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 a combination of unique geographic and hydrological factors.

The primary driver is the river confluence effect. The Mazhu Midstream Area is situated at a major convergence zone where multiple tributaries of the Yao River system meet. This geographic configuration creates an environment with enhanced local water vapor availability and facilitates the convergence of low-level airflow along the river valleys. Additionally, the region features a dense water network comprised of numerous rivers, lakes, and irrigation channels. This intricate web of water bodies significantly augments local moisture cycling through increased evaporation and transpiration, creating a self-sustaining feedback loop that favors precipitation. Furthermore, the central plains act as a natural collection zone for airflow descending from the surrounding elevated terrain, which enhances low-level moisture convergence and the orographic triggering of convection.

From an engineering perspective, this high rainfall has critical implications. The Mazhu area serves as the geographic core of the South Line diversion route, which conveys water from the Cao'e River to Ningbo. Its status as a rainfall maximum means it acts as a significant natural water collection zone, directly impacting the operation of key hydraulic nodes such as the Shushan Grand Sluice and the Yao River Grand Sluice. The abundance of local water resources in this area can effectively reduce the dependence on diverted water from the Cao'e River during wet periods. However, the associated high variability imposes strict requirements on the flood drainage capacity of the Yao River system. Operational protocols must carefully balance the intake of external water with the need to discharge excessive local runoff to prevent waterlogging.

A notable observation from the data is that the Yuyao Plain Mazhu Midstream Area receives 64% more daily rainfall than the Nansha Plain Area, despite their relatively close proximity of approximately 30 km. This remarkable gradient underscores the vital importance of local geographic factors in modulating regional precipitation patterns and necessitates highly differentiated management strategies for each sub-region.

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)

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. The 15 sub-regions are categorized into three groups based on their geographic characteristics and trend magnitudes.

4.2.3.1. Coastal High-Change-Rate Regions

The coastal zone exhibits the highest trend magnitudes among all regions, reflecting enhanced sensitivity to oceanic climate changes. The Cixi Plain Midstream Area records the highest trend in the entire study area, with a Sen’s slope of 7.99 mm/year; its time series shows a consistent upward trajectory from approximately 800 mm in the late 1960s to over 2000 mm in the 2020s, with strong positive anomalies frequently observed after 2010 (Figure 4).

The Nansha Plain Area, despite being the driest region with the lowest baseline rainfall, shows the second-highest trend magnitude of 7.95 mm/year, with rainfall increasing by approximately 50% over the study period; a major cluster of positive anomalies is evident from 2010 to 2022, indicating a rapid wetting trend in this historically drier western zone (Figure 5). The Cixi Plain East River Area displays a Sen’s slope of 7.15 mm/year with a clear increasing pattern particularly accelerated after 2000, exhibiting temporal evolution similar to the neighboring Cixi Midstream Area but with slightly lower magnitude (Figure 6). The Cixi Plain West River Area records a Sen’s slope of 6.42 mm/year, indicating a westward decrease in trend magnitude within the Cixi system, likely reflecting increasing distance from the primary moisture source of the East China Sea (Figure 7).

The trend characteristics of coastal regions are summarized in Table 4a.

Table 4a. Trend Characteristics of Coastal High-Change-Rate Regions

4.2.3.2. River and Inland Plain Regions

The river and inland plain regions exhibit moderate trend magnitudes, characterized by strong hydrological connectivity and pronounced decadal oscillations. The Yuyao Plain Yaojiang Downstream Area shows the highest trend within this group at 6.66 mm/year, featuring a large variability range of approximately 800-2300 mm, clear decadal oscillations, and strong precipitation increases after 2010 (Figure 8). The Yaojiang Upstream Area exhibits a Sen’s slope of 6.46 mm/year with a trend pattern closely mirroring the downstream area, reflecting strong hydrological connectivity and shared climatic influences within the Yaojiang river system (Figure 9).

Both the Yuyao Plain Upstream and Downstream areas show an identical Sen’s slope of 6.30 mm/year, indicating synchronized behavior and common climate forcing across the inland plains with a moderate growth rate typical of the central zone (Figures 10-11). The Mazhu Midstream Area is unique in this group, 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, and the extreme inter-annual variability partially masks the linear trend signal, resulting in a lower Z-value of 2.28 despite large absolute gains (Figure 12).

The Yubei Plain Midstream Area shows a Sen’s slope of 5.20 mm/year with a very consistent upward trend; despite the moderate slope magnitude, it has a high Z-value of 4.20, indicating a steady and significant increase over the study period (Figure 13). The Fenghui Plain Area records a Sen’s slope of 5.08 mm/year, representing a below-average trend for the central zone, characterized by relatively stable inter-annual variability compared to its neighbors (Figure 14).

The trend characteristics of river and inland plain regions are summarized in Table 4b.

Table 4b. Trend Characteristics of River and Inland Plain Regions

4.2.3.3. Hilly and Mountainous Regions

The hilly and mountainous regions exhibit the lowest trend magnitudes, likely due to terrain blocking effects and stable microclimates that buffer large-scale climate signals. The Shushan Plain Area, located in the western region, shows a Sen’s slope of 5.20 mm/year; while moderate, its variability is higher than that of coastal zones, reflecting its transitional geographic position (Figure 15). The Yubei Plain Upstream Area, influenced by hilly terrain, shows an identical Sen’s slope of 5.20 mm/year with a moderate but consistent trend typical of inland transition zones (Figure 16).

The Jiangbei Zhenhai Plain Area presents an interesting case: despite its coastal location, it records a Sen’s slope of only 4.91 mm/year, which is lower than other coastal regions, suggesting different synoptic influences or local microclimatic effects (Figure 17). The Shaoyu Plain Area exhibits the lowest trend in the entire study region at 4.00 mm/year; the surrounding hilly terrain likely creates a stable microclimate and terrain blocking effects that limit moisture advection, effectively buffering the large-scale warming signal (Figure 18).

The trend characteristics of hilly and mountainous regions are summarized in Table 4c.

Table 4c. Trend Characteristics of Hilly and Mountainous Regions

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)

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

4.3.1.1 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.

4.3.1.2 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)

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

4.3.2.1 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.

4.3.2.2 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)

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

4.3.3.1 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.

4.3.3.2 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 (3-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.