EFFECTS OF THE FORWARD MODEL NONLINEARITY ON THE INVERSE MODEL SOLUTION

The use of models to simulate complicated, dynamic processes often requires representing nonlinear interactions and boundary conditions. In these situations, obtaining reliable forward model solutions can be challenging. This work explores the impact of forward model nonlinearity on the inverse model solution. The questions posed are, 1) Does increased nonlinearity in the head solution (forward model) always result in increased nonlinearity of the inverse solution (estimation of hydraulic conductivity)? and 2) How does non-uniqueness in the forward model, which can be affected by solution method and starting guess, affect the inverse model? A simple groundwater-flow forward model is solved with both Picard and Newton iterations. The inverse model has both head and flow observations and is examined with UCODE-2005. Results show that the forward nonlinearity and inverse nonlinearity are separate and it is not universally true that increased forward model nonlinearity increases inverse model nonlinearity. However, nonlinearity in the forward model that manifests in the form of non-unique forward model solutions can 1) Cause sensitivity to the starting guess of the forward model, 2) Introduce local minima into the inverse model solution space, causing non-uniqueness, and, 3) Make the inverse problem more difficult to solve.