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Spatiotemporal Variation Characteristics and Trend Analysis of Rainfall in Eastern Zhejiang from 1961 to 2022

Abstract: This study investigates the spatiotemporal distribution characteristics of rainfall in 15 typical sub-regions of Eastern Zhejiang based on long-term sequence data from 1961 to 2022, employing Mann-Kendall test, Sen’s slope estimation, and sliding window analysis. Results show that daily average rainfall (3.47-5.68mm) exhibits a distinct “high-in-center, low-in-west, medium-in-east” spatial pattern, with the central high-value area (Yuyao Plain Mazhu Midstream Area) reaching 5.68mm and the western low-value area (Nansha Plain Area) only 3.47mm. Mann-Kendall tests indicate significant upward trends (p<0.05) across all regions, while Sen’s slope estimates reveal spatial variations in trend magnitude, showing a “high-in-coastal, medium-in-river, low-in-hilly” distribution: coastal areas have the highest rates (Cixi Plain Midstream Area 7.99mm/year), while hilly mountainous regions have the lowest (Shaoyu Plain Area 4.00mm/year). Multi-time scale analysis reveals rainfall’s scale dependence: 3-month scale shows significant seasonal fluctuations (trend variations ±16mm) with low regional correlation (0.578); 6-month scale exhibits reduced fluctuations (±5mm) with strengthened correlation (0.623); 12-month scale demonstrates more stable trends (±1.7mm) with further increased correlation (0.640). As time scale increases, regional rainfall patterns become more synchronized while maintaining spatial differentiation, reflecting the combined effects of large-scale climate factors and local geographical features. These findings provide scientific guidance for the Eastern Zhejiang Water Diversion Project. Keywords: Eastern Zhejiang; rainfall spatiotemporal distribution; trend analysis; sliding window; Mann-Kendall test; spatial correlation

0. Introduction The Eastern Zhejiang region is located on the eastern coast of Zhejiang Province, with an average annual precipitation of over 1400mm, but its spatiotemporal distribution is extremely uneven. The Eastern Zhejiang Water Diversion Project, launched in June 2014 (with an average annual diversion volume of 890 million m³), provides key support for solving regional water shortage problems. Based on long-term sequence data from 1961 to 2022, this study employs the Mann-Kendall test and Sen’s slope estimation method to analyze the spatiotemporal distribution characteristics and evolution laws of rainfall in 15 typical sub-regions.
1. Research Background and Significance 1.1 Regional Hydrological and Climate Characteristics In Eastern Zhejiang, the precipitation during the Meiyu season (June-July) and Typhoon season (August-September) accounts for over 60% of the annual total, and is often accompanied by rainstorms and flood disasters. This makes the area prone to mountain hazards such as landslides and debris flows. The Eastern Zhejiang Water Diversion Project began operation in June 2014. It is the largest cross-basin water transfer project in Zhejiang Province, involving 19 counties (cities, districts) within Hangzhou, Shaoxing, Ningbo, and Zhoushan, with an average annual diversion volume of 890 million m³. Recent studies indicate that precipitation patterns in this region are undergoing significant changes. While annual precipitation shows an overall increasing trend, regional differences are obvious, with frequent extreme precipitation events occurring in some areas. These changes directly affect the scheduling operation of the diversion project and regional water resource allocation, while also bringing new challenges for flood control and disaster reduction. 1.2 Current Status and Methodological Advantages Precipitation in Zhejiang Province shows significant differences across regions and seasons. For example, rainfall during the flood season has increased in the eastern region while decreasing in the southwest. Although some studies have used relatively long-term sequence data, challenges remain regarding data homogeneity and integrity. Variations in the number of stations and time spans used in different studies affect the comparability and consistency of results. The Mann-Kendall test, as a non-parametric test method, has unique advantages in the trend analysis of hydro-meteorological elements. It does not require data to follow a specific distribution and is insensitive to outliers, making it particularly suitable for identifying trends in non-normally distributed data like precipitation. Meanwhile, Sen’s slope method estimates trend magnitude and direction by calculating the median of differences between data pairs; it possesses high robustness and stability, and its insensitivity to outliers gives it broader applicability than traditional linear regression. However, the integrated application of these two methods in precipitation research in Eastern Zhejiang is still relatively rare, especially regarding systematic research at the regional scale. 1.3 Research Objectives and Content This paper focuses on the 15 sub-regions covered by the Eastern Zhejiang Water Diversion Project. Based on long-term observation data from 1961 to 2022, and utilizing the Mann-Kendall test and Sen’s slope estimation methods, the study conducts the following research centered on engineering requirements: Analysis of Rainfall Spatial Distribution Laws: Focus on studying rainfall differences among different water-receiving areas, revealing the differences in rainfall characteristics of receiving areas such as the Nansha-Shushan-Shaoyu Plain composite area, to provide a basis for the project’s supply-demand balance. Assessment of Rainfall Trend Change Characteristics: Identify rainfall evolution laws in key receiving areas by quantitatively analyzing the rate of change and statistical significance of rainfall trends in each receiving area, providing scientific support for the long-term operation of the project. Discussion on Factors Influencing Rainfall Distribution: Analyze the influence mechanisms of factors such as topography, geomorphology, water vapor transport channels, and underlying surface characteristics on the spatial distribution of rainfall. Based on the spatiotemporal variation characteristics of rainfall and the differences between different receiving areas, optimization schemes for project water supply scheduling are proposed.
2. Study Area and Data Characteristics 2.1 Overview of the Study Area The Eastern Zhejiang region includes 15 typical sub-regions across five main areas: Xiaoshan, Shaoyu, Yuyao, Cixi, and Ningbo (as shown in Figure 1). The multi-year average precipitation in the region ranges between 1273.5 mm and 1454.8 mm, with significant inter-annual variation; the maximum annual precipitation reached 2050.1 mm, while the minimum dropped to 682.2 mm. Precipitation is mainly concentrated in the main flood season (April-July, accounting for 39.9-44.1%) and the typhoon season (August-September, accounting for 21.0-26.6%). The study area spans multiple water systems, including the Qiantang River, Cao’e River, and Yao River, with varying river network densities and lake distributions across different sections. Influenced by topographical conditions, the regions have formed differentiated drainage systems dominated by sluice and dam controls. Concurrently, the combined effects of topography, water systems, and engineering facilities have created spatial differences in regional flood control capabilities and risk characteristics, providing suitable typical cases for studying rainfall response. 2.2 Rainfall Characteristics and Data Analysis The precipitation characteristics of the study area present significant spatiotemporal differentiation. Based on the analysis of long-term observation data from 1961 to 2022, the region’s multi-year average precipitation fluctuates between 1273.5 mm and 1454.8 mm, with significant inter-annual variation (maximum 2050.1 mm, minimum 682.2 mm). In terms of seasonal distribution, precipitation is mainly concentrated in the main flood season (April-July, 39.9-44.1%) and the typhoon season (August-September, 21.0-26.6%), while precipitation in other months accounts for a smaller proportion (October to the following March, 31.2-36.6%); this distribution characteristic is closely related to the regional monsoon climate and typhoon impacts. To ensure the reliability of the research results, this study established a strict data quality control system. In the preprocessing stage, continuity tests were used to identify time gaps, the criterion was used to screen for outliers, and the adjacent station interpolation method was used to supplement missing data. In the data correction stage, combined with the sliding t-test method and cross-validation of adjacent stations, the homogeneity and consistency of the data series were ensured.

Fig. 1 Study area (15 sub-regions) 3. Research Methods 3.1 Mann-Kendall Test The Mann-Kendall test is a non-parametric test method used to detect monotonic trends in time series data. It does not require the assumption that data follows a specific distribution and is suitable for non-normally distributed data. When |Z|>1.96, it indicates a significant trend at the 0.05 significance level. The calculation formula for the Mann-Kendall test statistic S is: █(S=∑(i=1)^(n-1)▒∑(j=i+1)^n▒sgn (x_j-x_i )#(1) ) Where sgn(θ) is the sign function: █(sgn(θ)={■(1,&θ>0@0,&θ=0@-1,&θ<0)┤#(2) ) When n≥8, the statistic S approximately follows a normal distribution: █(E(S)=0#(3) ) █(Var(S)=n(n-1)(2n+5)/18#(4) ) The standardized statistic Z is calculated as: █(Z={■((S-1)/√(Var(S) ),&S>0@0,&S=0@(S+1)/√(Var(S) ),&S<0)┤#(4) ) 3.2 Sen’s Slope Method Sen’s slope method is a non-parametric method used to estimate the magnitude and direction of trends in a time series. It is obtained by calculating the median of the differences between all possible pairs of data points and has high robustness. For every pair of data points in the time series, the slope is calculated: █(Q_k=(x_j-x_i)/(j-i)#(5) )

Where j>i，k=1,2,…,N and N=n(n-1)/2. The Sen’s slope estimate β is calculated as: █(β={■(Q_[(N+1)/2] ,&N"为odd" @(Q_[N/2] +Q_((N+2)/2]))/2,&N"为even" )┤#(6) )

3.3 Sliding Window Analysis Sliding window analysis calculates the changes in statistical characteristics within a window by moving a fixed-size window across the time series. For a time series and window size , the main statistics are calculated as follows: Arithmetic Mean: █(μ_k=1/w ∑_(i=k)^(k+w-1)▒x_i #(7) )

Standard Deviation: █(σ_k=√(1/(w-1) ∑_(i=k)^(k+w-1)▒(x_i-μ_k )^2 )#(8) )

Coefficient of Variation: █(CV_k=σ_k/μ_k #(9) )

Slope of Linear Trend within Window: █(a_k=(w∑(i=k)^(k+w-1)▒i x_i-∑(i=k)^(k+w-1)▒i ∑(i=k)^(k+w-1)▒x_i )/(w∑(i=k)^(k+w-1)▒i^2 -(∑_(i=k)^(k+w-1)▒i)^2 )#(10) )

Where: k is the starting position of the window （k = 1, 2, ..., N-w+1）. The study selected three time scales: 3 months, 6 months, and 12 months for analysis. 4. Analysis of Rainfall Spatiotemporal Distribution Characteristics 4.1 Basic Characteristics of Spatial Distribution (Regional Rainfall Distribution Map) The daily average rainfall in the study area presents a spatial pattern of “high in the center, low in the west, and medium in the east,” as shown in Figure 2, with a range of 3.47-5.68 mm. The central high-value area (Yuyao Plain Mazhu Midstream Area, Yuyao Plain Upstream Area, and Yubei Plain Midstream Area) has the highest daily average rainfall, reaching 5.68 mm in the Yuyao Plain Mazhu Midstream Area. The western low-value area (Nansha Plain Area and Shaoyu Plain Area) has the lowest daily average rainfall, with the Nansha Plain Area at only 3.47 mm.

Fig. 2 Daily average rainfall distribution in eastern Zhejiang sub-regions 4.2 Long-term Trend Evolution Characteristics The annual trend change map of rainfall for the 15 regions in Eastern Zhejiang from 1961 to 2022 displays distinct spatiotemporal differentiation characteristics. As shown in Table 1 (Mann-Kendall test analysis), coastal areas such as the Nansha Plain Area (), Yubei Plain Midstream Area (), and Cixi Plain (Midstream Area , East River Area ) have the strongest trends, while the Shaoyu Plain Area () and Yuyao Plain Mazhu Midstream Area () have weaker trends. Table 1 Mann-Kendall Test Analysis Results Region Trend Description Significance p-value z-value Nansha Plain Area Upward Significant 0 4.2702 Shushan Plain Area Upward Significant 0.003 2.9642 Shaoyu Plain Area Upward Significant 0.0231 2.2717 Yubei Plain Upstream Area Upward Significant 0.0052 2.7941 Yubei Plain Midstream Area Upward Significant 0 4.2033 Fenghui Plain Area Upward Significant 0.0056 2.7698 Yuyao Plain Upstream Area Upward Significant 0.0002 3.7173 Yuyao Plain Downstream Area Upward Significant 0.0002 3.7173 Yuyao Plain Mazhu Midstream Area Upward Significant 0.0224 2.2839 Yuyao Plain Yaojiang Upstream Area Upward Significant 0.0005 3.4987 Yuyao Plain Yaojiang Downstream Area Upward Significant 0.0006 3.4258 Cixi Plain West River Area Upward Significant 0.0004 3.5108 Cixi Plain Midstream Area Upward Significant 0 4.0818 Cixi Plain East River Area Upward Significant 0 4.1061 Jiangbei Zhenhai Plain Area Upward Significant 0.0048 2.8184 From Figure 3, it can be seen that the Eastern Zhejiang region presents obvious decadal variations. The years 1967, 1978-1979, and 2003 were periods of low rainfall for the entire region, while 1973, 1989, 2012, 2015, and 2019-2021 were periods of high rainfall for multiple regions. After 2010, both the frequency and amplitude of regional rainfall fluctuations increased, especially in the Yuyao Plain Mazhu Midstream Area, Yubei Plain Midstream Area, and Fenghui Plain Area, where rainfall increases were significant; this may be related to the increased frequency of extreme precipitation events in the context of climate change.

Fig. 3 Annual trend change chart Figure 4 shows the time series changes and linear trends of rainfall for the 15 sub-regions in Eastern Zhejiang from 1961 to 2022. The annual rainfall in the Nansha Plain Area steadily increased from about 1000 mm in the 1960s to about 1500 mm in the 2020s; although inter-annual fluctuations were significant, the long-term increasing trend is clear. Similarly, the Yuyao Plain Mazhu Midstream Area had the largest fluctuation range (1750-3250 mm); although its Sen’s slope was at a medium level (6.20 mm/year), its baseline rainfall was significantly higher than other regions. Most areas in Eastern Zhejiang experienced significant rainfall increase periods in the early 1980s, late 1990s, and after 2010.

Fig. 4 Rainfall observations and trend lines for 15 sub-regions in eastern Zhejiang Figure 5 spatially categorizes the Sen’s slopes of all regions, showing that rainfall changes in Eastern Zhejiang present a spatial pattern of “high in coastal areas, medium in river areas, and low in hilly areas”. The high change rate areas along the coast (Cixi Plain Midstream Area 7.99 mm/year, Nansha Plain Area 7.95 mm/year) show the greatest changes, while the hilly and mountainous areas (Shaoyu Plain Area 4.00 mm/year, Yubei Plain Upstream Area 4.35 mm/year) show smaller changes.

Fig. 5 Spatial pattern of rainfall in eastern Zhejiang From Figure 6, it can be seen that the 95% confidence intervals for the trends in all regions include zero. This indicates that although the Mann-Kendall test shows the existence of trends, considering the range of natural variability, the statistical significance of these upward trends at the 95% confidence level is insufficient. The width of the confidence intervals reflects the differences in rainfall variability across regions, with the Yuyao Plain Mazhu Midstream Area notably displaying the widest confidence interval, indicating the most significant inter-annual fluctuations in rainfall in this area.

Fig. 6 Rainfall change trend and 95% confidence interval in eastern Zhejiang 4.3 Multi-time Scale Variation Characteristics Sliding window analysis reveals the scale dependence of rainfall in Eastern Zhejiang. On the 3-month scale, precipitation exhibits high instability, with average precipitation ranging from 3.468 to 5.680 mm, a coefficient of variation of 0.525-0.574, and large trend fluctuation amplitudes (-16.442 to 16.596 mm). Taking the Cixi Plain East River Area as an example (Figure 7), daily average precipitation fluctuates between 0-10 mm, the coefficient of variation often exceeds 1.0, and trend fluctuations reach ±5 mm. At this scale, inter-regional correlation is low (lowest 0.578), especially between coastal and inland mountain areas, indicating significant spatial heterogeneity in short-term precipitation patterns.

Fig. 7 3-month sliding window analysis of Cixi Plain East River District On the 6-month scale, the precipitation range is similar (3.474-5.673 mm), but the coefficient of variation increases (0.603-0.651), and trend fluctuations weaken (-5.301 to 5.092 mm). The rainfall fluctuation in the Cixi Plain East River Area (Figure 8) becomes smoother (2.5-7.5 mm), and trend changes narrow to ±2 mm, indicating that precipitation tends to stabilize on the half-year scale. Inter-regional correlations strengthen (lowest 0.623), with correlation coefficients between adjacent regions mostly exceeding 0.8.

Fig. 8 6-month sliding window analysis of Cixi Plain East River District On the 12-month scale, the spatial distribution of precipitation is stable (3.470-5.664 mm), and trend changes are flatter (-1.579 to 1.729 mm). Rainfall in the Cixi Plain East River Area (Figure 9) stabilizes in the 2-5 mm range, with a coefficient of variation of 0.5-1.0, and trend changes of only ±0.5 mm. Regional correlations further improve (lowest 0.640), and spatial clustering becomes more obvious; internal correlation in coastal areas reaches 0.85-0.89, and 0.75-0.85 in river areas.

Fig. 9 12-month sliding window analysis of Cixi Plain East River District The Cixi Plain East River Area showed precipitation peaks in the early 1990s, early 2000s, and mid-2010s; periodicity is more obvious on the 12-month scale, possibly related to ENSO events. As the time scale increases, regional precipitation patterns tend to become consistent but maintain spatial differentiation, reflecting the combined effects of large-scale climate factors and local geographical factors. 4.4 Correlation Characteristics Based on Multi-time Scales As shown in Figure 10, as the analysis window expands from 3 months to 12 months, inter-regional correlations generally strengthen, with the average correlation coefficient increasing from 0.83 to 0.87, indicating that rainfall patterns in Eastern Zhejiang are more synergistic and consistent on long time scales. This is consistent with seasonal rainfall characteristics and the influence of large-scale climate factors; short-term variations are greatly affected by local factors, while long-term scales reflect common features of regional climate change. Internal correlation in coastal high-change-rate areas (Nansha Plain Area, Cixi Plain Midstream/East River/West River Areas, Yubei Plain Midstream Area) significantly strengthens with time scale (0.82 0.86). In particular, the correlation between Cixi Plain Midstream Area and West River Area increased from 0.899 to 0.941, an increase of 0.042, indicating that they are more obviously affected by similar marine climates on long time scales. Internal correlation changes in river and inland plain areas are more complex. The correlation between the Yuyao Plain Yaojiang Upstream and Downstream areas continued to strengthen (0.921 0.944), indicating tighter hydrological connections on long time scales. However, the Yuyao Plain Mazhu Midstream Area shows a unique “increase then decrease” pattern with most regions; for example, its correlation with the Nansha Plain Area (0.709 0.718 0.681) may be related to the area’s unique geographical location and hydrological characteristics. The increase in internal correlation in hilly and mountainous areas is relatively small (0.83 0.85), indicating that rainfall patterns in mountainous areas are relatively stable across different time scales, continuously influenced by terrain blocking effects. The correlation between the Jiangbei Zhenhai Plain Area and the Cixi Plain East River Area shows a characteristic of increasing first and then slightly decreasing (0.857 0.891 0.889), which may reflect differences in climate driving factors on seasonal and annual scales.

Fig. 10 Inter-regional correlations with 3-month sliding window

Fig. 11 Inter-regional correlations under 6-month sliding window

Fig. 12 Inter-regional correlations under12-month sliding window

5. Discussion and Conclusion Based on long-term sequence data from 1961 to 2022, this study systematically analyzed the spatiotemporal distribution characteristics of rainfall in 15 typical sub-regions of Eastern Zhejiang, reaching the following main conclusions: Daily average rainfall in the study area (3.47-5.68 mm) presents a spatial distribution pattern of “high in the center, low in the west, and medium in the east”. The central high-value area (Yuyao Plain Mazhu Midstream Area, 5.68 mm) is located at a river confluence with a dense water network and strong local water vapor cycling, where topography favors airflow convergence and uplift. The eastern medium-value area (Cixi Plain series, 3.90-4.04 mm) is greatly influenced by the ocean but lacks strong uplift mechanisms. The western low-value area (Nansha Plain Area and Shaoyu Plain Area, 3.47-3.63 mm) may be affected by airflow subsidence and terrain barriers, resulting in lower rainfall. Mann-Kendall tests show that all regions have significant upward trends (), but Sen’s slope estimates reveal a spatial pattern of trend intensity being “high in coastal areas, medium in river areas, and low in hilly areas”. Coastal areas (Cixi Plain Midstream Area 7.99 mm/year, Nansha Plain Area 7.95 mm/year) change the fastest; river basins (Yuyao Plain Yaojiang Downstream Area 6.66 mm/year) have moderate rates; and hilly mountainous areas (Shaoyu Plain Area 4.00 mm/year) grow more slowly. Although the 95% confidence interval analysis indicates that the statistical significance of these trends is insufficient, the spatial differentiation pattern still has important indicative significance. Multi-time scale analysis reveals the scale dependence of rainfall. On the 3-month scale, precipitation is highly unstable with large trend fluctuations (-16.442 to 16.596 mm) and low inter-regional correlation (lowest 0.578); on the 6-month scale, trend fluctuations weaken (-5.301 to 5.092 mm) and correlations strengthen (lowest 0.623); on the 12-month scale, trends are flatter (-1.579 to 1.729 mm) and correlations further improve (lowest 0.640). This indicates that rainfall on long time scales is driven more by large-scale climate factors, while short-term rainfall reflects local influences more. Inter-regional rainfall correlations show complex patterns with time scale changes. Internal correlations in coastal areas significantly strengthen with time scale (0.82 0.86); correlations in river and inland plain areas are complex and show “regional dependence” characteristics; correlations in hilly and mountainous areas show small increases (0.83 0.85). Notably, the Yuyao Plain Mazhu Midstream Area shows a unique “increase then decrease” correlation change pattern with most regions. Recommendations: Formulate differentiated water supply strategies for areas with different change rates, paying special attention to extreme event prevention in coastal high-change-rate areas. Establish a multi-time scale linkage mechanism based on 3-month, 6-month, and 12-month schedules, considering regional differences in the short term and adopting holistic strategies in the long term. Implement source-receiver coordinated optimization, utilizing the central high-value area as a key water source and strengthening water supply guarantees for areas with large inter-annual fluctuations. Perfect warning systems by focusing on spatiotemporal differentiation characteristics of rainfall and monitoring regional rainfall response differences under extreme climate events.