Automatic Differentiation: A Powerful Device for the Estimation of Hydraulic Parameters

Our aim is to estimate the hydraulic transmission parameter T, in the confined aquifer equation: [1] ∂ / ∂ x}( T ∂ h} / ∂ x}) + ∂ / ∂ y}( T ∂ h} / ∂ y})=S ∂ h} / ∂ t}+q,

which is typical case of an ill posed inverse problem. A widely used strategy to solve (1) in practice is to estimate T as the T0 solution of a certain kind of a nonlinear optimization problem such as: [2] minT F(T), F(T)= | hk(T)-h0 |2,

where h0 is a real observations vector and hk(T) is the solution of (1) related to the actual Tk solution of (2), obtained by some iterative process.

We shall present computational results of estimating T for the cuban Ariguanabo aquifer, emphasizing the use of automatic differentiation to solve the optimization problem (2), by comparing this alternative with the use of the divided differences method.