A Quantile-Based Encoder-Decoder Framework for Multi-Step Ahead Runoff Forecasting

Deep neural network (DNN) models have become increasingly popular in the hydrology community. However, most studies are related to (rainfall-) runoff simulation and comparatively fewer studies have focused on runoff forecasting. In this study, quantile-based (q = 0.05, 0.5, 0.95) encoder-decoder (ED) models that use long short -term memory network (LSTM) and dense network (DN) blocks were developed for three and five days ahead runoff forecasting. Through linear (LW) and non-linear (NLW) wavelet selection, hybrid models LSTM-DN, LSTM-DN-LW, LSTM-DN-NLW, ED, ED-LW, and ED-NLW were developed. For each lead time (LT = 3, 5) and value of q, different model configurations were created using different input lag lengths (IL = 15, 45, 180). The developed models were tested for runoff forecasting using three basins (with different characteristics) from the Catchment Attributes and MEteorology for Large-sample Studies (CAMELS) dataset. The models were compared using deterministic (e.g., the Kling-Gupta efficiency [KGE] metric) and probabilistic (e.g., reliability) statistical metrics. While the models showed high variability in performance across the three basins (KGE = 0.308-0.979 for the q = 0.5 models), very high accuracy (up to KGE = 0.979) was achieved for one of the basins with high snowmelt. The ED-NLW model was found to generally outperform the other models. Although the LSTM-DN model had the highest median KGE (0.434 across all configurations), the ED and ED-NLW models had higher reliability than LSTM-DN (90% and 91%, respectively, considering a 90% confidence level). Models coupled with NLW performed superior to those that used LW. All ED models had high reliability despite two of the basins achieving median KGE values of similar to 0.390, highlighting that quantile-based models can generate reliable forecast intervals even when the KGE of the median forecast (q = 0.5) is low. An additional experiment generated synthetic precipitation forecasts with varying degrees of accuracy. The models were trained using accurate precipitation forecasts and tested using both accurate and inaccurate precipitation forecasts. While up to a 120% improvement in KGE was found when accurate precipitation forecasts were used as input to the models, using inaccurate precipitation forecasts resulted in a substantial decrease in reliability. Overall, the results of this study can serve as a benchmark for future studies developing probabilistic DNN models for runoff forecasting.