Abstract
As the most water shortage and water polluted area in China, the water quality prediction is of utmost needed and important in Haihe River Basin for its water resource management. The long short-term memory (LSTM) has been a widely used tool for water quality forecast in recent years. The performance and adaptability of LSTM for water quality prediction of different indicators needs to be discussed before it adopted in a specific basin. However, literature contains very few studies on the comparative analysis of the various prediction accuracy of different water quality indicators and the causes, especially in Haihe River Basin. In this study, LSTM was employed to predict biochemical oxygen demand (BOD), permanganate index (CODMn), dissolved oxygen (DO), ammonia nitrogen (NH3–N), total phosphorus (TP), hydrogen ion concentration (pH), and chemical oxygen demand digested by potassium dichromate (CODCr). According to results under 24 different input conditions, it is demonstrated that LSTMs present better predicting on BOD, CODMn, CODCr, and TP (median Nash–Sutcliffe efficiency reaching 0.766, 0.835, 0.837, and 0.711, respectively) than NH3–N, DO, and pH (median Nash–Sutcliffe efficiency of 0.638, 0.625, and 0.229, respectively). Besides, the performance of LSTM to predict water quality is linearly related to the maximum value of temporal autocorrelation and cross-correlation coefficients of water quality indicators calculated by maximal information coefficient with the coefficients of determination of 0.79 to approximately 0.80. This study would provide new knowledge and support for the practical application and improvement of the LSTM in water quality prediction.
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Acknowledgements
The authors would like to acknowledge the Hebei Provincial Academy of Ecological Environmental Science, China (http://www.hebhky.cn/) for their data.
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This work was supported by the National Nature Science Foundation of China (no. 41807471) and the Open Research Fund Program of MNR Key Laboratory for Geo-Environmental Monitoring of Great Bay Area (SZU51029202010).
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All authors contributed to the study’s conception and design. QL and YW designed all experiments. QL conducted all experiments and analyzed the results. The first draft of the manuscript was written by QL, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Highlights
1. Different water quality indicators in the Haihe River Basin are predicted using LSTM.
2. LSTM is more accurate when increasing the time steps of input variables properly.
3. LSTM performs better forBOD, CODMn, CODCr, and TP than NH3–N, DO, and pH.
4. LSTM performance is linearly related to autocorrelation/cross-correlation of inputs.
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Appendix A LSTM model structure
Appendix A LSTM model structure
A memory block, whose state at time \(t\) is illustrated in Fig. 3, consists of a forget gate, an input gate, a memory cell, and an output gate (Hochreiter and Schmidhuber 1997). In the last computation at time \((t-1)\), both cell state \(({C}_{t-1})\) and output \(({h}_{t-1})\) are stored by the memory block, and the initial values of \({C}_{0}\) and \({h}_{0}\) are zero. At time \(t\), new inputs \({(X}_{t})\) are available. First, the forget gate, which determines what information to remove, generates a value \({(f}_{t})\) between 0 and 1 as a basis for determining the extent of allowing \({C}_{t-1}\) to pass by combing \({h}_{t-1}\) and \({X}_{t}\) into sigmoid function (Eq. (10)). Meanwhile, a new candidate cell state (\(\widetilde{{c}_{t}})\) and its coefficient can be generated by Eqs. (11) and (12), respectively. Thereafter, the new cell state \(({C}_{t})\) is determined according to Eq. (13). Next, the output gate produces a value \(({o}_{t})\) to determine the parts of the cell state to output based on Eq. (14). Finally, the output is calculated by Eq. (15).
In Eqs. (10), (11), (12), and (14), \(W\) denotes the matrices of weights for the gates or cells with the corresponding subscripts; \(b\) represents learnable biases. Besides, \(\sigma\) and \(\mathrm{tan}h\) denotes the sigmoid function and the tanh function, respectively.
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Li, Q., Yang, Y., Yang, L. et al. Comparative analysis of water quality prediction performance based on LSTM in the Haihe River Basin, China. Environ Sci Pollut Res 30, 7498–7509 (2023). https://doi.org/10.1007/s11356-022-22758-7
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DOI: https://doi.org/10.1007/s11356-022-22758-7