Linear system techniques applied to the Fuenmayor Karst Spring, Huesca (Spain)

Abstract

Black box identification techniques are very useful tools to study the relationship between rainfall and the discharge of karst aquifers. Autocorrelation, cross-correlation, cross-spectral, impulse response identification (Wiener–Hopf and error minimization methods) and parametric identification of transfer functions techniques have been used by different authors. A review of these techniques has been realized to assess the possibilities and limitations. The reviewed techniques are applied to a time rainfall–discharge series of Fuenmayor karst spring, (southern central Pyrenees, Spain) to establish the relative quality of the obtained models. The quality is evaluated with the Nash–Sutcliffe model efficiency coefficient. In addition, effective rainfall has been used to improve the performance of every model. The whitening technique has been used in the cross-correlation technique with good results. The studied spring shows a Fontestorbes type behavior. The linearity of the system has been analyzed by the coherence function. Fuenmayor has an acceptable linear response, except for high frequency events. The parametric identification provides the best efficiency value E = 0.8164 and provides a proper transfer function, with five parameters (one zero, two poles, the gain and the delay). The prediction power of this transfer function is validated with another time series, with an efficiency value of E = 0.7904.