Coupled inverse modelling of groundwater flow and mass transport and the worth of concentration data

This paper presents the extension of the self-calibrating method to the coupled inverse modelling of groundwater flow and mass transport. The method generates equally likely solutions to the inverse problem that display the variability as observed in the field and are not affected by a linearisation of the state equations. Conditioning to the state variables is measured by an objective function including, among others, the mismatch between the simulated and measured concentrations. Conditioning is achieved by minimising the objective function by gradient-based methods. The gradient contains the partial derivatives of the objective function with respect to: log conductivities, log storativities, prescribed heads at boundaries, retardation coefficients and mass sources. The derivatives of the objective function with respect to log conductivity are the most cumbersome and need the most CPU-time to be evaluated. For this reason, to compute this derivative only advective transport is considered. The gradient is calculated by the adjoint-state method. The method is demonstrated in a controlled, synthetic study, in which the worth of concentration data is analysed. It is shown that concentration data are essential to improve transport predictions and also help to improve aquifer characterisation and flow predictions, especially in the upstream part of the aquifer, even in the case that a considerable amount of other experimental data like conductivities and heads are available. Besides, conditioning to concentration data reduces the ensemble variances of estimated transmissivity, hydraulic head and concentration.