Sensitivity of groundwater models with respect to variations in transmissivity and storage

Sensitivity analysis is the study of a system's response to various disturbances. In this study, disturbances of aquifer parameters are considered. In the simulation of an aquifer the investigator must establish tolerances within which the parameters of the physical system may vary without appreciably affecting the model results. By means of a first‐order sensitivity formalism it is shown how to evaluate the perturbed hydraulic head for a small change in aquifer parameter. An expression for the sensitivity coefficient is obtained in this study by taking the partial derivative of the flow equation with respect to a particular parameter. The sensitivity coefficient is evaluated either analytically or by numerical techniques for some common models. The sensitivity formalism is applied to the Theis equation to study the general behavior of sensitivity coefficients and to determine the range of validity of the first‐order sensitivity formalism. The formalism is also applied to one‐ and two‐dimensional numerical models to see the effect of barrier and constant head boundaries. The perturbed hydraulic head is obtained for a change of transmissivity ( T ) and storage coefficient ( S ) by applying the first‐order sensitivity formalism. This procedure should be a valuable tool in calibrating models or establishing tolerances on T and S for a given acceptable error in hydraulic head. In general, a ±20% deviation in T or S may be handled adequately by the first‐order formalism discussed in this work.