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Further comments on sensitivities, parameter estimation, and sampling design in one‐dimensional analysis of solute transport in porous media
Author(s) -
Knopman Debra S.,
Voss Clifford I.
Publication year - 1988
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/wr024i002p00225
Subject(s) - sensitivity (control systems) , estimation theory , porous medium , boundary value problem , sampling (signal processing) , regression analysis , nonlinear regression , regression , inverse , statistics , mathematics , nonlinear system , biological system , computer science , porosity , mathematical analysis , physics , geology , engineering , geotechnical engineering , geometry , filter (signal processing) , quantum mechanics , electronic engineering , computer vision , biology
Sensitivities of solute concentration to parameters associated with first‐order chemical decay, boundary conditions, initial conditions, and multilayer transport are examined in one‐dimensional analytical models of transient solute transport in porous media. A sensitivity is a change in solute concentration resulting from a change in a model parameter. Sensitivity analysis is important because minimum information required in regression on chemical data for the estimation of model parameters by regression is expressed in terms of sensitivities. Nonlinear regression models of solute transport were tested on sets of noiseless observations from known models that exceeded the minimum sensitivity information requirements. Results demonstrate that the regression models consistently converged to the correct parameters when the initial sets of parameter values substantially deviated from the correct parameters. On the basis of the sensitivity analysis, several statements may be made about design of sampling for parameter estimation for the models examined: (1) estimation of parameters associated with solute transport in the individual layers of a multilayer system is possible even when solute concentrations in the individual layers are mixed in an observation well; (2) when estimating parameters in a decaying upstream boundary condition, observations are best made late in the passage of the front near a time chosen by adding the inverse of an hypothesized value of the source decay parameter to the estimated mean travel time at a given downstream location; (3) estimation of a first‐order chemical decay parameter requires observations to be made late in the passage of the front, preferably near a location corresponding to a travel time of times the half‐life of the solute; and (4) estimation of a parameter relating to spatial variability in an initial condition requires observations to be made early in time relative to passage of the solute front.