El Harrouni,et al.  Uncertainty analysis of groundwater flow with DRBEM , 1997 .

[18]  J. Doherty,et al.  The cost of uniqueness in groundwater model calibration , 2006 .

[19]  Steen Christensen,et al.  Evaluation of prediction intervals for expressing uncertainties in groundwater flow model predictions , 1999 .

[20]  E. Poeter,et al.  Documentation of UCODE; a computer code for universal inverse modeling , 1998 .

[21]  John Doherty,et al.  Ground Water Model Calibration Using Pilot Points and Regularization , 2003, Ground water.

[22]  Steen Christensen,et al.  User guide to the UNC process and three utility programs for computation of nonlinear confidence and prediction intervals using MODFLOW-2000 , 2006 .