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Variational sensitivity analysis, data requirements, and parameter identification in a leaky aquifer system
Author(s) -
Yeh William W.G.,
Sun NeZheng
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/wr026i009p01927
Subject(s) - aquifer , sensitivity (control systems) , discretization , nonlinear system , aquifer properties , identification (biology) , mathematics , computer science , control theory (sociology) , mathematical optimization , geology , engineering , mathematical analysis , geotechnical engineering , groundwater , physics , botany , electronic engineering , biology , control (management) , quantum mechanics , groundwater recharge , artificial intelligence
The adjoint state sensitivity method is developed to aid the analysis of a pumping test design for parameter identification in a leaky aquifer system. The system considered consists of an unconfined aquifer overlaying an aquitard which overspreads a confined aquifer. The adjoint equations are derived in the continuous form without discretizing the governing equations and are expressed in terms of “convection‐diffusion” equations with time dependent coefficients. The multiple cell balance (MCB) method is used to solve the nonlinear governing equations as well as their adjoint equations. Algorithms are developed for calculating sensitivity coefficients of heads in each layer of an aquifer with respect to various parameters. A concept called “contribution of an observation” is introduced which can be used to measure the usefulness of an observation in connection with data requirements for parameter identification. It links experimental design with observation errors and the requirement of model application. The sufficiency of an observation system for parameter identification can be evaluated at the design stage before extensive resources are committed to data collection. A numerical example is given to verify the proposed method and to explain its applicability to the design of a pumping test.