Analysis of Evolutionary Characteristics and Prediction of Annual Runoff in Qianping Reservoir

Abstract

Under the combined influence of climate change and human activities, the non-stationarity of reservoir runoff has significantly intensified, posing challenges for traditional statistical models to accurately capture its multi-scale abrupt changes. This study focuses on Qianping (QP) Reservoir and systematically integrates climate-driven mechanisms with machine learning approaches to uncover the patterns of runoff evolution and develop high-precision prediction models. The findings offer a novel paradigm for adaptive reservoir operation under non-stationary conditions. In this paper, we employ methods including extreme-point symmetric mode decomposition (ESMD), Bayesian ensemble time series decomposition (BETS), and cross-wavelet transform (XWT) to investigate the variation trends and mutation features of the annual runoff in QP Reservoir. Additionally, four models—ARIMA, LSTM, LSTM-RF, and LSTM-CNN—are utilized for runoff prediction and analysis. The results indicate that: (1) the annual runoff of QP Reservoir exhibits a quasi-8.25-year mid-short-term cycle and a quasi-13.20-year long-term cycle on an annual scale; (2) by using Bayesian estimators based on abrupt change year detection and trend variation algorithms, an abrupt change point with a probability of 79.1% was identified in 1985, with a confidence interval spanning 1984 to 1986; (3) cross-wavelet analysis indicates that the periodic associations between the annual runoff of QP Reservoir and climate-driving factors exhibit spatiotemporal heterogeneity: the AMO, AO, and PNA show multi-scale synergistic interactions; the DMI and ENSO display only phase-specific weak coupling; while solar sunspot activity modulates runoff over long-term cycles; and (4) The NSE of the ARIMA, LSTM, LSTM-RF, and LSTM-CNN models all exceed 0.945, the RMSE is below 0.477 × 10⁹ m³, and the MAE is below 0.297 × 10⁹ m³, Among them, the LSTM-RF model demonstrated the highest accuracy and the most stable predicted fluctuations, indicating that future annual runoff will continue to fluctuate but with a decreasing amplitude.

1. Introduction

QP Reservoir, located in the mountainous region of Western Henan Province, serves as a key control project within the Yi River system, a major tributary of the Yellow River Basin [1]. As an essential ecological barrier and water conservation area for the Huang-Huai-Hai Plain, the reservoir plays a critical role in safeguarding regional water supply security, stabilizing the downstream flood control system of the Yi River, and promoting ecological restoration of river channels [2]. However, driven by multiple pressures—including the reconstructed spatiotemporal distribution of precipitation under climate warming, the increasing demand for refined reservoir operation, and the sharp rise in agricultural irrigation water use within the basin—the inflow runoff into QP Reservoir has become increasingly complex, exhibiting intensified fluctuations, abrupt changes, and long-term evolutionary patterns. These complexities present severe challenges to traditional hydrological models, which struggle to capture the multi-scale coupling mechanisms of runoff processes [3,4,5]. Against this backdrop, systematically uncovering the multi-modal periodic oscillations, critical mutation thresholds, and teleconnection mechanisms between reservoir runoff series and large-scale climatic drivers, while developing intelligent prediction models that integrate physical mechanisms with data-driven approaches, is not only a cutting-edge scientific challenge for achieving coordinated governance of water resources, ecosystems, and economies in the Yellow River Basin but also a crucial technical pathway for upgrading reservoir functions from single-purpose flood control to multi-dimensional regulation of water quantity, quality, and ecology. This advancement holds significant practical value for ensuring regional water security and supporting the ecological protection and high-quality development strategy of the Yellow River Basin [6,7,8,9].

For a long time, runoff evolution analysis has primarily relied on statistical hydrological methods such as the Mann-Kendall trend test [10] and R/S fractal analysis [11]. However, these approaches exhibit limited capability in decomposing nonlinear and non-stationary signals. In recent years, advances in signal processing and machine learning techniques have opened up new avenues for runoff studies [12]. For example, Wang et al. [13] combined empirical mode decomposition (EMD) with time-varying filtering (TVF) to effectively reduce the complexity of raw runoff data. Liao et al. [14] integrated ensemble empirical mode decomposition (EEMD) with artificial neural networks (ANNs), significantly improving prediction accuracy. Guo et al. [15] applied complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) to handle nonlinear data and coupled it with a least squares support vector machine–gray model (LSSVM-GM(1,1)) to enhance model applicability and robustness. Zhang et al. [16] improved the smoothness of monthly runoff series by integrating variational mode decomposition (VMD) with singular spectrum analysis–bidirectional long short-term memory (SSA-BiLSTM). In addition, Gao et al. [17] combined wavelet transform with long short-term memory (LSTM) networks to enhance model interpretability and stability. He et al. [18] employed LSTM to perform daily runoff prediction and trend analysis in the Nanguo River Basin, while Hu et al. [19] achieved high predictive accuracy using random forest (RF) in the Huai River Basin. Despite these advancements, significant limitations remain. Existing studies often lack in-depth exploration of the synergistic effects of multi-scale periodic oscillations, the dynamic identification of abrupt changes, and the interpretation of multi-factor coupling mechanisms. These gaps are especially evident in river systems like the Yi River, which are subject to intense anthropogenic disturbances [20].

Based on a deepened understanding of multi-scale coupling mechanisms, this study, for the first time, targets the key hydraulic project in the Yi River Basin—the QP Reservoir—by integrating a triple-technology framework comprising Bayesian change point detection, climate–runoff multi-factor interaction analysis, and hybrid machine learning prediction. This framework systematically addresses the challenges of quantifying runoff evolution and achieving high-precision forecasting under intensified non-stationarity. To gain deeper insights into the evolution of annual runoff in QP Reservoir and to perform accurate predictions, this study integrates multiple advanced methodologies with a range of climate-driving factors [21]. The main methods include: employing extreme-point symmetric mode decomposition (ESMD) [22,23] to reveal the multi-scale characteristics of runoff; applying Bayesian decomposition for abrupt change point detection [24]; analyzing the time–frequency correlations and common periodicities between runoff and large-scale climate factors using cross-wavelet transform (XWT) [25,26,27]; and innovatively developing a dual hybrid machine learning framework that integrates ARIMA, LSTM, LSTM-RF, and LSTM-CNN models [28,29,30,31,32] to enhance the capability of capturing non-stationary features and improve prediction accuracy. This study aims to comprehensively analyze the evolution characteristics of annual runoff in QP Reservoir through the integrated application of multiple methods to reveal its underlying patterns and provide scientifically grounded forecasts of future runoff trends [33,34,35]. The findings are expected to offer a robust scientific basis for water resource management and allocation in QP Reservoir, thereby promoting sustainable water resource utilization in the region [36].

2. Materials and Methods

2.1. Data Description

QP Reservoir is classified as a large (Type II) reservoir, located in the middle reaches of the Yi River system within the Yellow River Basin. The reservoir dam controls a catchment area of 1320 km². Administratively, this area belongs to Luoyang City, Henan Province, which is situated between 111°10′–113°10′ E longitude and 33°38′–35°05′ N latitude [37]. The hydrological data used in this study consist of the annual runoff series observed at the hydrological station located at QP Reservoir dam site. These data are sourced from the Hydrological Yearbook of the People’s Republic of China, with observation responsibilities held by the Henan Hydrology and Water Resources Bureau under the Yellow River Conservancy Commission. The data series span from 1952 to 2017 and have been rigorously compiled and published, ensuring high standardization and reliability. This provides a solid and dependable foundation for analyzing and forecasting the long-term evolution of annual runoff in QP Reservoir. Through in-depth analysis of this long-term dataset, the study aims to provide scientific support for water resource management and optimized allocation in both QP Reservoir and the broader Yi River Basin [38]. Figure 1 presents an overview map of the study area.

2.2. Extreme-Point Symmetric Mode Decomposition

Extreme-point symmetric mode decomposition (ESMD) [39,40] is an optimized version of the Hilbert–Huang Transform (HHT), designed to explore global trends and differentiations in time series data. Developed in 2013 by Jinliang Wang and Zongjun Li, ESMD has been applied in a range of scientific and engineering fields, including informatics, atmospheric science, and ecology. Building upon the principles of empirical mode decomposition (EMD), ESMD identifies local extrema in the data series, constructs upper and lower envelopes using cubic spline interpolation, and computes their mean function m(t) as an “adaptive global mean line”.

$$m(t)={\displaystyle \frac{U(t)+L(t)}{2}}$$

(1)

where: U(t) represents the upper envelope and L(t) represents the lower envelope.

By subtracting the mean of the envelope curves from the original signal, the intermediate signal h(t) is obtained:

$$h(t)=X(t)+m(t)$$

(2)

where: X(t) represents the original signal (raw sequence).

The intermediate signal h(t) is checked to determine whether it satisfies the intrinsic mode function (IMF) conditions: that is, the number of local extrema and zero-crossings must be equal, or at most differ by one. Additionally, at any given time, the mean of the upper envelope of the local maxima and the lower envelope of the local minima must be zero. If the IMF conditions are not met, the procedure is iterated, refining the signal through filtering until the conditions are satisfied, resulting in the IMF component. The extracted IMF component is then subtracted from the original signal to obtain the residual signal R_i(t):

$$R_i(t)=X(t)+IM{F}_i(t)$$

(3)

The process is repeated to extract IMF components until the residual signal can no longer be decomposed. Ultimately, the original sequence is decomposed into a sum of multiple intrinsic mode functions (IMF components) and a trend component (R):

$$X(t)={\displaystyle \sum _{i=1}^{n}IM{F}_i(t)+R}$$

(4)

where: IMF_i(t) represents the i-th intrinsic mode function.

Each IMF has clear physical meaning and local characteristics, while R represents the adaptive global mean curve, which, in the sense of “nonlinear least squares,” can accurately reflect the specific variation process of the time series. ESMD has advantages such as adaptability, basis-free operation, smooth processing, and the ability to distinguish between large-scale cycles and nonlinear trends.

2.3. Bayesian Decomposition Algorithm

Bayesian integrated time series decomposition is a time series analysis technique based on Bayesian statistical methods. It decomposes a time series into multiple latent components, such as trend, seasonality, and residuals [41]. This decomposition method provides an in-depth understanding of the influences of different factors within time series data and can be used for tasks such as forecasting and anomaly detection. The basic model can be expressed as:

$$y_t={\mu }_t+{\gamma }_t+{\beta }^T{x}_t+{ϵ}_t$$

(5)

where: y_t represents the observation at time t; μ_t is the trend component, which is typically modeled as a random walk or autoregressive process; γ_t is the seasonal component, usually modeled using Fourier series; x_t is the exogenous variable, and β is the corresponding regression coefficient; and ϵ_t is the error term, typically assumed to be Gaussian white noise.

This algorithm is also used as a method for detecting change points in time series, with its core idea being to estimate the locations of change points and their associated parameters through Bayesian inference. The Bayesian change point analysis model can be expressed as follows:

$$y_t~\mathcal{N}({\mu }_1+{\beta }_1{x}_t,{\sigma }^2) \mathrm{for} t\le \tau$$

(6)

$$y_t~\mathcal{N}({\mu }_2+{\beta }_2{x}_t,{\sigma }^2) \mathrm{for} t>\tau$$

(7)

where: y_t represents the observation at time t; μ₁ and μ₂ are the intercepts; β₁ and β₂ are the slopes; σ² is the error variance; and τ is the change point location.

2.4. Cross-Wavelet Transform

The cross-wavelet transform (XWT) is an analytical method based on wavelet transform, used to reveal the correlation between two time series in the time–frequency domain. By combining wavelet transform and cross-spectral analysis, it can detect correlations at different time scales on the time–frequency plane. Compared with traditional cross-correlation methods, XWT is more effective in handling non-stationary signals and provides richer feature information. This method calculates the cross-wavelet spectrum of two signals, reflecting the degree of correlation in their time–frequency distribution—the larger the magnitude, the stronger the correlation between the two signals. Moreover, XWT can further analyze the phase relationship and common periodicity between signals through wavelet coherence, allowing a better understanding of their interactions. The cross-wavelet transform of two time series is defined as W^XY = W^XW^Y∗, where ⁎ denotes the complex conjugate. The cross-wavelet power spectrum is described as |W^XY|, while the complex argument arg (W^xy) represents the local relative phase between x_n and y_n in both time and frequency domains. The theoretical distribution of its power and background spectra $P_k^X$ and $P_k^X$ is given as follows: given 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:

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

(8)

where: $W_n^X(s)$ is the wavelet transform coefficient of time series X at scale s; $W_n^{Y\ast }(s)$ is the complex conjugate of the wavelet transform coefficient of time series Y at scale s; p is a threshold used to determine the significance of the correlation; Z_v (p) denotes the confidence level of the probability density function, which follows the square root distribution of the product of two-parameter ${\chi }^2$-distributed variables; σ_x and σ_y are the standard deviations of the two time series, respectively; and v denotes the degrees of freedom. $P_k^X$ and $P_k^Y$ represent the wavelet power spectra of time series X and Y at scale k, respectively.

2.5. Runoff Prediction Methods

2.5.1. ARIMA Model

ARIMA (autoregressive integrated moving average) is a classical time series analysis method used for forecasting future data [42]. The ARIMA model integrates the characteristics of the autoregressive (AR) model, differencing (I), and the moving average (MA) model. The basic principle of the ARIMA model is as follows:

$$ARIMA(p,d,q)$$

(9)

where: p is the order of the autoregressive terms, d is the degree of differencing, and q is the order of the moving average terms.

The autoregressive (AR) model assumes that the current value y_t is a linear combination of its p past values:

$$y_t=c+{\varphi }_1{y}_{t-1}+{\varphi }_2{y}_{t-2}+\dots +{\varphi }_p{y}_{t-p}+{ϵ}_t$$

(10)

where: c is the constant term, ϕ₁, ϕ₂, …, ϕ_p are the autoregressive coefficients, and ϵ_t is the white noise error term.

Differencing is a technique used to convert a non-stationary time series into a stationary one. The differencing order d represents the number of differencing operations required.

$$\nabla y_t=y_t-y_{t-1}$$

(11)

$${\nabla }^2{y}_t=\nabla y_t-\nabla y_{t-1}$$

(12)

The moving average (MA) model assumes that the current value y_t is a linear combination of the past q error terms.

$$y_t=\mu +{ϵ}_t+{\theta }_1{ϵ}_{t-1}+{\theta }_2{ϵ}_{t-2}+\dots +{\theta }_q{ϵ}_{t-q}$$

(13)

where: μ is the constant term, θ₁, θ₂, …, θ_p are the moving average coefficients, and ϵ_t is the white noise error term. Figure 2 shows the ARIMA flowchart.

2.5.2. LSTM Model

Long short-term memory (LSTM) is a special type of recurrent neural network (RNN) [43] that effectively captures long-term dependencies in time series data. The core of LSTM lies in its unit structure, as illustrated in Figure 3, which includes the forget gate, input gate, cell state, and output gate. The LSTM model is composed of the previous time step’s input, cell state, temporary cell state, hidden state, forget gate, input gate, and output gate. The computation process can be summarized as follows: at each time step, the model calculates the values of the forget gate, input gate, and output gate based on the previous hidden state and the current input. The forget gate determines which information to discard from the cell state, the input gate selectively updates the cell state, and the output gate determines which information to output. Through this mechanism, LSTM effectively retains useful information and discards irrelevant information, ensuring efficient information flow in subsequent computations. The hidden state is output at each time step, enabling accurate modeling of time series data.

The forget gate determines which information should be discarded from the cell state:

$$f_t=\sigma (W_f\cdot [h_{t-1}\cdot x_t]+b_f)$$

(14)

where: f_t is the output of the forget gate, W_f is the weight matrix, bf is the bias term, σ is the sigmoid activation function, ht−1 is the hidden state from the previous time step, and x_t is the input at the current time step.

The input gate determines which new information should be stored in the cell state:

$$i_t=\sigma (W_t\cdot [h_{t-1}\cdot x_t]+b_i)$$

(15)

$${\tilde{C}}_t=\tanh (W_c\cdot [h_{t-1}\cdot x_t]+b_c)$$

(16)

$$C_t=f_t\cdot C_{t-1}+i_i\cdot {\tilde{C}}_t$$

(17)

where: i_t is the output of the input gate, ${\tilde{C}}_t$ is the candidate cell state, W_i and W_C are the weight matrices, b_i and b_C are the bias terms, and C_t is the updated cell state.

The output gate determines which information should be output:

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

(18)

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

(19)

where: o_t is the output of the output gate, h_t is the hidden state at the current time step, W_o is the weight matrix, and b_o is the bias term.

2.5.3. LSTM-RF Model

Random forest (RF) is an ensemble learning method that improves model performance by constructing multiple decision trees and aggregating their predictions. Each decision tree is built based on randomly selected features and samples, which enhances the robustness and generalization ability of the model. Assuming the random forest consists of T decision trees, with each tree’s prediction denoted as ${\widehat{y}}_t(t=1,2,\dots ,T)$, the final prediction of the random forest, denoted as ${\widehat{y}}_{RF}$, is given by:

$${\widehat{y}}_{RF}={\displaystyle \frac{1}{T}}{\displaystyle \sum _{t=1}^T{\widehat{y}}_t}$$

(20)

Given the limited size of the dataset and to mitigate the risks of gradient explosion and overfitting, this study employs a hybrid model integrating a single-layer LSTM with an RF. The architecture of the proposed model is illustrated in Figure 4.

2.5.4. LSTM-CNN Model

Convolutional neural networks (CNNs) are deep learning models tailored for processing data with grid-like structures. Through the use of convolutional layers, pooling layers, and fully connected layers, CNNs can automatically extract features and perform classification or regression tasks. The typical architecture consists of five layers: an input layer, convolutional layer, pooling layer, activation function layer, and fully connected layer. The input layer receives the sample data, while the convolutional layers perform feature extraction. The convolution operation is defined as follows:

$$O(i,j)={\displaystyle \sum _{kh=0}^{K_h-1}{\displaystyle \sum _{kw=0}^{K_w-1}I}}(i+kh,j+kw)\cdot W(kh,kw)+b$$

(21)

where: O(i,j) is the value at position (i,j) in the output matrix, I is the input matrix, and W is the convolution kernel. K_h and K_W represent the height and width of the convolution kernel, respectively, and b is the bias term.

In this study, average pooling is used in the pooling layer. The activation function selected is the ReLU function:

$$f(x)=\max (0,x)$$

(22)

The formula for the fully connected layer is as follows:

$$y=W\cdot x+b$$

(23)

Due to the tendency of CNN to overfit when predicting with small datasets, this study combines a single-layer LSTM network with CNN, as shown in Figure 5.

3. Results

3.1. Characteristics of Annual Runoff Variation

In order to analyze the periodicity and trend characteristics of the annual runoff of QP Reservoir, this study used the ESMD method to decompose the annual runoff data. Compared with the traditional empirical mode decomposition (EMD) method [44], the extreme-point symmetric mode decomposition (ESMD) approach offers higher fitting accuracy, purer intrinsic components, greater computational efficiency, and improved stability. These advantages make ESMD particularly well suited for analyzing nonlinear and non-stationary data such as those commonly found in climate and hydrological studies. As shown in Figure 6, the annual runoff time series at the dam site of QP Reservoir is decomposed using ESMD. When the optimal decomposition order reaches 39, the variance ratio of the trend component R is minimized, and the ESMD decomposition stops automatically. Based on this, three IMF components and the trend component R were synthesized to reconstruct a time series, which is found to completely overlap with the original runoff time series. This indicates that the ESMD method is complete and the decomposition results are reliable. To analyze the inherent multi-scale time oscillations in the annual runoff series, the fast Fourier transform (FFT) was applied to determine the average period of each component. The main periods of IMF1, IMF2, and IMF3 are 8.25 years, 9.14 years, and 13.20 years, respectively. This suggests that the annual runoff of QP Reservoir exhibits quasi-8.25-year and quasi-13.20-year medium-short-term and long-term cyclical characteristics at the inter-annual scale.

As shown in Figure 7, the trend component R of the annual runoff in QP Reservoir, derived from the ESMD decomposition, represents the long-term trend variation of the annual runoff. The annual runoff series shows an increasing trend from 1952 to 1959, followed by a decreasing trend from 1959 to 1975, an increase from 1975 to 1985, a decrease from 1985 to 1995, an increase from 1995 to 2005, and a final decrease from 2005 to 2017. Additionally, the figure indicates that from 1952 to 2017, the annual runoff series of the reservoir exhibits regular oscillatory fluctuations, with volatility gradually decreasing over time and the amplitude of the peaks and valleys progressively diminishing.

The variance contribution rates obtained from

Table 1. Period, variance contribution rate, and correlation coefficient of the time series components of the annual runoff of QP Reservoir.

IMF Component	IMF1	IMF2	IMF3	R
Period (Year)	8.25	9.14	13.20
Variance Contribution Rate (%)	48.17	20.56	14.61	16.66
Correlation Coefficient	0.58	0.27	0.34	0.42

reveal the relative importance of each IMF component in the original series. The variance contribution rate of IMF1, corresponding to the quasi-8.25-year cycle, is the largest, accounting for 49.17%, indicating a strong oscillatory signal. This is followed by IMF2, with a variance contribution rate of 20.56% for the quasi-9.14-year cycle. From the variance contribution rates of the different IMF components, it is clear that the inter-annual oscillation (8.25 years) dominates the variability in the annual runoff series. The changes in the annual runoff of QP Reservoir are primarily determined by IMF1 and IMF2, with their first and second main cycles being 8.25 years and 9.14 years, respectively.

To better investigate the abrupt change characteristics of annual runoff in QP Reservoir, this study employs the Bayesian decomposition algorithm to analyze the runoff time series. Compared with heuristic segmentation algorithms [45] and the Pettitt test [46], the Bayesian approach provides a full probabilistic distribution of the change point locations, quantities, and associated uncertainties. This effectively addresses the limitations of heuristic and Pettitt-based methods in quantifying uncertainty and adapting to complex patterns. Figure 8 illustrates the dynamic temporal variation of the annual runoff data for QP Reservoir from 1952 to 2017, based on the Bayesian decomposition algorithm. The figure shows that the overall trend of the annual runoff from 1952 to 2017 is relatively stable, with the grey shaded area representing the 95% confidence interval. The narrow interval also indicates that the trend estimation is quite reliable. The annual variation in runoff is typically associated with various atmospheric factors. Overall, the probability of a change point in the annual runoff occurring around 1985 is 79.1%, with the confidence interval for this abrupt change spanning from 1984 to 1986. Furthermore, trend change points generally reflect a transition in the runoff from one dynamic mode to another, indicating trends of stable change, increase, or decrease in runoff. For QP Reservoir, there is a 40.3% probability of a single trend change point, which occurs in 1982, with the confidence interval for this change point spanning from 1976 to 1984. Additionally, the identified harmonic order changes before and after the change point, which enhances its applicability in runoff change detection.

3.2. Driving Mechanism of Climate Factors on Annual Runoff

This study utilized the cross-wavelet method to examine the relationship between nine large-scale climate drivers and the annual runoff of QP Reservoir. Due to missing data for some climate drivers in certain years, the analysis was based on data from 1960 to 2017.

The cross-wavelet results between climate drivers and annual runoff are presented in Figure 9 and Figure 10. The color bars represent the square of the wavelet correlation coefficient, with larger values indicating stronger coherence or power between the two time series in the local time domain. The conical contour lines mark the effective range of the spectral values in the cross-wavelet, and the region enclosed by the bold black solid line indicates that the correlation within this area passes the 95% significance level test. The arrows indicate the phase relationship between the two time series. A rightward arrow indicates that the two time series are in-phase, showing a positive correlation (i.e., as the climate driver increases, annual runoff also increases), while a leftward arrow indicates that the two time series are out-of-phase, showing a negative correlation (i.e., as the climate driver increases, annual runoff decreases).

Figure 9 shows that the Atlantic multidecadal oscillation (AMO) exhibits one positive correlation resonance period with annual runoff, corresponding to a 13.7~16 year cycle from 1980 to 1991. The Arctic oscillation (AO) shows two resonance periods with annual runoff: a positive correlation resonance period from 1980 to 1989 with a 5.9~7.8 year cycle, and a negative correlation resonance period from 1980 to 1987. The Pacific decadal oscillation (PDO) shows one positive correlation resonance period with annual runoff, corresponding to a 0~3.5 year cycle from 1971 to 1984. The Pacific–North American oscillation (PNA) shows one positive correlation resonance period with annual runoff, corresponding to a 13.6~16 year cycle from 1980 to 1996. No resonance periods were found between the Indian Ocean dipole mode index (DMI), El Niño–southern oscillation (ENSO), North Atlantic oscillation (NAO), North Pacific index (NPI), sunspot activity, and annual runoff.

The climate–runoff coupling characteristics revealed in Figure 10 indicate that the variability of annual runoff in QP Reservoir is primarily modulated by the synergistic effects of multi-scale climate oscillations. Figure 10 shows that the AMO exhibits one negative correlation resonance period with annual runoff, corresponding to a 2.1~3.7 year out-of-phase cycle from 1964 to 1970. The AO shows two positive correlation resonance periods with annual runoff: one from 1964 to 1970 with a 1.6~5 year cycle, and another from 1978 to 1989 with a 5.9~8.6 year cycle, both exhibiting in-phase resonance exciting a quasi-8.25-year mid-term oscillation. The DMI shows two positive correlation resonance periods: a 4~5.9 year cycle from 1967 to 1970 and a 4.2~6.7 year cycle from 1980 to 1989, but presents a directionally weak coupling pattern due to the dynamic barrier of the Tibetan Plateau. The ENSO shows two negative correlation resonance periods with annual runoff, corresponding to 2~4 year and 4~6.2 year out-of-phase cycles from 1966 to 1974 and 1980 to 1993, respectively, confirming a phase-lag effect caused by delayed teleconnections. The NAO shows no significant resonance periods with annual runoff. The NPI shows one positive correlation resonance period with annual runoff, corresponding to a 5~7.8 year in-phase cycle from 1983 to 1992. The PDO shows one short-term negative correlation resonance period, corresponding to a 0~1.5 year out-of-phase cycle from 1975 to 1977. The PNA pattern exhibits two positive correlation resonance periods: a 3.4~5 year cycle from 1964 to 1970 and a 4.2~7.1 year cycle from 1982 to 1993, jointly amplifying westerly jet variability with AO. Sunspot activity shows one negative correlation resonance period with annual runoff, corresponding to a 6.9~14 year out-of-phase cycle from 1972 to 1996, with its attenuation phase (1985–1995) exerting a suppressive effect on evapotranspiration and overlapping with a runoff mutation threshold.

Using cross-wavelet transform techniques, this study explored the driving mechanisms of climate drivers on the annual runoff of QP Reservoir. It is found that the periodic relationships between the annual runoff and different climate drivers exhibit significant spatiotemporal heterogeneity. AMO, AO, and PNA demonstrate multi-scale synergies, while DMI and ENSO show weak coupling only during specific periods. Additionally, sunspot activity modulates runoff variability through long-term cycles.

3.3. Future Projections of Annual Runoff Variability in QP Reservoir

To analyze the future trends of annual runoff in QP Reservoir, four models—ARIMA, LSTM, LSTM-RF, and LSTM-CNN—were employed for predictive analysis. Given the limited sample size of annual runoff data, the dataset was not split into training and testing subsets; instead, all four models utilized a rolling window approach with a uniform time step of three. The performance of the models was evaluated and compared using three key metrics: RMSE [47], MAE [48], and NSE [49], as presented in

Table 2. Annual runoff forecasting performance of the two models.

Model Name	RMSE (109 m3)	MAE (109 m3)	NSE
ARIMA	0.477	0.297	0.949
LSTM	0.437	0.331	0.951
LSTM-CNN	0.3272	0.192	0.973
LSTM-RF	0.219	0.129	0.988

. As shown in Table 2, the NSE values of all four models exceeded 0.945, the RMSE values were all below 0.477 × 10⁹ m³, and the MAE values were all below 0.297 × 10⁹ m³. These results indicate that all four models demonstrate high prediction accuracy and are well suited for forecasting the annual runoff of QP Reservoir.

As shown in Figure 11, a linear regression analysis was performed between the predicted and observed values for the four models. The results show that all models captured the same general trend as the observed data and exhibited a high degree of goodness of fit. It is worth noting that the LSTM-RF model performed the best, achieving a coefficient of determination as high as 0.988, with a corresponding linear regression equation of y = 0.9728x + 0.1355. In contrast, the other three models exhibited relatively lower goodness of fit. The ARIMA model achieved an R² of 0.949, with a corresponding linear regression equation of y = 0.9391x + 0.3884. The LSTM model achieved an R² of 0.951, with the corresponding linear regression equation y = 0.925x + 0.3061; meanwhile, the LSTM-CNN model yielded an R² of 0.973, with the equation y = 0.9971x − 0.0454. The LSTM-RF model significantly outperforms the other three models in terms of goodness of fit, indicating its higher accuracy and reliability in predicting annual runoff. It is better able to capture the dynamic variation patterns of annual runoff, thereby providing a more scientifically robust basis for forecasting the characteristic trend changes of QP Reservoir.

As shown in Figure 12, in order to better analyze the future trend of annual runoff variations in QP Reservoir, this study employed four validated high-accuracy models to predict runoff from 2018 to 2035. To mitigate potential biases arising from individual model predictions, a comparative analysis using all four models was conducted. Given the limited size of the annual runoff dataset and the focus of this study being solely on runoff forecasting for QP Reservoir, a rolling window approach was adopted without splitting the data into training and testing sets. In the figure, the gray shaded area represents the predicted runoff data for 2018–2035. The annual runoff of QP Reservoir exhibits a three-peak and three-trough fluctuation pattern, with smaller amplitudes in the first two cycles and a significantly increased amplitude in the final cycle, overall following a fluctuating evolutionary trend. This suggests a recurring fluctuating pattern in the annual runoff of QP Reservoir. When compared with historical trends, it is evident that the reservoir does not exhibit a sustained long-term increase or decrease. Instead, due to the variability in peak and trough magnitudes, the annual runoff of QP Reservoir is characterized by irregular and incomplete cyclic fluctuations. Although the four models differ in the precise locations of peaks and troughs, they all predict three distinct fluctuation cycles, with the amplitude significantly increasing in the last cycle. This fluctuation pattern may be influenced by factors such as climate change, human activities, or reservoir operation and management. Specifically, the LSTM-RF model forecasts relatively smaller but smoother amplitude variations, consistent with its high accuracy demonstrated in the fitting analysis. In contrast, the ARIMA model predicts larger amplitude fluctuations, which may reflect its sensitivity to random variations present in historical data. The prediction results of the LSTM and LSTM-CNN models fall between those of the LSTM-RF and ARIMA models, demonstrating the potential of deep learning approaches to capture complex temporal patterns. Additionally, the gray shaded areas represent the uncertainty ranges of the model predictions. Although predicted values occasionally fall outside these ranges in certain years, they generally remain within reasonable bounds, indicating the models’ overall reliability. To further improve prediction accuracy, future research could incorporate additional influencing factors such as climate patterns and land use changes or employ ensemble learning techniques to integrate multiple models. Such advancements would enable a more comprehensive characterization of annual runoff evolution, providing stronger support for water resource management and decision-making at QP Reservoir.

4. Discussion

This study systematically revealed the multi-scale periodic characteristics, abrupt change behaviors, and climate-driven mechanisms of annual runoff in QP Reservoir and achieved high-accuracy predictions using various machine learning models. These findings not only enrich the understanding of runoff variation mechanisms in the Yi River Basin but also provide technical support for the dynamic regulation of small-and medium-sized reservoirs in the Yellow River Basin. However, several key issues remain that warrant further investigation.

Firstly, regarding the periodic characteristics of annual runoff, this study identified oscillation periods of approximately 8.25 and 13.20 years, reflecting a multi-period coexistence pattern at interannual to interdecadal scales. This finding is consistent with previous studies on periodicity in hydrological series from other major river basins, such as the Yellow and Yangtze Rivers, indicating that the runoff of QP Reservoir is jointly modulated by regional climate systems and large-scale climate modes [50]. However, the amplitude of these periodic oscillations shows a weakening trend over time, which may reflect the long-term impacts of human activities (such as hydraulic engineering regulation and land use changes) on the natural hydrological cycle within the basin [51]. Therefore, future research should incorporate anthropogenic factors, including land cover change and the evolution of agricultural irrigation, into the analytical framework of periodic mechanisms to enhance the comprehensiveness of mechanism interpretation.

Secondly, the results of abrupt change detection indicate that around 1985, there was a high-probability shift point, which corresponds to the mid-1980s period marked by agricultural expansion, a sharp increase in irrigation areas, and anomalous drought conditions in the Yellow River Basin. This further confirms the dynamic response of the reservoir’s annual runoff to the coupled influence of climate variability and human activities [52]. However, some uncertainty remains in the confidence interval of the detected change point, partly due to the relatively low temporal resolution of runoff data and missing records in meteorological datasets. Therefore, future research should utilize higher temporal resolution data (such as seasonal or monthly scales) to conduct more refined detection of abrupt change mechanisms, thereby reducing uncertainty.

In terms of climate-driven mechanisms, cross-wavelet analysis reveals that the variability of annual runoff in QP Reservoir is primarily governed by a three-level synergistic forcing from the AMO, AO, and PNA climate modes. The warm phase of the AMO (1964–1970) suppressed the Western Pacific subtropical high, weakening monsoonal moisture transport and causing runoff declines with a 2.1~3.7 year periodicity. The positive phase of the AO (1978–1989), through coupling between the polar vortex and the westerly jet, excited a quasi-8.25-year oscillation. The positive phase of the PNA (1982–1993), acting as a transmission hub for ENSO, resonated with the AO to amplify meridional circulation variability, inducing high-frequency fluctuations of 4.2~7.1 years. The AMO modulates the AO, which in turn drives the PNA, forming a cascading inter-oceanic teleconnection chain that elucidates the physical essence of runoff evolution dominated by the Northern Hemisphere mid-to-high latitude system. In contrast, equatorial factors (DMI/ENSO) exhibit only weak coupling, constrained by geographic barriers and phase delays. This finding provides important insights for enhancing the climate adaptability of regional water resource management. However, the current analysis remains at the level of statistical coupling and does not fully elucidate the causal mechanisms. Future research could incorporate methods such as Granger causality tests and information flow analysis to further clarify the direct and indirect driving pathways of climate factors on runoff variability [53].

In addition, in terms of runoff prediction, the LSTM-RF and LSTM-CNN models demonstrated significantly higher predictive accuracy compared with the traditional ARIMA model, confirming the advantage of deep learning methods in modeling nonlinear and non-stationary hydrological series [54]. This study also found that the hybrid LSTM-RF and LSTM-CNN models significantly improve prediction accuracy. Specifically, the LSTM-CNN model combines temporal dependency modeling with local feature extraction, while the LSTM-RF model suppresses noise overfitting through feature selection. However, these hybrid architectures compromise computational efficiency and are highly dependent on hyperparameter tuning. Additionally, limitations such as limited sample size and incomplete incorporation of external climate variables constrain the models’ generalizability. Future work could enhance prediction stability and applicability by expanding datasets (e.g., multi-site runoff data) and optimizing model architectures (e.g., integrating Transformers and attention mechanisms).

Overall, while this study has made substantial progress in periodic feature extraction, change point detection, climate mechanism analysis, and runoff prediction model development, there remains room for improvement in terms of data temporal–frequency resolution, causal mechanism identification, and model extrapolation capacity. Future research should move toward the integration of multi-source data, multi-scale mechanism coupling, and the development of physics-informed data-driven models, thereby enabling more accurate support for intelligent scheduling and climate-adaptive water resource management in QP Reservoir and similar reservoirs.

5. Conclusions

This study investigates the evolutionary trends and characteristic changes of annual runoff in QP Reservoir by integrating ESMD, heuristic segmentation, cross-wavelet analysis, and four machine learning models. The main conclusions are summarized as follows:

(1)

The annual runoff series of QP Reservoir exhibits quasi-8.25-year short- to medium-term periodic characteristics and quasi-13.20-year long-term periodic characteristics on an interannual scale.

(2)

An annual abrupt change point with a probability of 79.1% was detected in the annual runoff of QP Reservoir in 1985, with a confidence interval spanning from 1984 to 1986.

(3)

The periodic correlations between the annual runoff of QP Reservoir and climate drivers vary spatially and temporally: AMO, AO, and PNA exhibit multi-scale synergy; DMI and ENSO show only phase-specific weak coupling; while solar sunspot activity exerts long-term modulation on runoff.

(4)

The NSE of the ARIMA, LSTM, LSTM-RF, and LSTM-CNN models all exceed 0.945, the RMSE is below 0.477 × 10⁹ m³, and the MAE is below 0.297 × 10⁹ m³, Among them, the LSTM-RF model demonstrated the highest accuracy and the most stable predicted fluctuations, indicating that future annual runoff will continue to fluctuate but with a decreasing amplitude.

This study establishes a “decomposition–attribution–prediction” framework by integrating multi-scale periodic diagnostics, abrupt change point validation, and climate–runoff mechanism analysis. It fills the research gap on runoff non-stationarity in heavily human-impacted areas of the Yi River basin and offers a novel paradigm for intelligent reservoir cascade operation in the Yellow River basin. Future work will couple climate and anthropogenic drivers (such as irrigation and regulation) and conduct transfer validation across reservoir groups in the Yellow River basin to enhance prediction robustness under extreme scenarios and improve mechanistic interpretability.