Infilling streamflow data using feed-forward back-propagation (BP) artificial neural networks: Application of standard BP and pseudo Mac Laurin power series BP techniques

Hydrological data (e.g. rainfall, river flow data) are used in water resource planning and management. Sometimes hydrological time series have gaps or are incomplete, or are not of good quality or are not of sufficient length. This problem seems to be more prevalent in developing countries than in developed countries. In this paper, feed-forward artificial neural networks (ANNs) techniques are used for streamflow data infilling. The standard back-propagation (BP) technique with a sigmoid activation function is used. Besides this technique, the BP technique with an approximation of the sigmoid function by pseudo Mac Laurin power series Order 1 and Order 2 derivatives, as introduced in this paper, is also used. Empirical comparisons of the predictive accuracy, in terms of root mean square error of predictions (RMSEp), are then made. A preliminary case study in South Africa (i.e. using the Diepkloof (control) gauge on the Wonderboomspruit River and the Molteno (target) gauge on Stormbergspruit River in the River summer rainfall catchment) was then done. Generally, this demonstrated that the standard BP technique performed just slightly better than the pseudo BP Mac Laurin Orders 1 and 2 techniques when using mean values of seasonal data. However, the pseudo Mac Laurin approximation power series of the sigmoid function did not show any substantial impact on the accuracy of the estimated missing values at the Molteno gauge. Thus, all three the standard BP and pseudo BP Mac Laurin orders 1 and 2 techniques could be used to fill in the missing values at the Molteno gauge. It was also observed that a linear regression could describe a strong relationship between the gap size (0 to 30 %) and the expected RMSEp (thus accuracy) for the three techniques used here. Recommendations for further work on these techniques include their application to other flow regimes (e.g. 4-month seasons, mean annual extreme, etc) and to streamflow series of a winter rainfall region.