Precipitation Variation Characteristics in Gannan Prefecture, China: Application of the Innovative Trend Analysis and the BEAST (Bayesian Estimator of Abrupt Change, Seasonality, and Trend) Ensemble Algorithm

Abstract

This study examined the trend changes as well as the spatial distribution of average precipitation and the abrupt change characteristics of precipitation in Gannan Prefecture, China, using daily precipitation monitoring data from 1980 to 2021 at eight meteorological stations. Analytical methods employed included the climate change trend rate, anomaly analysis, Innovative Trend Analysis (ITA), ITA-change boxes (ITA-CB), ArcGIS technology, and BEAST Ensemble Algorithm. Long-term average precipitation variability was comprehensively analyzed across multiple temporal scales. Results indicated that over the 42 years, interannual precipitation exhibited a significant increasing trend, with an annual rate of 14.363 mm/decade, and abrupt changes were detected in 1984, 2003, and 2018. The distribution of average precipitation varied substantially from year to year. July was the month with the highest average monthly precipitation, and December was the month with the lowest. Summer precipitation contributed the most to annual totals (51.33%), whereas winter precipitation contributed the least (2.01%). Interdecadal precipitation exhibited a pattern of an initial decrease followed by an increase over the study period. Based on the mean and standard deviation of the series’ first half, which was divided by the ITA method, we established a three-category classification for mean precipitation (low, medium, and high). Annual average and seasonal average precipitation showed non-monotonic variations. While the overall trend of annual average precipitation showed a modest augmentation, the increasing tendencies in the middle-value and high-value categories slowed. In spring, the decreasing trend in high-value categories slowed. In summer, decreasing trends in middle-value categories and overall zones slowed, with an enhanced increasing trend observed in autumn and winter overall. At the spatial scale, the average precipitation across Gannan Prefecture exhibited a decreasing trend from south to north. Higher precipitation was recorded at meteorological stations in the southwest (Maqu), west (Luqu), and south (Diebu), primarily influenced by the interaction between the Qinghai–Tibetan Plateau monsoon and westerly circulation, as well as regional topographic effects. The research findings have significant implications for agricultural and pastoral production planning and sustainable economic development in Gannan Prefecture, China.

1. Introduction

Precipitation is a key climatic variable that directly influences the severity of regional droughts, regulates vegetation health and hydrological cycle patterns, and has attracted considerable attention in climate research [1,2]. The Sixth Assessment Report (AR6) by the Intergovernmental Panel on Climate Change (IPCC) indicates that continued global warming will alter the spatiotemporal distribution of precipitation and reshape water resource allocation [3,4]. These changes will necessitate adaptive adjustments in agricultural and pastoral systems, including production structure optimization and species selection. Furthermore, interactions with human activities can trigger extreme precipitation events, which have been linked to secondary disasters such as crop yield reduction, soil erosion, and property damage due to precipitation-related droughts and floods [5,6,7]. Such events pose substantial threats to sustainable development. Therefore, investigating precipitation trends, distribution, and abrupt changes across multiple spatiotemporal scales holds significant scientific value for advancing regional water resource management and enhancing proactive drought/flood risk assessment.

Currently, global climate and hydrology scholars have increasingly focused on precipitation distribution, frequency, and long-term trends. For instance, Mirzaei et al. [8] examined daily precipitation inhomogeneity across Iran (1966–2018) using the Concentration Index (CI), Lorenz Asymmetry Coefficient (LAC), and Shannon’s Entropy (H). They reported that northwestern precipitation was distributed more uniformly than in the southwest and southeast. Chen et al. [9] analyzed Central Asian seasonal precipitation (1901–2013) via GPCC V7 data, calculating mean precipitation, Coefficient of Variation (CV), trend coefficient K, and applying Ensemble Empirical Mode Decomposition (EEMD) and the Empirical Orthogonal Function (EOF). Their results showed that, compared to the other seasons, spring precipitation was predominant, followed by summer. Both seasons exhibited declining spatial trends, and the summer EOF-1 patterns differed significantly from those of the other seasons. Yu et al. [10] investigated extreme precipitation characteristics in the Weihe River Basin, China (1973–2020), using correlation analysis, spatial feature analysis, and non-homogeneity testing. The results revealed a significant zonal distribution pattern, with extreme precipitation indices decreasing from south to north, while most indices exhibited increasing trends. Zhang et al. [11] applied thin-plate smoothing splines to interpolate Tibetan Plateau precipitation from 1967 to 2016, followed by wavelet analysis and the Theil-Sen estimate. They found that precipitation peaked in spring and summer and followed a general upward trend, accelerating after 2000 while exhibiting substantial variability before 1990. Wang et al. [12] examined multiscale precipitation changes in Shaanxi-Gansu-Ningxia (1973–2019) using EOF and wavelet transforms. Annual precipitation declined significantly in the Jingjiang River Basin, whereas summer and winter precipitation increased, but spring precipitation decreased. Collectively, these studies employed diverse analytical techniques to examine precipitation from different perspectives and regions. Their findings provide a solid scientific basis and decision-making support for the rational regulation of precipitation and the effective mitigation of secondary disasters, such as droughts and floods.

Gannan Prefecture plays a pivotal role in Gansu Province’s ecosystem, serving as a critical water conservation area for the upper reaches of the Yellow River and Yangtze River [13,14,15]. However, recent climate change has intensified regional drought and flood events, exerting significant impacts on the sustainable development of livestock farming and tourism. Previous research by Wang et al. [16] employed linear regression and wavelet analysis to examine spatiotemporal patterns and periodicity of flood-season (May–September) precipitation in Gannan (1976–2019). Their findings revealed that flood-season precipitation was concentrated in central Gannan, with lower volumes at northern and southern boundaries. Heavy-rainfall days showed an increasing trend, and the dominant interannual cycle was 14 years. Yang et al. [17] applied singular spectrum analysis, linear trend analysis, and climate abrupt change analysis to monthly precipitation (1983–2012), identifying an overall decreasing trend in annual precipitation (−6.3 mm/decade), an abrupt change in 1985, and a 12-month primary cycle. Cao et al. [18] analyzed the spatiotemporal distribution of precipitation levels across 60 stations in Gansu’s Hedong region (including Gannan) from April to September from 1973 to 2020, using empirical orthogonal function decomposition and correlation analysis. They found increasing total precipitation on the Gannan Plateau, with frequent light-to-moderate rainfall events. While these studies provided valuable insights, their methods relied on assumptions of data independence or specific distribution characteristics. Traditional approaches, such as linear regression, may oversimplify trends as monotonic curves, failing to capture nonlinear dynamics in precipitation time series. Such limitations can obscure sub-trends or varying rates of change across periods. To address these gaps, ŞEN [19,20] proposed the non-parametric Innovative Trend Analysis (ITA) in 2012. Unlike conventional methods, ITA requires no predefined statistical distribution, is less sensitive to distributional assumptions, and offers intuitive trend identification for meteorological and hydrological factors, effectively revealing micro-scale non-monotonic trends [21,22,23]. To enhance ITA’s quantitative capabilities, Alashan [24] developed ITA with Change Boxes (ITA-CB) in 2018. Building on ITA’s intuitive foundation, ITA-CB enables quantitative trend analysis, detects acceleration or deceleration in changes, and improves the method’s scientific rigor and accuracy.

This study utilized daily precipitation data from eight meteorological stations in Gannan Prefecture, covering the period from 1980 to 2021, to analyze climate change trend rates and the spatial variability of precipitation in the region. Precipitation patterns were examined across multiple temporal scales using climate trend rate analysis and anomaly detection methods. Furthermore, the study employed the BEAST ensemble algorithm, Innovative Trend Analysis (ITA), and the ITA-CB trend method to explore nonlinear trends and abrupt changes in precipitation. To enhance the investigation of spatial characteristics during the ArcGIS-based spatial distribution analysis, the ERA5-Land reanalysis dataset was incorporated. The primary objective of this research is to provide a robust scientific basis for decision-making aimed at optimizing the tourism industry structure, improving water resource management, and enhancing agricultural and livestock productivity in the study area.

2. Materials and Methods

2.1. Study Area Profile

Gannan Prefecture is situated in the southwestern Gansu Province, China, at the tri-provincial junction of Gansu, Qinghai, and Sichuan. The region forms a transitional zone between the northeastern margin of the Qinghai–Tibet Plateau and the western Loess Plateau. With a mean elevation of 2960 m above sea level, the prefecture covers approximately 45,000 km², accounting for about 10.6% of Gansu Province’s total area. Its geographical extent spans 100°46′–104°44′ E longitude and 33°06′–36°10′ N latitude, comprising one city and seven counties. The region experiences a plateau continental monsoon climate, characterized by short summers, prolonged winters, low mean annual temperatures (1.1–12.7 °C), large diurnal temperature variations, a frost-free period of only 85–180 days, abundant sunshine (1800–2600 h per year), and annual precipitation of 400 to 500 mm. Geomorphologically, the prefecture consists of three major subregions: (1) the western flat plateau pastoral area, (2) the southeastern Min-Die alpine gorge area, and (3) the northeastern mountainous and hilly farming-pastoral ecotone. The terrain slopes gradually from higher elevations in the northwest to lower elevations in the southeast, exhibiting pronounced spatial heterogeneity. This region lies within an ecologically fragile cold zone, rendering it highly sensitive to climate change [25,26,27].

2.2. Data Sources

Daily precipitation data (1980–2021) for Gannan Prefecture were obtained from the China Meteorological Science Data Service Platform (http://data.cma.cn/; accessed 23 January 2025). The datasets were standardized to ensure consistency, and missing or anomalous values in the original datasets were corrected using mean interpolation. Monthly, seasonal, and annual average precipitation values were subsequently calculated [28].

Monthly mean temperature data from the ERA5-Land reanalysis dataset were downloaded from the Medium-Range Weather Forecasts (ECMWF) (https://cds.climate.copernicus.eu/datasets; accessed 18 September 2025). The dataset covers the same time span as the meteorological stations, extending from 1980 to 2021. With a spatial resolution of 0.1° (approximately 9 km), the study extracted ERA5-Land grid precipitation data corresponding to the coordinates of 33 distinct points. The distribution of the 33 points is shown in Figure 7. This ERA5-Land precipitation data was bias-corrected using the ground observations obtained from the meteorological stations.

Seasons were defined as spring (March–May), summer (June–August), autumn (September–November), and winter (December–February of the following year). The study area is illustrated in Figure 1.

3. Methods

3.1. Climate Change Trend Rate

A linear regression equation for annual climate elements is established as follows:

$$y=ax+b,$$

(1)

where $y$ is a climate element, e.g., precipitation or temperature; $x$ represents time (year sequence); $a$ indicates the climate change trend rate; and $10\times a$ expresses the climate change over a 10-year period. $a>0$ indicates that the climate elements have increased over time, whereas $a<0$ indicates that the climate elements have decreased over time. $b$ is the $y$-intercept [29].

3.2. Anomaly and Cumulative Anomaly

For a time series $y_1,y_2,y_3\cdots y_n$, the anomaly $\Delta y_i$ is calculated as follows:

$$\Delta y_i=y_i-\overline{y}$$

(2)

where

$$\overline{y}={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{y}_i}$$

(3)

where $n$ is the length of the time series.

The cumulative anomaly method is widely used to directly analyze long-term trends from data curves. In this method, an upward trend in the cumulative anomaly curve indicates an increase in the anomaly values over time, whereas a downward trend indicates a decrease [30]. For a time series $y_1,y_2,y_3\cdots y_n$, the cumulative anomaly $S_t$ at a certain time $t$ is defined as:

$$S_t={\displaystyle \sum _{i=1}^t\Delta y_i=}{\displaystyle \sum _{i=1}^t(y_i-\overline{y})},t=1,2,\cdots n$$

(4)

Analysis of the cumulative anomaly curve’s fluctuations allows the identification of the long-term evolutionary trend within a time series and the approximate timing of potential abrupt changes. Specifically, this method can be applied to characterize the intra-annual variability of precipitation.

3.3. Innovation Trend Analysis (ITA)

Innovative Trend Analysis (ITA), a non-parametric statistical method proposed by Şen in 2012 [19], is used to analyze time series data without relying on serial auto-correlation, normality, or record length assumptions. For non-monotonic trends, classifying the data into low, medium, and high value categories is a necessary step in Innovative Trend Analysis to provide a complete characterization of the data behavior through the trend slope parameter. The methodology is conducted as follows:

(1) Segmentation of the time series

In the ITA method, a time series $x_1,x_2,x_3\cdots x_n$ is divided into two equal sub-series, denoted as $y_1$ and $y_2$, which are then sorted in ascending order. The first half ($y_1$) is plotted on the X-axis, and the second half ($y_2$) is plotted on the Y-axis in a Cartesian coordinate system.

If the data points fall on the 1:1 line ($y=x$), it indicates that the series exhibits no trend. However, if the data points are distributed above the 1:1 line ($y=x$), this indicates an increasing trend; while those distributed below the 1:1 line ($y=x$) indicate a decreasing trend [31].

(2) Classification of low, medium, and high value categories

To characterize trends across data intervals in non-monotonic scenarios, value categories are stratified using the methods outlined in [32,33], which allows for a more granular interpretation.

The low, medium, and high value categories are defined according to temporal variation within the first sub-series $y_1$. Specifically, the mean ${\overline{y}}_1$ and standard deviation $SD$ of the first part series $y_1$ are calculated, and the value categories are then classified as follows:

$$\left\{\begin{array}{l}lowvaluecategories:y_1\le {\overline{y}}_1-SD\hfill \\ mediumvaluecategories:{\overline{y}}_1-SD<y_1<{\overline{y}}_1+SD\hfill \\ highvaluecategories:y_1\ge {\overline{y}}_1+SD\hfill \end{array}\right.$$

(5)

(3) Calculation of the trend slope under the ITA method

The trend slope $S$ is calculated as follows:

$$S={\displaystyle \frac{2({\overline{y}}_1-{\overline{y}}_2)}{n}}$$

(6)

where ${\overline{y}}_1$ and ${\overline{y}}_2$ represent the averages of the first and the second sub-sequence; $n$ is the length of the time series. $S>0$ indicates an upward trend. $S<0$ indicates a downward trend.

3.4. ITA-Change Boxes (ITA-CB)

The ITA-change boxes (ITA-CB) method, introduced by Alashan in 2018 [24], was developed to numerically quantify and visualize changes in time series data using ITA scatter plots. While the ITA method expresses changes as absolute quantities, the ITA-CB method represents them as percentages relative to the mean. The lower and upper ranges of ITA-CB define the expected minimum and maximum change domains within a time series, thereby improving the interpretability of trend variability. These ranges are derived statistically from the mean and standard deviation to establish theoretical bounds for change domains in the time series. The ITA-change boxes (ITA-CB) method comprises the following steps:

(1) Calculate the Relative Rate of Change $K$

The relative rate of change ($K$) for each value category is calculated as:

$$K={\displaystyle \frac{y_2-y_1}{y_1}}\times 100\%$$

(7)

where $y_1$ is the first sub-series of the time series, $y_2$ is the second sub-series. These calculations are repeated for $n/2$ times, where $n$ is the total number of data points in the time series.

(2) Statistical Characterization and Visualization

The minimum, maximum, and mean values are calculated for the low, medium, and high categories of the time series. Box plots are then generated to visualize the distribution of $K$ across categories. Subsequently, the changes are plotted within their respective categories and visualized using box plots. The horizontal axis represents the stratification groups (e.g., low, medium, high, and whole), while the vertical axis displays the change percentages.

(3) Trend Analysis in ITA-change boxes (ITA-CB)

A category exhibits a rising trend when its mean value is greater than zero, and a decreasing trend when the mean value is less than zero. A smaller difference between the median and maximum values in the box plot corresponds to an increasing trend slope, indicating that the trend is strengthening. Conversely, a larger difference between the median and maximum values corresponds to a decreasing trend slope, suggesting that the trend is weakening. This visualization approach facilitates a detailed quantitative examination of temporal variations by enabling direct interpretation of distributional characteristics.

3.5. BEAST Ensemble Algorithm

The Bayesian Ensemble Algorithm (BEAST), proposed by Zhao [34] in 2019, is a Bayesian model averaging framework that integrates multiple competing models to detect abrupt changes, trends, and seasonal variations through time-series decomposition. The model generates physically plausible nonlinear trends and well-calibrated uncertainty measures. Abrupt change detection in BEAST identifies both the number and locations of abrupt changes by evaluating the prior and posterior distributions of the time-series data.

The time series decomposition is represented as:

$$Y(t)=Trend(t)+Seasonality(t)+AbruptChanges+\epsilon (t)$$

(8)

where $Trend(t)$ describes long-term trends; $Seasonality(t)$ describes periodic changes; $Seasonality(t)$ captures abrupt points; and $\epsilon (t)$ is the residual term.

4. Results

4.1. Precipitation Variability Analysis

4.1.1. Analysis of Interannual Precipitation Variability

The mean annual precipitation in Gannan Prefecture from 1980 to 2021 was 536.54 mm, showing a gradual increase with a climatic trend rate of 14.363 mm/ decade (p < 0.05). As shown in Figure 2a, the average annual precipitation reached 703.75 mm in 2020, which was 31.16% above the multi-year average, whereas the minimum value of 424.3 mm occurred in 2002, 20.92% below the multi-year average. Despite significant interannual fluctuations, an overall increasing trend was observed. According to Figure 2b, over the 42 years from 1980 to 2021, 23 years (54.8%) recorded positive precipitation anomaly values. Before 2011, near-normal and moderately dry years alternated. From 2011 to 2021, positive precipitation anomalies persisted consecutively except in 2015, with 2018–2020 characterized by wet conditions and a pronounced increasing precipitation trend. During the study period, the years with interannual cumulative anomaly values greater than 100 mm were 1984, 2003, 2018, and 2020. Precipitation in these years exceeded the multi-year average, indicating periods of anomalously high precipitation. In contrast, 1996, 2000, 2002, and 2015 showed interannual cumulative anomaly values less than −80 mm, representing periods of anomalously low precipitation. The cumulative precipitation anomaly series from 1980 to 2021 reached minima in 2002 and 2015, allowing division into three distinct phases: a fluctuating decline period (1980–2002), an oscillatory period (2003–2015), and a significant increase period (2016–2021).

The Innovative Trend Analysis (ITA) and ITA-change boxes (ITA-CB) methods were employed to analyze micro-trends in annual precipitation across Gannan Prefecture. As illustrated in Figure 3a, in the low-value categories of the average annual precipitation from 1980 to 2021, one data point was located below the 1:1 line, while all other data points lay above it, indicating an upward trend. The data within both the median-value and high-value categories consistently appeared above the 1:1 line, confirming an upward trend. Figure 3b shows that the average trend change rate in the low-value categories of ITA was 0.32%. The mean line was approximately equidistant from the maximum and minimum lines, suggesting that the trend change was not statistically significant. In contrast, the median-value and high-value categories exhibited trend magnitudes of 6.69% and 9.03%, respectively, with mean line approaching the minima line, indicating a deceleration in the upward trend for these categories. The overall trend magnitude for annual precipitation (1980–2021) was 5.92%, with the mean line close to the maximum line, signifying a moderate upward trend.

4.1.2. Analysis of Interdecadal Precipitation Variation

The variation in interdecadal precipitation reflects long-term trends in precipitation changes over extended periods [35,36]. As shown in

Table 1. Interdecadal changes in average precipitation, seasonal average precipitation in Gannan Prefecture (1980–2021).

Period	Annual Average Precipitation/mm	Average Precipitation in Spring/mm	Average Precipitation in Summer/mm	Average Precipitation in Autumn/mm	Average Precipitation in Winter/mm
1980–1989 (1980s)	533.92	120.65	274.59	129.67	8.00
1990–1999 (1990s)	514.31	117.12	282.89	102.54	9.78
2000–2009 (2000s)	523.15	110.76	261.60	141.12	7.87
2010–2019 (2010s)	557.53	129.18	274.53	141.99	11.66
1980–2021	536.54	119.97	275.37	130.45	9.62

, Gannan Prefecture exhibited a fluctuating upward trend in average interdecadal precipitation over the past 42 years. Specifically, average annual precipitation decreased from 533.92 mm in the 1980s to 514.31 mm in the 1990s, falling below the multi-year average and indicating a downward trend. Subsequently, precipitation gradually increased, with the 2010s average exceeding the multi-year mean. Seasonally, spring precipitation declined from the 1980s to the 2000s, remaining below the multi-year average during the 1990s–2000s before rising significantly after the 2000s. Summer precipitation increased from the 1980s to the 1990s, peaked in the 1990s, declined through the 2000s, and subsequently rebounded. This pattern may reflect variability in northwesterly winds and a strengthened western Pacific subtropical high-pressure system during summer. Autumn precipitation decreased from the 1980s to the 1990s before rising gradually. Winter precipitation mirrored the summer pattern but with smaller rates of change. From the 2000s to the 2010s, all seasons demonstrated an overall upward trend in precipitation.

4.1.3. Analysis of Precipitation Variability Within the Year

According to

Table 2. Monthly distribution of precipitation in Gannan Prefecture (1980–2021).

Statistical Item	Spring			Summer			Autumn			Winter
	March	April	May	June	July	August	September	October	November	December	January	February
Precipitation/mm	15.38	34.12	70.47	82.15	101.82	91.41	80.48	43.66	6.30	1.62	3.57	5.55
Proportion of average annual precipitation %	2.87	6.36	13.13	15.31	18.98	17.04	15.00	8.14	1.18	0.30	0.67	1.04
	22.36			51.33			24.32			2.01

, the average monthly precipitation in Gannan Prefecture (1980–2021) exhibited a unimodal distribution, with precipitation concentrated from May to September. July recorded the highest precipitation (101.82 mm), accounting for 18.98% of the annual mean, while December recorded the lowest (1.62 mm), representing only 0.30% of the annual mean. Seasonally, precipitation showed substantial differences: summer precipitation > autumn precipitation > spring precipitation > winter precipitation. Linear regression analysis of seasonal precipitation (Figure 4) revealed upward trends in spring (3.23 mm/decade), summer (2.57 mm/decade), and winter (1.12 mm/decade). In contrast, autumn showed no significant trend (0.008 mm/decade).

Subsequently, the Innovative Trend Analysis (ITA) and ITA-change boxes (ITA-CB) methods were applied to conduct a micro-trend analysis of seasonal precipitation in Gannan Prefecture, as shown in Figure 5.

As shown in Figure 5(a1), scatter points in the low-value categories of spring precipitation in Gannan Prefecture were primarily distributed above the 1:1 line (y = x), with only a few points below it, indicating an overall upward trend. In the median-value categories, all points were located above the 1:1 line, confirming an upward trend. Conversely, scatter points in the high-value categories were entirely positioned below the 1:1 line, signifying a downward trend. Figure 5(a2) quantifies these trends: the average trend change rate was +6.06% in the low-value categories, indicating an upward trend, although the acceleration or deceleration of this trend was not statistically significant; +6.63% in the median-value categories, and −2.55% in the high-value categories. The proximity of the median-value categories and high-value categories to their respective lower bounds suggested a decelerating upward trend in the median-value categories and a gradual decline in the high-value categories. Notably, outliers in the median-value categories implied potential extreme precipitation events. The overall average trend change rate was +5.18%, with the mean value near the lower bound, indicating a slow upward trend.

Figure 5(b1) illustrates that in the low-value and median-value categories of summer precipitation in Gannan Prefecture, some scatter points fell below the 1:1 line, but most data clustered around this line, indicating no significant trend in these categories. In contrast, all scatter points in the high-value categories were located above the y = x line, suggesting a slight upward trend. As quantified in Figure 5(b2), the average trend change rates were +0.62% (low-value categories), −0.95% (median-value categories), and +3.06% (high-value categories), with an overall rate of −0.15%. The proximity of means to upper bounds in the low-value categories implied a slight upward trend, while the high-value categories exhibited a stronger upward trend. The median-value categories showed a slight downward trend, with the overall trend indicating a marginal decrease at a decelerating rate. Notably, outlier in median-value categories suggested potential extreme precipitation events.

Figure 5(c1) demonstrates that scatter points for the low-value, median-value, and high-value categories of autumn precipitation in Gannan Prefecture all lie above the 1:1 line, indicating upward trends. However, the trends exhibited non-monotonic behavior within these categories, making it unclear whether the upward trends were accelerating or decelerating. Figure 5(c2) shows that the average trend change rate was +19.71% in the low-value categories (mean closer to the maximum value, suggesting a moderately strengthened upward trend), +25.86% in the median-value categories (mean approaching the maximum value, demonstrating a pronounced upward trend), and +17.23% in the high-value categories (mean near the minimum categories, indicating a slow upward trend). The overall average trend change rate for autumn was +22.52%, with the mean slightly closer to the maximum value, reflecting a moderately strengthened upward trend.

Figure 5(d1) illustrates that scatter points for winter precipitation in Gannan Prefecture exhibited distinct temporal trends: low-value category points lay on or below the 1:1 line, indicating a downward trend; median-value category points predominantly clustered above the line (with some on it), indicating an upward trend; and high-value category points all lay above the line, confirming an upward trend. Overall, the data demonstrated a non-monotonic upward trend, although it remained unclear whether this trend was accelerating or decelerating. As quantified in Figure 5(d2), the average trend change rates were −14.67% for the low-value categories (with the mean equidistant from the maximum and minimum bounds, suggesting no significant intensification or deceleration of the downward trend), +15.76% for the median-value categories (with the mean closer to the minimum value, indicating a gradual upward trend), and +22.86% for the high-value categories (with the mean closer to the maximum value, reflecting a strengthening upward trend). The overall average trend change rate was +14.21%, with the mean approaching the maximum value, signifying a moderately strengthening upward trend.

4.2. Spatial Distribution of the Annual Mean Precipitation

The spatial variability of the annual mean precipitation (1980–2021) across eight meteorological stations in Gannan Prefecture was visually represented using ArcGIS technology through graded color mapping. Figure 6 illustrates the spatial distribution of annual and seasonal average precipitation across the Gannan Prefecture based on these data, revealing a relatively consistent precipitation pattern at the regional scale while highlighting the differences in mean precipitation among individual stations. However, due to the relatively sparse spatial distribution of the existing stations, it remains challenging to adequately capture the fine-scale spatial variability of precipitation. To enhance the analysis of regional precipitation characteristics, this study further incorporated monthly precipitation data from 33 points derived from the ERA5-Land reanalysis dataset. Spatial interpolation was subsequently conducted using the kriging method in ArcGIS, version 10.8 (Figure 7).

4.2.1. Spatial Distribution of the Annual Mean Precipitation Patterns

Figure 6(a1) shows a spatial gradient in annual average precipitation across Gannan Prefecture, decreasing from southwest (609.26 mm) to northeast (437.81 mm). The southwest (Maqu), west (Luqu), and south (Diebu) regions exhibited higher annual average precipitation than the surrounding areas. Figure 7(a1), which incorporates the ERA5-Land reanalysis data, corroborates this primary pattern, clearly delineating the southwest (Maqu), west (parts of Luqu), and south (Diebu) regions as the high-precipitation belt (ranging from 596.07 mm to 743.12 mm).

Figure 6(a2) indicates a general west-to-east decline in precipitation trends, with west (Luqu) region showing the largest average increase rate (+25.35 mm/decade, p < 0.05), followed by the southwest (Maqu) region, both were classified as high-growth areas. In contrast, the northeastern (Lintan), eastern (Zhuoni), and southeastern (Zhouqu) regions showed an increase below the regional mean, forming low-growth areas. Conversely, Figure 7(a2) suggests that annual precipitation overall exhibits an increasing trend across Gannan Prefecture, with the largest increase observed in the southeast (Zhouqu) region. Notably, the eastern part of Maqu and the southern part of Diebu show significant annual increases (ranging from +2.22 mm/ decade to 3.32 mm/decade). Regions like northwest (Xiahe), central-west (Hezuo), northeastern (Lintan), and parts of Zhuoni show only slight increases, while the northern edge exhibits a slight decreasing trend. Overall, the trend in Figure 7(a2) presents a north-to-south gradient, with precipitation increase diminishing northward.

4.2.2. Seasonal Precipitation Spatial Patterns

Figure 6(b1–e1) reveals that precipitation patterns in summer, autumn, and winter were broadly consistent with the annual average precipitation distribution, though seasonal variations were evident at the station and regional scales. For instance, northwest (Xiahe) Station recorded the lowest spring precipitation (less than 100 mm), whereas eastern (Zhuoni) and south (Diebu) stations received the highest values (more than 130 mm). In summer, heavy precipitation (more than 300 mm) was observed in the southwest (Maqu)-west (Luqu)-south (Diebu) region, while the southeastern (Zhouqu) station recorded less than 220 mm. Autumn precipitation was relatively high along the southwest (Maqu)-west (Luqu)-south (Diebu) (over 140 mm), with northwest(Xiahe) and southeastern (Zhouqu) stations recording lower totals (less than 220 mm). Winter precipitation was generally minimal across the region, with northwest (Xiahe), south (Diebu), and southeastern (Zhouqu) stations each receiving less than 10 mm. Figure 7(b1–e1) show that the spatial distribution of spring precipitation was consistent with that of the annual mean precipitation, with higher rainfall concentrated in Maqu, southeastern Luqu, Diebu, southern Zhuoni, and eastern Zhouqu, while lower values occurred in the northwestern region, forming a south–high–north–low pattern. Summer precipitation was mainly concentrated in the southwest and along the northwestern margins, whereas the eastern regions received relatively less precipitation. In autumn, higher precipitation was observed across southeastern Maqu–southeastern Luqu–southern Diebu, as well as Hezuo and Zhuoni, while lower precipitation occurred in western Maqu and Zhouqu. Winter precipitation was generally low across the entire prefecture.

Seasonal precipitation climate tendency rate (Figure 6(b2–e2)) further highlighted regional-scale contrasts. Spring precipitation showed a decreasing trend in the northwest, with the west (Luqu) station exhibiting a slight decline (−1.99 mm/decade, p < 0.05), indicating a weak negative growth signal. Most other stations had growth rates below 10 mm/decade, which belonged to the low-growth area of precipitation. Summer precipitation indicated a decreasing trend in the eastern region, particularly in northeast (Lintan), eastern (Zhuoni), south (Diebu), and southeastern (Zhouqu) stations, with all stations except west (Luqu) station showing growth rates below 10 mm/decade, classifying them as low-growth zones. Autumn precipitation showed a significant increase in the west (Luqu) and south (Diebu)stations (>10 mm/decade), while other regions remained in low-growth categories. Winter precipitation trend rates ranged from 0.36 to 2.07 mm/decade (p < 0.05), indicating uniformly low growth across the region, with south (Diebu) showing a marginally higher increase. Figure 7(b2–e2) reveal that spring precipitation showed a marked increasing trend in the southeastern (Zhouqu), southern (Diebu), parts of Zhuoni, and portions of Maqu regions. The summer precipitation increase was most pronounced in the southwestern Maqu area, followed by southern Luqu, Diebu, and southwestern Zhouqu, while other regions exhibited relatively weak summer trends. Autumn precipitation showed notable increases in Zhouqu, Diebu, the southern margin of Luqu, and southeastern Maqu, whereas other regions displayed relatively weak trends. Winter precipitation across Gannan Prefecture showed little overall change.

ITA trend slopes analysis (Figure 6(b3–e3)) corroborated these findings. Spring precipitation in the west (Luqu) and south (Diebu) stations showed negative slopes (−0.26 and −0.12, respectively), while summer precipitation exhibited negative growth in northwest (Xiahe), northeastern (Lintan), eastern (Zhuoni), south (Diebu), and southeastern (Zhouqu) stations. By contrast, autumn precipitation displayed positive slopes across all stations, with west (Luqu) and south (Diebu) showing relatively higher increases. Winter ITA slopes ranged from −0.01 to 0.11, reflecting low variability, with slightly higher values at the south (Diebu) and slightly lower values at the west (Luqu). Overall, these results highlight consistent regional-scale patterns and average precipitation station differences, while fine-scale local variability cannot be fully resolved, given the sparsity of the current station network. Figure 7(b3–e3) show that the ITA trend slopes for spring, summer, and winter are basically consistent with the climate tendency rate analysis. However, the autumn ITA trend slope in Figure 7(d3) reveals a strong precipitation belt extending from the southeast to the northwest, differing slightly from the tendency rate map.

4.3. Precipitation Abrupt Change

4.3.1. Analysis of Abrupt Changes in Annual Average Precipitation

Abrupt changes in annual average precipitation across Gannan Prefecture were detected using the Mann–Kendall (M-K) test and BEAST Ensemble Algorithm (Figure 8). The M-K test (Figure 8a) identified a statistically significant abrupt change point (95% confidence interval) in 2016, marked by the intersection of the UF (forward sequence statistic) and UB (backward sequence statistic) curves. After this, precipitation trends accelerated notably: from 1980 to 2016, mean annual precipitation increased at a rate of 1.11 mm/decade, but from 2016 to 2021, it climbed at a rate of 59.42 mm/decade (p < 0.05) (Figure 8b). Inflection points were indicated by red dashed circles. BEAST analysis (Figure 8c) revealed three abrupt change points in annual precipitation within the 42-year study period, occurring in 1984, 2003, and 2018 (The gray shaded area represents the 95% credible interval for the long-term annual mean precipitation trend. The green shaded area shows the posterior probability of an abrupt change occurring in different years, where higher peaks indicate a greater likelihood of a change point). The corresponding phase-specific trends (Figure 8d) indicated the characterized precipitation regimes: an upward trend during 1980–1984, a downward trend from 1984 to 2003, an upward trend from 2003 to 2018, and a downward trend from 2018 to 2021.

4.3.2. Analysis of Abrupt Changes in Seasonal Average Precipitation

Table 3. Abrupt Changes in Seasonal Precipitation in Gannan Prefecture.

Season	Mann–Kendall Test for Change-Point Detection		BEAST Integrated Algorithm
	Year of Abrupt Changes	Trend Variability Before and After the Abrupt Change (mm/decade, p < 0.05)	Peak Year of Abrupt Changes	The Trend Variation Rate Before and After the Peak Year of Abrupt Changes (mm/decade, p < 0.05)
Spring	1981, 1991, 2012, 2015	(1980–1981) +10.88 (1981–1991) +24.39 (1991–2012) −0.56 (2012–2015) −65.66 (2015–2021) +6.85	1995, 1999, 2004, 2008, 2018	(1980–1995) −2.70 (1995–1999) +3.71 (1999–2004) +44.87 (2004–2008) −30.04 (2008–2018) +51.69 (2018–2021) −165.54
Summer	1981, 1984, 1990, 1998, 2003, 2018	(1980–1981) +350.5 (1981–1984) +330.11 (1984–1990) −120.49 (1990–1998) +18.53 (1998–2003) −22.25 (2003–2018) −15.67 (2018–2021) −262.30	1984, 2003, 2015	(1980–1984) +190.23 (1984–2003) −23.68 (2003–2015) −56.32 (2015–2021) +126.22
Autumn	2014, 2018	(1980–2014) +5.01 (2014–2018) −26.04 (2018–2021) +158.69	2005	(1980–2005) +0.931 (2005–2021) +2.94
Winter	1982, 1990, 1992, 2017	(1980–1982) +19.25 (1982–1990) +9.04 (1990–1992) +123.75 (1992–2017) −0.50 (2017–2021) +8.96	1992, 2011, 2018	(1980–1992) +6.66 (1992–2011) −1.65 (2011–2018) +5.17 (2018–2021) −1.81

reveals distinct seasonal characteristics of abrupt precipitation changes, with spring, summer, and winter experiencing more frequent abrupt changes than autumn. A methodological comparison between the Mann–Kendall (M-K) test and the BEAST algorithm highlights discrepancies: the M-K test tended to identify temporally concentrated abrupt change points, with gradual shifts in slopes before and after most detected years (e.g., spring 1981: +10.88 to +24.39 mm/decade; summer 1981: +350.5 to +330.11 mm/decade; autumn 2003: −22.25 to −15.67 mm/decade). In contrast, the BEAST ensemble algorithm detected more temporally dispersed change points with clearer differences in slopes, thereby offering a more explicit indication of increasing or decreasing precipitation.

5. Discussion

Analysis of precipitation data from eight meteorological stations across Gannan Prefecture (1980–2021) revealed an overall upward trend in annual average precipitation (14.36 mm/ decade, p < 0.05), characterized by three distinct phases: a fluctuating downward trend (1980–2002), a quasi-stable oscillation (2003–2015), and a pronounced increase (2016–2021). During the pronounced increasing period, consecutive positive anomalies were strongly correlated with enhanced southwestward transport of warm, moist air. This intensification was associated with the westward extension, northward shift, and strengthening of the Western Pacific Subtropical High. While this finding was consistent with Che et al. [37], it contrasted with the results reported by Wei et al. [38] and Yang et al. [17]. These discrepancies likely resulted from differences in data sources and study periods. Short study periods can be dominated by the ascending or descending phase of a strong natural interdecadal oscillation within that era. Consequently, when analyzing precipitation trends, the Climate Change Trend Rate, and the trend slope derived from the Innovative Trend Analysis (ITA) method over a longer period (typically more than 30 years), the influence of short-term oscillations tends to be averaged out. This allows for a clearer revelation of the actual precipitation trend under the backdrop of global climate warming.

Trend analysis using ITA and ITA-CB demonstrated that the overall precipitation increase was primarily driven by growth in medium-value and high-value categories (+6.69% and +9.03%, respectively), suggesting an elevated risk of extreme heavy precipitation events. For intra-annual precipitation distribution, July recorded the highest monthly precipitation while December had the minimum, a pattern consistent with findings by Yang et al. [39] and Huang et al. [40]. Seasonal average precipitation trend analysis (climatic trend rate and ITA/ITA-CB methods) revealed a 75% consistency between the two approaches. Spring average precipitation exhibited a gradual upward trend, while winter average precipitation showed an accelerating upward trend; autumn displayed a non-significant intensification and slowdown of the upward trend. Summer average precipitation demonstrated greater complexity: it presented an upward trend (2.57 mm/ decade), consistent with findings by Zhang et al. [41], though ITA-CB revealed a gradual decline in median-value categories and overall summer precipitation. Integrating findings from this study with previous research by Caloiero et al. [42] and Benzater et al. [43], the innovative trend analysis (ITA) demonstrated greater sensitivity in detecting precipitation change characteristics. This approach enabled more precise detection of detailed trend determination and statistical significance across low-value categories, medium-value categories, and high-value categories.

The spatial distribution patterns derived from meteorological station observations and the ERA5-Land reanalysis dataset were generally consistent. Both datasets indicate that the main precipitation centers in Gannan Prefecture for annual, summer, and autumn precipitation are concentrated in the southwestern (Maqu), western (Luqu), and southern (Diebu) regions, exhibiting a gradual decrease from south to north. Winter precipitation is generally low throughout the prefecture, with minimal spatial variability. However, discrepancies were observed in Zhouqu regarding precipitation trends. Climate tendency rate analysis based on annual mean precipitation classified Zhouqu as a low-growth area according to meteorological station observations, whereas ERA5-Land reanalysis suggested that it experienced the largest increase in annual precipitation. This divergence likely arises from differences in spatial resolution, observational methods, and the data assimilation processes of the two datasets. Despite calibration of ERA5-Land data using ground-based observations, precipitation was still generally overestimated, particularly in the complex terrain of Zhouqu, possibly due to its unique geographic location and local topographic shielding effects. Seasonal analyses further highlight the complex spatiotemporal variability of precipitation across Gannan Prefecture. In spring, station observations identified eastern (Zhuoni) and southern (Diebu) regions as primary precipitation zones, while ERA5-Land reanalysis extended high-value precipitation areas to Maqu, southeastern Luqu, Diebu, southern Zhuoni, and eastern Zhouqu. During summer, station observations indicated the highest precipitation in Maqu, whereas ERA5-Land reanalysis shifted the peak slightly toward the southwestern edge of Maqu and identified a secondary high in the northern margin of Xiahe. In autumn, both datasets showed generally consistent spatial distributions, although ERA5-Land reanalysis captured local heterogeneity more precisely, emphasizing southeastern Maqu as a prominent high-precipitation area.

Against the backdrop of 20th-century global warming, extreme precipitation events have become increasingly frequent, and both annual average precipitation and seasonal average precipitation in Gannan Prefecture displayed significant abrupt changes. To address limitations of the Mann–Kendall (M-K) change-point test—including sensitivity to time series length, data characteristics, and reduced responsiveness to outliers—this study also applied the BEAST integrated algorithm. BEAST analysis identified 1984, 2003, and 2018 as peak years for abrupt changes in annual precipitation, consistent with the extreme values revealed by cumulative anomaly analysis. The spatiotemporal variability of precipitation is influenced by multiple interacting factors, including global warming, atmospheric circulation, longitude, latitude, elevation, and topography [44,45].

This study employed multi-methodological and multi-temporal approaches to characterize regional precipitation variability. To overcome the challenge of finely resolving local-scale precipitation variations (a limitation imposed by the sparse network of ground meteorological stations in Gannan Prefecture), we incorporated the ERA5-Land reanalysis dataset for spatial distribution analysis. While traditional methods, such as the Mann–Kendall (M-K) test and the BEAST algorithm, effectively identify abrupt changes in regional mean precipitation, their capacity to provide insight into local fine-scale dynamics is inherently limited. Therefore, future research should leverage Artificial Intelligence (AI) techniques to bias-correct high-resolution gridded data, remote sensing products, and reanalysis datasets, thus providing a more comprehensive and reliable basis for detecting and validating abrupt changes in localized precipitation.

6. Conclusions

Based on daily surface meteorological data from the China Meteorological Science Data Service Platform (1980–2021), this study calculated the monthly average precipitation for Gannan Prefecture. Through multiscale analysis across temporal scales, regional-scale spatial distribution, and abrupt changes, we systematically examined annual average precipitation patterns and characteristics over 42 years. The main conclusions are as follows.

Between 1980 and 2021, annual average precipitation in Gannan Prefecture exhibited a significant upward trend of 14.363 mm/decade (p < 0.05), with abrupt changes identified in 1984, 2003, and 2018. Average precipitation distribution demonstrates substantial heterogeneity across interannual, decadal, and intra-annual timescales. Interannually, three distinct phases were identified: a fluctuating decline period (1980–2002), an oscillatory period (2003–2015), and a significant increase period (2016–2021). At the interdecadal scale, precipitation remained below the long-term average from the 1980s to the 2010s, yet it has accelerated at varying rates since the 1990s. Intra-annually, the monthly average precipitation peaks in July and reaches its minimum in December, with 78.6% concentrated in late spring (May), summer (June–August), and early autumn (September). Summer precipitation dominated annual totals (51.33%), while winter contributed minimally (2.01%). ITA and ITA-CB analyses revealed non-monotonic trends in annual average precipitation and seasonal average precipitation. Annual average precipitation showed decelerated upward trends in medium-value categories and high-value categories, despite an overall intensified upward tendency. Spring average precipitation exhibited weakened downward trends in high-value categories; summer displayed diminished downward trends in medium-value categories and overall. Autumn and winter demonstrated upward trends. At the spatial scale of annual mean precipitation distribution, the patterns derived from meteorological station observations and the ERA5-Land reanalysis dataset were generally consistent. Annual as well as summer and autumn precipitation in Gannan Prefecture was primarily concentrated in the southwestern (Maqu), western (Luqu), and southern (Diebu) regions, exhibiting a gradual decrease from south to north. This spatial pattern is largely attributed to the interaction between the plateau monsoon and westerly winds, combined with orographic enhancement, resulting in relatively higher precipitation in these areas.