Nonlinear System Engineering Techniques Applied to the Fuenmayor Karst Spring, Huesca (Spain)

Fuenmayor is a modest karst spring that tapes a small limestone aquifer near Huesca, Spain. A previous paper proposes a transfer function between effective rainfall and discharge concluding that Fuenmayor has an acceptable linear response. However, the linear model does not estimate adequately the response to some events where the nonlinearities are evidenced. To deal with the nonlinear characteristics of Fuenmayor, it is proposed a black-box model based on the Hammerstein-Wiener block-oriented structure. It is composed by a linear dynamic system surrounded by two static nonlinearities at its input and output. Seven different configurations of blocks are presented. Their efficiency has been evaluated by the Nash–Sutcliffe model efficiency coefficient. A good result is obtained with a configuration where the linear block is a second-order transfer function, with a zero and seven unit delays. The first nonlinear block is a piecewise polynomial and the second block has been suppressed. The running test draws out a maximum Nash-Sutcliffe efficiency of E = 0.9383.