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Coupled inverse problems in groundwater modeling: 2. Identifiability and experimental design
Author(s) -
Sun NeZheng,
Yeh William W.G.
Publication year - 1990
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr026i010p02527
Subject(s) - identifiability , equivalence (formal languages) , uniqueness , mathematics , mathematical optimization , salient , context (archaeology) , inverse , computer science , statistics , mathematical analysis , artificial intelligence , geometry , paleontology , discrete mathematics , biology
Parameter identifiability and experimental design in the context of solving the coupled inverse problem in groundwater modeling are considered in part 2 of the two‐paper series. The following three new definitions of extended identifiability for a distributed parameter system are presented: interval identifiability (INI), prediction equivalence identifiability (PEI), and management equivalence identifiability (MEI). The uniqueness requirement of the inverse solution is relaxed by these definitions. An identified parameter is said to be extendedly identifiable if it is able to satisfy an accuracy requirement in a specific application of the model. When a generalized least squares norm is used, the proposed identifiabilities are applicable to any coupled problems in which the state variables and parameters may have different order of magnitudes. A salient feature of the new definitions is that the extended identifiabilities are closely related to experimental design. Consequently, the sufficiency of an experimental design for assuring a given level of an extended identifiability can be estimated prior to field experiments. The methodology developed can be used to determine the reliability of an experimental design even for nonlinear models. A numerical example on the management of a wastewater disposal is given to explain how the concepts and methods presented in this paper can be used for solving practical problems.