Volume 8 Issue 3
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Article Navigation >  Water Science and Engineering  > 2015  >  8(3): 175-194
Tian-chyi J. Yeh, De-qiang Mao, Yuan-yuan Zha, Jet-chau Wen, Li Wan, Kuo-chin Hsu, Cheng-haw Lee. 2015: Uniqueness, scale, and resolution issues in groundwater model parameter identification. Water Science and Engineering, 8(3): 175-194. doi: 10.1016/j.wse.2015.08.002
Citation: Tian-chyi J. Yeh, De-qiang Mao, Yuan-yuan Zha, Jet-chau Wen, Li Wan, Kuo-chin Hsu, Cheng-haw Lee. 2015: Uniqueness, scale, and resolution issues in groundwater model parameter identification. Water Science and Engineering, 8(3): 175-194. doi: 10.1016/j.wse.2015.08.002
shu

Uniqueness, scale, and resolution issues in groundwater model parameter identification

doi: 10.1016/j.wse.2015.08.002
  • a.

    Department of Hydrology and Water Resources, The University of Arizona, Tucson 85721, USA

  • b. Department of Resources Engineering, National Cheng Kung University, Tainan 701, PR China

  • c. Department of Geophysics, Colorado School of Mines, Golden 80401, USA

  • d. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, PR China

  • e. Department of Safety Health and Environmental Engineering, National Yunlin University of Science and Technology, Touliu 64002, PR China

  • f. Research Center for Soil & Water Resources and Natural Disaster Prevention, National Yunlin University of Science and Technology, Touliu 64002, PR China.

Funds:  This work was supported by the Strategic Environmental Research and Development Program (Grant No. ER-1365), the Environmental Security and Technology Certification Program (Grant No. ER201212), and the Earth Sciences of the National Science Foundation (Grant No. 1014594).
More Information
  • Corresponding author: Tian-chyi J. Yeh
  • Received Date: 2015-06-19
  • Rev Recd Date: 2015-07-17
    Abstract
  • This paper first visits uniqueness, scale, and resolution issues in groundwater flow forward modeling problems. It then makes the point that non-unique solutions to groundwater flow inverse problems arise from a lack of information necessary to make the problems well defined. Subsequently, it presents the necessary conditions for a well-defined inverse problem. They are full specifications of (1) flux boundaries and sources/sinks, and (2) heads everywhere in the domain at at least three times (one of which is t = 0), with head change everywhere at those times must being nonzero for transient flow. Numerical experiments are presented to corroborate the fact that, once the necessary conditions are met, the inverse problem has a unique solution. We also demonstrate that measurement noise, instability, and sensitivity are issues related to solution techniques rather than the inverse problems themselves. In addition, we show that a mathematically well-defined inverse problem, based on an equivalent homogeneous or a layered conceptual model, may yield physically incorrect and scenario-dependent parameter values. These issues are attributed to inconsistency between the scale of the head observed and that implied by these models. Such issues can be reduced only if a sufficiently large number of observation wells are used in the equivalent homogeneous domain or each layer. With a large number of wells, we then show that increase in parameterization can lead to a higher-resolution depiction of heterogeneity if an appropriate inverse methodology is used. Furthermore, we illustrate that, using the same number of wells, a highly parameterized model in conjunction with hydraulic tomography can yield better characterization of the aquifer and minimize the scale and scenario-dependent problems. Lastly, benefits of the highly parameterized model and hydraulic tomography are tested according to their ability to improve predictions of aquifer responses induced by independent stresses not used in the inverse modeling efforts.

     

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