A Novel Daily Runoff Probability Density Prediction Model Based on Simplified Minimal Gated Memory–Non-Crossing Quantile Regression and Kernel Density Estimation

Abstract

Reliable and accurate daily runoff predictions are critical to water resource management and planning. Probability density predictions of daily runoff can provide decision-makers with comprehensive information by quantifying the uncertainty of forecasting. Models based on quantile regression (QR) have been proven to achieve good probabilistic prediction performance, but the predicted quantiles may crossover with each other, seriously reducing the reliability of the prediction. This paper proposes non-crossing quantile regression (NCQR), which guarantees that the intervals between adjacent quantiles are greater than 0, which avoids the occurrence of quantile crossing. In order to apply NCQR to the prediction of nonlinear runoff series, this paper combines NCQR with recurrent neural network (RNN) models. In order to reduce the model training time and further improve the model accuracy, this paper simplifies the minimal gated memory (MGM) model and proposes a new RNN model, called the simplified minimal gated memory (SMGM) model. Kernel density estimation (KDE) is used to transform the discrete quantiles predicted using SMGM-NCQR into a continuous probability density function (PDF). This paper proposes a novel daily density prediction model that combines SMGM-NCQR and KDE. Three daily runoff datasets in the Yangtze River Basin in China are taken as examples and compared with the advanced models in current research in terms of five aspects: point prediction evaluation, interval prediction evaluation, probability density prediction evaluation, the degree of quantile crossing and training time. The experimental results show that the model can provide high-quality and highly reliable runoff probability density predictions.