Analytical sensitivity analysis of transient groundwater flow in a bounded model domain using the adjoint method. Issue 7 (3rd July 2015)

• Record Type: Journal Article
• Authors: Lu, Zhiming; Vesselinov, Velimir V.
• Is Part Of: Water resources research. Volume 51:Issue 7(2015:Jul.)
• Page Start: 5060
• Page End: 5080
• Publication Date: 2015-07-03
• Subjects: sensitivity analysis -- adjoint method -- analytical solutions -- transient flow; Hydrology -- Periodicals; 333.91
• DOI: 10.1002/2014WR016819
• Languages: English
• ISSNs: 0043-1397

Abstract

Abstract: Sensitivity analyses are an important component of any modeling exercise. We have developed an analytical methodology based on the adjoint method to compute sensitivities of a state variable (hydraulic head) to model parameters (hydraulic conductivity and storage coefficient) for transient groundwater flow in a confined and randomly heterogeneous aquifer under ambient and pumping conditions. For a special case of two‐dimensional rectangular domains, these sensitivities are represented in terms of the problem configuration (the domain size, boundary configuration, medium properties, pumping schedules and rates, and observation locations and times), and there is no need to actually solve the adjoint equations. As an example, we present analyses of the obtained solution for typical groundwater flow conditions. Analytical solutions allow us to calculate sensitivities efficiently, which can be useful for model‐based analyses such as parameter estimation, data‐worth evaluation, and optimal experimental design related to sampling frequency and locations of observation wells. The analytical approach is not limited to groundwater applications but can be extended to any other mathematical problem with similar governing equations and under similar conceptual conditions. Key Points: Analytic approach to compute transient sensitivities using the adjoint method Model parameters include distributed transmissivity and storativity Parameter fields can be correlated or uncorrelated