Runoff Evolution Characteristics and Predictive Analysis of Chushandian Reservoir

Abstract

The Chushandian Reservoir, a key control project on the Huaihe River, is vital for flood control, water allocation, and maintaining ecological baseflow. This study analyzes runoff evolution and provides predictive insights for sustainable water management. Methods employed include Extremum Symmetric Mode Decomposition (ESMD) for decomposing complex signals, a mutation detection algorithm to identify significant changes in time-series data, and cross-wavelet transform to examine correlations and phase relationships between time series across frequencies. Additionally, the hybrid models GM-BP and CNN-LSTM were used for runoff forecasting. Results show cyclical fluctuations in annual runoff every 2.3, 5.3, and 14.5 years, with a significant decrease observed in 2010. Among climate factors, the Atlantic Multidecadal Oscillation (AMO) had the strongest correlation with runoff variability, while ENSO and PDO showed more localized impacts. Model evaluations indicated strong predictive performance, with Nash–Sutcliffe Efficiency (NSE) scores of 0.884 for GM-BP and 0.909 for CNN-LSTM. These findings clarify the climatic drivers of runoff variability and provide valuable tools for water resource management at the Chushandian Reservoir under future climate uncertainties.

1. Introduction

With the intensification of global climate change and human activities, the hydrological cycle system is facing unprecedented disturbances, leading to increasingly pronounced nonlinear and unstable characteristics in runoff processes [1]. Particularly in reservoir-regulated basins, runoff evolution is influenced by both natural climate variability and anthropogenic interventions, resulting in more complex trends [2]. The Chushandian Reservoir in Xinyang City, located in the middle reaches of the Huai River Basin, serves as a critical water resource regulation project in the region. Accurately identifying the evolutionary trends and dominant factors of its runoff characteristics holds significant practical importance for flood control, water resource optimization, and ecological conservation [3,4]. However, the scarcity of hydrological data and the complexity of change mechanisms in this basin pose challenges as traditional hydrological analysis and prediction methods exhibit high uncertainty in medium- to long-term assessments.

In recent years, data-driven approaches have emerged as essential tools in hydrological modeling. The Extreme-point Symmetric Mode Decomposition (ESMD), an advanced signal analysis technique, effectively extracts periodic information from nonstationary hydrological series and has been widely applied in climate and hydrological data analysis [5,6]. ESMD offers superior adaptability in decomposing data, enabling the identification of multi-scale runoff variations [7]. For change-point detection, the heuristic segmentation method is widely used in basin mutation studies due to its high sensitivity and computational efficiency.

Teleconnection factors such as ENSO, PDO, NAO, and AMO are key climatic drivers influencing runoff variability in China [8,9]. Cross-wavelet transform (XWT) can reveal time–frequency coupling relationships between two time series, making it an effective method for exploring the response of runoff to teleconnection influences [10]. Existing studies indicate significant regional differences in the dominance of teleconnection factors; for instance, runoff in the upper Yangtze River is strongly influenced by PDO, while South China is primarily modulated by ENSO [11,12]. The impact of AMO on precipitation and runoff in central and northern China has gained increasing attention, with some studies demonstrating its significant positive correlation with runoff at decadal scales [13,14].

Notably, teleconnection factors often exhibit synergistic or competitive interactions, with their effects varying across temporal scales and seasons, necessitating in-depth analysis through wavelet coherence and resonance techniques. Additionally, long-term factors such as solar activity and the Indian Ocean Dipole (IOD), though indirect, may perturb regional water cycles in specific years [15,16,17].

In hydrological forecasting, accurate and reliable medium-term runoff prediction is crucial for optimizing the allocation of water resources [18,19,20] and so recent advancements have shifted from traditional physically based models to data-driven approaches. Gray system models (GMs), due to their effectiveness in small-sample modeling, are widely used for medium- to long-term runoff prediction, Combining GMs with BP neural networks enhances prediction accuracy by compensating for the linear assumptions of gray models [21,22]. Convolutional Neural Networks (CNNs) have been widely applied in the field of time-series prediction. The structure of a CNN typically consists of an input layer, convolutional layers, pooling layers, and fully connected layers. The convolutional layers reduce the number of model parameters, thus significantly alleviating the overfitting problem [23,24]. LSTM models have shown significant advantages in hydrological prediction [25,26]. Their memory unit design captures long-term dependencies in time series, balancing high accuracy and computational efficiency in runoff and water quality forecasting. Integrated CNN-LSTM models further optimize multi-scale hydrological signal analysis through complementary mechanisms: the CNN extracts local temporal features while the LSTM captures long-term dependencies [27,28,29,30]. Leveraging strong fitting capabilities for nonlinear dynamics, these deep learning models have become mainstream in hydrological forecasting.

Despite these advancements, most existing studies focus on signal decomposition or runoff prediction separately and often fail to adequately capture the coupling effects of multiscale climatic signals and nonstationary runoff processes in reservoir systems. Few studies integrate ESMD with CNN-LSTM to study the long-term trends and periodic characteristics of reservoir runoff, particularly under the influence of teleconnection factors. This study addresses this gap by constructing an integrated analysis–prediction framework combining ESMD, heuristic segmentation, cross-wavelet analysis, and hybrid deep learning models (CNN-LSTM and GM-BP). This approach allows for both improved understanding of runoff evolution mechanisms and more accurate prediction of future changes. The novelty of this work lies in its multi-method fusion of signal processing, climate signal attribution, and deep learning forecasting, applied to a highly regulated and climate-sensitive reservoir basin. The results contribute to runoff modeling under complex environmental conditions, supporting adaptive management strategies in regions affected by both natural and human-induced hydrological variability.

2. Materials and Methods

2.1. Data Description

Located in Xinyang City, Henan Province, China, the Chushandian Water Control Project serves as a critical regulatory node within the Huai River Basin, geographically situated in Chushandian Village, Youhe Township, Shihe District. This hydraulic complex holds dual strategic roles in the basin management framework: (1) functioning as a pivotal control point for the regional flood defense system, and (2) operating as core infrastructure for optimized water resource allocation. Through its multi-objective operational mechanisms, the project simultaneously safeguards urban–rural water supply security and maintains ecological baseflow requirements. This engineering–ecological multifunctional framework exemplifies the modern transition of water conservancy projects from single-purpose disaster mitigation to comprehensive service provision. For this study, natural runoff data spanning 58 years (1960–2017) from the Chushandian Reservoir were selected for in-depth hydrological analysis (see Figure 1).

This study employs the runoff dataset from the Chushandian Hydrological Station in the Huaihe River Basin spanning from 1960 to 2017 (see

Table 1. Data from the Chushandian Hydrological Station.

	Maximum Value	Minimum Value	Mean Value
Annual runoff (billion m3)	2.45029	0.15012	1.047

). To ensure robust model training and evaluation, 80% of the dataset was allocated as the training set, with the remaining 20% serving as the test set. The training dataset was then inputted into the model for parameter calibration. Additionally, data for nine teleconnection factors were acquired from the Physical Sciences Laboratory (PSL) of the National Oceanic and Atmospheric Administration (NOAA).

This study employs the Extreme-point Symmetric Mode Decomposition (ESMD), heuristic segmentation method, cross-wavelet analysis, and predictive models (GM-BP and CNN-LSTM) to analyze the runoff data from 1960 to 2017 collected at the Chushandian Hydrological Station in the Huaihe River Basin. The ESMD algorithm, implemented using an existing software package (Java 1.8.0), was configured with a maximum of 40 iterations (the default value; this can be reduced to 10 for large datasets to minimize computation time), a parameter value selected based on empirical data from similar studies to balance computational efficiency and decomposition accuracy. Both the heuristic segmentation method and cross-wavelet analysis were performed using custom scripts in MATLAB (R2021b), with the cross-wavelet analysis utilizing the Morlet wavelet basis function. The predictive models were coded in Python (version 3.9.7).

2.2. Extreme-Point Symmetric Mode Decomposition

Developed by Wang Jinliang [31] et al. as an advancement of the Empirical Mode Decomposition (EMD) algorithm, Extreme-point Symmetric Mode Decomposition (ESMD) represents a novel methodology. The core innovation of ESMD lies in replacing EMD’s conventional envelope-based cubic spline interpolation approach with an internal extreme-point symmetric interpolation method, thereby achieving enhanced interpolation precision for raw data sequences [32]. In this study, algorithmic enhancements were introduced to the ESMD framework by innovatively incorporating a variational constraint mechanism during signal decomposition. Specifically, an adaptive global baseline was constructed based on the least squares criterion, and a functional optimization model linking terminal residual components with baseline functions was established. This advancement enables intelligent optimization of sifting iteration counts, significantly improving decomposition efficiency and accuracy.

For a hydrological sequence data Y = {x₁, x₂, …, x_n}, the ESMD algorithm is executed as follows:

Step 1. Find all the local extreme points (maxima points plus minima points) in the sequence Y and numerate them by F_i with 1 ≤ i ≤ n.

Step 2. Connect all the adjacent F_i with line segments, and mark their midpoints by F_i with 1 ≤ i ≤ n.

Step 3. Add the left and right boundary midpoints F₀ and F_n with a specific approach.

Step 4. Construct p interpolating curves L₁, …, L_p (p ≥ 1) with all these n + 1 midpoints, and calculate their mean value by L* = (L₁ + … + L_p)/p.

Step 5. Repeat the above four steps on Y − L* until ∣L*∣ ≤ ε (ε is a permitted error) or the sifting times attain a preset maximum number K. At this point in time, we obtain the first mode M₁.

Step 6. Repeat the above five steps on the residual Y − M₁, and obtain M₂ and M₃, until the last residual R has no more than a certain number of extreme points.

Step 7. Change the maximum number K in a finite integer interval [K_min, K_max], and repeat the above six steps. Then, calculate the variance σ₂ of Y − R, and plot a figure with σ/σ₀ and K, where σ₀ is the standard deviation of Y.

Step 8. Find the number K₀, which agrees with a minimum σ/σ₀ on [K_min, K_max]. Then, use K₀ to repeat the previous six steps and output the whole modes. At this point in time, the last residual R is actually an optimal Adaptive Global Mean (AGM) curve.

2.3. Heuristic Segmentation

Developed by Bernaola-Galván et al. [33,34] in the context of electrocardiogram sequence analysis, the heuristic segmentation algorithm effectively identifies abrupt change points in nonlinear and non-stationary time series. Compared to conventional abrupt change detection methods, this approach employs a t-test to partition non-stationary sequences into multiple stationary sub-sequences characterized by distinct mean values and physical characteristics [35]. The mean values of each sub-sequence segment can be adaptively adjusted as required, while the absence of fixed constraints enhances its flexibility and practicality as a robust change-point detection technique.

Assuming a time series x(t) with N points, the composite deviation $s_D(i)$ at point i is as follows:

$$s_D(i)={\left({\displaystyle \frac{(N_1-1)\times s_1{(i)}^2+(N_2-1)\times s_2{(i)}^2}{N_1+N_2-2}}\right)}^{1/2}\times {\left({\displaystyle \frac{1}{N_1}}+{\displaystyle \frac{1}{N_2}}\right)}^{1/2}$$

(1)

where $N_{\mathrm{n}}$ is the number of points on both sides of i, $s_D(i)$ denotes the standard deviation, and u_n(i) represents the mean value, calculated sequentially from left to right.

The t-test statistic T(i) is computed as follows, such that higher values of T correspond to more significant differences between the mean values of the left-side and right-side segments relative to point i:

$$T(i)=\left|{\displaystyle \frac{{\mu }_1(i)-{\mu }_2(i)}{s_D(i)}}\right|$$

(2)

The method assumes that the input time series can be partitioned into approximately stationary sub-sequences, each with a distinct mean. While robust to moderate levels of noise, it is sensitive to non-stationarity and assumes homoscedastic variance within each segment. Therefore, the runoff series underwent preliminary detrending prior to segmentation to improve stationarity. The threshold was empirically determined through sensitivity testing across the range of 0.5–0.95, ensuring sufficient sensitivity to meaningful hydrological changes while minimizing the detection of pseudo-change points induced by noise.

2.4. Cross-Wavelet Analysis

Cross-wavelet transform (XWT) is an advanced time–frequency analysis technique developed from the conventional continuous wavelet transform, which is particularly suitable for multi-signal and multi-scale analysis. This method can effectively examine the correlation between two time series while revealing their phase structures and detailed characteristics in both time and frequency domains. The cross-wavelet power spectrum provides insights into the interrelationships between the two sequences within high-energy regions [36,37].

Given the two discrete time series X = {x₁, x₂, …, x_n} and Y = {y₁, y₂, …, y_n}, the cross-wavelet transform between these sequences can be defined as follows:

$$W_n^{xy}\left(s\right)=W_n^x\left(s\right)·W_n^{y\ast }\left(s\right)$$

(3)

where $W_n^{xy}\left(s\right)$ represents the correlation strength between the two sequences; $W_n^{y\ast }\left(s\right)$ denotes the complex conjugate of $W_n^y\left(s\right)$; and s is the time delay.

The power and theoretical distribution of the background power spectra A and B are given as follows:

$$D(\left|{\displaystyle \frac{W_n^X(s)W_n^{Y\ast }(s)}{{\sigma }_X{\sigma }_Y}}\right|<p)={\displaystyle \frac{Z_v(p)}{v}}\sqrt{P_k^X{P}_k^Y}$$

(4)

where $Z_v(p)$ represents the confidence level of the probability density function, which follows a square-root distribution of the product of two-parameter ${\chi }^2$ distributions; ${\sigma }_X$ and ${\sigma }_Y$ denote the standard deviations of the two time series, respectively; and v stands for the degrees of freedom.

This study selected nine teleconnection factors closely related to the hydrological processes in the study area (such as ENSO, PDO, NAO, etc.) as time-series pairs, each forming an analysis object with the annual runoff data of the target basin. Through cross-wavelet transform, the energy-coupling characteristics and phase-lag relationships between them at multiple timescales were explored, providing time–frequency domain evidence for revealing the remote climatic driving mechanisms of runoff variations.

To comprehensively capture the key climatic variability signals affecting watershed water cycles and their interactions, the study selected nine circulation indices, including the El Niño-Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO), and North Atlantic Oscillation (NAO), based on their significant impacts on climatic elements in the East Asian monsoon region (including eastern China and the Huaihe River Basin) and existing research foundations. ENSO profoundly alters the East Asian summer monsoon circulation by regulating the position and intensity of the Western Pacific Subtropical High, directly influencing the precipitation pattern and drought/flood risks in the Huaihe River Basin; the positive/negative phases of PDO significantly modulate the intensity and spatial distribution of ENSO’s impacts on East Asian climate; phase changes in the Arctic Oscillation (AO) and NAO affect the path and intensity of cold air, influencing the occurrence risks of cold waves and spring droughts in eastern China; the Atlantic Multidecadal Oscillation (AMO) has been proven to have significant correlations and physical linkages with the East Asian monsoon (including precipitation in the Huaihe River Basin); the Dipole Mode Index (DMI) indirectly affects precipitation in the Yangtze and Huaihe River Basins by influencing the Indian monsoon or East Asian subtropical high; as a marker of mid-latitude atmospheric activity centers in the North Pacific, the North Pacific Index (NPI) is also associated with East Asian climate; and long-term solar activity (SUNSPOT) is regarded as one of the natural external forcing factors potentially affecting the decadal oscillation of the East Asian monsoon.

2.5. Runoff Prediction Methods

This study employs two predictive models for comprehensive analysis and forecasting of annual runoff data: a GM-BP hybrid prediction model and a CNN-LSTM hybrid deep learning model.

2.5.1. Gray Prediction Model and BP Neural Network Method

The gray model (GM) demonstrates outstanding accuracy in short-term forecasting but exhibits weak adaptability to long-term fluctuating data. In contrast, the BP neural network excels at capturing nonlinear characteristics, yet suffers from slow convergence, susceptibility to local minima, and time-consuming training processes. The coupling of these two methods achieves complementary advantages as the GM provides baseline short-term predictions while the BP corrects for nonlinear fluctuations, with weight optimization enhancing overall forecasting accuracy. The architecture of the combined model is illustrated in Figure 2.

$$X={\displaystyle \sum _{i=1}^n{l}_G}{\widehat{\mathcal{X}}}_{G\mathrm{t}}+l_B{\widehat{\mathcal{X}}}_{\mathrm{Bt}}$$

(5)

X is the runoff prediction value, 10,000 m³; t is the prediction time period; and $l_G,{\widehat{\mathcal{X}}}_{G\mathrm{t}},l_B,{\widehat{\mathcal{X}}}_{\mathrm{Bt}}$ are the prediction values and combination weight coefficients of the combined model at different time periods t. Different weight coefficients are calculated according to Equation (6), which is as follows:

$$l_k={\displaystyle \frac{{\displaystyle \sum _{i=1,i\ne k}^n{d}_i}}{{\displaystyle \sum _{i=1}^n{d}_i}}}\cdot {\displaystyle \frac{1}{n-1}}$$

(6)

where ${\mathrm{l}}_{\mathrm{k}}$ is the weight coefficient of the different combined models and ${\mathrm{d}}_{\mathrm{i}}$ is the sum of squared residuals of different models during the prediction period. In this method, the number of combined models used is 2, and their weight coefficient calculation equations are as follows:

$$l_B={\displaystyle \frac{d_G^{\prime }}{d_B^{\prime }+d_G^{\prime }}}$$

(7)

$$l_G={\displaystyle \frac{d_B^{\prime }}{d_B^{\prime }+d_G^{\prime }}}$$

(8)

where ${\mathrm{l}}_B$ is the combination weight coefficient of the gray model; ${\mathrm{l}}_G$ is the combination weight coefficient of the BP neural network model; and $d_B^{\prime },d_G^{\prime }$ is the sum of squared residuals of the two models during the prediction period.

2.5.2. CNN-LSTM Hybrid Deep Learning Model

As one of the core neural network models in the field of deep learning, Convolutional Neural Networks (CNNs) can achieve feature extraction through automatic hierarchical processing when handling large-scale data information. By leveraging convolutional kernel structures, this model significantly reduces the number of network parameters, not only effectively mitigating model overfitting issues but also substantially improving the computational efficiency of the network model [38,39]. Each convolutional layer can be expressed as follows:

$$h_{ij}^k=f\left({(W^k\times x)}_{ij}+b_k\right)$$

(9)

where $h_{ij}^k$ represents the output after performing the convolution operation on the input; f denotes the activation function; $W^{\mathrm{k}}$ represents the weight of the convolution kernel associated with the k-th feature map; * indicates the convolution operation; and $b_k$ denotes the bias.

In the LSTM model, the design of the input gate, output gate, and forget gate enables selective learning and memorization of effective information while discarding irrelevant data, as illustrated in Figure 3. This mechanism ensures long-term screening and retention of information within unique neuronal structures, thereby effectively mitigating the information loss problem caused by increasing network depth. Furthermore, the gating mechanism of memory cells can alleviate gradient attenuation during backpropagation, effectively addressing common training challenges such as vanishing and exploding gradients [40]. The output computation formula of this model at time step t is as follows:

$$o_t=\sigma (W_0\cdot [h_{t-1},x_t]+b_o)$$

(10)

$$h_t=o_t\times \tanh (C_t)$$

(11)

where $o_t$ represents the output at time t; $b_o$ denotes the bias value; $W_0$ indicates the weight value of the hidden layer; and $C_t$ is the cell state at the time step.

The classic LSTM model enhances the storage capacity of temporal dimensional features through the introduction of gated memory units. However, its sequential recursive computation paradigm still struggles to effectively model cross-cycle dependencies in sequential data. This structural characteristic leads to systematic biases in modeling correlations of periodic fluctuation features.

The CNN employs a sliding computation mechanism with multi-layer convolutional kernels to precisely extract spatial local patterns from input data. When combined with temporal abstraction layers constructed by gated recurrent units, it enables the modeling of multi-level temporal evolution patterns (see Figure 4).

3. Results

3.1. Periodic and Trend Characteristics

This study applies the Extreme-point Symmetric Mode Decomposition (ESMD) method to conduct multi-scale analysis on the runoff time-series data of the Chushandian Reservoir from 1960 to 2017, with a focus on elucidating the periodic patterns and long-term evolutionary characteristics of the watershed runoff.

The decomposition results yield a series of trend terms R and intrinsic mode functions (IMFs), which constitute the final analytical outcomes. Based on the statistical independence of the IMF, this study employs spectral analysis to extract periodic features from the decomposition results. First, the discrete Fourier transform is applied to calculate the dominant oscillation periods of each modal component. Subsequently, combined with modal energy contribution analysis, the study quantitatively evaluates the dominant role and fluctuation characteristics of interannual-scale signals in the original runoff series. The results are presented in

Table 2. Period, variance contribution rate, and correlation coefficient of annual runoff time-series components at Chushandian station.

IMF Components	IMF1	IMF2	IMF3	IMF4	IMF5	R
Period/year	2.32	5.27	14.50	19.33	29.00
Variance contribution rate	59.72%	21.37%	12.25%	3.48%	1.93%	1.26%
Correlation coefficient	0.76	0.35	0.36	0.23	−0.09	−0.16

.

In ESMD (Ensemble Symmetric Mode Decomposition), the correlation coefficient of IMF (intrinsic mode function) components, typically the Pearson correlation coefficient, serves as a core indicator for quantifying the linear correlation strength between each mode and the original signal. The closer the absolute value of this coefficient is to one, the stronger the interpretive ability of the IMF for the original signal, which usually corresponds to oscillation patterns with clear physical mechanisms (such as interannual climatic cycles). Conversely, components with absolute values approaching 0 mostly represent noise interference. The trend term R is the final residual component obtained after decomposing the original time series via ESMD. Essentially, it serves as an adaptive global mean curve based on the “least squares” criterion, reflecting the long-term variation trend of the time series. It effectively strips the high-frequency fluctuations and seasonal components from the original series, clearly demonstrating the macroevolution direction of the data. The trend term R plays a critical role in time-series analysis, undertaking key functions such as trend judgment and data preprocessing, thus providing an important foundation for subsequent prediction and feature analysis.

According to Table 1, the annual runoff data of the Chushandian River were decomposed using the ESMD method. When the screening number reached seven, the variance ratio of the trend component R reached its minimum, and the decomposition automatically terminated, yielding the IMF components and the trend component R. To verify the accuracy of the decomposition, IMF1 to IMF5 and the trend component R were reconstructed, and the results matched the original annual runoff series, confirming the reliability of the ESMD method. To analyze the multi-timescale fluctuations embedded in the annual runoff series, FFT analysis was performed. The dominant periods of IMF1 to IMF5 were 2.32 years, 5.27 years, 14.5 years, 19.33 years, and 29 years, respectively. This indicates that the annual runoff exhibits quasi-2.32-year and quasi-5.27-year cycles on an interannual scale, as well as a quasi-14.5-year cycle characteristic on a decadal scale [41].

The correlation coefficients in Table 2 show that the correlation for IMF3 and subsequent components is relatively weak, which suggests that while these components may reveal potential long-term periodic fluctuations, their role in capturing the dominant periodic features of runoff is limited. Therefore, these components make a smaller contribution to actual predictions. Future research may consider excluding these low-correlation IMF components from analysis and focusing on the short-period components like IMF1 and IMF2 to improve the model’s effectiveness (see Figure 5).

The trend component R of the ESMD for the annual runoff time series of the Chushandian Reservoir from 1960 to 2017 is shown in Figure 6. Based on the linear regression analysis of annual runoff from 1960 to 2017, a statistically significant positive trend was identified (slope = 0.0972, p = 5.16 × 10⁻⁶ < 0.05). Although runoff decreased in some years, an overall upward trend was observed.

3.2. Mutation Detection

The mutation year test for the annual runoff time series of the Chushandian Reservoir from 1960 to 2017 was conducted using the heuristic segmentation method, with the results shown in Figure 7. In this test, the minimum segmentation length was set to 20, and the significance level was 0.65. As illustrated in Figure 7, the annual runoff series of the Chushandian Reservoir exhibited a significant abrupt decrease in 2010.

3.3. The Influence of Teleconnection Factors on Runoff

This study employs the cross-wavelet technique to systematically elucidate the coupling mechanisms between runoff and large-scale climatic drivers (including nine circulation indices such as the El Niño-Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO), and North Atlantic Oscillation (NAO)) [42,43]. The time–frequency coherence spectrum constructed using cross-wavelet transform (Figure 8) reveals that the color gradient represents the intensity distribution of coherence coefficients, with warm-toned regions indicating high-coherence characteristics. Significant spectral segments exceeding a coherence value of 0.6 (validated by Monte Carlo significance testing at p < 0.05) delineate the coupling features between climatic patterns and hydrological elements across time–frequency domains. The cone-shaped boundary demarcates the effective domain of wavelet spectral analysis, while the area outside this boundary is subject to edge effects. Statistically significant regions exceeding the 95% confidence level are outlined by bold black contours, verified through Monte Carlo testing. Vector arrows characterize phase relationships, where right-pointing arrows denote synchronous variations (in-phase oscillations) and left-pointing arrows signify anti-phase relationships [44,45,46,47].

From Figure 8, the periodic resonance analysis between runoff and the Atlantic Multidecadal Oscillation (AMO) reveals a statistically significant positive correlation resonance period of 5–11.1 years during 1982–2005. In contrast, the periodic resonance analysis between runoff and the Arctic Oscillation (AO) identifies two distinct statistically significant periods: a 3.7–6-year synchronous oscillation with negative correlation observed during 1966–1974 and a 6.5–8.5-year synchronous oscillation with positive correlation during 1979–1987. There exists a weak negative correlation resonance period of 4–6 years between runoff and the Indian Ocean Dipole Index (DMI). The analysis of runoff and the El Niño-Southern Oscillation (ENSO) shows weak positive correlation resonance periods of 0–2 years and 3–3.5 years, as well as a weak negative resonance period of 3.8–4.5 years, during 1963–1990. Runoff and the North Atlantic Oscillation (NAO) exhibit weak positive and negative resonance periods: a 0–3-year positive correlation resonance period during 1965–1975 and a 0–4.5-year negative correlation resonance period during 1975–1985. The analysis of runoff and the North Pacific Index (NPI) indicates a significant positive correlation resonance period of 7–9 years during 1982–1995. Runoff and the Pacific Decadal Oscillation (PDO) also show weak positive and negative resonance periods: a 0–2-year negative correlation resonance period during 1963–1968 and a 4.5–5.4-year positive correlation resonance period during 1969–1975. For runoff and the Pacific-North American Oscillation Index (PNA), three statistically significant resonance periods are identified: 3–6 years (positive correlation) during 1965–1975, 0–2.2 years (positive correlation) during 1987–1994, and a 0–3.6-year resonance period (negative correlation) during 2008–2015. Sunspot activity (SUNSPOT) shows a weak negative correlation resonance period of 0–2 years with annual runoff during 1982–2005.

Table 3. Wavelet coherence power spectrum between annual runoff at Chushandian station and teleconnection factors: main parameters.

Climate Index	Resonance Period (Years)	Time Period	Correlation
Atlantic Multidecadal Oscillation (AMO)	5–11.1	1982–2005	Positive
Arctic Oscillation (AO)	3.7–6	1966–1974	Negative
	6.5–8.5	1979–1987	Positive
Indian Ocean Dipole Index (DMI)	4–6	1985–2010	Negative
El Niño-Southern Oscillation (ENSO)	0–2	1985–1990	Positive
	3–3.5	1970–1978	Positive
	3.8–4.5	1985–1993	Negative
North Atlantic Oscillation (NAO)	0–3	1965–1975	Positive
	0–4.5	1975–1985	Negative
North Pacific Index (NPI)	7–9	1982–1995	Positive
Pacific Decadal Oscillation (PDO)	0–2	1963–1968	Negative
	4.5–5.4	1969–1975	Positive
Pacific-North American Oscillation Index (PNA)	3–6	1965–1975	Positive
	0–2.2	1987–1994	Positive
	0–3.6	2008–2015	Negative
Sunspot Activity (SUNSPOT)	0–2	1982–2005	Negative

presents the wavelet coherence power spectrum between annual runoff at Chushandian station and teleconnection factors.

From Figure 9, the analysis reveals two statistically significant positive resonance periods between the Atlantic Multidecadal Oscillation (AMO) and annual runoff: a 2.3–4.7-year period during 1966–1972 and a 7.4–9.2-year period during 1985–1998. The Arctic Oscillation (AO) exhibits one positive and one negative significant resonance period with annual runoff: a 2.5–5.6-year period (1965–1972) and a 6.7–9.3-year period (1981–1994), respectively. The Indian Ocean Dipole Index (DMI) demonstrates a single significant negative resonance period of 3.5–6 years with annual runoff during 1965–1974. The El Niño-Southern Oscillation (ENSO) shows a significant positive resonance period of 2.3–5.6 years with annual runoff during 1966–1974. In contrast, no statistically significant resonance period is identified between the North Atlantic Oscillation (NAO) and annual runoff. The North Pacific Index (NPI) exhibits a significant positive resonance period of 6–9 years with annual runoff during 1985–1994, while the Pacific Decadal Oscillation (PDO) displays a significant negative resonance period of 7.7–10.6 years during 1998–2005. The Pacific-North American pattern (PNA) demonstrates a significant positive resonance period of 3.2–5.7 years with annual runoff during 1965–1973. Sunspot activity (SUNSPOT) exhibits a significant positive resonance period of 7–11.4 years with annual runoff during 1976–2004. These results highlight AMO as the dominant driver of annual runoff variability, exerting profound impacts on hydrological cycles through cross-temporal-scale ocean–atmosphere coupling mechanisms. Specifically, its two significant positive resonance periods span interannual to decadal-scale synergistic variations, reflecting sustained multiscale influences on runoff dynamics. In contrast, other factors (e.g., PDO, ENSO) predominantly play secondary roles within specific temporal or regional contexts, whilst solar activity exerts indirect and long-term modulating effects.

Table 4. Cross-wavelet power spectrum of annual runoff at Chushandian station and teleconnection factors: main parameters.

Climate Index	Resonance Period (Years)	Time Period	Correlation
Atlantic Multidecadal Oscillation (AMO)	2.3–4.7	1966–1972	Positive
	7.4–9.2	1985–1998
Arctic Oscillation (AO)	2.5–5.6	1965–1972	Positive
	6.7–9.3	1981–1994	Negative
Indian Ocean Dipole Index (DMI)	3.5–6	1965–1974	Negative
El Niño-Southern Oscillation (ENSO)	2.3–5.6	1966–1974	Positive
North Atlantic Oscillation (NAO)	No significant resonance period	-	-
North Pacific Index (NPI)	6–9	1985–1994	Positive
Pacific Decadal Oscillation (PDO)	7.7–10.6	1998–2005	Negative
Pacific-North American Pattern (PNA)	3.2–5.7	1965–1973	Positive
Sunspot Activity (SUNSPOT)	7–11.4	1976–2004	Positive

presents the cross-wavelet power spectrum of annual runoff at Chushandian station and teleconnection factors.

3.4. Runoff Prediction

3.4.1. Model Parameter Configuration

The parameter settings of the CNN-LSTM model affect its runoff prediction performance to a certain extent, and the settings of relevant parameters are shown in

Table 5. Model parameter configuration.

Model Parameters	Parameter Setting
Number of layers	2 (1 Conv1D, 1 LSTM)
Neurons (units)	16 (Conv1D layer), 32 (LSTM layer)
Activation function	ReLU (Conv1D), Tanh (LSTM)
Dropout	0.3 (after LSTM layer)
Training epochs	300
Data normalization	StandardScaler (z-score normalization) applied after detrending
Early stopping	Patience of 10 epochs

.

The code includes the use of polynomial fitting to extract the trend component from the time-series data. The detrended data is obtained by subtracting this trend component from the original data. Additionally, the Monte Carlo Dropout (MC Dropout) method is employed for uncertainty quantification.

3.4.2. Model Prediction Performance

This study uses the mean squared error (MSE), mean absolute error (MAE), and Nash–Sutcliffe Efficiency coefficient (NSE) as evaluation metrics. The GM-BP prediction model takes a continuous ten-year historical runoff observation sequence as the input feature, with the next year’s runoff as the prediction target for training. Through dynamic iterative optimization of the neural network’s weight parameters, the model gradually establishes a nonlinear mapping relationship between historical data and future runoff. After training, the model predicts annual runoff for 1970–2017 (the prediction period after inputting ten years of data) and compares the results with actual observations for analysis. The CNN-LSTM prediction model effectively captures the spatiotemporal characteristics of runoff data through the synergistic effect of CNN’s local feature extraction and LSTM’s long-term dependency modeling. The model prediction results are shown in

Table 6. Model evaluation metrics.

Prediction Model	MSE (Billion m3)	MAE (Billion m3)	NSE
GM-BP	3.25 × 103	1.42 × 10−1	0.884
CNN-LSTM	2.39 × 103	1.21 × 10−1	0.940
	2.62 × 103	1.26 × 10−1	0.909

. From Table 6, it can be seen that both models are suitable for predicting runoff changes in the Chushandian watershed.

As shown in Table 6, the model evaluation metrics demonstrate that the CNN-LSTM model outperforms the GM-BP model, with a 2.83% higher Nash–Sutcliffe Efficiency coefficient (NSE). This set of optimized metrics indicates that the CNN-LSTM model, by integrating the spatial feature extraction capability of convolutional neural networks (CNNs) for hydrological sequences and the temporal dependency capture advantage of long short-term memory networks (LSTMs), effectively reduces the deviation between predicted values and measured runoff data. Physically, the significant decrease in MSE reflects the model’s improved fitting accuracy for extreme flow events, while the optimization of MAE demonstrates better consistency between predicted values and actual observations in overall trends. The positive growth of the NSE further validates that, compared to the combined prediction mechanism of the GM-BP model, the end-to-end learning framework of CNN-LSTM can more fully excavate the nonlinear dynamic characteristics in hydrological data, thus exhibiting superior generalization ability and prediction reliability in the simulation of complex runoff systems. The CNN-LSTM model exhibits an average 95% confidence interval width of 1.20 billion m³ for annual runoff predictions over the next decade, while the GM-BP model shows a corresponding interval of 1.04 billion m³. These results demonstrate both models’ relatively precise capture of short-term hydrological dynamics.

Analysis of Figure 10 reveals that the reservoir’s annual runoff is characterized primarily by intense interannual fluctuations without a clear long-term increasing or decreasing trend, although it exhibits periodic high–low alternations. Both models are suitable for predicting highly variable runoff without distinct cyclical patterns.

4. Discussion

This study investigates the multi-timescale periodic characteristics of runoff in the Chushandian Reservoir from 1960 to 2017 using Extreme-point Symmetric Mode Decomposition (ESMD), heuristic segmentation, and cross-wavelet analysis. The results reveal distinct periodic fluctuations in annual runoff: quasi-2.32-year and quasi-5.27-year cycles at interannual scales and a quasi-14.5-year oscillation at decadal scales. These multi-scale periodic features are closely associated with large-scale climate oscillations such as ENSO and AMO. Previous studies have demonstrated that climatic factors serve as key drivers of runoff variability, with their correlations exhibiting temporal-scale dependence, as evidenced by cross-wavelet analysis in delineating runoff–climate interactions across multiple timescales.

The abrupt decrease in annual runoff of the Chushandian Reservoir is the result of the combined effects of climate change and land use changes. Sustained temperature rise in the basin has intensified evapotranspiration, while the uneven spatiotemporal distribution of precipitation has directly reduced runoff recharge. High temperatures have also weakened soil water storage capacity, decreasing the contribution of base flow to rivers. The expansion of construction land (e.g., 5.33 hectares of new industrial, mining, and rural land added in Chushandian village) has increased the impervious area, causing the rainwater infiltration rate to drop by over 40%. Surface runoff converges rapidly but with shortened duration, leading to a reduced base flow during dry periods. Under the influence of these multiple factors, the abrupt decrease in runoff occurred in 2010.

Cross-wavelet analysis indicates that the Atlantic Multidecadal Oscillation (AMO) exhibits the strongest association with annual runoff variability, demonstrating a significant positive correlation and emerging as the dominant climatic driver. In contrast, the Pacific Decadal Oscillation (PDO) and El Niño-Southern Oscillation (ENSO) exert secondary influences during specific periods, displaying time-lagged and phase-dependent effects. Solar activity exerts more indirect and long-term impacts. Although the 58-year annual runoff dataset (1960–2017) provides a temporal basis, it may be insufficient to fully capture long-term climatic shifts or very-low-frequency hydrological trends—particularly for natural climate oscillations like the Atlantic Multidecadal Oscillation (AMO) or Pacific Decadal Oscillation (PDO), which operate on multi-decadal to centennial timescales. Second, while large-scale climatic factors (e.g., ENSO, AMO) were analyzed for their impact on runoff, their effects exhibit significant spatial heterogeneity across the Huaihe River Basin. Local climatic variations, elevation gradients, and land use changes (e.g., urbanization, deforestation) introduce complex hydrological responses that vary notably from upstream to downstream regions. This spatial non-uniformity underscores the need for future studies to incorporate high-resolution spatial datasets and multi-site monitoring networks to better characterize basin-scale hydrological dynamics.

In the prediction model, there are two main sources of uncertainty. First, the annual runoff data only covers 58 years, which is relatively limited and may affect the training and prediction results of the models. Second, the selection of model parameters directly influences the prediction outcomes. In this research, the control variable method was adopted for parameter selection, and multiple training sessions were conducted to ensure that the selected parameters fall within the optimal range. However, whether there are better parameters beyond this range remains unknown.

Although this paper elaborates on the construction of CNN-LSTM and GM-BP models and their performance analysis in annual runoff prediction, several limitations remain. First, due to the nonlinearity and complexity of annual runoff indicators, runoff prediction is a complex problem. The hyperparameters in the current models represent local optima rather than global optima. Consequently, the search for hyperparameters is constrained within an empirical range, introducing uncertainties into our results. Finally, deep learning models contribute to addressing acute social needs and revealing underlying mechanisms, with this study primarily focusing on the former. Further research is required to uncover the underlying mechanisms of deep learning applications, thereby further enhancing the accuracy of runoff prediction.

5. Conclusions

This study collected 58 years of annual runoff data from the Chushandian Reservoir and employed methods such as Extreme-point Symmetric Mode Decomposition, heuristic segmentation, and cross-wavelet analysis to investigate the trends and characteristic variations in annual runoff from 1960 to 2017.

(1)

On the interannual scale, the annual runoff at Chushandian exhibited quasi-periodic features of approximately 2.32 and 5.27 years, while on the decadal scale it showed quasi-periodic fluctuations of about 14.5 years.

(2)

A significant abrupt decrease in the annual runoff series occurred in 2010. But the overall trend is upward.

(3)

The Atlantic Multidecadal Oscillation (AMO) was identified as the primary factor influencing annual runoff variability, demonstrating a significant positive correlation with runoff. In contrast, other factors (e.g., PDO, ENSO) played secondary roles in specific periods or regions, while solar activity exerted a more indirect and long-term influence.

For practitioners in the field of water resource management, the findings of this study provide practical guidance for addressing climate-driven runoff fluctuations. Decision-makers can adopt proactive management measures to optimize water allocation plans, scientifically regulate reservoir storage, and maintain ecosystem sustainability in the context of climate change. Notably, the identified runoff mutation events (such as the significant decline observed in 2010) can serve as key references for constructing early-warning systems against extreme weather events like droughts and formulating impact mitigation strategies.

(4)

Although the CNN-LSTM model effectively captures the nonlinear characteristics and abrupt changes in runoff, the prediction performance still has room for improvement due to the limited current data. Acquiring larger-scale training data will further optimize the runoff prediction model proposed in this study. Future runoff prediction research should consider more influencing factors, such as environmental factors, to enhance the model’s adaptability and prediction accuracy in complex scenarios.

The application scope of the model system can be extended to regions beyond the Chushandian Reservoir, promising to provide technical support for other areas facing similar hydrological challenges. By adapting the models to different reservoir scenarios and incorporating more climatic influencing factors, these predictive models can become the core technical support in regional and national water resource management systems. Furthermore, the deep integration of real-time monitoring data and predictive models creates new possibilities for dynamic water resource management, significantly enhancing the responsiveness to real-time hydrological changes. Future research will focus on model optimization and iteration, embedding uncertainty quantification methods, and expanding applications to broader hydrological forecasting scenarios so as to provide stronger technical support for resilient water management strategies in the face of climate uncertainties.