Analysis of High–Low Runoff Encounters Between the Water Source and Receiving Areas in the Xinyang Urban Water Supply Project

Abstract

The construction of the Xinyang Urban Water Supply Project, centered on the Chushandian Reservoir, required a thorough investigation of high–low runoff encounters between the water source and receiving areas to optimize water allocation and operational scheduling. Based on the hydrological stations at Changtaiguan (CTG) on the main stream of the Huaihe River (HR) in the water source area and Miaowan (MW) on the main stream of the Honghe River in the receiving area, the trends and abrupt change characteristics of monthly runoff from 2014 to 2024 were analyzed using methods such as extremum symmetry mode decomposition (ESMD) and heuristic segmentation, with spatial encounter patterns determined using Copula functions. The results indicate that (1) the runoff in the water source area showed a quasi-6.05-month periodic characteristic on a monthly scale, while the runoff in the receiving area exhibited a quasi-6.72-month periodic characteristic on a monthly scale; (2) the water source area experienced runoff mutation in August 2015 (extreme drought) and June 2024 (extreme precipitation), with the receiving area responding 7 months earlier than the water source area, revealing differences in system vulnerability; (3) synchronous hydrological states were significantly more likely to occur (51.2%) compared with asynchronous conditions (25.2%), with the highest probability of “concurrent drought” (19.8%) and a high-risk “normal water source—receiving area drought” combination (14.1%). These findings provide theoretical and technical support for the optimized scheduling of the Chushandian Reservoir, improving the resilience and adaptability of the Xinyang Urban Water Supply Project to climate fluctuations and extreme hydrological events.

1. Introduction

Water resources serve as a critical foundation for supporting the sustainable development of regional economies and societies. With the rapid expansion of urban and rural water supply networks toward greater complexity and scale in China, inter-basin water transfer projects have emerged as a strategic measure to address the uneven spatiotemporal distribution of water resources [1,2]. The stable operation of regional water resource systems and the security of water supply fundamentally depend on the spatiotemporal synergistic effects of hydrological regimes between the water source and receiving areas. This synergistic relationship not only determines the rationality of water resource allocation but also directly influences the operational efficiency and risk resilience of water supply systems [3,4]. As a core tool for water resource management, high–low runoff encounter analysis quantifies the synchronous occurrence probability of high, normal, and low runoff conditions in different regions, providing a scientific basis for joint water resource dispatching and risk management [5,6]. Recent studies indicate that, under the dual impacts of climate change and human activities, regional hydrological sequences exhibit significant non-stationary and nonlinear characteristics [7,8,9]. The Intergovernmental Panel on Climate Change (IPCC) Sixth Assessment Report reveals that over the past 30 years, temperatures in the Huaihe River Basin (HRB) have risen at a rate of 0.28 °C per decade, with precipitation variability increasing by 15%, leading to a notable rise in the frequency of extreme hydrological events [10,11]. Meanwhile, human activities such as reservoir group operations and agricultural irrigation have increasingly disrupted natural runoff processes, further complicating the spatiotemporal patterns of hydrology [12,13]. Against this backdrop, traditional hydrological analysis methods face limitations in applicability due to their inability to accurately capture the non-stationarity and complex dependence structures of hydrological sequences [14]. There is an urgent need to develop multivariate joint analysis methods suitable for nonlinear and non-stationary hydrological data to scientifically reveal the coupling relationships between the water source and receiving areas. Such advancements would provide theoretical support for rational water resource allocation and risk management in river basins [15,16,17].

Runoff, as the primary indicator of surface water resources in a watershed, is directly influenced by climate change and human activities, which in turn affects the rational allocation and utilization of regional water resources. Understanding the evolutionary patterns and trends of watershed runoff is crucial for the sustainable management of water resources. With continuous socio-economic development, underlying surface conditions have undergone significant changes, leading to substantial alterations in river runoff, which no longer exhibits natural characteristics. Therefore, studying the characteristics of runoff variation, analyzing trends in runoff series, and diagnosing mutations are of profound significance. Guo et al. [18] analyzed the periodic characteristics of the Wei River main stream runoff based on the Mann–Kendall (MK) method. Cui et al. [19] applied the Theil–Sen median method to examine runoff trends in the Yellow River Basin, revealing a decreasing trend in runoff depth at a rate of 0.3 mm per year from 1982 to 2012. However, existing research mainly targets large-scale basins, with insufficient coupled analysis of non-stationary hydrological characteristics and spatial correlation patterns in medium-small watersheds like the Huai River (HR) tributaries [20]. These medium–small basins, characterized by limited regulation capacity and high ecological vulnerability, actually demand more refined investigations [21,22].

Currently, multivariate hydrological analysis mainly includes multivariate normal distribution [23], empirical frequency method [24], and Copula function method [25]. Among these, the multivariate normal distribution method requires the variables to follow a normal distribution and be linearly correlated. However, actual hydrological series often exhibit skewed characteristics. For example, the skewness coefficient of runoff in the HRB generally exceeds 1.2, limiting the applicability of the model [26]. The empirical frequency method is based on the sorting of historical data, making it simple and intuitive to calculate. However, it is difficult to construct continuous joint probability distributions, and it cannot accurately quantify the occurrence probability of any joint flood–drought state, thus restricting its practical value in risk assessment and water resource scheduling [27]. In contrast, the Copula function separates the marginal distributions and dependence structures of multivariate data, offering flexibility in capturing nonlinear and asymmetric dependency characteristics. It is particularly effective in revealing the tail dependence between variables in extreme hydrological events, making it the mainstream method for current multivariate joint probability analysis [28]. For example, Wan et al. [29] constructed a joint flood–drought probability model for multiple reservoirs in the lower reaches of the Luanhe River Basin in Hebei Province, China, based on the Copula function, providing a basis for the optimal joint water supply scheduling of urban reservoir clusters. Guan et al. [30] used the Copula function to reveal the joint probability distribution of runoff and precipitation in the Yellow River Basin, identifying dry–wet encounter scenarios and probabilities, offering scientific reference for optimal water resource allocation. Nevertheless, risk assessments of high–low runoff encounters for newly constructed water projects, such as the Chushan Dian Reservoir, is relatively scarce [31], creating constraints for optimizing operational strategies and impeding precision in water resource management.

To address the aforementioned issues, this study focused on the newly constructed Chushandian Reservoir, a key component of the Xinyang Urban Water Supply Project. Its key innovation lies in the systematic analysis of runoff trends, periodic variations, and mutation characteristics across both the water source and receiving areas, with a focus on medium and small tributaries of the HR. Using monthly runoff data (2014–2024) from the Changtaiguan (CTG) on the main stream of the HR in the water source area and the Miaowan (MW) station on the main stream of the Honghe River in the water receiving area, we integrated extremum symmetry mode decomposition (ESMD) [32] and a heuristic segmentation algorithm [33] to detect trends and mutation characteristics. Additionally, the Copula function was used to construct a joint probability model of high–low runoff encounters between the water source and receiving areas. This approach provided a comprehensive characterization of the spatial correlation and joint risk features of hydrological states, establishing a scientific quantitative basis for regional water resource planning. The findings provide technical support for operational management while enhancing the resilience of the water supply system to extreme events [34,35].

2. Materials and Methods

2.1. Study Area

The Xinyang Urban Water Supply Project is located in the Shihe and Pingqiao districts of Xinyang City, Henan Province. Water is sourced from the Chushandian Reservoir, supplying water to the central urban area of Xinyang City and the Mingang Airport Zone, while also serving Zhumadian’s Zhengyang County, Pingyu County, and towns along the Mingang line, meeting the water demands for urban living and industrial use [36]. This project is a crucial measure to address water shortages in southern Henan, with a designed annual water supply of 213 million cubic meters, benefiting a population of over 3 million. Xinyang City is situated in the upper reaches of the HR (Figure 1), with geographic coordinates ranging from 113°45′ E to 115°55′ E and 30°23′ N to 32°27′ N. The city covers a total area of 18,900 km², with its terrain being higher in the south and lower in the north, dominated by hills and uplands [37]. The climate is transitional between the subtropical and warm temperate zones, with an average annual rainfall of 1116 mm. Precipitation is unevenly distributed throughout the year, with 66% falling between May and September. July receives the most rainfall, at 214.6 mm, while December receives the least, at 26.3 mm [38].

2.2. Datasets

This study selected the CTG station (32°31′ N, 114°06′ E, drainage area 3090 km²), located downstream of the Chushandian Reservoir on the main stream of the HR in the water source area, and the MW station (33°08′ N, 114°68′ E, drainage area 2660 km²), a representative station on the main stream of the Honghe River in the water receiving area, as the research subjects (Figure 1). The data used in this study consist of monthly runoff observation sequences from July 2014 to July 2024, provided by the Huaihe River commission of the Ministry of Water Resources, P.R.C. The average annual runoff at the CTG station is 1.23 billion m³, while at the MW station it is 380 million m³. The raw data underwent consistency checks (eliminating the impact of station relocation) and missing value treatment (using the K-nearest neighbors (KNN) interpolation method, with a filling ratio of less than 5%), resulting in a continuous 120-month synchronized analysis dataset.

2.3. Methodology

In this study, we employed a comprehensive analytical framework to characterize runoff dynamics between the water source and receiving areas. The ESMD method was first applied to quantify periodic patterns and trend characteristics in the runoff series. Subsequently, the heuristic segmentation algorithm was implemented to detect abrupt change points. Finally, Copula functions were utilized to analyze the high–low runoff encounter features between the two regions. The complete methodological workflow is illustrated in Figure 2.

2.3.1. Extremum Symmetry Mode Decomposition

The ESMD method, a recent development of the Hilbert–Huang transform, was co-developed by Jinliang Wang and Zongjun Li in 2013. It can be applied to various fields involving data processing in scientific research and engineering, such as ocean and atmospheric sciences, information science, and ecology [39]. This method draws on the concept of empirical mode decomposition (EMD) [40] and employs a “least squares” approach to optimize the final residual mode, making it an “adaptive global mean line” for the entire data set. Through this, the optimal filtering number is determined. ESMD is a data-driven, adaptive, nonlinear, time-varying signal decomposition method with strong local characteristics and adaptability, making it suitable for analyzing non-stationary and nonlinear time series. This method is one of the latest techniques for extracting the trend and period of time series. After decomposition, the original time series can be expressed as the sum of a series of intrinsic mode functions (IMFs) and a trend component [41].

The fast Fourier transform (FFT) is an efficient algorithm for computing the discrete Fourier transform (DFT) and its inverse. It is used to convert signals from the time or spatial domain into a frequency-domain representation. The core idea of FFT is to apply a divide-and-conquer strategy, breaking down large-scale DFT computations into smaller subproblems, thereby significantly reducing computational complexity. The improvement in efficiency is particularly notable when processing large datasets [42]. The FFT is applied to estimate the average period of the IMF components derived from ESMD decomposition.

2.3.2. Heuristic Segmentation Algorithm

The heuristic segmentation algorithm, proposed by Bernaola-Galvá et al. in their study of electrocardiogram sequences, is a method suitable for detecting abrupt changes in nonlinear and non-stationary time series [43]. Compared with traditional change detection methods such as the MK test [44], Cramér’s method [45], Lepage’s method [46], and Pettitt’s method [47], this approach uses the t-test to divide non-stationary sequences into multiple stationary subsequences with different means. Each subsequence represents different physical backgrounds. The scales of the mean segments obtained through decomposition are variable and not restricted by the method itself, making it an effective new approach for detecting changes.

2.3.3. Copula Function

Sklar’s theorem states that within an n-dimensional continuous random variable system X = (x₁, x₂, …, x_n), assuming each random variable x_i has its corresponding marginal cumulative distribution function F_i, there exists a unique Copula function C that can precisely construct the joint distribution function H of system X, as expressed by the following formula:

$$H(X)=C[F_1(x_1),F_2(x_2),\dots ,F_n(x_n)],x\in R^n$$

(1)

where the Copula function C is a mapping from [0,1]ⁿ to [0,1], and it satisfies the following properties: C (F₁, F₂, …, F_n) is a monotonically increasing function, and its value is always non-negative within any n-dimensional interval. If for any i < n, F_i = 0, then C (F₁, F₂, …, F_n) = 0 [48].

To use Copula for the joint distribution of two variables, six commonly used three-parameter distribution functions (Logn, GP, P-III, Log-L, GEV, Wbl) are selected from

Table 1. Six distribution functions used in this study.

Name	Cumulative Distribution Function (CDF)	Parameters
Lognormal (Logn)	$F(x)=\mathrm{\Phi }({\displaystyle \frac{\ln (x-y)-\mu }{\sigma }})$	$\mu ,\sigma ,\gamma$
Gen. Pareto (GP)	$F(x)=1-{\left[1-{\displaystyle \frac{k}{\alpha }}(x-\epsilon )\right]}^{1/k}$	$k,\alpha ,\epsilon$
Pearson Type III (P-III)	$F(x)={\displaystyle \frac{1}{\alpha \mathrm{\Gamma }(\beta )}}{\displaystyle {\int }_{\gamma }^x(\frac{x-\gamma }{\alpha }}{)}^{\beta -1}{e}^{-({\displaystyle \frac{x-y}{\alpha }})}$	$\alpha ,\beta ,\gamma$
Log-Logistic (Log-L)	$F(x)={\left[1+{({\displaystyle \frac{\beta }{x-\gamma }})}^{\alpha }\right]}^{-1}$	$\alpha ,\beta ,\gamma$
Gen. Extreme Value (GEV)	$F(x)=\exp \left(-\exp \left(k^{-1}\ln \left(1-{\displaystyle \frac{k(x-\mu )}{\sigma }}\right)\right)\right)$	$k,\sigma ,\mu$
Weibull (Wbl)	$F(x)=1-\exp \left(-{\left({\displaystyle \frac{x-\gamma }{\beta }}\right)}^{\alpha }\right)$	$\alpha ,\beta ,\gamma$

to fit the marginal distributions of runoff in the water source and receiving areas, with parameters estimated using the maximum likelihood method and goodness-of-fit tests conducted via the Kolmogorov–Smirnov (K-S) test and Anderson–Darling (A-D) test methods [49]. The K-S test is a non-parametric method based on the difference between the empirical cumulative distribution function of the sample data and the theoretical cumulative distribution function. Its core principle lies in calculating the maximum absolute difference between the two functions and determining whether to reject the null hypothesis based on the probability distribution of this statistic. The A-D test is another non-parametric method used to assess whether sample data follow a specific theoretical distribution. Its key principle involves measuring the goodness of fit by calculating a weighted squared difference between the empirical and theoretical cumulative distribution functions, where the weight is related to the probability density function of the theoretical distribution.

The selection of optimal marginal distribution types for each runoff series from six candidate distributions, based on K-S and A-D tests, serves as a prerequisite for constructing Copula-based probability models in both regions. At a significance level of p = 0.05, if a distribution passes the K-S test, the one with the smallest A-D statistic is chosen as the optimal distribution for the runoff in different regions, while distributions failing the K-S test are discarded.

The Copula functions used in this study are shown in

Table 2. Five Copula functions used in this study.

Name	Function Expression	Parameter Range
Clayton	$(u^{-\theta }+v^{-\theta }-1{)}^{-1/\theta }$	$\theta \in [0,\infty )$
Gumbel	$\exp (-{({(-\ln u)}^{\theta }+{(-\ln v)}^{\theta })}^{1/\theta })$	$\theta \in [1,\infty )$
Frank	$-{\displaystyle \frac{1}{\theta }}\ln (1+{\displaystyle \frac{(e^{-\theta u}-1)(e^{-\theta v}-1)}{e^{-\theta }-1}})$	$\theta \in R\backslash 0$
Gaussian	${\displaystyle {\int }_{-\infty }^{{\mathrm{\Phi }}^{-1}(u)}{\displaystyle {\int }_{-\infty }^{{\mathrm{\Phi }}^{-1}(v)}\frac{1}{2\pi \sqrt{1-{\theta }^2}}}}\exp ({\displaystyle \frac{2\theta xy-x^2-y^2}{2(1-{\theta }^2)}})dxdy$	$\theta \in \left[-1,1\right]$
Student t	${\displaystyle {\int }_{-\infty }^{t_{\vartheta }^{-1}(u)}{\displaystyle {\int }_{-\infty }^{t_{\vartheta }^{-1}(v)}\frac{\mathrm{\Gamma }((\vartheta +2)/2)}{\mathrm{\Gamma }(\theta /2)\pi \vartheta \sqrt{1-{\theta }^2}}}}{(1+{\displaystyle \frac{x^2-2\theta xy+y^2}{\delta }})}^{(\vartheta +2)/2}dxdy$	$\theta \in \left[-1,1\right]$

. After identifying the optimal marginal distribution functions for runoff in both the water source and receiving areas, the degree of association between the candidate Copula functions and the empirical Copula function is measured using root mean square error (RMSE) and Nash–Sutcliffe efficiency (NSE). The optimal Copula function is then selected based on the goodness-of-fit test results, which are used to establish the joint distribution of runoff between the source and receiving areas.

3. Results

3.1. Periodic and Trend Characteristics of Runoff

3.1.1. Temporal Evolution Characteristics of Runoff in the Water Source Area

As shown in Figure 3, the ESMD decomposition was applied to the monthly runoff series of the CTG station in the water source area. The decomposition automatically terminated when the optimal screening count reached 22 iterations, at which point the trend component R achieved the minimum variance ratio. In ESMD (Ensemble Symmetric Mode Decomposition), the correlation coefficient of IMF (intrinsic mode function) components, typically the Pearson correlation coeffi-cient, 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 usu-ally corresponds to oscillation patterns with clear physical mechanisms (such as in-terannual climatic cycles). Conversely, components with absolute values approaching 0 mostly represent noise interference. This process yielded six IMF components and one trend component R. It was found that the original runoff sequence was the sum of various IMF components and the trend component R, indicating that the ESMD method is complete and that the decomposition results are reliable. For analyzing the inherent multi-timescale oscillations in the monthly runoff series, FFT was employed to determine the average periods of each component. The dominant periods of IMF1–IMF6 were found to be 6.05 months, 12.10 months, 24.20 months, 40.33 months, 40.33 months, and 60.50 months, respectively. These results indicate that the monthly runoff of the HR main stream in the water source area has a quasi-6.05-month periodic characteristic at the monthly scale and a quasi-12.10-month periodic characteristic at the interannual scale. The variance contribution rates (VCR) in

Table 3. Period, VCR and correlation coefficient of the runoff time series components at the water source area.

IMF Components	IMF1	IMF2	IMF3	IMF4	IMF5	IMF6	R
Period (months)	6.05	12.10	24.20	40.33	40.33	60.50
VCR (%)	24.67	35.59	11.52	12.18	4.82	1.24	9.99
Correlation coefficient	0.26	0.54	0.14	0.24	0.26	0.06	0.17

indicate the relative importance of each IMF component to the original series. IMF2, with its quasi-12.10-month period, demonstrates the highest VCR at 35.59%, exhibiting particularly pronounced oscillatory signals. This is followed by IMF1’s quasi-6.05-month period, which shows a VCR of 24.67%. Analysis of VCR across different IMF components reveals that interannual oscillations (12.10-month) dominate the monthly runoff series variations. The monthly runoff changes in the main stream HR’s source area are primarily determined by IMF1 and IMF2, with the first and second principal periods being 6.05 months and 12.10 months, respectively.

The trend component R obtained through ESMD decomposition for the runoff series at CTG station in the water source area represents the long-term overall variation trend of monthly runoff, as illustrated in Figure 3g. The runoff sequence showed a decreasing trend from September 2018 to May 2020, dropping to the lowest value on record for the same period of 2.33 m³/s in May 2020. This was partly related to the reduction in runoff during the construction of the Chushandian Reservoir, which started in early 2019 and was completed in 2021. On the other hand, the HRB experienced consecutive dry years from 2018 to 2019 [50], with the precipitation in Xinyang City in 2019 being only 665 mm, approximately 50% of the multi-year average precipitation. The runoff began to rise in June 2020. In July of the same year, affected by the subtropical high, severe rainstorms and floods hit the HRB, with the HR system experiencing a relatively large basin-wide flood [51], and the runoff reaching 203.17 m³/s. In July 2024, the HRB was hit by another 9 heavy rainfall events, resulting in another basin-wide flood following the one in July 2020. Therefore, the runoff has shown an overall upward trend since 2020.

3.1.2. Temporal Evolution Characteristics of Runoff in the Water Receiving Area

As illustrated in Figure 4, the ESMD decomposition of the monthly runoff sequence at MW station in the water receiving area was performed. When the optimal selection number reached 8, the variance ratio corresponding to the trend component R was minimized, and the ESMD decomposition automatically stopped. Based on this, six IMF components and one trend component R were obtained. To analyze the inherent multi-time-scale oscillations in the monthly runoff sequence, the FFT was applied to calculate the average period of each component. The main periods of IMF1–IMF6 were found to be 6.72 months, 17.29 months, 20.17 months, 24.20 months, 60.50 months, and 60.50 months, respectively. This indicates that the monthly runoff in the main stream of the Honghe River at the water receiving area exhibits a quasi-6.72-month cycle at the monthly scale and a quasi-20.17-month period at the interannual scale, synchronized with the 2-year cycle of El Niño-Southern Oscillation (ENSO), reflecting the influence of climate teleconnections [52]. From the VCR of the different IMF components, it can be seen that in the interannual oscillation, the interannual oscillation (20.17 months) dominates the variation of the monthly runoff sequence. The changes in the monthly runoff of the main stream of the Honghe River at the water receiving area are primarily determined by IMF2 and IMF3, with the second and third main periods being 17.29 months and 20.17 months, respectively. The period, variance contribution rate (VCR), and correlation coefficient of the runoff time series components in the water receiving area are shown in

Table 4. Period, VCR and correlation coefficient of the runoff time series components at the water receiving area.

IMF Components	IMF1	IMF2	IMF3	IMF4	IMF5	IMF6	R
Period (months)	6.72	17.29	20.17	24.20	60.50	60.50
VCR (%)	14.69	23.00	30.77	3.45	11.66	4.78	11.66
Correlation coefficient	0.36	0.23	0.30	0.25	0.15	0.06	0.22

.

As can be seen from Figure 4, the runoff sequence showed a decreasing trend from October 2018 to June 2020. The water receiving area experienced consecutive dry years, with the runoff maintaining at 3.41 m³/s and dropping to the minimum value of 0.81 m³/s in May 2020. From August 2019 to July 2024, the runoff presented an upward trend. As a tributary of the HR, the Honghe River was affected by floods in the HRB, with floods occurring in July 2020 and July 2024, respectively, and the runoff reaching 65.72 m³/s and 128.33 m³/s. In September 2021, affected by extreme rainstorms in the upper reaches, the runoff increased to 84.23 m³/s. This change is consistent with the variation law of runoff in the water source area, further confirming the dominant role of regional climate drivers. In addition, the figure also shows that the runoff in the water receiving area is unevenly distributed, with most of it concentrated in the flood season (June–September), and affected by complex weather systems, making the water-receiving area prone to severe floods and droughts.

3.2. Mutation Characteristics of Runoff

Based on the heuristic segmentation algorithm, the mutation detection of monthly runoff time series from July 2014 to July 2024 was performed for hydrological stations in both the water source and receiving areas. The test results are shown in Figure 5, with a minimum segmentation length of 20 and a significance level of 0.85. As seen in Figure 5, the monthly runoff sequence at the CTG station in the water source area experienced a sudden decrease in August 2015, which corresponds to the severe drought event in the HRB during the summer of 2015 (with precipitation 40% lower than the normal annual amount) [11]. A sudden increase occurred in June 2024, raising concerns about whether it was caused by an extreme precipitation event (such as 350 mm of precipitation in June 2024), leading to a short-term disturbance [53]. It is necessary to continuously verify whether this is a trend reversal. The monthly runoff sequence at the MW station at the water receiving area experienced a sudden decrease in January 2015, 7 months earlier than in the water source area, reflecting the more sensitive response of the Honghe River Basin to drought, which may be related to the smaller regulation reservoir capacity [54,55].

3.3. Analysis of the Characteristics of High–Low Runoff Encounters

3.3.1. Marginal Distribution Functions in the Water Source and Receiving Areas

Table 5. Optimal marginal distribution functions and parameters for runoff in the water source and receiving areas.

Name	K-S Test						A-D Statistic						Optimal Distribution	Parameters
	Logn	GP	P-III	Log-L	GEV	Wbl	Logn	GP	P-III	Log-L	GEV	Wbl
Water source area	√	√	√	√	√	√	1.25	1.23	1.10	0.80	1.50	2.29	Log-L	$\mu$= 1.02 $\sigma$= 2.33 $\gamma$= 11.04
Water receiving area	√	×	×	√	√	×	1.37	3.07	4.12	1.06	0.79	3.99	GEV	k = −0.61 σ = 5.50 μ = 4.82

Note: “√” means passing the K-S test, and “×” means failing the K-S test.

lists the goodness-of-fit test results for each distribution of runoff in different regions, as well as the parameters for the optimal distribution, with the optimal distribution highlighted in bold black font. As shown in Table 5, the optimal marginal distribution function for the water source area runoff is Log-L. The optimal marginal distribution function for the water receiving area runoff is GEV, which is suitable for describing the peak characteristics of Honghe runoff, as shown in Figure 6.

Figure 7 demonstrates the fitting performance between theoretical and empirical frequencies of the optimal marginal distributions. As visually evident from the plot, data points are consistently clustered closely around the 1:1 reference line. This pattern confirms that the optimally selected distributions for runoff data in both the water source and receiving areas exhibit strong agreement between theoretical and empirical frequencies, thereby validating the reliability of the distribution selection process.

3.3.2. Copula Functions in the Water Source and Receiving Areas

The results are shown in

Table 6. Goodness-of-fit test results for Copula functions.

Copula Function	NSE	RMSE	θ
Gaussian	0.9876	0.3411	0.6141
T	0.9810	0.4235	2.1531
Clayton	0.9820	0.4112	0.9312
Frank	0.9873	0.3450	4.2222
Gumbel	0.9883	0.3316	1.6649

, which summarizes the goodness-of-fit test results of each Copula function and lists the parameter estimates of the best Copula function. A decrease in RMSE values and an increase in NSE values indicate an improvement in the fitting effect, with the best-performing Copula function highlighted in bold. By comprehensively comparing the three test metrics of the five candidate Copula functions, it is concluded that the Gumbel Copula function performs best in terms of fitting. Based on this, the joint distribution probability of monthly runoff between the two areas can be obtained.

3.3.3. Probability Analysis of High–Low Runoff Encounters

Joint probability contours for runoff in the water source and receiving areas, constructed with the Gumbel Copula, are presented in Figure 8. These contours enable quantitative calculation of joint probabilities for various runoff combination states across different timescales. Figure 8a illustrates the joint return period distribution between CTG station (source area) and the MW station (receiving area), reflecting the probability characteristics of runoff in different combinations. From the figure, it can be observed that most of the observed data are concentrated in the region where CTG’s runoff ≤ 60 m³/s and MW’s runoff ≤ 40 m³/s, indicating frequent co-occurrence of low-runoff events. When CTG’s runoff > 160 m³/s and MW’s runoff > 100 m³/s, their joint probability is less than 10%, demonstrating rare high-runoff co-occurrence. The univariate return period analysis reveals that the return period for CTG’s runoff > 200 m³/s and MW’s runoff > 120 m³/s is over 100 years. This figure effectively characterizes the joint return characteristics of “synchronized drought,” “synchronized flood,” and misaligned runoff combinations, providing quantitative evidence for water resource allocation and extreme event management.

Figure 8b shows that when CTG’s runoff ≤ 20 m³/s and MW’s runoff ≤ 20 m³/s, the corresponding joint probability exceeds 60%, revealing significant synchronous drought risk under current climatic conditions. This indicates that under the current climate and operational background, there is a higher risk of synchronized drought in both areas, and the system resilience is relatively weak. Once this “synchronized drought” phenomenon occurs, it will significantly reduce the flexibility of water resource allocation, increase the uncertainty and risk of urban water supply, and become a key bottleneck in ensuring water resource security. Furthermore, from the overall distribution pattern of the contour map, the joint distribution exhibits significant asymmetry and tail dependence characteristics, particularly in the low-runoff combination region, which exhibits more pronounced clustering behavior. This reflects the tail dependence between the water source and receiving areas during extreme drought events, further validating the effectiveness of the Copula model in capturing extreme joint states.

The Copula function methodology was applied to analyze high–low runoff encounters patterns between the water source and receiving areas. Based on standardized classification thresholds for high, normal, and low runoff regimes, a systematic bivariate analysis of runoff status combinations was performed. The two systems each demonstrated three distinct runoff conditions (high/normal/low), with their joint probability distribution detailed in

Table 7. Joint probability table of high–low runoff encounters between the water source and receiving areas.

Probability %	Receiving-Wet	Receiving-Normal	Receiving-Dry
Source-wet	16.5	9.9	2.5
Source-normal	6.6	14.9	14.1
Source-dry	5.8	9.9	19.8

. The results indicate that (1) synchronous hydrological conditions occur with significantly greater frequency than asynchronous states, showing a consistent hierarchy of co-dry > co-wet > co-normal events and that (2) among asynchronous combinations, source-normal and receiving-dry > source-wet/dry and receiving-normal > source-normal and receiving-wet > source-dry and receiving-wet > source-wet and receiving-dry.

According to the table above, the probability of synchronous dry conditions is higher than that of synchronous wet conditions, further confirming the regional climate pattern of “drought-flood co-occurrence” in the area, and highlighting the risk characteristics of this pattern in the region [56]. Accordingly, corresponding scheduling response measures are proposed [57,58,59], as shown in

Table 8. High–low runoff encounters scenarios and corresponding scheduling response measures.

High–Low Runoff Encounters Scenarios	Probability	Scheduling Response Measures
Co-dry	19.8%	Activating backup water sources, limiting high-water-consuming industries
Source-normal and receiving-dry	14.1%	20% reservoir capacity reservation
Co-wet	16.5%	Enhanced ecological water supplementation and power generation
Source-wet and receiving-dry	2.5%	Conventional operation

. When the runoff synchronization between the water source and receiving areas fall to ≤20 m³/s (with a joint probability > 50%), the proposed measures include activating backup water sources, limiting high-water-consuming industries, and reserving 20% of the reservoir capacity in a normal water year to address the “source-normal & receiving-dry” scenario. These results provide a theoretical basis for formulating regional scheduling and emergency plans for the Xinyang Urban Water Supply Project. Therefore, in the process of water resource management and scheduling strategy formulation, it is essential not to rely solely on the wet–dry analysis of point runoff but to consider the joint hydrological response relationships between regions. Particularly during dry periods, priority should be given to regions with a higher probability of “synchronous dry” conditions, and a dynamic scheduling mechanism based on joint probability thresholds should be established to enhance the adaptability and resilience of the water supply system in the context of climate variability. Consequently, joint probability distribution analysis not only improves the accuracy of extreme scenario identification but also helps shift the management paradigm from “passive response” to “active early warning,” which is of significant practical importance for ensuring regional water resource security.

4. Discussion

This study reveals significant differences in the periodic characteristics of runoff between the CTG station (HR, water source area) and MW station (Honghe River, water receiving area) in the Xinyang Urban Water Supply Project. The monthly runoff in the water source area exhibits a dual dominant cycle with periods of approximately 6.05 months and 12.10 months, directly influenced by the seasonal precipitation of the East Asian monsoon, with 66% of the annual precipitation occurring between May and September. In contrast, the monthly runoff in the receiving area shows cycles of approximately 6.72 months and 20.17 months, which are closely related to the delayed effect of local surface storage and regulation [60]. This difference reveals the distinct response mechanisms to climate drivers in different regions: the source area’s runoff periodicity closely follows climatic rhythms due to the regulation capacity of the large Chushandian Reservoir; while the receiving area, lacking regulation infrastructure and with a catchment area of only 2660 km², shows a more pronounced nonlinear characteristic in its runoff process.

The change-point detection results further corroborate the compounding impacts of anthropogenic activities and extreme climate events. The abrupt decline in August 2015 at the source area corresponds to a severe drought in the HRB, with precipitation for the year being 40% lower than the average. However, the receiving area exhibited hydrological discontinuity as early as January of the same year, seven months ahead of the water source area. This delayed response highlights the vulnerability of the Honghe River Basin’s ecosystem, with its small reservoir capacity making it prone to runoff interruption early in the drought period. Of particular concern is the significant change point in the water source area in June 2024, which is directly linked to a 350 mm extreme rainfall event in a single month. This aligns with the IPCC’s warning about the frequent occurrence of extreme events in the HRB, and future attention should be given to the potential impact of such sudden hydrological processes on newly constructed water supply projects.

The joint probability model constructed using the Copula function indicates that the synchronization probability of wet and dry periods between the water source and receiving areas is 51.2%, significantly higher than that of asynchronous combinations. Among these, the probability of both being dry (19.8%) exceeds that of both being wet (16.5%). This finding has major implications for the Xinyang Urban Water Supply Project. When both areas experience drought simultaneously, the runoff at MW station is often below 20 m³/s, and the project must ensure a water supply for 3 million people and an annual supply of 213 million cubic meters with limited water resources, leading to a sharp increase in system vulnerability. More critically, the combined probability of source-normal and receiving-dry conditions reaches 14.1%, which becomes a high-frequency risk scenario. This requires a shift in the engineering scheduling approach, breaking away from the traditional thinking of local balance, and fully utilizing the Chushandian Reservoir’s storage and regulation capacity to pre-adjust water supply to the receiving area during normal water periods to mitigate the frequent water source mismatch crisis.

From a methodological perspective, this study combined ESMD, heuristic segmentation, and the Gumbel Copula function, providing an effective tool for non-stationary hydrological analysis in small-to-medium-sized watersheds. The heuristic segmentation successfully captured the turning point where the runoff sequence decays into a jump, with 2019 being a key turning point. The Gumbel Copula, due to its ability to model the tail dependence of extreme drought conditions, showed a joint probability of 60% in low-runoff areas, making it more suitable for drought-dominated regions when compared with other functions [61]. However, it should be noted that this study has certain limitations: Firstly, the exclusive use of 10-year monthly runoff data makes it difficult to capture longer-term decadal hydrological oscillations, which may affect the accuracy of extreme event recurrence period assessments. Secondly, the failure to isolate the independent impacts of human activities such as reservoir operations (e.g., runoff reduction during the construction phase of Chushandian Reservoir) and agricultural irrigation on runoff mutations results in unclear attribution of contributions between natural and anthropogenic driving factors.

Future research should focus on expanding the following three aspects: First, extend the hydrological time series to over 30 years to validate the cyclical stability of the model and capture potential decadal oscillation characteristics. Second, deeply integrate reservoir scheduling with human activity disturbances such as irrigation water extraction, and develop a comprehensive regulation model driven by both natural and social factors. Lastly, based on the probability of drought and flood encounters, design dynamic adaptive scheduling strategies. These studies will significantly enhance the resilience and adaptability of water supply systems to climate fluctuations and extreme hydrological events.

5. Conclusions

This study revealed significant differences in the periodic and mutation characteristics of runoff between the water source area (main stream of the HR) and receiving area (main stream of the Honghe River) in the Xinyang Urban Water Supply Project. Using the Gumbel Copula model, the probability of high–low runoff encounters was quantified. The findings are summarized below:

(1)

Periodic Patterns: The runoff in the water source area was controlled by the East Asian monsoon, showing a quasi-6.05-month periodicity at the monthly scale and a quasi-12.10-month periodicity at the interannual scale. In the receiving area, due to the regulation effect of the underlying surface, the runoff exhibited a quasi-6.72-month periodicity at the monthly scale and a quasi-20.17-month periodicity at the interannual scale. This difference requires the engineering scheduling to account for the regional hydrological response lag effect (approximately 2–3 months).

(2)

Mutation Characteristics: The 2015 drought event caused a 40% reduction in the runoff of the water source area. In the receiving area, due to the small reservoir capacity (only 2660 km² of catchment area), the abrupt change occurred 7 months earlier, highlighting the vulnerability of the tributary system. The 2024 abrupt change, which increased in magnitude, is associated with extreme precipitation of 350 mm, suggesting that future responses to sudden hydrological events need to be strengthened.

(3)

Risk Management: The Gumbel Copula model demonstrated that synchronous hydrological states exhibited higher occurrence probabilities (51.2%) than asynchronous conditions (48.8%), with a distinct frequency hierarchy as follows: co-dry (19.8%) > co-wet (16.5%) > co-normal (14.9%) > source-normal and receiving-dry (14.1%) > source-wet/dry and receiving-normal (9.9%) > source-normal and receiving-wet (6.6%) > source-dry and receiving-wet (5.8%) > source-wet and receiving-dry (2.5%). The analysis conclusions of this study can support the new round of water resource planning and scheduling in Xinyang City.