ANN-based interval forecasting of streamflow discharges using the LUBE method and MOFIPS

The estimation of prediction intervals (PIs) is a major issue limiting the use of Artificial Neural Networks (ANN) solutions for operational streamflow forecasting. Recently, a Lower Upper Bound Estimation (LUBE) method has been proposed that outperforms traditional techniques for ANN-based PI estimation. This method construct ANNs with two output neurons that directly approximate the lower and upper bounds of the PIs. The training is performed by minimizing a coverage width-based criterion (CWC), which is a compound, highly nonlinear and discontinuous function. In this work, we test the suitability of the LUBE approach in producing PIs at different confidence levels (CL) for the 6 h ahead streamflow discharges of the Susquehanna and Nehalem Rivers, US. Due to the success of Particle Swarm Optimization (PSO) in LUBE applications, variants of this algorithm have been employed for CWC minimization. The results obtained are found to vary substantially depending on the chosen PSO paradigm. While the returned PIs are poor when single-objective swarm optimization is employed, substantial improvements are recorded when a multi-objective framework is considered for ANN development. In particular, the Multi-Objective Fully Informed Particle Swarm (MOFIPS) optimization algorithm is found to return valid PIs for both rivers and for the three CL considered of 90%, 95% and 99%. With average PI widths ranging from a minimum of 7% to a maximum of 15% of the range of the streamflow data in the test datasets, MOFIPS-based LUBE represents a viable option for straightforward design of more reliable interval-based streamflow forecasting models.