Error handling strategies in multiphase inverse modeling

Parameter estimation by inverse modeling involves the repeated evaluation of a function of residuals. These residuals represent both errors in the model and errors in the data. In practical applications of inverse modeling of multiphase flow and transport, the error structure of the final residuals often significantly deviates from the statistical assumptions that underlie standard maximum likelihood estimation using the least-squares method. Large random or systematic errors are likely to lead to convergence problems, biased parameter estimates, misleading uncertainty measures, or poor predictive capabilities of the calibrated model. The multiphase inverse modeling code iTOUGH2 supports strategies that identify and mitigate the impact of systematic or non-normal error structures. We discuss these approaches and provide an overview of the error handling features implemented in iTOUGH2.

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

[2]  D. Cox,et al.  An Analysis of Transformations , 1964 .

[3]  W. Bouten,et al.  Validity of First-Order Approximations to Describe Parameter Uncertainty in Soil Hydrologic Models , 2002 .

[4]  D. F. Andrews,et al.  Robust Estimates of Location: Survey and Advances. , 1975 .

[5]  Stefan Finsterle,et al.  A truncated Levenberg-Marquardt algorithm for the calibration of highly parameterized nonlinear models , 2011, Comput. Geosci..

[6]  C. J. Lawrence.  Robust estimates of location : survey and advances , 1975 .

[7]  S. P. Neuman,et al.  Estimation of Aquifer Parameters Under Transient and Steady State Conditions: 1. Maximum Likelihood Method Incorporating Prior Information , 1986 .

[8]  Stefan Finsterle,et al.  Multiphase Inverse Modeling: Review and iTOUGH2 Applications , 2004 .

[9]  G. Keller.  K-T boundary issues. , 1994, Science.

[10]  E. Somersalo,et al.  Statistical and computational inverse problems , 2004 .

[11]  Stefan Finsterle,et al.  Robust estimation of hydrogeologic model parameters , 1998 .

[12]  N Oreskes,et al.  Verification, Validation, and Confirmation of Numerical Models in the Earth Sciences , 1994, Science.

[13]  J. Craggs.  Applied Mathematical Sciences , 1973 .

[14]  S. Weisberg.  Applied Linear Regression , 1981 .

[15]  Stefan Finsterle,et al.  Joint Hydrological-Geophysical Inversion for Soil Structure Identification , 2006 .

[16]  A. Lehikoinen,et al.  Dynamic inversion for hydrological process monitoring with electrical resistance tomography under model uncertainties , 2010 .

[17]  Stefan Finsterle,et al.  Determining permeability of tight rock samples using inverse modeling , 1997 .

[18]  John Doherty,et al.  A short exploration of structural noise , 2010 .

[19]  Richard L. Cooley,et al.  A method of estimating parameters and assessing reliability for models of steady state Groundwater flow: 2. Application of statistical analysis , 1979 .