An extended identifiability in aquifer parameter identification and optimal pumping test design

An extended identifiability, called “δ identifiability”, is developed for groundwater modeling and management. Some fundamental concepts are developed for establishing a criterion in connection with the problem of optimal experimental design, such as the design of an optimum pumping test to assist aquifer parameter identification. In practice, the quantity and quality of data prohibits a unique solution of the inverse problem of parameter identification. The proposed “δ identifiability” is based upon the concept of weak uniqueness. The determination of the admissibility of a given design is formulated as a nonlinear programming problem. The original constrained problem is transformed into solving a sequence of unconstrained problems by a penalty function method. Numerical experiments are conducted to illustrate the proposed concept and algorithm.