Sensitivity analysis of two-dimensional steady-state aquifer flow equations. Implications for groundwater flow model calibration and validation

This paper presents the analytical properties of the sensitivity of the two-dimensional, steady-state groundwater flow equation to the flow parameters and to the boundary conditions, based on the perturbation approach. These analytical properties are used to provide guidelines for model design, model calibration and monitoring network design. The sensitivity patterns are shown to depend on the nature of both the perturbed parameter and the variable investigated. Indeed, the sensitivity of the hydraulic head to the hydraulic conductivity extends mainly in the flow direction, while the sensitivity to the recharge spreads radially. Besides, the sensitivity of the flow longitudinal velocity to the hydraulic conductivity propagates in both the longitudinal and transverse directions, whereas the sensitivity of the flow transverse velocity propagates in the diagonal directions to the flow. The analytical results are confirmed by application examples on idealized and real-world simulations. These analytical findings allow some general rules to be established for model design, model calibration and monitoring network design. In particular, the optimal location of measurement points depends on the nature of the variable of interest. Measurement network design thus proves to be problem-dependent. Moreover, adequate monitoring well network design may allow to discriminate between the possible sources of error.