Rainfall Trends and Multi-scale Variability in the Water-receiving Area of the Zhejiang East Water Diversion Project.

Authors

ZENG Tian-li¹, ZUO Xiao-xia¹, YANG Yu¹, DAI Huan¹, WU Mu-hong², ZHONG Lü-bin², CHEN Shu-yang³

1. Zhejiang Design Institute of Water Conservancy and Hydroelectric Power Co., LTD., Hangzhou 310002, China
2. Qingyuan County Water Conservancy Bureau, Lishui, Zhejiang 323800, China
3. Zhejiang Yansi Information Technology Co., Ltd., Hangzhou, Zhejiang 310051, China

Abstract

This study systematically investigates the spatiotemporal distribution characteristics, long-term trends, multi-scale variability, and regional correlation of rainfall in 15 typical sub-regions of Eastern Zhejiang based on long-term daily rainfall observation data from 1961 to 2022 (62 years). Employing the Mann-Kendall (MK) trend test, Sen's slope estimation, Hurst exponent analysis, and multi-scale sliding window analysis, this research provides comprehensive insights into rainfall dynamics within the influence area of the Eastern Zhejiang Water Diversion Project.

Regarding spatial distribution, daily average rainfall ranges from 3.47 mm to 5.68 mm, exhibiting a distinct "high-in-center, low-in-west, medium-in-east" spatial pattern. The central high-value area (Yuyao Plain Mazhu Midstream Area) reaches 5.68 mm, while the western low-value area (Nansha Plain Area) records only 3.47 mm.

In terms of long-term trends, Mann-Kendall tests reveal that all 15 sub-regions exhibit statistically significant upward trends (p<0.05). Sen's slope estimates demonstrate spatial differentiation in trend magnitude following a "high-in-coastal, medium-in-river, low-in-hilly" pattern. Hurst exponent analysis (H > 0.5) confirms that the observed upward trends possess long-term persistence.

The multi-scale variability analysis through sliding window reveals pronounced scale dependence. At the 3-month scale, precipitation exhibits high instability with large trend fluctuations (±16 mm) and low correlation. At the 12-month scale, trends become more stable (±1.7 mm) with improved correlation, indicating that long-term patterns are controlled by large-scale climate factors.

With respect to regional correlation, inter-regional correlations strengthen with increasing time scale, rising from 0.83 (3-month) to 0.87 (12-month). Notably, the Yuyao Plain Mazhu Midstream Area displays a unique "increase-then-decrease" correlation pattern, reflecting its special hydro-geographic conditions.

For engineering implications, the post-2010 intensification of rainfall fluctuations necessitates optimized scheduling strategies for the Eastern Zhejiang Water Diversion Project to enhance flood control and supply security under changing climate conditions.

Keywords

Eastern Zhejiang Water Diversion Project; rainfall spatiotemporal distribution; Mann-Kendall test; Sen's slope estimation; Hurst exponent; multi-scale analysis; scale dependence

1. Introduction

1.1 Regional Hydrological and Climate Context

The Eastern Zhejiang region, situated on the eastern coast of Zhejiang Province, China, is characterized by a typical subtropical monsoon climate with annual precipitation exceeding 1400 mm. However, the spatiotemporal distribution of water resources is extremely uneven. Over 60% of the annual rainfall is concentrated in the Meiyu season (June-July) and the Typhoon season (August-September), often leading to alternating flood and drought disasters.

The Eastern Zhejiang Water Diversion Project, which commenced operation in June 2014, represents the largest cross-basin water transfer infrastructure in Zhejiang Province. It serves 19 counties (districts) across Hangzhou, Shaoxing, Ningbo, and Zhoushan, with an average annual diversion volume of 890 million m³. In the context of global climate change, recent hydro-meteorological observations indicate that precipitation patterns in this region are undergoing significant shifts. The frequency of extreme precipitation events has increased, posing new challenges to the project's water source stability, conveyance safety, and scheduling optimization. Therefore, a systematic analysis of rainfall trends and variability in the project's receiving areas is essential for scientific management.

1.2 Research Progress on Precipitation Variability

1.2.1 Global and National Trends

The Intergovernmental Panel on Climate Change (IPCC) Sixth Assessment Report (AR6) confirms that human influence has intensified the global water cycle, leading to increased precipitation variability in mid-latitude land areas since the 1950s [1]. This intensification is consistent with the Clausius-Clapeyron relationship, which predicts a ~7% increase in atmospheric water-holding capacity per degree of warming [2].

Global studies have documented widespread increasing trends in annual maximum daily precipitation [4]. Donat et al. [5] further demonstrated that both dry and wet regions are experiencing more extreme precipitation events. In China, precipitation patterns exhibit significant regional differentiation. While northern China has seen some drying trends, eastern and southern regions generally show increasing precipitation intensity [15,16]. Specific to the Yangtze River Basin and Eastern China, studies have consistently identified upward trends in rainfall indices [20,21], often linked to changes in large-scale circulation patterns such as the westward extension of the Western Pacific Subtropical High and variations in the East Asian Monsoon [19].

1.2.2 Methodological Approaches

Statistical trend detection relies heavily on non-parametric methods. The Mann-Kendall (MK) test [6,7] and Sen's slope estimator [11] have become standard tools for assessing trend significance and magnitude in hydrological series, as they are robust against outliers and non-normal distributions [8]. To assess the reliability of these trends, the Hurst exponent [12] provides crucial insights into long-term persistence, indicating whether a trend is likely to continue or reverse. Furthermore, multi-scale sliding window analysis has emerged as a powerful technique to examine variability across different temporal aggregation scales [13,14], revealing how statistical characteristics evolve from short-term weather noise to long-term climate signals.

1.2.3 Research Gaps

Despite substantial progress in precipitation research, critical gaps remain regarding the specific context of the Eastern Zhejiang Water Diversion Project:

Despite substantial progress, critical gaps remain in the specific context of the Eastern Zhejiang Water Diversion Project. First, most existing studies focus on provincial or basin scales, leaving local variations in the 15 specific sub-regional receiving areas poorly characterized. Second, few studies systematically combine trend significance (MK), magnitude (Sen's), and persistence (Hurst) into a unified framework for robust trend characterization. Third, the scale dependence of rainfall variability and inter-regional correlations in this coastal transition zone remains under-investigated. Finally, most climatic research lacks direct translation into operational recommendations for large-scale water diversion systems, particularly regarding source-receiver coordination.

1.3 Research Objectives

This study focuses on the 15 sub-regions of the Eastern Zhejiang Water Diversion Project. Based on a continuous 62-year dataset (1961-2022), it addresses four key objectives:

This study addresses four key objectives. The first objective involves spatial analysis to quantify the multi-year average daily rainfall and identify spatial clustering patterns (high/medium/low-value areas) to inform regional water balance assessments. The second objective focuses on trend assessment to detect trend significance, quantify magnitudes, and evaluate persistence using the integrated MK-Sen-Hurst framework, identifying areas with rapid climate response. The third objective encompasses multi-scale analysis to characterize rainfall variability and inter-regional correlation evolution at 3-, 6-, and 12-month scales, distinguishing between local weather noise and regional climate signals. The fourth objective concerns engineering application to provide scientific recommendations for differentiated water supply strategies, multi-scale scheduling mechanisms, and adaptive management to enhance the project's resilience to climate change.

2. Study Area and Data

2.1 Overview of the Study Area

2.1.1 Geographic Location and Topography

The study area is located in the eastern part of Zhejiang Province, China, covering 15 typical sub-regions distributed across five administrative zones: Xiaoshan, Shaoyu, Yuyao, Cixi, and Ningbo (Figure 1). This region serves as the primary water receiving area for the Eastern Zhejiang Water Diversion Project.

The topography features a complex transition from coastal plains in the east to inland hills in the west, which significantly influences regional hydrological processes. The characteristics of the three major topographic zones are summarized in Table 1a.

Table 1a. Topographic Zones and Characteristics

Table 1. The 15 Sub-regions of the Study Area

2.1.2 Hydro-climate Characteristics

The region is characterized by a subtropical monsoon climate with substantial precipitation variability. Annual precipitation multi-year averages range between 1273.5 mm and 1454.8 mm, with high inter-annual variability as historical maximums reach 2050.1 mm and minimums drop to 682.2 mm. Regarding seasonal distribution, rainfall is highly concentrated in the Meiyu season (June-July) and Typhoon season (August-September), which together account for over 60% of the annual total. This concentration often leads to alternating flood and drought risks.

Figure 1. Location of the study area and distribution of 15 sub-regions

2.2 Data Sources

This study utilizes daily precipitation observation records from 1961 to 2022 (62 years) for 15 representative meteorological/hydrological stations within the study area. Data were obtained from the Zhejiang Provincial Meteorological Bureau and local hydrological monitoring networks. The dataset includes 22,630 daily values per station, capturing multiple decadal climate cycles and providing a robust foundation for long-term trend analysis.

2.3 Data Quality Control

To ensure the reliability of the research results, a rigorous four-stage data quality control system was applied. The first stage involved continuity assessment, which systematically identified time series gaps; missing data accounted for less than 2% for any station. The second stage focused on outlier detection, applying the 3σ criterion (Pauta criterion) to flag statistical anomalies; flagged values were cross-checked against adjacent stations and synoptic records to distinguish measurement errors from genuine extreme events. The third stage addressed interpolation, where small gaps were filled using linear regression with the most highly correlated neighboring stations, validated against seasonal climatology. The fourth stage comprised homogeneity testing, employing the Standard Normal Homogeneity Test (SNHT) and sliding t-test methods to detect and correct breakpoints caused by station relocations or instrument changes.

The final quality-controlled dataset exceeds 98% completeness and has been verified for homogeneity.

3. Research Methods

This study employs four complementary analytical methods to comprehensively characterize rainfall spatiotemporal patterns: (1) Mann-Kendall trend test for significance assessment, (2) Sen's slope estimation for trend magnitude quantification, (3) Sliding window analysis for multi-scale variability characterization, and (4) Hurst exponent analysis for trend persistence evaluation.

3.1 Mann-Kendall (MK) Trend Test

The Mann-Kendall test is a rank-based non-parametric method widely used to detect monotonic trends in hydro-climatic time series. Its primary advantages are its robustness against outliers and its capability to handle non-normally distributed data [6,7].

For a time series $\{x\_{1},x\_{2},...,x\_{n}\}$, the test statistic $S$ is calculated as:

$S=\sum\_{i=1}^{n-1}\sum\_{j=i+1}^{n}sgn(x\_{j}-x\_{i}) (Equation 1)$

where $sgn(θ)$ is the sign function:

$sgn(θ)=\left\{\begin{matrix}+1,&if θ>0\\0,&if θ=0\\-1,&if θ<0\end{matrix}\right.$

For sample sizes $n\geq 8$, the statistic $S$ is approximately normally distributed with mean $E(S)=0$ and variance:

$Var(S)=\frac{n(n-1)(2n+5)-\sum\_{p=1}^{g}t\_{p}(t\_{p}-1)(2t\_{p}+5)}{18}$

where $g$ is the number of tied groups and $t\_{p}$ is the number of observations in the $p$-th tied group.

The standardized test statistic $Z$ is computed to assess significance:

$Z=\left\{\begin{matrix}\frac{S-1}{\sqrt{Var(S)}},&if S>0\\0,&if S=0\\\frac{S+1}{\sqrt{Var(S)}},&if S<0\end{matrix}\right. (Equation 2)$

A positive $Z$ indicates an upward trend, while a negative $Z$ indicates a downward trend. The null hypothesis of no trend is rejected at the significance level $α$ if $|Z|>Z\_{1-α/2}$. In this study, significance levels of $α=0.05$ ($|Z|>1.96$) and $α=0.01$ ($|Z|>2.576$) are used.

3.2 Sen's Slope Estimation

Sen's slope estimator [11] is used to estimate the true magnitude of the linear trend. Unlike linear regression, it is insensitive to outliers. For all data pairs $(x\_{i},x\_{j})$ where $j>i$, the slope $Q\_{k}$ is calculated:

$Q\_{k}=\frac{x\_{j}-x\_{i}}{j-i} (Equation 3)$

The Sen's slope $β$ is defined as the median of all $N=n(n-1)/2$ calculated slopes. A positive $β$ signifies an increasing trend (mm/year). The 95% confidence interval for the slope is estimated using a non-parametric procedure based on the normal distribution of the rank statistic.

3.3 Sliding Window Analysis

To characterize the scale dependence and non-stationarity of rainfall, a sliding window approach is applied. This study uses three distinct window sizes to capture variability at different temporal scales, as shown in Table 3a.

Table 3a. Sliding Window Configurations

For a window of size $w$, four statistical moments are calculated at each time step $k$. The arithmetic mean ($μ\_{k}$) is computed as $μ\_{k}=\frac{1}{w}\sum\_{i=k}^{k+w-1}x\_{i}$. The standard deviation ($σ\_{k}$) is calculated as $σ\_{k}=\sqrt{\frac{1}{w-1}\sum\_{i=k}^{k+w-1}(x\_{i}-μ\_{k})^{2}}$. The coefficient of variation ($CV\_{k}$) is derived as $CV\_{k}=\frac{σ\_{k}}{μ\_{k}}$, providing a normalized measure of variability. The trend slope within window ($a\_{k}$) represents the instantaneous rate of change within the window.

3.4 Hurst Exponent Analysis

The Hurst exponent ($H$) quantifies the long-term memory or persistence of a time series [12], estimated via Rescaled Range (R/S) analysis. The procedure involves three steps: first, dividing the series into sub-series of length $n$; second, calculating the range of cumulative deviations ($R$) and standard deviation ($S$) for each sub-series; and third, fitting the power law relationship $(R/S)\_{n}∝n^{H}$.

The value of $H$ ranges from 0 to 1, with interpretations summarized in Table 3b.

Table 3b. Hurst Exponent Interpretation

3.5 Inter-Regional Correlation Analysis

To assess spatial coherence, Pearson correlation coefficients ($r$) are calculated between all pairs of the 15 sub-regions. Correlation matrices are computed for data aggregated at 3-month, 6-month, and 12-month scales. This scale-dependent correlation analysis reveals how spatial synchronization evolves from local weather scales to regional climate scales.

4. Results and Analysis

4.1 Rainfall Spatial Distribution Characteristics

4.1.1 Overview of Spatial Pattern

Analysis of the 62-year (1961-2022) daily rainfall records reveals that the study area exhibits a distinct spatial distribution pattern characterized as "high-in-center, low-in-west, medium-in-east" (Figure 2). The daily average rainfall across the 15 sub-regions ranges from 3.47 mm to 5.68 mm, with an overall regional average of 3.98 mm.

This spatial pattern reflects the combined influences of maritime moisture availability from the East China Sea, topographic modification of regional airflow, local water body distributions and evapotranspiration, and confluence effects in river valley systems.

Figure 2. Spatial distribution of daily average rainfall (mm) across 15 sub-regions in Eastern Zhejiang (1961-2022)

4.1.2 Western Low-Value Area

The western zone, encompassing three sub-regions, records the lowest daily average rainfall with a zonal mean of 3.80 mm.

The lower rainfall in the western zone can be attributed to several factors. First, airflow subsidence effects occur because the western portions lie in the lee side of regional topographic features, potentially experiencing subsidence of air masses that reduces precipitation efficiency. Second, the transitional hills between the western plains and adjacent highlands act as terrain barriers that may intercept moisture-bearing air masses, creating a partial rain shadow effect. Third, compared to coastal areas, the western zone is farther from the primary maritime moisture source (East China Sea), resulting in reduced moisture availability.

4.1.3 Central High-Value Area

The central zone represents the rainfall maximum of the study area, with six sub-regions recording a zonal mean of 4.26 mm—12% higher than the western zone.

The central high-value area, particularly the Yuyao Plain Mazhu Midstream Area with its exceptional 5.68 mm daily average, owes its elevated rainfall to:

River Confluence Effects: The Mazhu Midstream Area is located at a major confluence zone where multiple tributaries of the Yao River system converge. This creates enhanced local water vapor availability and potential convergence of low-level airflow along river valleys.

Dense Water Network: The presence of numerous rivers, lakes, and irrigation channels significantly augments local moisture cycling through increased evaporation and transpiration.

Topographic Convergence: The central plains represent a natural collection zone for airflow from surrounding elevated terrain, enhancing low-level moisture convergence and orographic triggering of convection.

Notable Observation: The Yuyao Plain Mazhu Midstream Area (5.68 mm) receives 64% more daily rainfall than the Nansha Plain Area (3.47 mm), despite their relatively close proximity (~30 km). This remarkable gradient underscores the importance of local geographic factors in modulating regional precipitation patterns.

4.1.4 Eastern Medium-Value Area

The eastern zone, comprising six sub-regions along the coast and in the Yao River downstream area, records an intermediate zonal mean of 3.88 mm.

Despite direct exposure to maritime air masses from the East China Sea, the eastern coastal zone does not record the highest rainfall. This apparent "Coastal Paradox" is explained by:

Lack of Lifting Mechanisms: The flat coastal terrain provides minimal orographic lift to incoming maritime air masses.

Marine Boundary Layer Stability: The stable marine boundary layer over the cool East China Sea can suppress convective development.

Coastal Wind Effects: Strong onshore winds can transport moisture inland before significant precipitation occurs.

Internal Gradient: An interesting pattern emerges within the Cixi Plain series, showing a westward decrease from Midstream (3.90 mm) to West River (3.63 mm), potentially reflecting local moisture dynamics.

4.1.5 Summary of Spatial Distribution

Table 2. Daily Average Rainfall Statistics by Zone

The higher coefficient of variation (CV = 0.172) in the central zone reflects the exceptional status of the Yuyao Plain Mazhu Midstream Area, while the low CV (0.042) in the eastern zone indicates more homogeneous conditions among coastal sub-regions.

4.2 Long-term Trend Evolution Characteristics

This section presents a comprehensive analysis of rainfall trends across the 15 sub-regions of Eastern Zhejiang from 1961 to 2022, including Mann-Kendall test results, Sen's slope estimates, decadal variations, spatial patterns of trend intensity, uncertainty assessment, and Hurst exponent persistence analysis.

4.2.1 Trend Significance Analysis (Mann-Kendall Test)

Overall Results

The Mann-Kendall test was applied to the annual rainfall series of all 15 sub-regions. Results demonstrate that all regions exhibit statistically significant upward trends at the 0.05 significance level (Table 1).

Table 3. Mann-Kendall Test Results for Annual Rainfall (1961-2022)

Spatial Pattern: The Z-values reveal clear spatial differentiation. The strongest trends (Z > 4.0) are concentrated in the western Nansha area and the central/eastern coastal plains (Yubei Midstream, Cixi East/Midstream). In contrast, the hilly areas (Shaoyu) and the highly variable Mazhu Midstream area show relatively weaker signals (Z < 2.3), though still statistically significant.

4.2.2 Decadal Variations and Inter-annual Patterns

Figure 3 presents the annual trend change chart showing simultaneous variations across all 15 sub-regions from 1961 to 2022. The region exhibits pronounced decadal-scale oscillations superimposed on the long-term upward trend.

Figure 3. Annual trend change chart of daily average rainfall (1961-2022)

The key temporal features are summarized in Table 3c.

Table 3c. Key Temporal Features of Rainfall Variation (1961-2022)

A critical observation is the post-2010 intensification, characterized by increased frequency and amplitude of fluctuations. The Yuyao Plain Mazhu Midstream Area reached a record high of approximately 9 mm/day in 2021. This intensification suggests a shift toward more extreme precipitation regimes under climate change.

4.2.3 Individual Sub-region Trend Analysis

Detailed trend analysis was performed for each sub-region using Sen's slope estimation.

1. Coastal High-Change-Rate Regions

Cixi Plain Midstream Area (Figure 4)

The Cixi Plain Midstream Area exhibits the highest trend among all regions, with a Sen's slope of 7.99 mm/year. The time series shows a consistent upward trajectory from approximately 800 mm in the late 1960s to over 2000 mm in the 2020s. Notably, strong positive anomalies are frequently observed after 2010, suggesting an enhanced sensitivity to oceanic climate changes in this coastal zone.

Figure 4. Trend analysis in Cixi Midstream Area

Nansha Plain Area (Figure 5)

Despite being the driest region with the lowest baseline rainfall, the Nansha Plain Area shows the second-highest trend magnitude of 7.95 mm/year. Rainfall has increased by approximately 50% over the study period. A major cluster of positive anomalies is evident in the period from 2010 to 2022, indicating a rapid wetting trend in this historically drier western zone.

Figure 5. Trend analysis in Nansha Plain Area

Cixi Plain East River Area (Figure 6)

With a Sen's slope of 7.15 mm/year, the Cixi Plain East River Area displays a clear increasing pattern, particularly accelerated after the year 2000. Its temporal evolution is similar to the neighboring Cixi Midstream Area but with a slightly lower magnitude of change.

Figure 6. Trend analysis in Cixi East River Area

Cixi Plain West River Area (Figure 7)

The Cixi Plain West River Area records a Sen's slope of 6.42 mm/year. This value indicates a westward decrease in trend magnitude within the Cixi system, likely reflecting the increasing distance from the primary moisture source of the East China Sea.

Figure 7. Trend analysis in Cixi West River Area

2. River and Inland Plain Regions

Yuyao Plain Yaojiang Downstream Area (Figure 8)

This region shows the highest trend within the river group, with a Sen's slope of 6.66 mm/year. It is characterized by a large variability range (~800-2300 mm), clear decadal oscillations, and a strong increase in precipitation after 2010.

Figure 8. Trend analysis in Yaojiang Downstream Area

Yuyao Plain Yaojiang Upstream Area (Figure 9)

The Yaojiang Upstream Area exhibits a Sen's slope of 6.46 mm/year. Its trend pattern closely mirrors that of the downstream area, reflecting the strong hydrological connectivity and shared climatic influences within the Yaojiang river system.

Figure 9. Trend analysis in Yaojiang Upstream Area

Yuyao Plain Upstream & Downstream Areas (Figures 10-11)

Both the Yuyao Plain Upstream and Downstream areas show an identical Sen's slope of 6.30 mm/year. This synchronized behavior indicates common climate forcing across the inland plains, with a moderate growth rate typical of the central zone.

Figure 10. Trend analysis in Yuyao Upstream Area

Figure 11. Trend analysis in Yuyao Downstream Area

Yuyao Plain Mazhu Midstream Area (Figure 12)

The Mazhu Midstream Area is unique, exhibiting the largest variability (range 1250-3250 mm) and highest baseline rainfall in the region. Although its Sen's slope is a moderate 6.20 mm/year, the absolute increases are substantial, with a historic high approaching 3250 mm in 2021. The extreme inter-annual variability partially masks the linear trend signal, resulting in a lower Z-value (2.28) despite the large absolute gains.

Figure 12. Trend analysis in Mazhu Midstream Area

Yubei Plain Midstream Area (Figure 13)

With a Sen's slope of 5.20 mm/year, this area shows a very consistent upward trend. Despite the moderate slope magnitude, it has a high Z-value (4.20), indicating a steady and significant increase over the study period.

Figure 13. Trend analysis in Yubei Midstream Area

Fenghui Plain Area (Figure 14)

The Fenghui Plain Area records a Sen's slope of 5.08 mm/year, representing a below-average trend for the central zone. It is characterized by relatively stable inter-annual variability compared to its neighbors.

Figure 14. Trend analysis in Fenghui Plain Area

3. Hilly and Mountainous Regions

Shushan Plain Area (Figure 15)

Located in the western region, the Shushan Plain Area shows a Sen's slope of 5.20 mm/year. While moderate, its variability is higher than that of the coastal zones, reflecting its transitional geographic position.

Figure 15. Trend analysis in Shushan Plain Area

Yubei Plain Upstream Area (Figure 16)

This area, influenced by hilly terrain, shows a Sen's slope of 5.20 mm/year. The trend is moderate but consistent, typical of the inland transition zones.

Figure 16. Trend analysis in Yubei Upstream Area

Jiangbei Zhenhai Plain Area (Figure 17)

Despite its coastal location, the Jiangbei Zhenhai Plain Area records a Sen's slope of 4.91 mm/year, which is lower than other coastal regions. This suggests it may experience different synoptic influences or local microclimatic effects.

Figure 17. Trend analysis in Jiangbei Zhenhai Plain Area

Shaoyu Plain Area (Figure 18)

The Shaoyu Plain Area exhibits the lowest trend in the entire region, with a Sen's slope of 4.00 mm/year. The surrounding hilly terrain likely creates a stable microclimate and terrain blocking effects that limit moisture advection, buffering the large-scale warming signal.

Figure 18. Trend analysis in Shaoyu Plain Area

4.2.4 Spatial Pattern of Trend Magnitude

Figure 19 synthesizes the Sen's slope estimates, revealing a "Coastal > River Basin > Hilly" spatial pattern. Coastal areas show ~50% stronger trends (avg 7.45 mm/yr) than hilly areas (avg 4.91 mm/yr), indicating greater sensitivity to marine climate warming.

Figure 19. Spatial pattern of rainfall trend magnitudes

4.2.5 Trend Uncertainty Analysis (95% Confidence Intervals)

Figure 20 presents the 95% confidence intervals for Sen's slope estimates. A critical finding is that the 95% confidence intervals for ALL 15 sub-regions include zero. This indicates substantial statistical uncertainty in the magnitude of the trend, primarily due to the high inter-annual variability of the monsoon climate. While the MK test confirms the existence of trends, their precise rate of change varies significantly. The Mazhu Midstream Area displays the widest confidence interval (~400 mm/year), consistent with its extreme fluctuations.

Figure 20. Rainfall variation trends and 95% confidence intervals

4.2.6 Trend Persistence Analysis (Hurst Exponent)

To evaluate trend reliability, Hurst exponent ($H$) analysis was performed.

The Hurst exponent analysis yields consistent results across all 15 sub-regions, with all H values exceeding 0.5 (range: 0.5595 to 0.6257). The Nansha Plain Area exhibits the highest persistence ($H=0.6257$), aligning with its strong trend. In contrast, the Mazhu Midstream Area shows the lowest persistence ($H=0.5595$), where high variability reduces the persistence signal.

The consistent finding of $H>0.5$ across all regions confirms that the observed upward trends possess long-term memory and are likely to continue in the near future, rather than being random fluctuations. This provides robust evidence for long-term water resource planning.

Table 2. Hurst Exponent Values for Annual Rainfall (1961-2022)

4.3 Multi-time Scale Variation Characteristics

Sliding window analysis was employed to examine the scale-dependent behavior of rainfall in Eastern Zhejiang. By analyzing statistical characteristics at 3-month, 6-month, and 12-month scales, this section reveals how rainfall variability, trends, and patterns evolve across different temporal aggregation levels. The Cixi Plain East River Area is used as the representative case for detailed illustration, with regional comparisons provided.

4.3.1 Three-Month Scale Analysis (Seasonal/Intra-seasonal)

Representative Case: Cixi Plain East River Area

Figure 21 presents the 3-month sliding window analysis results, displaying four key statistics: daily average rainfall, standard deviation, coefficient of variation, and trend slope.

Figure 21. 3-month sliding window analysis for Cixi Plain East River Area

Detailed Observations

The daily average rainfall exhibits rapid, high-amplitude oscillations ranging from 0 to 10 mm, with clear seasonal signals showing summer maxima and winter minima. Peak values approach 10 mm during strong monsoon periods, while troughs drop near zero. The standard deviation ranges from 0 to 8 mm, tracking rainfall seasonality, with peaks exceeding 6 mm during periods of high variability such as typhoon sequences. The coefficient of variation frequently exceeds 1.0 (range 0 to 1.5+), indicating extreme relative variability where the standard deviation often surpasses the mean. The trend slope shows chaotic oscillations with rapid sign reversals within a range of ±5 mm; at this scale, "trends" are dominated by noise and lack persistence.

Regional Statistics at 3-Month Scale

Across all 15 sub-regions, the 3-month scale is characterized by a trend fluctuation range of ±16 mm (-16.44 to +16.60 mm) and a minimum correlation of 0.578. The key finding is that precipitation at this scale exhibits high instability and spatial heterogeneity, driven largely by local convective systems and terrain effects rather than large-scale climate patterns.

4.3.2 Six-Month Scale Analysis (Semi-annual)

Representative Case: Cixi Plain East River Area

Figure 22 presents the 6-month sliding window analysis, revealing how aggregation to half-year scales modifies statistical characteristics.

Figure 22. 6-month sliding window analysis for Cixi Plain East River Area

Detailed Observations

The daily average rainfall fluctuations smooth out to a range of 2.5-7.5 mm, with the annual cycle becoming clearer and reduced extremes compared to the 3-month scale. The standard deviation peak values are reduced by approximately 30% (range 1.5-5.5 mm). The coefficient of variation stabilizes around 0.7-0.8, with fewer events exceeding 1.0. The trend slope fluctuation range reduces significantly to ±2 mm, with trends showing longer wavelengths and fewer reversals, indicating emerging persistence.

Regional Statistics at 6-Month Scale

At the 6-month scale, the trend fluctuation range narrows to ±5 mm (-5.30 to +5.09 mm), representing a 70% reduction in volatility compared to the 3-month scale. The minimum correlation increases to 0.623. The key finding is that semi-annual aggregation filters out high-frequency weather noise, revealing clearer decadal patterns and improved spatial coherence.

4.3.3 Twelve-Month Scale Analysis (Annual)

Representative Case: Cixi Plain East River Area

Figure 23 presents the 12-month (annual) sliding window analysis, demonstrating the most stable characterization of rainfall behavior.

Figure 23. 12-month sliding window analysis for Cixi Plain East River Area

Detailed Observations

The daily average rainfall shows smooth, quasi-sinusoidal oscillations within a constrained range of 2-5 mm, with long-term decadal variations becoming the dominant feature (e.g., early 1990s peak, mid-2010s rise). The coefficient of variation drops to a stable range of 0.4-1.0, indicating predictable relative variability. The trend slope fluctuations are drastically reduced to ±0.5 mm, with annual-scale trends showing high persistence and reversing only with major climate shifts.

Regional Statistics at 12-Month Scale

At the 12-month scale, the trend fluctuation range narrows to ±1.7 mm (-1.58 to +1.73 mm), representing approximately 90% reduction from the 3-month scale. The minimum correlation reaches 0.640, the highest among all scales. The key finding is that at the annual scale, rainfall patterns are controlled by large-scale climate modes (e.g., ENSO, Monsoon) rather than local weather, resulting in maximum stability and spatial synchronization.

4.3.4 Scale Dependence Synthesis

The analysis confirms a strong scale dependence in rainfall characteristics. Regarding variability reduction, trend fluctuation amplitude decreases by approximately 90% from 3-month (±16 mm) to 12-month (±1.7 mm) scales. In terms of correlation enhancement, spatial coherence improves as the analysis window widens, with minimum correlation increasing from 0.578 to 0.640. The physical interpretation of this hierarchy reflects the transition from weather-dominated processes (stochastic, local) at short scales to climate-dominated processes (organized, regional) at long scales. This finding suggests that annual statistics provide the most reliable basis for long-term water resource planning, while short-term operations must account for extreme instability.

4.4 Scale Dependence of Regional Rainfall Correlation

This section examines the inter-regional correlation patterns of rainfall across the 15 sub-regions of Eastern Zhejiang. Correlation matrices were computed for 3-month, 6-month, and 12-month aggregated series to reveal how spatial coherence evolves with temporal scale.

4.4.1 Three-Month Scale Correlation Analysis

Figure 24 presents the correlation matrix at the 3-month scale.

Figure 24. Inter-regional correlation matrix (2-month scale)

Statistical Overview and Spatial Patterns

The correlation analysis at the 3-month scale reveals an average correlation coefficient of 0.83 across the region, with values ranging from a minimum of 0.709 to a maximum of 1.000. The lowest correlation (0.709) is observed between the Yuyao Plain Mazhu Midstream Area and the Nansha Plain Area.

Geographically, distinct clusters emerge even at this short time scale. The Coastal Cluster exhibits high internal coherence; for instance, the correlation between Cixi East River and Cixi Midstream reaches 0.905. Similarly, the River Basin Cluster demonstrates strong hydrological connectivity, evidenced by the perfect correlation (1.000) between Yuyao Upstream and Downstream areas. However, the Yuyao Plain Mazhu Midstream Area stands out as an anomalous region, showing systematically lower correlations with most other regions (e.g., 0.709 with Nansha). This decoupling likely reflects its unique hydro-geographic conditions and high local variability, which are more pronounced at seasonal scales.

Interpretation

At the seasonal scale (3-month), local meteorological factors such as convective systems and terrain effects play a dominant role. This dominance results in significant spatial heterogeneity across the study area, leading to relatively lower inter-regional correlations compared to longer time scales.

4.4.2 Six-Month Scale Correlation Analysis

Figure 25 presents the correlation matrix at the 6-month scale.

Figure 25. Inter-regional correlation matrix (6-month scale)

Statistical Changes and Cluster Strengthening

As the aggregation scale extends to 6 months, the average correlation coefficient increases slightly to 0.85, representing a net gain of 0.02 compared to the 3-month scale. The minimum observed correlation also improves to 0.718.

This scale extension leads to a noticeable strengthening of regional clusters. The coastal cluster, in particular, shows significant improvement in internal coherence; for example, the correlation between Cixi Midstream and West River rises from 0.899 to 0.938. This enhancement suggests that semi-annual aggregation effectively filters out a portion of the high-frequency noise associated with short-term weather events, thereby revealing stronger underlying oceanic climate signals, especially in coastal zones.

4.4.3 Twelve-Month Scale Correlation Analysis

Figure 26 presents the correlation matrix at the 12-month (annual) scale, showing the highest overall spatial coherence.

Figure 26. Inter-regional correlation matrix (12-month scale)

Overall Coherence and Anomalous Patterns

The 12-month scale analysis demonstrates the highest level of spatial synchronization, with the average correlation reaching 0.87 (an increase of 0.04 from the 3-month scale). Correlation coefficients across the matrix range from 0.681 to 1.000.

A notable finding is the "Increase-then-Decrease" pattern observed in the Yuyao Mazhu Midstream Area. For several region pairs, such as with Nansha, the correlation first increases from the 3-month scale (0.709) to the 6-month scale (0.718), but then unexpectedly decreases at the 12-month scale (0.681). This anomaly suggests that while seasonal aggregation initially improves coherence, the annual total rainfall in the Mazhu area may be decoupled from regional patterns. This could be due to specific local hydrological processes, such as moisture recycling, which operate on different timescales than the broader regional climate.

In terms of spatial patterns, the Coastal Cluster reaches maximum coherence with an average correlation of approximately 0.93, driven by common large-scale marine climate forcing. In contrast, the Hilly Cluster shows the smallest increase in correlation, indicating that terrain-induced heterogeneity persists even when data are aggregated to annual scales.

4.4.4 Summary of Correlation Evolution

Table 4. Correlation Statistics Across Time Scales

Implications for Management

The scale-dependent correlation patterns have direct implications for water resource management. High-correlation regions, such as the Coastal and River Basin clusters, can be managed as coordinated systems for long-term planning, leveraging their synchronized climate response. Conversely, low-correlation regions like the Mazhu Midstream Area require independent operational strategies and robust risk management plans, as their hydrological behavior may diverge significantly from the regional average, especially during extreme years.

5. Discussion and Conclusions

5.1 Discussion

5.1.1 Mechanisms of Spatial Differentiation

The study reveals a distinct "high-in-center, low-in-west" rainfall pattern. The exceptional rainfall in the Mazhu Midstream Area (5.68 mm/day) is likely driven by confluence zone enhancement. As a major convergence point of the Yao River tributaries, this area experiences channelized airflow and forced uplift. Furthermore, the dense network of rivers and wetlands enhances local evapotranspiration, creating a moisture recycling feedback loop that sustains high precipitation. In contrast, the Nansha Plain Area (3.47 mm/day) in the west likely suffers from lee-side subsidence effects and terrain barriers that intercept moisture transport from the coast.

5.1.2 Climate Change Signatures and Comparison

The universal upward trends (4.00-7.99 mm/year) across all 15 sub-regions align with the global "wet-gets-wetter" paradigm documented in IPCC reports [1] and global analyses [4]. Our finding of a "Coastal Enhancement" pattern (average trend 7.45 mm/year) is consistent with studies in the Yangtze River Delta [22] and Zhejiang Province [25], which link enhanced coastal precipitation to warming sea surface temperatures and intensified moisture flux from the East China Sea.

Significantly, we observed a post-2010 intensification of rainfall variability, with record highs occurring in 2021 (e.g., ~3250 mm in Mazhu). This aligns with findings by Su et al. [21] regarding increased extremes in the Yangtze Basin. The high Hurst exponents ($H>0.5$) for all regions provide novel evidence that these upward trends are not temporary fluctuations but persistent climate shifts.

5.1.3 Implications for Engineering Operations

The findings have direct implications for the Eastern Zhejiang Water Diversion Project. A notable source-receiver mismatch exists: the primary water source area (Mazhu) has the highest rainfall but also the highest variability, while the key recipient areas (Nansha, Shaoyu) have the lowest baseline rainfall but are experiencing the fastest increasing trends. This dynamic requires flexible allocation strategies. Regarding scale-dependent management, the increase in spatial correlation from 0.83 (3-month) to 0.87 (12-month) suggests that strategic planning can be coordinated regionally based on annual climate coherence. However, tactical operations for flood control must remain independent at the sub-regional level due to lower short-term correlations and high local variability.

5.2 Conclusions

Based on the systematic analysis of 62 years of daily rainfall data (1961-2022), this study draws five main conclusions. First, regarding spatial pattern, rainfall follows a distinct "high-in-center, low-in-west" distribution, with the Central zone (Mazhu Midstream) receiving 64% more rainfall than the Western zone (Nansha), driven by river confluence effects and local topography. Second, in terms of universal increase, all 15 sub-regions show statistically significant upward trends ($p<0.05$), with trend magnitudes exhibiting a clear spatial gradient: Coastal (7.45 mm/yr) > River Basin (6.38 mm/yr) > Hilly (4.91 mm/yr). Third, concerning trend persistence, Hurst exponent analysis yields values between 0.56 and 0.63 for all regions, confirming that the observed upward trends are persistent and likely to continue in the near future. Fourth, with respect to scale dependence, rainfall characteristics are highly scale-dependent; as analysis scales extend from 3 to 12 months, trend fluctuation amplitude decreases by approximately 90% (from ±16 mm to ±1.7 mm), and inter-regional correlation improves by 5-11%, indicating that long-term patterns are controlled by regional climate factors while short-term patterns are dominated by local weather noise. Fifth, regarding the correlation anomaly, the Mazhu Midstream Area exhibits a unique "increase-then-decrease" correlation pattern, reflecting its distinctive hydro-geographic behavior as a semi-independent confluence zone.

5.3 Recommendations

Based on the research findings, the following recommendations are proposed, summarized in Table 5.

Table 5. Recommendations for Water Diversion Project Management

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