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Runoff prediction using a multi-scale two-phase processing hybrid model

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Xuehua Zhao
Xuehua Zhao
Xuehua Zhao
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Huifang Wang
Huifang Wang
Huifang Wang
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Qiucen Guo
Qiucen Guo
Qiucen Guo
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Jiatong An
Jiatong An
Jiatong An
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Abstract and Figures

Accurate and timely runoff prediction is essential for effective water resource management and controlling floods and droughts. However, the stochasticity of runoff due to environmental changes and human activities poses a significant challenge in achieving reliable predictions. This paper presents a multi-scale two-phase processing strategy to develop a hybrid model for runoff prediction. In the first phase of model design, the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) is utilised to identify significant frequencies in the non-stationary target data series. The inputs to the model are decomposed into intrinsic modal functions during this stage. In the second phase, the swarm decomposition (SWD) is used to decompose high-frequency components with consistently high values of time-shift multi-scale weighted permutation entropy (TSMWPE) into sub-sequences. This permits further identification and establishment of data attributes that are incorporated into the extreme learning machine (ELM) algorithm. The ELM then simulates the series of component data, creating a comprehensive tool for runoff prediction. The hybrid model demonstrates exceptional accuracy, achieving a Nash-Sutcliffe efficiency greater than 0.95 and a qualification rate exceeding 0.93. This model can be utilised in decision-making systems as an efficient and accurate solution for generating reliable predictions, particularly for hydrological challenges characterized by non-stationary data.
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ORIGINAL PAPER
Stochastic Environmental Research and Risk Assessment (2025) 39:1059–1076
https://doi.org/10.1007/s00477-025-02907-3
al. 2024b). Process-driven modeling is complex and has
stringent data requirements, which many watersheds often
cannot meet (Granata and Fabio Di Nunno 2024; Xu et al.
2021). In contrast, data-driven modeling requires less infor-
mation, oers greater adaptability, and demonstrates better
prediction performance. As a result, data-driven modeling
is becoming increasingly popular in practical applications
(Wu et al. 2023). In data-driven modeling, traditional pre-
diction methods, such as auto-regressive moving average
model and multiple linear regression model, are commonly
used. While these methods have a fast computational speed,
they often struggle to provide satisfactory predictions for
nonlinear and non-stationary runo series (AlDahoul et al.
2023).
The application of articial intelligence has led to machine
learning (ML) becoming the most widely used method for
forecasting (Ditthakit et al. 2023). ML can uncover deep
connections within time series data, build complex nonlin-
ear high-dimensional models, and establish corresponding
mathematical relationships to address nonlinear problems,
thereby enhancing the reliability of nonlinear time series
1 Introduction
Runo is a crucial stochastic variable in various environ-
mental processes, and its spatial and temporal variability
directly impacts local and global water, energy and matter
cycles. Accurate and reliable runo forecasting is vital for
preventing oods and droughts, as well as for the ecient
and rational utilisation of water resources. This is signicant
for promoting sustainable development of society (Wang
and Peng 2024a). However, runo is highly stochastic and
non-stationarity in nature due to the inuence of multiple
factors, which makes accurate runo prediction challenging
(Zhao et al. 2021).
There are currently two approaches to predicting run-
o: process-driven and data-driven methods (Wang et
Xuehua Zhao
zhaoxh688@126.com
1 College of Water Resources Science and Engineering,
Taiyuan University of Technology, Taiyuan 030024, China
Abstract
Accurate and timely runo prediction is essential for eective water resource management and controlling oods and
droughts. However, the stochasticity of runo due to environmental changes and human activities poses a signicant
challenge in achieving reliable predictions. This paper presents a multi-scale two-phase processing strategy to develop a
hybrid model for runo prediction. In the rst phase of model design, the improved complete ensemble empirical mode
decomposition with adaptive noise (ICEEMDAN) is utilised to identify signicant frequencies in the non-stationary tar-
get data series. The inputs to the model are decomposed into intrinsic modal functions during this stage. In the second
phase, the swarm decomposition (SWD) is used to decompose high-frequency components with consistently high values
of time-shift multi-scale weighted permutation entropy (TSMWPE) into sub-sequences. This permits further identication
and establishment of data attributes that are incorporated into the extreme learning machine (ELM) algorithm. The ELM
then simulates the series of component data, creating a comprehensive tool for runo prediction. The hybrid model dem-
onstrates exceptional accuracy, achieving a Nash-Sutclie eciency greater than 0.95 and a qualication rate exceeding
0.93. This model can be utilised in decision-making systems as an ecient and accurate solution for generating reliable
predictions, particularly for hydrological challenges characterized by non-stationary data.
Keywords ICEEMDAN · ELM · Runo prediction · SWD · TSMWPE
Accepted: 3 January 2025 / Published online: 19 January 2025
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025
Runo prediction using a multi-scale two-phase processing hybrid
model
XuehuaZhao1· HuifangWang1· QiucenGuo1· JiatongAn1
1 3
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
... It consists primarily of two strategies: divide and conquer and data reconstruction. Common data processing techniques include EMD, EEMD and VMD Wang et al. 2024;Zhao et al. 2025). Tan et al. (2018) developed a hybrid method for predicting runoff using EEMD and ANN model. ...
... Previous research applied EMD to process runoff signals and adaptively decompose data into various intrinsic mode functions (IMFs) with multiple wavelengths (Zhao et al. 2025). However, EMD exhibits modal mixing, where a single IMF may contain multiple scales of signals or have the same scale of signals, or exist in different IMFs simultaneously . ...
... This study evaluates point forecasting effects (monthly and daily scales) using MAE, MAPE, RMSE, and MdAPE Zhao et al. 2025). For interval forecasting, three evaluation indicators ) are considered. ...
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