Neural network simulation of spring flow in karst environments

Daily discharges of two springs lying in a karstic environment were simulated for a period of 2.5 years with the use of a multi-layer perceptron back-propagation neural network. Two models were developed for the springs, one relying on the original data and another where the missing discharge values were supplemented by assuming linear relationships during base flow conditions. For both springs the mean square error of the two models did not differ significantly, with an improvement exhibited at the extremes, during the network’s training phase, by the model that utilized the extended data set, the results of which are reported here. The time lag between precipitation and spring discharge differed significantly for the two springs indicating that in karstic environments hydraulic behavior is dominated, even within a few hundred meters, by local conditions. Optimum training results were attained with a Levenberg–Marquardt algorithm resulting in a network architecture consisting of two input layer neurons, four hidden layer neurons, and one output layer neuron, the spring’s discharge. The neural network’s predictions captured the behavior for both springs and followed very closely the discontinuities in the discharge time series. Under-/over-estimation of observed discharges for the two springs remained below 3 %, with the exception of a few local maxima where the predicted discharges diverged more strongly from observed values. Inclusion of temperature data did not add to the improvement of predictions. Finally, optimum predictions were attained when past discharge data were added to the input record and discharge differentials rather than direct discharges were calculated resulting in elimination of any local maximum discrepancy between observed and predicted discharge values.