| Abstrakt: |
Runoff prediction with a small number of observations is an important but challenging topic in hydrological research. In this study, a coupled nonlinear dynamical model based on randomly distributed embedding (RDE) is proposed, which fully extracts the spatial correlation between runoff series to achieve accurate prediction of small sample runoff. First, ensemble empirical mode decomposition (EEMD) is employed to make the data smooth. Second, phase space reconstruction (PSR) is performed, which not only expands the dimensionality of the data but also reconstructs the high-dimensional attractors of the nonlinear dynamical system. Finally, RDE is applied to generate enough non-delay attractors from the high-dimensional observations to map the delay attractors of the target variable. Each mapping converts the spatial information of the high-dimensional data into the future information of the target variable. An application for predicting the monthly runoff at the Xianyang, Zhangjiashan, and Zhuangtou stations in the Weihe River, China, is performed to evaluate the performance of RDE, convolutional neural network (CNN), long short-term memory (LSTM), and CNN-LSTM, and the sensitivity of RDE to the training sample size is analysed. The results show that RDE improves the root mean square error (RMSE) by approximately 16.74–45.61% over the other models. Moreover, RDE maintains high accuracy as the training sample size decreases. With only 12.31% of the training samples, a satisfactory result is still obtained. RDE is reliable and robust, and the prediction results remain almost unchanged as the sample size decreases. Therefore, RDE will be of great value for runoff prediction in situations when only small numbers of samples are available. [ABSTRACT FROM AUTHOR] |
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