MF6-ADJ: A Non-Intrusive Adjoint Sensitivity Capability for MODFLOW 6

Adjoint sensitivity analysis provides an efficient alternative to direct methods when evaluating the influence of many uncertain parameters on a limited number of performance measures in hydrologic and hydrogeologic models. However, most adjoint implementations are "intrusive", requiring extensive modifications of the forward simulation code. This creates significant development and maintenance burdens that limit broad adoption. To address these needs, we present MF6-ADJ, a "non-intrusive" adjoint sensitivity capability for the MODFLOW 6 groundwater flow process that leverages the MODFLOW Application Programming Interface (API) to interact with the forward groundwater flow solution without altering its core code. MF6-ADJ supports both confined and unconfined flow conditions, structured and unstructured grids, and is compatible with both the Standard and Newton-Raphson solution schemes. It computes sensitivities of a wide range of general performance measures, including hydraulic heads, boundary fluxes, and weighted residuals, with respect to key model parameters such as hydraulic conductivity, storage coefficient, injection/extraction rate, recharge rate, boundary head, and boundary conductance. Sensitivities are computed at each node, enabling fine-grained diagnostic and calibration analysis. Validation against analytical solutions and the finite-difference perturbation method confirms excellent agreement, while demonstrating speedups ranging from hundreds to tens of thousands of times depending on grid discretization, since the adjoint state method computes sensitivities efficiently at the grid-block level. This non-intrusive design makes MF6-ADJ highly accessible and maintainable, offering efficient and scalable sensitivity analysis in complex groundwater modeling workflows.