Optimal experimental design for parameter estimation in column outflow experiments -: art. no. 1186

Inverse modeling is increasingly used for water flow and reactive solute transport in the unsaturated zone to determine unknown parameters, e.g., soil hydraulic parameters, degradation rates or dispersion coefficients. However, experimental data are frequently not suitable for parameter estimation leading instead to practically singular estimation problems. Optimal experimental design aims at identifying experimental conditions and sampling schemes that deliver measurement data which are most sensitive to unknown parameters. A new numerical approach to optimize experimental designs for parameter estimation in coupled partial differential equations (PDEs) and ordinary differential equation (ODEs) arising from transport and degradation processes is presented. The optimal experimental design problem is embedded in the framework of optimal control theory. This results in an intricate, nonlinear, constrained optimization problem that is solved by a direct approach based on a structured SQP method. These methods are used to investigate several scenarios for a column outflow experiment in a simulation study. Simultaneously, experimental conditions, such as irrigation schemes, substance concentrations, and sampling schemes are optimized. Result is an enormous reduction of parameter uncertainty. Additionally, it is demonstrated that it is possible to estimate both soil hydraulic and solute transport parameters together in one experiment on the basis of leachate data only. The usefulness of the numerical approach for practical applications is discussed.