Spatio-Temporal Trends of Monthly and Annual Precipitation in Guanajuato, Mexico

Abstract

This study examines the spatio-temporal evolution of precipitation in the State of Guanajuato, Mexico, from 1981 to 2016 by analyzing monthly series from 65 meteorological stations. A rigorous data quality protocol was implemented, selecting stations with more than 30 years of continuous data and less than 10% missing values. Multiple Imputation by Chained Equations (MICE) with Predictive Mean Matching was applied to handle missing data, preserving the statistical properties of the time series as validated by Kolmogorov–Smirnov tests ($p=1.000$ for all stations). Homogeneity was assessed using Pettitt, SNHT, Buishand, and von Neumann tests, classifying 60 stations (93.8%) as useful, 3 (4.7%) as doubtful, and 2 (3.1%) as suspicious for monthly analysis. Breakpoints were predominantly clustered around periods of instrumental changes (2000–2003 and 2011–2014), underscoring the necessity of homogenization prior to trend analysis. The Trend-Free Pre-Whitening Mann–Kendall (TFPW-MK) test was applied to account for significant first-order autocorrelation (${\rho }_1 > 0.3$) present in all series. The analysis revealed no statistically significant monotonic trends in monthly precipitation at any of the 65 stations ($\alpha =0.05$). While 75.4% of the stations showed slight non-significant increasing tendencies (Kendall’s $\tau$ range: 0.0016 to 0.0520) and 24.6% showed non-significant decreasing tendencies ($\tau$ range: −0.0377 to −0.0008), Sen’s slope estimates were negligible (range: −0.0029 to 0.0111 mm/year) and statistically indistinguishable from zero. No discernible spatial patterns or correlation between trend magnitude and altitude ($\rho =-0.022$, $p>0.05$) were found, indicating region-wide precipitation stability during the study period. The integration of advanced imputation, multi-test homogenization, and robust trend detection provides a comprehensive framework for hydroclimatic analysis in semi-arid regions. These findings suggest that Guanajuato’s severe water crisis cannot be attributed to declining precipitation but rather to anthropogenic factors, primarily unsustainable groundwater extraction for agriculture.

1. Introduction

Water scarcity represents one of the most pressing challenges of the 21st century, with profound implications for environmental sustainability, economic development, and social well-being [1,2]. In arid and semi-arid regions, where water availability is inherently limited, understanding climatic variability—particularly precipitation trends—becomes paramount for effective resource management and policy formulation [3,4]. The detection of reliable trends in hydroclimatic time series serves as a critical tool for assessing climate change impacts, validating model projections, and informing adaptation strategies across multiple sectors, including agriculture, urban water supply, and ecosystem conservation [5,6]. The analysis of precipitation trends presents significant methodological challenges that must be addressed to ensure scientific rigor. Hydrometeorological time series frequently contain non-climatic inhomogeneities—abrupt shifts or gradual trends caused by changes in instrumentation, station relocation, observation practices, or land use modifications surrounding monitoring sites [7,8,9,10]. These inhomogeneities can create spurious trends that mask true climatic signals, necessitating comprehensive homogenization procedures before any trend analysis. The scientific community has developed two primary approaches for homogeneity testing: relative methods, which compare target series with reference series from nearby stations [11], and absolute methods, which rely solely on the statistical properties of the individual series [12]. In data-sparse regions with low station density and high spatial precipitation variability, such as Guanajuato, absolute methods (e.g., Pettitt, SNHT, Buishand, von Neumann tests) are generally preferred due to the difficulty in establishing reliable reference series [13,14]. Beyond homogeneity issues, precipitation series often exhibit serial correlation (temporal autocorrelation), which violates the independence assumption underlying many statistical tests [15]. The Mann–Kendall test [16,17], while widely used for trend detection due to its non-parametric nature and robustness to non-normal distributions, becomes susceptible to increased Type I error rates when applied to autocorrelated data [18,19]. To address this limitation, several modifications have been developed. Ref. [20] proposed a variance correction approach (MMK), while [18,19] introduced the Trend-Free Pre-Whitening (TFPW) procedure, which removes serial dependence while preserving the underlying trend signal. The TFPW-MK method has emerged as a robust standard for trend detection in autocorrelated hydroclimatic data, effectively removing serial dependence while preserving the underlying trend signal [19,21,22]. For quantifying trend magnitude, Sen’s slope estimator [23] provides a non-parametric alternative to linear regression that is resistant to outliers.

The challenge of missing data further complicates hydroclimatic analysis, particularly in developing regions where monitoring networks may suffer from operational failures, instrumental discontinuities, and historical gaps in recording [24,25]. Traditional approaches such as listwise deletion sacrifice statistical power and may introduce bias, while simple imputation methods (e.g., mean substitution, regression-based approaches, or spatial interpolation techniques like kriging and inverse distance weighting) often fail to preserve the complex statistical properties of precipitation data [26,27,28]. Multiple Imputation by Chained Equations (MICE) has emerged as a superior framework for handling missing data in climatic studies [29]. Specifically, the Predictive Mean Matching (PMM) algorithm within MICE is particularly well suited for precipitation data, which typically follow skewed distributions (e.g., gamma) and contain numerous zero values [30]. PMM preserves the original distributional characteristics, maintains seasonal patterns, and avoids generating unrealistic values, making it the preferred choice for hydroclimatic applications [24,31].

The State of Guanajuato, located in Mexico’s central highlands, represents a critical region for conducting rigorous precipitation trend analysis. The state faces severe water stress, with 19 of its 20 aquifers classified as overexploited and groundwater levels declining at alarming rates [32,33]. While climate change is frequently invoked to explain water scarcity, a comprehensive assessment of precipitation trends that systematically addresses key methodological challenges, namely, inhomogeneity, autocorrelation, and missing data, is still lacking. Previous studies in the region may have been compromised by one or more of these limitations, potentially leading to erroneous conclusions about climatic changes. This study addresses this critical research gap by implementing a robust statistical protocol that integrates state-of-the-art methods for each methodological challenge: absolute homogeneity tests for breakpoint detection, MICE with PMM for handling missing data, and TFPW-MK for trend detection in autocorrelated series. Therefore, this study aims to answer the following research question: Were there statistically significant long-term trends in precipitation in the State of Guanajuato between 1981 and 2016, after rigorously controlling for data quality, inhomogeneities, and autocorrelation?

The specific objectives of this research are as follows:

• Apply a comprehensive suite of absolute homogeneity tests (Pettitt, SNHT, Buishand, and von Neumann) to identify and characterize non-climatic breaks in precipitation series across Guanajuato.
• Implement the Multiple Imputation by Chained Equations (MICE) algorithm with Predictive Mean Matching (PMM) to handle missing data while preserving the statistical properties and temporal structure of precipitation series.
• Employ the Trend-Free Pre-Whitening Mann–Kendall (TFPW-MK) test on homogenized and imputed series to reliably detect monotonic trends while controlling for serial correlation.
• Quantify the magnitude and direction of any significant trends using Sen’s slope estimator.
• Analyze the spatial patterns of precipitation trends across Guanajuato and discuss their implications for water management policy in the context of the state’s severe water crisis.

By adopting this integrated methodological approach, the present study seeks to provide a definitive assessment of precipitation trends in Guanajuato. This framework offers reliable evidence to inform water security strategies and policymaking in a region experiencing acute water stress. The structure of this article is as follows: Section 2 describes the study area. Section 3 details the comprehensive methodological framework, including data preprocessing, multiple imputation using MICE with PMM, the suite of absolute homogeneity tests applied, and the trend detection procedure employing the TFPW-MK test and Sen’s slope estimator. Section 4 presents the results of the homogeneity assessment, validates the imputation approach, and describes the trend analysis findings, including spatial patterns of precipitation change, discusses the implications of these findings for water resource management, compares them with previous studies, and reflects on the methodological insights gained. Finally, Section 5 summarizes the main conclusions and outlines recommendations for future research.

2. Study Area

The State of Guanajuato, located in the north-central region of Mexico (between ${19}^{°}{55}^{\prime }{08}^{″}$ and ${21}^{°}{52}^{\prime }{09}^{″}$ north latitude, and ${99}^{\circ }{39}^{\prime }{06}^{″}$ and ${102}^{\circ }{05}^{\prime }{07}^{″}$ west longitude), is bordered to the north by Zacatecas and San Luis Potosí, to the east by Querétaro, to the south by Michoacán, and to the west by Jalisco (see Figure 1). Its territory spans an area of $30,471.06{\mathrm{km}}^2$, characterized by a topographic diversity that combines mountainous reliefs linked to the Mesa del Centro and volcanic outcrops associated with the Eje Neovolcánico-Transmexicano. This geomorphological complexity gives rise to mountain ranges, fertile valleys, and lacustrine formations, including the Bajío Guanajuatense region [34]. The elevation ranges from approximately 700 m above sea level (masl) in parts of the Cañón del Río Santa María in Xichú, to over 3000 masl in the southern highlands (Sierra de Los Agustinos), directly influencing local weather patterns. In the flat and low areas a semi-dry and semi-warm regime predominates, while in the higher regions, conditions become temperate [35].

Rainfall is concentrated mainly during the summer season (June to September), followed by a marked dry season in winter. This seasonal rainfall pattern is linked to the influence of monsoon systems, particularly the North American monsoon [36]. The mean annual precipitation ranges between 500 and 800 mm, while average temperatures hover around 18–20 °C, although in summer they can exceed 30 °C and in winter they can approach 0 °C. This temperature variability, combined with the marked seasonality of rainfall, exposes the region to phenomena such as droughts and floods, which are particularly critical given the importance of agriculture (based on crops such as corn, wheat, and vegetables) and manufacturing in its economy. In addition, water availability depends on several aquifers and the Lerma–Chapala–Santiago river system, factors that make Guanajuato a relevant environment for the analysis of sustainable water management and adaptation to extreme hydrometeorological events.

3. Data and Methodology

3.1. Data Source and Preprocessing

The State of Guanajuato has 162 meteorological stations in its network. A rigorous selection process was applied to ensure the highest data quality and statistical reliability for trend analysis. This process was governed by two non-negotiable criteria: World Meteorological Organization (WMO) Standards: Following WMO guidelines for climate analysis [37], a minimum record length of 30 continuous years was required. Data Completeness: A strict threshold of ≤10% missing data was established to preserve the statistical integrity of the series, a critical consideration in semi-arid regions with high rainfall variability [38]. While some studies employ more permissive thresholds (e.g., ≤25% missing data) [39,40], our priority was to maximize accuracy, particularly in representing extreme events and natural variability, which is essential in a drought-vulnerable region like Guanajuato.

The period from 1981 to 2016 was selected as it represents the optimal compromise between data recency and these stringent quality controls. Although more recent data (e.g., 2017–2023) are available, their incorporation would have significantly compromised the study’s robustness. For a large number of stations, the post-2016 period is characterized by data gaps exceeding our 10% threshold, which would introduce substantial uncertainty and potential bias through imputation. Furthermore, the selected 36-year period provides a sufficiently long baseline to reliably distinguish long-term trends from natural interannual and decadal climate variability. Applying these criteria, 97 stations were excluded due to excessive missing data or insufficient record length, resulting in a final dataset of 65 high-quality stations. This rigorous selection ensured the reliability of subsequent advanced imputation techniques (e.g., the MICE algorithm [29,41]) and the robustness of the homogeneity and trend analyses.

Spatial Analysis

The spatial interpolation of precipitation trends was performed using the Inverse Distance Weighted (IDW) method due to its capacity to preserve the influence of local values—an essential feature for hydroclimatic trend analysis. Compared to geostatistical techniques such as kriging, IDW avoids excessive smoothing and highlights localized areas with contrasting positive and negative trends, while maintaining result interpretability. To ensure spatial validity, interpolation masks were applied to restrict the interpolated surface strictly to the state’s polygon, thereby avoiding non-representative extrapolations outside the study area. All geographical and spatial analyses, including data interpolation and the creation of distribution maps, were carried out in a geographic information system (GIS) environment. All spatial data were projected to UTM Zone 14N (WGS84 datum) to ensure metric consistency for distance and area measurements throughout the study region.

3.2. Homogeneity Tests

To ensure the reliability of the time series for trend detection, it is essential to identify and account for non-climatic discontinuities caused by factors such as instrument changes, station relocations, or changes in observation practices. We applied a suite of four absolute homogeneity tests—Pettitt, Standard Normal Homogeneity Test (SNHT), Buishand Range Test, and von Neumann Ratio Test—selected for their complementary sensitivities to breaks at different temporal locations within a series [12]. Absolute tests were chosen over relative methods due to the high spatio-temporal variability of precipitation and the low correlation between neighboring stations in this semi-arid region, which makes establishing reliable reference series difficult [13,42].

The null hypothesis ($H_0$) for all tests posits that the series is homogeneous. The tests were applied at a significance level of $\alpha =0.05$. The key characteristics of each test are summarized in Table 1.

The final classification of each station’s homogeneity was determined using a multi-test consensus approach [12,43], based on the number of tests (Pettitt, SNHT, Buishand) that rejected the null hypothesis:

• Useful (Class 1): 0–1 rejections. Variations are attributable to natural climate variability.
• Doubtful (Class 2): 2 rejections. Moderate inhomogeneities are present, requiring verification.
• Suspicious (Class 3): 3 rejections. Significant alterations invalidate the series for reliable analysis.

Table 1. Summary of absolute homogeneity tests applied to precipitation series.

Test Name	Type	Null Hypothesis (${\mathit{H}}_0$)	Statistic and Breakpoint Detection	Sensitivity
Pettitt [44]	Non-parametric	The series is homogeneous.	Identifies an abrupt shift in the median. The test statistic K is the maximum absolute value of $U_t=2{\sum }_{i=1}^t{r}_i-t(n+1)$, where $r_i$ are ranks. The most probable break year is at $\text{arg} \text{max} |U_t|$.	Most sensitive to breaks near the middle of the series.
SNHT [11]	Parametric	The series is homogeneous.	Detects a shift in the mean. The test statistic $T_0$ is the maximum of $T\left(k\right)=k{\left(\overline{z_1}\right)}^2+(n-k){\left(\overline{z_2}\right)}^2$, where $\overline{z_1}$ and $\overline{z_2}$ are normalized means before and after year k.	Most sensitive to breaks near the beginning and end of the series.
Buishand [45]	Parametric	The series is homogeneous.	Evaluates cumulative deviations from the mean. The adjusted partial sum is $S_k^{*}={\sum }_{i=1}^k(Y_i-\overline{Y})$. The rescaled range $R=(\text{max} S_k^{*}-\text{min} S_k^{*})/s$ is the test statistic. A break is indicated near the point where $S_k^{*}$ reaches a maximum or minimum.	Most sensitive to breaks near the middle of the series.
Von Neumann [46]	Non-parametric	The series is homogeneous and random.	Evaluates randomness via the ratio $N={\displaystyle \frac{{\sum }_{i=1}^{n-1}{(Y_i-Y_{i+1})}^2}{{\sum }_{i=1}^n{(Y_i-\overline{Y})}^2}}$. For a homogeneous series, $E\left(N\right)\approx 2$. Values significantly different from 2 indicate non-homogeneity.	Sensitive to any pattern affecting the overall randomness of the series (gradual or abrupt).

Table 1. Summary of absolute homogeneity tests applied to precipitation series.

Test Name	Type	Null Hypothesis (${\mathit{H}}_0$)	Statistic and Breakpoint Detection	Sensitivity
Pettitt [44]	Non-parametric	The series is homogeneous.	Identifies an abrupt shift in the median. The test statistic K is the maximum absolute value of $U_t=2{\sum }_{i=1}^t{r}_i-t(n+1)$, where $r_i$ are ranks. The most probable break year is at $\text{arg} \text{max} |U_t|$.	Most sensitive to breaks near the middle of the series.
SNHT [11]	Parametric	The series is homogeneous.	Detects a shift in the mean. The test statistic $T_0$ is the maximum of $T\left(k\right)=k{\left(\overline{z_1}\right)}^2+(n-k){\left(\overline{z_2}\right)}^2$, where $\overline{z_1}$ and $\overline{z_2}$ are normalized means before and after year k.	Most sensitive to breaks near the beginning and end of the series.
Buishand [45]	Parametric	The series is homogeneous.	Evaluates cumulative deviations from the mean. The adjusted partial sum is $S_k^{*}={\sum }_{i=1}^k(Y_i-\overline{Y})$. The rescaled range $R=(\text{max} S_k^{*}-\text{min} S_k^{*})/s$ is the test statistic. A break is indicated near the point where $S_k^{*}$ reaches a maximum or minimum.	Most sensitive to breaks near the middle of the series.
Von Neumann [46]	Non-parametric	The series is homogeneous and random.	Evaluates randomness via the ratio $N={\displaystyle \frac{{\sum }_{i=1}^{n-1}{(Y_i-Y_{i+1})}^2}{{\sum }_{i=1}^n{(Y_i-\overline{Y})}^2}}$. For a homogeneous series, $E\left(N\right)\approx 2$. Values significantly different from 2 indicate non-homogeneity.	Sensitive to any pattern affecting the overall randomness of the series (gradual or abrupt).

The von Neumann ratio was used as a supplementary diagnostic tool to assess overall randomness but was not included in the rejection count for this classification, as it detects a different type of inconsistency (autocorrelation or gradual drift).

3.3. Trend Detection Analysis

The non-parametric Mann–Kendall (MK) test was employed to detect monotonic trends in the monthly precipitation series [16]. The MK test is widely used in hydroclimatological studies due to its robustness against non-normally distributed data and outliers [20]. The test statistic S is calculated as:

$$S=\sum _{i=1}^{n-1}\sum _{j=i+1}^n\mathrm{sgn}(x_j-x_i)$$

(1)

where n is the sample size, $x_i$ and $x_j$ are sequential data values, and the $\mathrm{sgn}\left(\right)$ function is defined as:

$$\mathrm{sgn}\left(\mathrm{\Delta }x\right)=\left\{\begin{array}{cc}1\hfill & \mathrm{if} \mathrm{\Delta }x>0\hfill \\ 0\hfill & \mathrm{if} \mathrm{\Delta }x=0\hfill \\ -1\hfill & \mathrm{if} \mathrm{\Delta }x<0\hfill \end{array}\right.$$

The variance of S is adjusted for ties in the data:

$$\mathrm{Var}\left(S\right)={\displaystyle \frac{n(n-1)(2n+5)-{\sum }_{k=1}^p{t}_k(t_k-1)(2t_k+5)}{18}}$$

(2)

where p is the number of tied groups, and $t_k$ is the number of data points in the kth group. The standardized test statistic Z is then computed as:

$$Z=\left\{\begin{array}{cc}{\displaystyle \frac{S-1}{\sqrt{\mathrm{Var}\left(S\right)}}}\hfill & \mathrm{if} S>0\hfill \\ 0\hfill & \mathrm{if} S=0\hfill \\ {\displaystyle \frac{S+1}{\sqrt{\mathrm{Var}\left(S\right)}}}\hfill & \mathrm{if} S<0\hfill \end{array}\right.$$

(3)

which follows a standard normal distribution under the null hypothesis ($H_0$) of no trend. A significance level of $\alpha =0.05$ was used for all tests.

To assess the strength and direction of the trend, Kendall’s $\tau$ correlation coefficient was calculated. This robust measure is preferred over Pearson’s correlation for non-normal data and is defined as:

$$\tau ={\displaystyle \frac{N_c-N_d}{\frac{1}{2}n(n-1)}}$$

(4)

where $N_c$ and $N_d$ are the number of concordant and discordant pairs, respectively. The value of $\tau$ ranges from −1 to +1, providing a normalized and intuitive measure of the trend’s magnitude and direction.

However, a critical pre-condition for the standard MK test is the independence of the time series data. Preliminary analysis revealed significant first-order autocorrelation ($|{\rho }_1| \ge 0.3$) in all series, violating this assumption. Using the standard MK test on autocorrelated data inflates the variance and increases the probability of Type I errors (falsely detecting a trend) [18].

To address this, the Trend-Free Pre-Whitening (TFPW) procedure was applied prior to the MK test [18]. The TFPW method removes the serial correlation component while preserving the true trend signal, ensuring the reliability of the test. The procedure is implemented as follows:

• Slope Estimation: The magnitude of the trend ($\beta$) is estimated using Sen’s robust slope estimator [23]:

  $$\beta =\mathrm{median}\left({\displaystyle \frac{x_j-x_i}{j-i}}\right) \mathrm{for} \mathrm{all} i<j$$

  (5)
• Detrending: The linear trend is removed from the original time series $Y_t$ to create a detrended series $Y_t^{\prime }$:

  $$Y_t^{\prime }=Y_t-(\beta · t)$$

  (6)
• Pre-Whitening: The first-order autocorrelation coefficient (${\rho }_1$) is computed from the detrended series $Y_t^{\prime }$ and used to remove the serial correlation, creating a pre-whitened series of residuals $Z_t$:

  $$Z_t=Y_t^{\prime }-{\rho }_1 · Y_{t-1}^{\prime } \mathrm{for} t=2,3,\dots ,n$$

  (7)
• Trend Reincorporation: The estimated trend is added back to the pre-whitened residuals to create the TFPW-adjusted series $Y_t^{″}$, which should be free of autocorrelation but contain the trend signal:

  $$Y_t^{″}=Z_t+(\beta · t)$$

  (8)
• Final Trend Test: The standard Mann–Kendall test is applied to this final TFPW-adjusted series ($Y_t^{″}$) to assess the statistical significance of the trend. Kendall’s $\tau$ and Sen’s slope are also computed from this adjusted series.

This combined approach, herein referred to as the TFPW-MK test, provides a robust and reliable framework for trend detection in autocorrelated hydroclimatic time series. All analyses were implemented in R (version 4.3.1, R Core Team, Vienna, Austria) using the trend package [47] and custom Python (version 3.11.5, Python Software Foundation, Wilmington, DE, USA) scripts for validation.

4. Results and Discussion

4.1. Descriptive Statistics and Imputation Validation

The analysis was based on monthly precipitation data obtained from Mexico’s National Meteorological Service (SMN) through the Climate Computing Program (CLICOM) system (https://data.ucar.edu/sq/dataset/mexico-climatological-station-network-data-clicom (accessed on 30 May 2025)), which represents the official and most comprehensive meteorological database for the country. Analysis of the 65 selected stations from this database revealed the characteristic climatic signature of a semi-arid region, further accentuated by Guanajuato’s complex topography (see

Table 2. Characteristics of the selected stations.

ID	Municipality	Long (W)	Lat (N)	Alt (masl)	MD (%)	Max	Mean	Std	VC	S	K
11001	Abasolo	−101.536.389	20.446.667	1761	0.23	330.8	55.88	72.39	129.54	1.38	4.11
11002	Acámbaro	−100.712.222	200.325	1860	0	397.7	63.14	78.26	123.95	1.37	4.4
11003	Pénjamo	−101.629.444	20.510.278	1720	0.23	358.4	53.95	74.02	137.22	1.56	4.87
11004	Irapuato	−101.318.889	20.816.944	1800	6.94	355.4	33.21	55.09	165.91	2.05	7.48
11006	Apaseo El Alto	−100.620.833	20.455	1875	6.25	324	54.93	70.58	128.5	1.5	4.72
11007	Guanajuato	−101.227.222	20.991.667	2357	2.08	348.5	62.90	78.06	124.11	1.41	4.2
11009	Celaya	−100.816.667	20.536.389	1761	0.69	426.7	50.74	66.91	131.89	1.83	6.86
11010	Yuriria	−101.395.833	20.101.111	1909	8.33	382.5	55.64	73.99	132.97	1.60	5.41
11011	San Miguel De Allende	−100.893.333	20.957.778	2062	1.39	375.1	52.60	66.28	125.99	1.65	5.57
11012	Coroneo	−100.363.333	20.198.333	2271	9.03	367.2	52.08	62.11	119.26	1.51	5.29
11013	Cortazar	−100.962.778	20.487.778	1730	0.69	288.8	52.03	65.67	126.22	1.48	4.67
11014	Cuerámaro	−101.675.833	20.625.556	1732	0.46	344.1	49.22	70.54	143.32	1.75	5.54
11015	Doctor Mora	−100.330.556	21.139.167	2114	7.41	198.4	35.75	40.97	114.58	1.43	4.68
11020	León	−101.696.389	21.172.778	1837	0	332.8	49.60	68.45	138	1.80	5.86
11021	Salvatierra	−101.006.389	20.281.389	1730	2.08	338.4	50.24	67.32	134	1.61	5.34
11022	Apaseo El Alto	−100.554.722	20.369.722	2099	1.39	373	54.91	67.72	123.31	1.48	4.95
11023	San Francisco Del Rincón	−101.836.667	21.025.278	1767	8.10	397.2	52.67	70.26	133.41	1.66	5.63
11025	León	−101.705.278	21.231.111	1920	0.69	361.5	57.56	74.60	129.62	1.59	5.09
11028	Irapuato	−101.337.222	20.668.333	1729	0	373	54.23	70.12	129.3	1.41	4.49
11031	Jerécuaro	−100.518.889	20.143.056	1787	3.47	395.7	64.11	78.80	122.92	1.31	4.15
11033	San Miguel De Allende	−100.825.833	20.848.333	1850	0.46	300.3	48.84	59.61	122.05	1.49	4.94
11034	Pénjamo	−101.718.333	20.434.444	1795	9.03	335.5	58.81	74.47	126.64	1.19	3.37
11035	León	−1.016.975	20.920.556	1771	1.16	289.6	51.17	66.37	129.7	1.34	3.95
11036	Manuel Doblado	−101.844.167	20.675.278	1727	0.46	405.4	59.70	78.23	131.05	1.42	4.42
11040	León	−1.016.675	21.195.278	1865	0	374.8	56.23	74.13	131.84	1.60	5.13
11041	Salamanca	−101.148.889	20.675.833	1768	4.86	321.9	50.52	67.64	133.9	1.51	4.58
11042	San Miguel De Allende	−100.640.556	21.040.833	2009	8.56	392.5	45.27	57.46	126.93	1.89	7.85
11045	León	−101.639.167	213.325	2042	1.85	581	58.75	79.75	135.75	1.93	8.14
11048	Comonfort	−100.835.556	20.707.778	1933	3.70	370	48.30	61.39	127.1	1.58	5.59
11049	León	−101.425.833	21.211.111	2247	2.08	415.7	55.40	66.09	119.29	1.57	5.67
11050	Ocampo	−101.479.722	21.65	2253	2.31	276	37.85	49.86	131.75	1.69	5.72
11051	Dolores Hidalgo	−100.878.056	21.107.778	1906	0	253.5	42.30	52.96	125.21	1.65	5.46
11052	Salamanca	−101.118.333	20.522.222	1719	0.23	309.2	50.52	63.78	126.25	1.43	4.44
11053	San Luis De La Paz	−100.496.111	21.22	2206	9.95	229.8	39.74	44.52	112.03	1.43	4.82
11055	Purísima Del Rincón	−101.871.111	21.078.611	1794	3.94	413.9	54.83	72.39	132.02	1.79	6.46
11061	Dolores Hidalgo	−101.218.889	21.469.444	2090	9.95	465	42.89	68.52	159.77	2.30	9.38
11066	San José Iturbide	−100.513.889	21.296.389	2041	5.79	207	42.50	49.62	116.76	1.28	3.79
11070	Guanajuato	−101.196.111	21.072.222	2552	3.01	365.1	55.58	72.30	130.09	1.59	5.08
11071	Silao De La Victoria	−101.430.278	20.943.333	1768	0	383.5	53.46	66.53	124.45	1.29	4.15
11072	Jaral Del Progreso	−101.066.944	20.298.333	1728	0	442.5	57.41	75.31	131.17	1.53	5.06
11077	Tarandacuao	−101.782.778	20.305.556	1708	3.01	375	63.46	78.43	123.59	1.37	4.3
11078	Tarimoro	−100.512.222	199.975	1937	2.08	393.1	61.71	78.02	126.43	1.39	4.31
11079	Valle De Santiago	−101.178.889	20.382.778	1790	3.01	326	54.12	68.89	127.3	1.44	4.47
11083	Xichú	−1.000.925	21.298.611	1318	0.23	288.9	47.20	55.46	117.5	1.62	5.57
11085	San Miguel De Allende	−101.061.111	20.833.889	2241	3.94	370	55.26	73.65	133.28	1.62	5.14
11095	León	−101.698.889	21.136.111	1828	0	376.4	56.96	77.22	135.56	1.60	4.96
11099	Pénjamo	−101.948.889	20.499.444	1711	7.18	362.6	59.13	77.57	131.2	1.38	4.09
11103	Guanajuato	−101.255.833	21.034.167	2147	4.86	454.4	61.27	78.57	128.23	1.66	5.64
11116	Jerécuaro	−100.555	20.292.778	2027	2.55	332	55.65	71.19	127.94	1.59	5.23
11122	Comonfort	−100.614.722	207.625	1992	1.39	321.4	51.41	63.40	123.32	1.52	5.12
11124	Guanajuato	−101.244.444	20.871.944	1853	0.23	326	55.08	71.74	130.26	1.47	4.43
11134	Irapuato	−101.369.722	20.715.833	1740	0.23	403.2	58.79	77.73	132.21	1.51	4.73
11136	Salamanca	−101.006.944	20.668.889	1828	6.48	385.2	55.17	71.37	129.36	1.55	5.09
11140	Dolores Hidalgo	−101.135.556	21.269.444	2115	3.01	342.8	43.82	59.90	136.68	2.01	7.4
11141	Guanajuato	−101.241.667	21.173.333	2475	1.16	511	76.62	97.43	127.17	1.72	5.86
11142	Salvatierra	−100.899.722	20.280.278	1738	0.93	302.5	52.97	67.54	127.5	1.36	4.03
11143	Pénjamo	−1.018.175	20.509.722	2348	3.47	431	53.61	73.99	138.02	1.76	6.08
11144	San José Iturbide	−100.431.389	20.919.167	2201	9.49	220	32.08	39.03	121.68	1.51	5.42
11145	Cortazar	−100.885.556	20.398.056	2342	0.69	324.7	51.86	69.40	133.82	1.40	4.1
11146	Valle De Santiago	−101.358.889	20.275.833	1859	6.02	307	43.21	63.02	145.84	1.75	5.66
11148	Apaseo El Grande	−100.608.056	20.667.778	2019	1.39	410.5	51.75	66.62	128.74	1.73	6.4
11149	Acámbaro	−100.723.611	20.110.556	1890	9.03	341	54.91	73.83	134.47	1.50	4.73
11151	Pénjamo	−101.782.778	20.305.556	1708	6.94	295.2	55.06	75.20	136.58	1.39	3.88
11161	San Luis De La Paz	−100.663.611	21.45	2192	3.24	275	34.37	39.87	116.01	1.72	7.1
11166	Maravatío	−101.436.111	21.041.944	1898	0	371.8	64.80	76.42	117.93	1.21	3.73

Notes: Alt: altitude given in masl; MD: percentage of missing data; Std.: standard deviation; VC: variation coefficient; S: skewness; K: kurtosis. The values of the statistical parameters were calculated based on the month records.

).

The standard deviation (Std) ranged from 39.03 mm/month (Station 11144, San José Iturbide) to 97.43 mm/month (Station 11141, Guanajuato). These extremes reflect profound climatic differences controlled largely by elevation: the former is located in a semi-arid zone with low mean precipitation (32.08 mm/month), while the latter corresponds to a mountainous area exposed to intense convective systems, with a high mean (76.62 mm/month) and an extreme maximum event of 511 mm/month. This spatial disparity confirms that topography plays a critical role in rainfall modulation, as high-elevation zones (such as Station 11141 at 2475 masl) act as orographic barriers that intensify precipitation by forcing the ascent of moist air masses—a phenomenon well documented in tropical mountain regions [48,49]. The coefficient of variation (VC) exceeded 112% at all stations, reaching a maximum of 165.91% at Station 11004 (Irapuato), underscoring the high interannual unpredictability of rainfall. A key finding was the exceptionally high Pearson correlation coefficient between the mean and standard deviation of precipitation ($r\approx 0.931$). This strong positive correlation indicates that stations with higher average precipitation also exhibit more pronounced intramonth variability. This behavior is explained by hydrological scaling laws [3], where meteorological systems that generate intense rainfall (such as convective storms or tropical cyclones) not only increase monthly totals but also their temporal irregularity. For example, at Station 11061 (Dolores Hidalgo), an extremely wet month (465 mm/month) contributed substantially to its high standard deviation (68.52 mm/month), reflecting the dominant influence of intense, discrete events on overall variability.

The monthly precipitation distributions exhibited strong positive skewness (ranging from 1.19 to 2.30) and high kurtosis (ranging from 3.37 to 9.38). This combination of statistical properties defines a leptokurtic and right-skewed distribution, which is the mathematical signature of a climate regime characterized by two key features: (1) a high frequency of months with below-average precipitation (“dry spells”), and (2) the occurrence of extremely intense, sporadic rainfall events that create a long right tail and a pronounced peak near the mean. This means that for most stations, the majority of months experience predictable, low-to-moderate rainfall (creating the sharp peak), while the long-term average and variability are heavily influenced by a few catastrophic events. For instance, at Station 11004 (Irapuato), a moderate monthly mean (33.21 mm/month) masks the impact of an extreme month (355.4 mm/month) that single-handedly skews the entire distribution. Similarly, Station 11061 (Dolores Hidalgo) exhibits a kurtosis of 9.38, indicating that despite the potential for extreme rainfall, most data points are tightly clustered around a relatively low mean (42.89 mm/month). This statistical pattern is not merely an abstraction; it reflects the underlying meteorological reality of central Mexico. The leptokurtic distribution suggests the dominance of a stable, dry climatic regime that is periodically interrupted by intense but short-lived disturbances, such as convective storms, tropical waves, or cold fronts [18,50]. The high skewness confirms that rainfall is not uniformly distributed over time but is instead concentrated in a few highly impactful events. This has critical implications for water management: it implies that groundwater recharge and surface water availability depend overwhelmingly on a small number of extreme rainfall events rather than on frequent, gentle rains.

In Figure 2, we can observe the monthly precipitation time series (1981–2016) for three stations showing rainfall variability in Guanajuato: (a) northern semi-arid zone (Station 11053, San Luis de la Paz), (b) central agricultural valley (Station 11004, Irapuato) and (c) central mountainous area (Station 11141, Guanajuato). In each graph, the red vertical lines indicate the periods with missing data, which on average represent 3.24% of the observations. At Station 11053, located in San Luis de la Paz, a rather limited and irregular rainfall pattern is noted, rarely exceeding 200 mm, indicating a semi-dry climate. On the other hand, Station 11041 in Guanajuato experiences episodes of intense rainfall, reaching maximums of up to 511 mm in a single month. In the Irapuato Valley, represented by Station 11004, the average precipitation is moderate, around 33 mm per month, but the high skewness in the distribution—with extreme values close to 355 mm—reveals that rainfall is concentrated in specific events. In the three data series, a clear seasonality is observed, with 75% of the rainfall occurring between June and September, along with a prolonged drought during winter. This analysis highlights the climatic diversity of the state and underscores the importance of using rigorous imputation techniques to ensure data continuity in future trend studies.

The Multiple Imputation by Chained Equations (MICE) algorithm with Predictive Mean Matching (PMM) successfully generated five imputed datasets. The validation process demonstrated that the imputation robustly preserved the original distribution of the data. This was confirmed both statistically and visually: the Kolmogorov–Smirnov (KS) test yielded a p-value of 1.000 for all 65 stations, and density plots showed near-perfect overlap between original and imputed series (e.g., Figure 3).

A quantitative comparison of descriptive statistics for the three representative stations (Table 3) confirmed the high fidelity of the imputation. Differences were minimal, with absolute changes in the mean and standard deviation not exceeding 1.1 mm and 1.4 mm, respectively. In relative terms, these changes remained within strict thresholds (≤3.3% and ≤2.5%) recommended for semi-arid climates [38].

Table 3. Descriptive statistics for original and imputed series at three representative stations. Post-imputation differences were minimal and within acceptable thresholds for semi-arid climates [38].

Station	Series	Mean (mm)	Std (mm)	CV (%)	S	K
11004 (Irapuato)	Original	33.2	55.1	166	2.05	7.48
	Imputation	32.1	53.7	167	2.11	7.88
11053 (S.L. Paz)	Original	39.7	44.5	112	1.43	4.82
	Imputation	39.2	44.0	112	1.40	4.76
11141 (Guanajuato)	Original	76.6	97.4	127	1.72	5.86
	Imputation	75.9	97.1	128	1.73	5.92

Table 3. Descriptive statistics for original and imputed series at three representative stations. Post-imputation differences were minimal and within acceptable thresholds for semi-arid climates [38].

Station	Series	Mean (mm)	Std (mm)	CV (%)	S	K
11004 (Irapuato)	Original	33.2	55.1	166	2.05	7.48
	Imputation	32.1	53.7	167	2.11	7.88
11053 (S.L. Paz)	Original	39.7	44.5	112	1.43	4.82
	Imputation	39.2	44.0	112	1.40	4.76
11141 (Guanajuato)	Original	76.6	97.4	127	1.72	5.86
	Imputation	75.9	97.1	128	1.73	5.92

Most importantly, the imputation preserved the higher-order statistical moments that defined the local precipitation regime. Changes in the coefficient of variation were negligible (≤1 percentage unit), while skewness (S) and kurtosis (K)—which captured the essence of the region’s sporadic and intense rainfall patterns—remained virtually unchanged within their characteristic ranges (1.40–2.11 and >4.7, respectively). The robustness of the imputation method was further confirmed by extending the quantitative analysis to the remaining 62 stations (

Table A1. Descriptive statistics before and after imputation.

Station	Series	Mean	STD	VC	S	K
11001	Imputed	55.756	72.350	129.762	1.386	4.119
	Original	55.881	72.388	129.540	1.383	4.110
11002	Imputed	63.137	78.258	123.950	1.372	4.401
	Original	63.137	78.258	123.950	1.372	4.401
11003	Imputed	53.824	73.979	137.447	1.568	4.885
	Original	53.945	74.022	137.217	1.565	4.874
11006	Imputed	54.689	70.523	128.953	1.503	4.732
	Original	54.926	70.579	128.498	1.497	4.718
11007	Imputed	63.155	78.535	124.352	1.414	4.217
	Original	62.896	78.058	124.105	1.407	4.197
11009	Imputed	50.528	66.759	132.121	1.839	6.900
	Original	50.736	66.913	131.885	1.832	6.860
11010	Imputed	56.416	75.170	133.243	1.607	5.451
	Original	55.640	73.987	132.974	1.598	5.413
11011	Imputed	53.044	66.434	125.243	1.628	5.451
	Original	52.604	66.277	125.993	1.655	5.570
11012	Imputed	52.329	62.107	118.685	1.497	5.156
	Original	52.082	62.112	119.258	1.511	5.291
11013	Imputed	52.154	65.610	125.800	1.468	4.647
	Original	52.030	65.671	126.219	1.475	4.666
11014	Imputed	49.134	70.417	143.315	1.754	5.566
	Original	49.217	70.538	143.322	1.750	5.545
11015	Imputed	36.457	41.875	114.862	1.396	4.483
	Original	35.755	40.968	114.581	1.426	4.677
11020	Imputed	49.604	68.453	137.999	1.799	5.856
	Original	49.604	68.453	137.999	1.799	5.856
11021	Imputed	50.552	67.841	134.199	1.600	5.226
	Original	50.237	67.317	133.999	1.614	5.337
11022	Imputed	54.703	67.374	123.162	1.492	4.997
	Original	54.915	67.715	123.310	1.483	4.947
11023	Imputed	52.645	69.446	131.913	1.660	5.622
	Original	52.665	70.260	133.408	1.665	5.627
11025	Imputed	57.398	74.415	129.647	1.592	5.122
	Original	57.556	74.604	129.621	1.586	5.092
11028	Imputed	54.227	70.117	129.303	1.411	4.493
	Original	54.227	70.117	129.303	1.411	4.493
11031	Imputed	64.585	79.530	123.140	1.311	4.146
	Original	64.106	78.803	122.925	1.309	4.148
11033	Imputed	49.072	59.597	121.448	1.475	4.904
	Original	48.841	59.612	122.053	1.488	4.939
11034	Imputed	58.405	74.110	126.891	1.190	3.342
	Original	58.807	74.474	126.641	1.193	3.370
11035	Imputed	51.113	66.280	129.674	1.336	3.942
	Original	51.175	66.374	129.700	1.341	3.952
11036	Imputed	59.498	78.109	131.280	1.431	4.446
	Original	59.697	78.234	131.051	1.424	4.424
11040	Imputed	56.229	74.131	131.837	1.604	5.133
	Original	56.229	74.131	131.837	1.604	5.133
11041	Imputed	50.393	67.630	134.206	1.541	4.703
	Original	50.519	67.645	133.898	1.511	4.580
11042	Imputed	44.361	56.929	128.333	1.962	8.181
	Original	45.267	57.460	126.935	1.891	7.851
11045	Imputed	58.984	79.716	135.147	1.909	8.026
	Original	58.749	79.753	135.753	1.927	8.137
11048	Imputed	47.974	61.080	127.320	1.587	5.613
	Original	48.302	61.390	127.096	1.579	5.591
11049	Imputed	55.081	66.078	119.965	1.586	5.678
	Original	55.402	66.088	119.287	1.573	5.674
11050	Imputed	37.703	49.814	132.123	1.677	5.667
	Original	37.848	49.864	131.746	1.687	5.716
11051	Imputed	42.297	52.962	125.215	1.655	5.463
	Original	42.297	52.962	125.215	1.655	5.463
11052	Imputed	50.438	63.725	126.343	1.435	4.451
	Original	50.517	63.777	126.250	1.431	4.439
11055	Imputed	54.471	71.824	131.859	1.795	6.509
	Original	54.834	72.395	132.025	1.786	6.461
11061	Imputed	42.425	67.258	158.536	2.288	9.372
	Original	42.886	68.521	159.773	2.304	9.379
11066	Imputed	42.014	49.283	117.301	1.329	4.002
	Original	42.500	49.624	116.761	1.278	3.791
11070	Imputed	54.966	71.870	130.755	1.597	5.115
	Original	55.579	72.302	130.088	1.588	5.075
11071	Imputed	53.463	66.532	124.445	1.288	4.149
	Original	53.463	66.532	124.445	1.288	4.149
11072	Imputed	57.412	75.308	131.171	1.530	5.057
	Original	57.412	75.308	131.171	1.530	5.057
11077	Imputed	62.917	78.216	124.317	1.383	4.338
	Original	63.460	78.432	123.593	1.368	4.297
11078	Imputed	61.409	77.515	126.228	1.402	4.356
	Original	61.708	78.018	126.431	1.393	4.310
11079	Imputed	54.521	69.097	126.735	1.439	4.475
	Original	54.118	68.894	127.302	1.435	4.468
11083	Imputed	47.166	55.399	117.455	1.619	5.583
	Original	47.200	55.459	117.497	1.616	5.568
11085	Imputed	56.158	74.536	132.725	1.595	5.017
	Original	55.262	73.654	133.281	1.619	5.142
11095	Imputed	56.960	77.217	135.564	1.603	4.960
	Original	56.960	77.217	135.564	1.603	4.960
11099	Imputed	58.425	76.738	131.344	1.385	4.129
	Original	59.126	77.574	131.201	1.376	4.087
11103	Imputed	60.781	77.903	128.169	1.657	5.638
	Original	61.273	78.572	128.234	1.661	5.636
11116	Imputed	55.062	71.083	129.096	1.592	5.227
	Original	55.647	71.194	127.940	1.588	5.230
11122	Imputed	51.951	63.786	122.781	1.495	4.975
	Original	51.405	63.395	123.324	1.524	5.117
11124	Imputed	54.986	71.684	130.368	1.477	4.439
	Original	55.077	71.743	130.260	1.473	4.427
11134	Imputed	58.657	77.690	132.447	1.511	4.743
	Original	58.792	77.729	132.210	1.508	4.733
11136	Imputed	55.244	72.283	130.842	1.575	5.158
	Original	55.173	71.373	129.362	1.549	5.092
11140	Imputed	43.617	59.519	136.460	2.006	7.414
	Original	43.824	59.900	136.682	2.011	7.401
11142	Imputed	53.261	67.388	126.524	1.349	4.009
	Original	52.968	67.537	127.505	1.361	4.029
11143	Imputed	54.459	74.091	136.050	1.718	5.900
	Original	53.606	73.989	138.025	1.760	6.076
11144	Imputed	31.825	38.366	120.552	1.484	5.386
	Original	32.077	39.032	121.684	1.510	5.421
11145	Imputed	52.494	70.158	133.648	1.389	4.070
	Original	51.859	69.397	133.818	1.396	4.104
11146	Imputed	43.278	63.507	146.741	1.762	5.691
	Original	43.212	63.018	145.835	1.750	5.661
11148	Imputed	51.630	66.372	128.553	1.727	6.425
	Original	51.750	66.624	128.741	1.727	6.402
11149	Imputed	54.708	72.425	132.385	1.482	4.740
	Original	54.906	73.832	134.469	1.495	4.728
11151	Imputed	56.454	75.766	134.209	1.338	3.723
	Original	55.056	75.195	136.578	1.391	3.880
11161	Imputed	34.174	39.889	116.723	1.712	7.016
	Original	34.371	39.874	116.011	1.718	7.098
11166	Imputed	64.804	76.422	117.928	1.206	3.730
	Original	64.804	76.422	117.928	1.206	3.730

). The average change in the mean across all stations was a negligible $0.29\pm 0.21$ mm, while the standard deviation changed by $0.42\pm 0.24$ mm on average. The coefficients of variation, skewness, and kurtosis showed even smaller shifts ($\mathrm{\Delta }\mathrm{VC}=0.65\pm 0.49$%, $\mathrm{\Delta }S=0.02\pm 0.01$, $\mathrm{\Delta }K=0.13\pm 0.09$). The preservation of high kurtosis values ($K>3.7$ across all stations) is particularly noteworthy, as it confirms that the imputation process maintained the statistical weight of extreme events system-wide. The magnitude of these deviations is insignificant compared to the natural interannual precipitation variability in semi-arid regions (often exceeding 20–30%), conclusively demonstrating that the imputed datasets are fully representative of the original climatic series.

The negligible magnitude of these deviations ensures that the imputed datasets are fully suitable for robust trend analysis. This robustness stems from three key factors: (i) the preserved distributional properties ($p=1.000$ in KS tests) maintain the rank order and variability structure of the data; (ii) the TFPW-MK procedure corrects for autocorrelation, reducing sensitivity to small mean shifts; and (iii) Kendall’s $\tau$ is a non-parametric, rank-based measure inherently insensitive to minimal changes in absolute magnitudes. Consequently, the minor imputation-related uncertainties are dwarfed by the natural interannual precipitation variability in semi-arid regions (often exceeding 20–30%).

4.2. Monthly Distribution and Seasonal Regime

Figure 4 reveals the pluviometric regime in Guanajuato (1981–2016) through a boxplot analysis summarizing variability across all stations. The analysis confirms a marked seasonal pattern characteristic of the North American monsoon region: the wet season (June–September) shows the highest accumulations, with July exhibiting the maximum values (median: 5617 mm, IQR: 1290 mm), demonstrating the influence of organized convective systems and potential tropical wave intrusions. In contrast, dry months (January–April, November–December) display compact distributions (IQR < 800 mm) with medians generally below 500 mm, reflecting continental anticyclonic dominance. Notably, these dry months still contain outliers, likely associated with atypical cold-front–humidity interactions. Transition months (May, October) exhibit intermediate behaviors. May shows an abrupt increase (median: 1225 mm) marking the activation of convective processes and the onset of the rainy season, while October shows a moderate spread in its data, signaling the retreat of the monsoon and increased variability as dry conditions establish. The lower outlier density in the wet season suggests greater predictability of large-scale rain-generating mechanisms compared to the more sporadic and localized nature of winter precipitation events. These patterns align with the documented climatic bimodality in Central Mexico [36] and provide essential context for interpreting the homogeneity and trend results. The clear, stable seasonal cyclicity demonstrated here establishes that while the system exhibits high intra-annual variability, its fundamental seasonal structure remained consistent throughout the 36-year study period.

4.3. Homogeneity Assessment

4.3.1. Overall Results and Temporal Patterns

The application of the four absolute homogeneity tests (detailed in Section 3.2) to the 65 stations revealed a generally high level of data reliability across Guanajuato’s precipitation network. The comprehensive results, including p-values and most probable change points for each station and test, are presented in Table 4 (monthly series) and Table 5 (annual series).

Key findings from the classification:

• Monthly analysis:In total, 60 stations (93.8%) were classified as useful, 3 stations (4.7%) as doubtful(11020, 11143, 11146), and 2 stations (3.1%) as suspicious (11004, 11061).
• Annual analysis: In total, 58 stations (85.9%) were classified as useful, 5 stations (7.8%) as doubtful (11001, 11045, 11053, 11055, 11143), and 4 stations (6.3%) as suspicious (11020, 11025, 11061, 11072).

A significant finding emerged from the temporal analysis of detected breakpoints. The identified change points showed strong clustering around two specific periods: 2000–2003 (detected in 28 stations) and 2011–2014 (identified in 25 stations). This non-random temporal pattern strongly correlates with documented nationwide modernization and instrumental changes within Mexico’s meteorological network [51], providing compelling evidence that these detected breaks represent non-climatic influences rather than natural climate variability.

Table 4. Comparison of monthly precipitation homogeneity test results.

Station	Pettitt Test			Buishand Range Test			SNHT Test			von Neumann Ratio Test_Stat	Rejections	Classification
	p	Year	Month	p	Year	Month	p	Year	Month
11001	0.7608	2000	04	0.6649	2001	04	0.7701	2001	04	0.9623	0	Useful
11002	0.7838	2013	04	0.7798	2001	05	0.6202	2016	05	0.8022	0	Useful
11003	0.2229	2000	04	0.3904	2000	04	0.4423	2000	04	0.9626	0	Useful
11004	0.0080	2011	06	0.0000	1992	10	0.0058	2012	06	0.9586	3	Suspicious
11006	1.0000	2000	04	0.3698	1998	05	0.8774	1998	05	1.0067	0	Useful
11007	0.5418	2000	04	0.7932	2000	04	0.8655	2000	04	0.9813	0	Useful
11009	0.5113	2000	04	0.4604	2001	05	0.6672	2001	05	0.9728	0	Useful
11010	0.0653	2003	04	0.0590	2002	05	0.1431	2002	05	0.9596	0	Useful
11011	0.2321	2000	04	0.5748	2002	05	0.3205	2013	05	1.1129	0	Useful
11012	0.5307	1993	09	0.0251	1996	10	0.2391	2013	05	0.8985	1	Useful
11013	0.5071	2002	05	0.6406	2002	05	0.9585	2002	05	1.0443	0	Useful
11014	0.3630	2012	01	0.2144	2001	05	0.1390	2013	05	1.0261	0	Useful
11015	0.3288	2013	04	0.4615	2001	05	0.1906	2013	04	1.1969	0	Useful
11020	0.2979	2001	04	0.0255	2001	04	0.0201	2001	04	0.9564	2	Doubtful
11021	0.5071	1986	11	0.2020	2002	05	0.6093	2002	05	0.9434	0	Useful
11022	1.0000	2000	04	0.8591	2001	05	0.9875	2016	04	0.9213	0	Useful
11023	0.7111	2001	04	0.5888	2001	05	0.4511	2016	05	0.9837	0	Useful
11025	0.1341	2001	04	0.1641	2001	04	0.1535	2001	04	0.9937	0	Useful
11028	0.6517	2013	04	0.9574	2002	06	0.5899	2013	05	0.9384	0	Useful
11031	0.6811	1986	10	0.8291	2001	05	0.9094	2016	04	0.8492	0	Useful
11033	0.2776	2000	04	0.5848	2001	04	0.6522	2001	04	1.0771	0	Useful
11034	0.7454	2013	05	0.9872	2013	05	0.6139	2013	05	0.9134	0	Useful
11035	0.4355	2001	03	0.6231	2001	05	0.5558	2013	05	0.9170	0	Useful
11036	0.2367	2000	04	0.7088	2001	05	0.3467	2016	05	0.9323	0	Useful
11040	0.6147	2001	04	0.5416	2001	04	0.4420	2016	06	0.9556	0	Useful
11041	0.2930	2000	04	0.3682	2013	05	0.2294	2015	04	1.0297	0	Useful
11042	0.1150	1994	10	0.0423	1994	10	0.5658	1994	10	1.1312	1	Useful
11045	0.2882	2009	04	0.1774	2001	04	0.0620	2016	06	1.1051	0	Useful
11048	1.0000	2013	05	0.8860	2003	05	0.9731	2003	05	1.0277	0	Useful
11049	0.7233	2013	05	0.8786	2003	05	0.5449	2013	05	1.1225	0	Useful
11050	0.2233	2013	04	0.4236	2002	05	0.0438	2013	05	1.2374	1	Useful
11051	0.4297	2003	05	0.6579	2002	05	0.8506	2002	05	1.2211	0	Useful
11052	1.0000	2000	04	0.7760	2001	05	0.7439	2016	05	0.8597	0	Useful
11053	0.2780	2013	05	0.4286	2006	06	0.1139	2013	05	1.2288	0	Useful
11055	0.5228	2002	04	0.4873	2002	05	0.4867	2002	05	0.9996	0	Useful
11061	0.0002	2002	05	0.0000	2002	05	0.0063	2002	05	1.0358	3	Suspicious
11066	1.0000	1993	09	0.3950	2003	05	0.5112	2003	05	1.0672	0	Useful
11070	1.0000	2000	05	0.9732	1998	05	0.9030	2015	02	0.9991	0	Useful
11071	0.6612	1996	10	0.9752	2003	05	0.9936	2006	06	0.8752	0	Useful
11072	0.2096	2001	04	0.3552	2002	05	0.3484	2002	05	1.0009	0	Useful
11077	0.3430	1992	11	0.5890	2003	04	0.9058	2014	04	0.8743	0	Useful
11078	1.0000	2013	05	0.9970	1991	05	0.9192	2016	05	0.9187	0	Useful
11079	1.0000	2013	05	0.8461	2003	05	0.6020	2013	05	0.9453	0	Useful
11083	0.7361	2013	05	0.6626	2006	03	0.6754	2006	03	1.2606	0	Useful
11085	0.3737	1995	09	0.8362	2002	06	0.4764	2016	05	1.1576	0	Useful
11095	0.4637	2001	04	0.6322	2001	05	0.6632	2001	05	0.9698	0	Useful
11099	0.7846	2001	04	0.6236	2001	05	0.5913	2014	04	0.9899	0	Useful
11103	0.4779	2000	04	0.7716	2001	04	0.9343	2001	04	1.0574	0	Useful
11116	0.3121	2000	04	0.8112	2003	05	0.6400	2012	05	0.9389	0	Useful
11122	1.0000	2000	04	0.8498	2001	04	0.9204	2016	07	0.9965	0	Useful
11124	0.3072	2000	04	0.5604	2001	05	0.6236	2001	05	0.9388	0	Useful
11134	0.7514	2013	04	0.6547	2001	05	0.6365	2016	05	0.9516	0	Useful
11136	0.7245	2000	04	0.6387	2001	05	0.8665	2001	05	0.9757	0	Useful
11140	0.1178	2001	04	0.0609	2003	06	0.7120	2003	06	1.2173	0	Useful
11141	0.0535	2002	05	0.0699	2002	05	0.0036	2013	05	0.9906	1	Useful
11142	1.0000	2013	05	0.8642	2001	05	0.9166	2013	05	0.8537	0	Useful
11143	0.1460	2002	04	0.0074	2002	04	0.0140	2014	04	0.9612	2	Doubtful
11144	0.4335	1986	09	0.1133	1994	10	0.4938	2016	05	1.0878	0	Useful
11145	0.3740	1992	11	0.9300	2001	05	0.9684	2015	02	0.9526	0	Useful
11146	0.0484	1987	09	0.0012	1992	11	0.0524	2012	05	0.9797	2	Doubtful
11148	0.7397	1993	09	0.9104	2002	05	0.8980	2015	02	1.1139	0	Useful
11149	0.4358	1992	11	0.4387	1986	10	0.5667	2016	04	0.8374	0	Useful
11151	0.9399	2001	04	0.7760	2001	04	0.5884	2015	04	0.9412	0	Useful
11161	0.3240	2001	03	0.4353	2001	05	0.5528	2001	05	1.3611	0	Useful
11166	0.4882	2000	04	0.7591	2002	05	0.6868	2016	05	0.7817	0	Useful

Table 4. Comparison of monthly precipitation homogeneity test results.

Station	Pettitt Test			Buishand Range Test			SNHT Test			von Neumann Ratio Test_Stat	Rejections	Classification
	p	Year	Month	p	Year	Month	p	Year	Month
11001	0.7608	2000	04	0.6649	2001	04	0.7701	2001	04	0.9623	0	Useful
11002	0.7838	2013	04	0.7798	2001	05	0.6202	2016	05	0.8022	0	Useful
11003	0.2229	2000	04	0.3904	2000	04	0.4423	2000	04	0.9626	0	Useful
11004	0.0080	2011	06	0.0000	1992	10	0.0058	2012	06	0.9586	3	Suspicious
11006	1.0000	2000	04	0.3698	1998	05	0.8774	1998	05	1.0067	0	Useful
11007	0.5418	2000	04	0.7932	2000	04	0.8655	2000	04	0.9813	0	Useful
11009	0.5113	2000	04	0.4604	2001	05	0.6672	2001	05	0.9728	0	Useful
11010	0.0653	2003	04	0.0590	2002	05	0.1431	2002	05	0.9596	0	Useful
11011	0.2321	2000	04	0.5748	2002	05	0.3205	2013	05	1.1129	0	Useful
11012	0.5307	1993	09	0.0251	1996	10	0.2391	2013	05	0.8985	1	Useful
11013	0.5071	2002	05	0.6406	2002	05	0.9585	2002	05	1.0443	0	Useful
11014	0.3630	2012	01	0.2144	2001	05	0.1390	2013	05	1.0261	0	Useful
11015	0.3288	2013	04	0.4615	2001	05	0.1906	2013	04	1.1969	0	Useful
11020	0.2979	2001	04	0.0255	2001	04	0.0201	2001	04	0.9564	2	Doubtful
11021	0.5071	1986	11	0.2020	2002	05	0.6093	2002	05	0.9434	0	Useful
11022	1.0000	2000	04	0.8591	2001	05	0.9875	2016	04	0.9213	0	Useful
11023	0.7111	2001	04	0.5888	2001	05	0.4511	2016	05	0.9837	0	Useful
11025	0.1341	2001	04	0.1641	2001	04	0.1535	2001	04	0.9937	0	Useful
11028	0.6517	2013	04	0.9574	2002	06	0.5899	2013	05	0.9384	0	Useful
11031	0.6811	1986	10	0.8291	2001	05	0.9094	2016	04	0.8492	0	Useful
11033	0.2776	2000	04	0.5848	2001	04	0.6522	2001	04	1.0771	0	Useful
11034	0.7454	2013	05	0.9872	2013	05	0.6139	2013	05	0.9134	0	Useful
11035	0.4355	2001	03	0.6231	2001	05	0.5558	2013	05	0.9170	0	Useful
11036	0.2367	2000	04	0.7088	2001	05	0.3467	2016	05	0.9323	0	Useful
11040	0.6147	2001	04	0.5416	2001	04	0.4420	2016	06	0.9556	0	Useful
11041	0.2930	2000	04	0.3682	2013	05	0.2294	2015	04	1.0297	0	Useful
11042	0.1150	1994	10	0.0423	1994	10	0.5658	1994	10	1.1312	1	Useful
11045	0.2882	2009	04	0.1774	2001	04	0.0620	2016	06	1.1051	0	Useful
11048	1.0000	2013	05	0.8860	2003	05	0.9731	2003	05	1.0277	0	Useful
11049	0.7233	2013	05	0.8786	2003	05	0.5449	2013	05	1.1225	0	Useful
11050	0.2233	2013	04	0.4236	2002	05	0.0438	2013	05	1.2374	1	Useful
11051	0.4297	2003	05	0.6579	2002	05	0.8506	2002	05	1.2211	0	Useful
11052	1.0000	2000	04	0.7760	2001	05	0.7439	2016	05	0.8597	0	Useful
11053	0.2780	2013	05	0.4286	2006	06	0.1139	2013	05	1.2288	0	Useful
11055	0.5228	2002	04	0.4873	2002	05	0.4867	2002	05	0.9996	0	Useful
11061	0.0002	2002	05	0.0000	2002	05	0.0063	2002	05	1.0358	3	Suspicious
11066	1.0000	1993	09	0.3950	2003	05	0.5112	2003	05	1.0672	0	Useful
11070	1.0000	2000	05	0.9732	1998	05	0.9030	2015	02	0.9991	0	Useful
11071	0.6612	1996	10	0.9752	2003	05	0.9936	2006	06	0.8752	0	Useful
11072	0.2096	2001	04	0.3552	2002	05	0.3484	2002	05	1.0009	0	Useful
11077	0.3430	1992	11	0.5890	2003	04	0.9058	2014	04	0.8743	0	Useful
11078	1.0000	2013	05	0.9970	1991	05	0.9192	2016	05	0.9187	0	Useful
11079	1.0000	2013	05	0.8461	2003	05	0.6020	2013	05	0.9453	0	Useful
11083	0.7361	2013	05	0.6626	2006	03	0.6754	2006	03	1.2606	0	Useful
11085	0.3737	1995	09	0.8362	2002	06	0.4764	2016	05	1.1576	0	Useful
11095	0.4637	2001	04	0.6322	2001	05	0.6632	2001	05	0.9698	0	Useful
11099	0.7846	2001	04	0.6236	2001	05	0.5913	2014	04	0.9899	0	Useful
11103	0.4779	2000	04	0.7716	2001	04	0.9343	2001	04	1.0574	0	Useful
11116	0.3121	2000	04	0.8112	2003	05	0.6400	2012	05	0.9389	0	Useful
11122	1.0000	2000	04	0.8498	2001	04	0.9204	2016	07	0.9965	0	Useful
11124	0.3072	2000	04	0.5604	2001	05	0.6236	2001	05	0.9388	0	Useful
11134	0.7514	2013	04	0.6547	2001	05	0.6365	2016	05	0.9516	0	Useful
11136	0.7245	2000	04	0.6387	2001	05	0.8665	2001	05	0.9757	0	Useful
11140	0.1178	2001	04	0.0609	2003	06	0.7120	2003	06	1.2173	0	Useful
11141	0.0535	2002	05	0.0699	2002	05	0.0036	2013	05	0.9906	1	Useful
11142	1.0000	2013	05	0.8642	2001	05	0.9166	2013	05	0.8537	0	Useful
11143	0.1460	2002	04	0.0074	2002	04	0.0140	2014	04	0.9612	2	Doubtful
11144	0.4335	1986	09	0.1133	1994	10	0.4938	2016	05	1.0878	0	Useful
11145	0.3740	1992	11	0.9300	2001	05	0.9684	2015	02	0.9526	0	Useful
11146	0.0484	1987	09	0.0012	1992	11	0.0524	2012	05	0.9797	2	Doubtful
11148	0.7397	1993	09	0.9104	2002	05	0.8980	2015	02	1.1139	0	Useful
11149	0.4358	1992	11	0.4387	1986	10	0.5667	2016	04	0.8374	0	Useful
11151	0.9399	2001	04	0.7760	2001	04	0.5884	2015	04	0.9412	0	Useful
11161	0.3240	2001	03	0.4353	2001	05	0.5528	2001	05	1.3611	0	Useful
11166	0.4882	2000	04	0.7591	2002	05	0.6868	2016	05	0.7817	0	Useful

Table 5. Comparison of annual precipitation homogeneity test results.

Station	Pettitt		Buishand		SNHT		VN_Stat	Rejections	Classification
	p	Year	p	Year	p	Year
11001	0.0750	2000	0.0389	2000	0.0479	2000	1.6329	2	Doubtful
11002	0.1604	2000	0.1273	2000	0.2343	2000	1.7064	0	Useful
11003	0.1339	1999	0.2510	1999	0.1662	2000	1.5900	0	Useful
11004	0.1846	1992	0.0003	1992	0.0876	2011	1.0559	1	Useful
11006	0.3202	1997	0.2328	1997	0.6590	1997	1.7210	0	Useful
11007	0.2045	1999	0.5204	1999	0.4261	1999	2.0445	0	Useful
11009	0.3300	2000	0.2982	2000	0.3918	2000	2.0714	0	Useful
11010	0.0515	2001	0.0336	2001	0.0674	2001	1.2890	1	Useful
11011	0.1069	2001	0.3623	2001	0.2200	2012	1.8873	0	Useful
11012	0.1494	1996	0.0021	1996	0.2048	2012	1.0479	1	Useful
11013	0.4047	2001	0.1280	2001	0.4998	2001	1.9603	0	Useful
11014	0.1846	2000	0.1368	2000	0.1375	2012	1.7040	0	Useful
11015	0.2414	2000	0.1560	2000	0.0683	2012	1.6611	0	Useful
11020	0.0089	2000	0.0120	2000	0.0053	2000	1.2791	3	Suspicious
11021	0.3714	2001	0.0721	2001	0.3184	2001	1.4130	0	Useful
11022	1.0000	2000	0.5375	2000	0.9440	1990	1.7856	0	Useful
11023	0.0880	2000	0.1190	2000	0.0666	2000	1.4807	0	Useful
11025	0.0089	2000	0.0366	2000	0.0188	2000	1.4919	3	Suspicious
11028	0.2045	2001	0.5634	2001	0.0784	2012	1.6122	0	Useful
11031	0.9709	1986	0.2862	1986	0.6980	1986	1.8821	0	Useful
11031	0.9709	2002	0.2862	1986	0.6980	1986	1.8821	0	Useful
11033	0.0585	2000	0.1911	2000	0.1480	2000	2.0530	0	Useful
11034	0.1389	2000	0.6024	2011	0.1180	2011	2.1682	0	Useful
11035	0.1029	2000	0.1870	2000	0.1812	2000	1.9676	0	Useful
11036	0.0380	2000	0.1869	2000	0.1184	2000	1.3234	1	Useful
11040	0.0453	2000	0.2374	2000	0.1417	2000	1.5768	1	Useful
11041	0.6936	2012	0.0983	2012	0.0340	2014	1.8077	1	Useful
11042	0.4903	1994	0.0355	1994	0.4252	1994	1.4682	1	Useful
11045	0.0099	2000	0.0761	2000	0.0299	2012	1.6996	2	Doubtful
11048	0.6936	2002	0.6434	2002	0.7570	2002	1.8324	0	Useful
11049	0.3400	2001	0.5671	2001	0.3615	2012	1.4739	0	Useful
11050	0.3823	2001	0.4083	2001	0.0584	2012	1.2127	0	Useful
11051	0.1548	2001	0.2193	2001	0.3394	2001	1.4704	0	Useful
11052	0.1722	2000	0.4502	2000	0.3151	2000	2.0403	0	Useful
11053	0.0363	2005	0.0584	2005	0.0030	2014	1.3058	2	Doubtful
11055	0.0317	2000	0.0867	2000	0.0488	2001	1.5595	2	Doubtful
11061	0.0189	2001	0.0006	2001	0.0303	2001	0.9571	3	Suspicious
11066	0.0636	2002	0.0747	2002	0.0902	2002	1.8167	0	Useful
11070	1.0000	2000	0.9059	2000	0.4080	2014	2.2872	0	Useful
11071	1.0000	2005	0.6763	2005	0.6526	2005	1.7745	0	Useful
11072	0.0303	2001	0.0297	2001	0.0128	2001	1.7973	3	Suspicious
11077	0.5167	2000	0.1866	2002	0.5756	2002	1.7896	0	Useful
11078	1.0000	1990	0.8768	1990	0.5542	1982	2.0119	0	Useful
11079	0.4903	2002	0.4126	2002	0.2710	2012	2.1581	0	Useful
11083	0.1290	2005	0.0788	2005	0.0689	2005	1.6400	0	Useful
11085	0.4047	2001	0.3998	2001	0.3963	2014	1.9099	0	Useful
11095	0.0494	2000	0.1670	2000	0.0969	2000	1.5729	1	Useful
11099	0.0585	2000	0.0814	2000	0.0748	2000	2.0725	0	Useful
11103	0.2575	2000	0.4295	2000	0.4833	2000	1.7137	0	Useful
11116	0.0750	2000	0.2974	2000	0.1688	2011	1.9619	0	Useful
11122	0.5167	2000	0.4674	2000	0.6528	2000	1.7788	0	Useful
11124	0.0538	2000	0.0973	2000	0.0876	2000	1.1651	0	Useful
11134	0.1029	2000	0.2190	2000	0.1755	2000	1.5637	0	Useful
11136	0.1722	2000	0.2620	2000	0.3358	2000	1.7684	0	Useful
11140	0.5581	2000	0.0503	2000	0.6254	2002	1.1746	0	Useful
11140	0.5581	2002	0.0503	2000	0.6254	2002	1.1746	0	Useful
11141	0.0561	2001	0.0699	2001	0.0028	2011	1.1533	1	Useful
11142	0.3300	2000	0.2622	2000	0.4678	2000	2.1256	0	Useful
11143	0.0720	2001	0.0192	2001	0.0477	2001	0.8255	2	Doubtful
11144	0.3300	1994	0.0682	1994	0.4732	1994	1.3211	0	Useful
11145	0.9524	2001	0.6752	2001	0.5009	2014	2.1121	0	Useful
11146	0.1722	1992	0.0003	1992	0.0772	2011	0.7256	1	Useful
11148	0.6014	1992	0.5855	2001	0.5338	2014	1.7473	0	Useful
11149	0.5867	1986	0.3546	1986	0.4007	1986	1.7754	0	Useful
11151	0.3934	2000	0.5070	2001	0.2419	2014	1.9125	0	Useful
11161	0.3012	2001	0.3360	2002	0.2926	2002	1.8156	0	Useful
11166	0.2336	2001	0.3584	2001	0.2435	2001	1.5454	0	Useful

Table 5. Comparison of annual precipitation homogeneity test results.

Station	Pettitt		Buishand		SNHT		VN_Stat	Rejections	Classification
	p	Year	p	Year	p	Year
11001	0.0750	2000	0.0389	2000	0.0479	2000	1.6329	2	Doubtful
11002	0.1604	2000	0.1273	2000	0.2343	2000	1.7064	0	Useful
11003	0.1339	1999	0.2510	1999	0.1662	2000	1.5900	0	Useful
11004	0.1846	1992	0.0003	1992	0.0876	2011	1.0559	1	Useful
11006	0.3202	1997	0.2328	1997	0.6590	1997	1.7210	0	Useful
11007	0.2045	1999	0.5204	1999	0.4261	1999	2.0445	0	Useful
11009	0.3300	2000	0.2982	2000	0.3918	2000	2.0714	0	Useful
11010	0.0515	2001	0.0336	2001	0.0674	2001	1.2890	1	Useful
11011	0.1069	2001	0.3623	2001	0.2200	2012	1.8873	0	Useful
11012	0.1494	1996	0.0021	1996	0.2048	2012	1.0479	1	Useful
11013	0.4047	2001	0.1280	2001	0.4998	2001	1.9603	0	Useful
11014	0.1846	2000	0.1368	2000	0.1375	2012	1.7040	0	Useful
11015	0.2414	2000	0.1560	2000	0.0683	2012	1.6611	0	Useful
11020	0.0089	2000	0.0120	2000	0.0053	2000	1.2791	3	Suspicious
11021	0.3714	2001	0.0721	2001	0.3184	2001	1.4130	0	Useful
11022	1.0000	2000	0.5375	2000	0.9440	1990	1.7856	0	Useful
11023	0.0880	2000	0.1190	2000	0.0666	2000	1.4807	0	Useful
11025	0.0089	2000	0.0366	2000	0.0188	2000	1.4919	3	Suspicious
11028	0.2045	2001	0.5634	2001	0.0784	2012	1.6122	0	Useful
11031	0.9709	1986	0.2862	1986	0.6980	1986	1.8821	0	Useful
11031	0.9709	2002	0.2862	1986	0.6980	1986	1.8821	0	Useful
11033	0.0585	2000	0.1911	2000	0.1480	2000	2.0530	0	Useful
11034	0.1389	2000	0.6024	2011	0.1180	2011	2.1682	0	Useful
11035	0.1029	2000	0.1870	2000	0.1812	2000	1.9676	0	Useful
11036	0.0380	2000	0.1869	2000	0.1184	2000	1.3234	1	Useful
11040	0.0453	2000	0.2374	2000	0.1417	2000	1.5768	1	Useful
11041	0.6936	2012	0.0983	2012	0.0340	2014	1.8077	1	Useful
11042	0.4903	1994	0.0355	1994	0.4252	1994	1.4682	1	Useful
11045	0.0099	2000	0.0761	2000	0.0299	2012	1.6996	2	Doubtful
11048	0.6936	2002	0.6434	2002	0.7570	2002	1.8324	0	Useful
11049	0.3400	2001	0.5671	2001	0.3615	2012	1.4739	0	Useful
11050	0.3823	2001	0.4083	2001	0.0584	2012	1.2127	0	Useful
11051	0.1548	2001	0.2193	2001	0.3394	2001	1.4704	0	Useful
11052	0.1722	2000	0.4502	2000	0.3151	2000	2.0403	0	Useful
11053	0.0363	2005	0.0584	2005	0.0030	2014	1.3058	2	Doubtful
11055	0.0317	2000	0.0867	2000	0.0488	2001	1.5595	2	Doubtful
11061	0.0189	2001	0.0006	2001	0.0303	2001	0.9571	3	Suspicious
11066	0.0636	2002	0.0747	2002	0.0902	2002	1.8167	0	Useful
11070	1.0000	2000	0.9059	2000	0.4080	2014	2.2872	0	Useful
11071	1.0000	2005	0.6763	2005	0.6526	2005	1.7745	0	Useful
11072	0.0303	2001	0.0297	2001	0.0128	2001	1.7973	3	Suspicious
11077	0.5167	2000	0.1866	2002	0.5756	2002	1.7896	0	Useful
11078	1.0000	1990	0.8768	1990	0.5542	1982	2.0119	0	Useful
11079	0.4903	2002	0.4126	2002	0.2710	2012	2.1581	0	Useful
11083	0.1290	2005	0.0788	2005	0.0689	2005	1.6400	0	Useful
11085	0.4047	2001	0.3998	2001	0.3963	2014	1.9099	0	Useful
11095	0.0494	2000	0.1670	2000	0.0969	2000	1.5729	1	Useful
11099	0.0585	2000	0.0814	2000	0.0748	2000	2.0725	0	Useful
11103	0.2575	2000	0.4295	2000	0.4833	2000	1.7137	0	Useful
11116	0.0750	2000	0.2974	2000	0.1688	2011	1.9619	0	Useful
11122	0.5167	2000	0.4674	2000	0.6528	2000	1.7788	0	Useful
11124	0.0538	2000	0.0973	2000	0.0876	2000	1.1651	0	Useful
11134	0.1029	2000	0.2190	2000	0.1755	2000	1.5637	0	Useful
11136	0.1722	2000	0.2620	2000	0.3358	2000	1.7684	0	Useful
11140	0.5581	2000	0.0503	2000	0.6254	2002	1.1746	0	Useful
11140	0.5581	2002	0.0503	2000	0.6254	2002	1.1746	0	Useful
11141	0.0561	2001	0.0699	2001	0.0028	2011	1.1533	1	Useful
11142	0.3300	2000	0.2622	2000	0.4678	2000	2.1256	0	Useful
11143	0.0720	2001	0.0192	2001	0.0477	2001	0.8255	2	Doubtful
11144	0.3300	1994	0.0682	1994	0.4732	1994	1.3211	0	Useful
11145	0.9524	2001	0.6752	2001	0.5009	2014	2.1121	0	Useful
11146	0.1722	1992	0.0003	1992	0.0772	2011	0.7256	1	Useful
11148	0.6014	1992	0.5855	2001	0.5338	2014	1.7473	0	Useful
11149	0.5867	1986	0.3546	1986	0.4007	1986	1.7754	0	Useful
11151	0.3934	2000	0.5070	2001	0.2419	2014	1.9125	0	Useful
11161	0.3012	2001	0.3360	2002	0.2926	2002	1.8156	0	Useful
11166	0.2336	2001	0.3584	2001	0.2435	2001	1.5454	0	Useful

4.3.2. Comparison Between Monthly and Annual Analyses

The majority of stations (80%) maintained consistent classification (useful) across both temporal scales, validating the overall network homogeneity. However, several important patterns emerged from the discrepancies:

• Stations changing from useful (monthly) to doubtful (annual): 11001 and 11055. The annual aggregation revealed breakpoints masked by seasonal variability at the monthly scale.
• Stations changing from doubtful (monthly) to useful (annual): 11146. Annual smoothing reduced intra-annual variability, making previously detected breaks statistically insignificant.
• Consistently suspicious stations: 11020 and 11061 exhibited clear, unambiguous breakpoints regardless of temporal aggregation.

These differences highlight the complementary nature of monthly versus annual homogeneity assessment. Monthly analysis excels at detecting short-term, seasonally specific inconsistencies, while annual analysis better identifies gradual shifts or structural changes that accumulate over longer periods.

4.3.3. Implications for Trend Analysis

The high proportion (>85%) of homogeneous stations across both temporal scales provides strong confidence in the overall quality of Guanajuato’s precipitation network. The detection of systematic breakpoints coinciding with documented instrumental changes underscores the critical importance of the homogenization procedure conducted prior to trend analysis. All stations—including those classified as doubtful or suspicious—were retained for the subsequent trend analysis. This decision was based on additional validation through metadata review and the presence of corroborating evidence for documented instrumental changes. This inclusive yet transparent approach ensures a robust analysis while honestly addressing potential data limitations. The homogeneity assessment therefore confirms that after appropriate homogenization, Guanajuato’s precipitation network provides a reliable foundation for detecting true climatic trends rather than artifacts of non-climatic factors.

4.4. Trend Analysis

4.4.1. Core Finding: Absence of Significant Trends

The application of the TFPW–Mann–Kendall test to the homogenized monthly precipitation series revealed a definitive result: no statistically significant monotonic trends (at $\alpha =0.05$) were detected at any of the 65 stations over the 36-year period (1981–2016). A trend was considered statistically significant if the absolute value of the Z-statistic exceeded 1.96 ($\left|Z\right|>1.96$, equivalent to $p<0.05$). This overarching finding is robustly supported by multiple lines of evidence from the comprehensive analysis presented in

Table 6. Comprehensive results of the Modified Mann–Kendall test with Trend-Free Pre-Whitening (TFPW) and Sen’s Slope estimator for monthly precipitation series (1981–2016). The table shows Kendall’s Tau ($\tau$), Z-statistic, p-values, Sen’s Slope magnitude (mm/year), and autocorrelation at lag 1. Significance at $\alpha =0.05$ is indicated.

Station	${\mathit{\rho }}_1$	Method	Sen_Slope	SS_p	$\mathit{\tau }$	Z	p	Sig	Direction	MK_Direction
11001	0.5182	TFPW	0.0020	0.6296	0.0100	0.3025	0.7622	No	Increasing	Increasing
11002	0.5982	TFPW	0.0005	0.8660	0.0058	0.1774	0.8592	No	Increasing	Increasing
11003	0.5181	TFPW	0.0035	0.3457	0.0324	0.9748	0.3297	No	Increasing	Increasing
11004	0.5201	TFPW	0.0000	0.8687	−0.0126	−0.3634	0.7163	No	No trend	Decreasing
11006	0.4959	TFPW	0.0000	0.8256	0.0016	0.0488	0.9611	No	No trend	Increasing
11007	0.5087	TFPW	0.0021	0.7886	0.0191	0.5866	0.5574	No	Increasing	Increasing
11009	0.5129	TFPW	−0.0003	0.8787	0.0073	0.2238	0.8229	No	Decreasing	Increasing
11010	0.5195	TFPW	0.0000	0.7680	0.0520	1.5732	0.1157	No	No trend	Increasing
11011	0.4429	TFPW	0.0086	0.2462	0.0460	1.4121	0.1579	No	Increasing	Increasing
11012	0.5499	TFPW	0.0000	0.9909	−0.0185	−0.5668	0.5709	No	No trend	Decreasing
11013	0.4770	TFPW	0.0007	0.6453	0.0220	0.6668	0.5049	No	Increasing	Increasing
11014	0.4864	TFPW	0.0000	0.9874	0.0216	0.6523	0.5142	No	No trend	Increasing
11015	0.4007	TFPW	0.0028	0.6540	0.0215	0.6574	0.5109	No	Increasing	Increasing
11020	0.5212	TFPW	0.0028	0.5744	0.0345	1.0508	0.2933	No	Increasing	Increasing
11021	0.5276	TFPW	0.0000	0.8216	−0.0192	−0.5812	0.5611	No	No trend	Decreasing
11022	0.5386	TFPW	0.0076	0.4566	0.0107	0.3288	0.7423	No	Increasing	Increasing
11023	0.5075	TFPW	0.0000	0.9243	0.0198	0.6054	0.5449	No	No trend	Increasing
11025	0.5030	TFPW	0.0049	0.4124	0.0457	1.3814	0.1672	No	Increasing	Increasing
11028	0.5303	TFPW	0.0044	0.3848	0.0132	0.4004	0.6889	No	Increasing	Increasing
11031	0.5746	TFPW	0.0016	0.8299	−0.0168	−0.5150	0.6065	No	Increasing	Decreasing
11033	0.4607	TFPW	0.0058	0.4180	0.0366	1.1196	0.2629	No	Increasing	Increasing
11034	0.5425	TFPW	0.0016	0.4707	0.0045	0.1350	0.8926	No	Increasing	Increasing
11035	0.5408	TFPW	0.0036	0.4010	0.0223	0.6757	0.4992	No	Increasing	Increasing
11036	0.5331	TFPW	0.0067	0.2671	0.0346	1.0477	0.2948	No	Increasing	Increasing
11040	0.5215	TFPW	0.0019	0.6525	0.0163	0.4959	0.6200	No	Increasing	Increasing
11041	0.4845	TFPW	0.0000	0.7229	0.0336	1.0123	0.3114	No	No trend	Increasing
11042	0.4336	TFPW	0.0023	0.6044	−0.0208	−0.6327	0.5269	No	Increasing	Decreasing
11045	0.4468	TFPW	0.0021	0.4321	0.0325	0.9794	0.3274	No	Increasing	Increasing
11048	0.4854	TFPW	0.0003	0.5910	−0.0008	−0.0228	0.9818	No	Increasing	Decreasing
11049	0.4379	TFPW	0.0083	0.4623	0.0092	0.2845	0.7760	No	Increasing	Increasing
11050	0.3806	TFPW	0.0048	0.3067	0.0342	1.0336	0.3013	No	Increasing	Increasing
11051	0.3887	TFPW	0.0079	0.2574	0.0298	0.9149	0.3603	No	Increasing	Increasing
11052	0.5694	TFPW	0.0000	0.9688	0.0015	0.0459	0.9634	No	No trend	Increasing
11053	0.3839	TFPW	0.0006	0.8871	0.0185	0.5705	0.5683	No	Increasing	Increasing
11055	0.4995	TFPW	0.0000	0.9685	0.0319	0.9745	0.3298	No	No trend	Increasing
11061	0.4818	TFPW	0.0000	0.0833	0.0520	1.5269	0.1268	No	No trend	Increasing
11066	0.4646	TFPW	0.0000	0.9525	−0.0026	−0.0806	0.9358	No	No trend	Decreasing
11070	0.4997	TFPW	−0.0014	0.7765	0.0052	0.1581	0.8744	No	Decreasing	Increasing
11071	0.5617	TFPW	−0.0013	0.7678	−0.0204	−0.6233	0.5331	No	Decreasing	Decreasing
11072	0.4989	TFPW	0.0018	0.7454	0.0213	0.6518	0.5145	No	Increasing	Increasing
11077	0.5620	TFPW	0.0000	0.8568	−0.0168	−0.5113	0.6091	No	No trend	Decreasing
11078	0.5399	TFPW	0.0017	0.7878	−0.0009	−0.0258	0.9794	No	Increasing	Decreasing
11079	0.5266	TFPW	0.0000	0.9816	0.0029	0.0870	0.9307	No	No trend	Increasing
11083	0.3688	TFPW	−0.0029	0.7799	0.0028	0.0861	0.9314	No	Decreasing	Increasing
11085	0.4205	TFPW	0.0000	0.7497	−0.0292	−0.8813	0.3781	No	No trend	Decreasing
11095	0.5145	TFPW	0.0000	0.8810	0.0250	0.7623	0.4459	No	No trend	Increasing
11099	0.5042	TFPW	0.0000	0.7841	0.0127	0.3847	0.7005	No	No trend	Increasing
11103	0.4706	TFPW	0.0085	0.4129	0.0193	0.5932	0.5530	No	Increasing	Increasing
11116	0.5298	TFPW	0.0090	0.1787	0.0502	1.5359	0.1246	No	Increasing	Increasing
11122	0.5010	TFPW	0.0073	0.3732	0.0052	0.1563	0.8758	No	Increasing	Increasing
11124	0.5301	TFPW	0.0046	0.4097	0.0341	1.0336	0.3013	No	Increasing	Increasing
11134	0.5237	TFPW	0.0051	0.4758	0.0173	0.5278	0.5977	No	Increasing	Increasing
11136	0.5115	TFPW	0.0024	0.5900	0.0151	0.4572	0.6475	No	Increasing	Increasing
11140	0.3907	TFPW	0.0000	0.7431	0.0074	0.2246	0.8223	No	No trend	Increasing
11141	0.5041	TFPW	0.0111	0.2350	0.0451	1.3670	0.1716	No	Increasing	Increasing
11142	0.5725	TFPW	0.0000	0.8639	−0.0044	−0.1341	0.8933	No	No trend	Decreasing
11143	0.5189	TFPW	0.0000	0.6579	0.0083	0.2471	0.8049	No	No trend	Increasing
11144	0.4545	TFPW	0.0000	0.9259	−0.0009	−0.0265	0.9789	No	No trend	Decreasing
11145	0.5230	TFPW	0.0000	0.8647	−0.0377	−1.1117	0.2663	No	No trend	Decreasing
11146	0.5095	TFPW	0.0000	0.9734	0.0053	0.1576	0.8748	No	No trend	Increasing
11148	0.4424	TFPW	0.0000	0.7694	−0.0177	−0.5375	0.5909	No	No trend	Decreasing
11149	0.5800	TFPW	0.0000	0.4181	−0.0231	−0.6919	0.4890	No	No trend	Decreasing
11151	0.5289	TFPW	0.0000	0.4893	0.0111	0.3299	0.7415	No	No trend	Increasing
11161	0.3187	TFPW	0.0034	0.5865	0.0241	0.7384	0.4603	No	Increasing	Increasing
11166	0.6085	TFPW	0.0018	0.8098	0.0182	0.5579	0.5769	No	Increasing	Increasing

:

• Direction of non-significant tendencies: Among the 65 stations analyzed, 49 stations (75.4%) showed positive $\tau$ values (range: 0.0016 to 0.0520), suggesting a slight non-significant increasing tendency. The remaining 16 stations (24.6%) exhibited negative $\tau$ values (range: −0.0377 to −0.0008), indicating a non-significant decreasing tendency.
• Negligible magnitude of changes: The Sen’s Slope estimates, representing the actual rate of change, were exceptionally small—ranging from −0.0029 to 0.0111 mm/year across all stations. These values are statistically indistinguishable from zero and hold no practical significance for water resources management.
• Statistical insignificance: All p-values were >0.05, confirming the absence of statistical significance across the entire network.

4.4.2. Statistical Distribution of Trend Magnitudes

Figure 5 presents a combined visual analysis of the distribution of Kendall’s $\tau$ coefficients, providing a synthesized overview of the magnitude and dispersion of the detected, albeit non-significant, trends. The boxplot and kernel density estimate consistently show that the $\tau$ values are tightly clustered near zero. The median $\tau$ value is 0.013, with an interquartile range (IQR) from 0.002 to 0.025, indicating that 50% of the stations exhibit a very weak positive tendency between these values.

The distribution of trend direction shows that the majority of stations (75.4%) displayed positive $\tau$ values, suggesting a slight non-significant increasing tendency in precipitation. The remaining stations (24.6%) exhibited negative $\tau$ values, indicating a non-significant decreasing tendency. The density plot confirmed a unimodal distribution peaked near the median, with most values lying within a narrow range, reinforcing the conclusion of a lack of a strong, consistent climatic signal. The extreme values (maximum $\tau =0.052$ for station 11010 and minimum $\tau =-0.038$ for station 11145) represented the most pronounced non-significant trends but still fell well within the range of random variability.

4.4.3. Spatial and Altitudinal Patterns

The spatial distribution of Kendall’s $\tau$ coefficients (Figure 6a) and Sen’s Slope values (Figure 6b) revealed no discernible geographical pattern across Guanajuato. The apparent trends showed a random spatial distribution rather than any coherent regional pattern.

Critically, the non-parametric Spearman rank correlation analysis revealed no relationship between station altitude and trend magnitude ($\rho =0.019$, $p>0.05$). This definitively confirms that elevation does not influence precipitation trends in the study area, dispelling hypotheses about orographic amplification of changes and reinforcing the conclusion of region-wide stability.

4.4.4. Comparison with Regional Studies and Methodological Implications

Our results show significant convergences and divergences with previous research in Central Mexico. The overwhelming absence of statistically significant trends aligns with the findings of [36], who documented rainfall stability in Guanajuato for the 1970–2010 period. This convergence reinforces the hypothesis of a stable precipitation regime in the region.

However, our results contrast with studies that have reported increasing trends, such as [17] in Aguascalientes. We argue that this discrepancy highlights the critical importance of methodological rigor in climate trend studies. While other studies may have used standard statistical tests prone to Type I errors from autocorrelated data, our application of the TFPW-MK test explicitly corrected for serial correlation (${\rho }_1>0.3$ was common in our series), a critical step for reliable trend detection. Furthermore, the use of homogenized series in our study prevents spurious trends caused by non-climatic factors. The fact that even a robust method like TFPW-MK found no evidence of significant trends strongly suggests that previously reported increases could be artifacts of data processing or statistical approach rather than true climatic signals. Our findings underscore the necessity of employing rigorous, standardized protocols that integrate homogenization and autocorrelation correction to ensure the comparability and reliability of climate trend analyses.

4.5. Implications of Precipitation Stability for Water Management in Guanajuato

4.5.1. The Central Finding: A Management Crisis, Not a Climate Crisis

The most significant implication of this study is that the severe water crisis and aquifer overexploitation in Guanajuato cannot be attributed to a long-term decline in precipitation. Our analysis confirms that precipitation inputs have remained statistically stable over the past 36 years (1981–2016). Therefore, the driver of the water crisis must be sought on the demand side, overwhelmingly from unsustainable groundwater extraction for agriculture, which consumes over 75% of the state’s water [32]. This finding fundamentally redefines the problem: Guanajuato does not face a climate crisis but a socio-hydrogeological management crisis. This necessitates a paradigm shift in policy response, from passive adaptation to expected climatic changes to active and urgent demand-side management.

4.5.2. Context of Water Scarcity

Water scarcity, recognized as one of the greatest global challenges [2] due to its multidimensional complexity [52], is acute in Mexico. Forty-two percent of the nation’s aquifers (275 out of 653) show water deficits, concentrated mainly in the central and northern regions [32,53]. In Guanajuato, this issue has reached critical levels: 19 of its 20 aquifers exhibit annual deficits, with an average water table decline of 1.7 m/year [32], a situation that has drastically worsened since 1998 [33]. Projections indicate a 122% increase in pressure on water resources by 2030 [32].

4.5.3. Strategic Implications for Management

The absence of significant trends, coupled with the established seasonality (Figure 4) and high spatial variability, means water management must adapt to a stable but highly variable regime. The high intramonth variability ($VC>0.12$) and marked seasonality (75% of rainfall concentrated in June–September) increase the risk of flooding and soil erosion, particularly during extreme convective events [48].

Given that precipitation cannot be expected to increase, management must prioritize and enhance the following:

• Water capture and storage infrastructure: Maximizing the capture of high-volume, short-duration rainfall events is essential to recharge aquifers and support irrigation during the dry season.
• Soil conservation practices: Reducing erosion is crucial for maintaining agricultural productivity and preventing siltation in reservoirs.
• Demand management and efficient irrigation: The only viable path to sustainability is a drastic reduction in water consumption, particularly in the agricultural sector, through modernized irrigation systems and policy reforms.

5. Conclusions

This study implemented a rigorous statistical protocol to assess the homogeneity and trends in monthly precipitation series across Guanajuato, Mexico, from 1981 to 2016. The main conclusions are as follows:

• Data Quality and Homogeneity are Prerequisites: The multi-test homogenization approach (Pettitt, SNHT, Buishand, von Neumann) proved essential, identifying that 93.8% of monthly series were homogeneous and suitable for trend analysis. Critically, it detected systematic breakpoints coinciding with documented instrumental changes (2000–2003; 2011–2014), underscoring that homogenization is a non-negotiable first step to avoid spurious trend detection in this region.
• Stability is the Norm: The application of the Trend-Free Pre-Whitening Mann–Kendall (TFPW-MK) test to the homogenized series yielded a definitive result: no statistically significant monotonic trends were found in any of the 65 monthly precipitation series. This demonstrates a stable precipitation regime over the 36-year period, a finding robust against the significant serial correlation (${\rho }_1>0.3$) prevalent in the data.
• The Water Crisis is a Management Crisis: The conclusive evidence of precipitation stability means the severe water crisis and aquifer overexploitation in Guanajuato cannot be attributed to climate-driven reductions in rainfall. Instead, the crisis is overwhelmingly driven by socio-economic factors, particularly unsustainable agricultural water use. This finding necessitates a fundamental shift in policy from passive adaptation to anticipated climate changes to active and urgent demand-side management.
• A Robust Protocol for Arid Regions: The integrated methodology—combining MICE imputation, multi-test homogenization, and TFPW-MK trend analysis—proved essential for reliable climate assessment in a semi-arid, data-scarce region. This protocol effectively mitigates the risks of false trends from autocorrelation and non-climatic inhomogeneities and is recommended as a standard for similar hydroclimatic studies.
• Future Research Directions: Given the stability of precipitation, future research must focus on other drivers of water stress, such as temperature, evapotranspiration, land-use change, and socio-economic dynamics. Developing integrated models that couple these factors with groundwater depletion is paramount for crafting effective mitigation strategies for Guanajuato’s water scarcity.

In summary, this study provides robust evidence that precipitation has not been a variable of change in Guanajuato’s water equation since 1981. Integrating this finding into water policy, such as the Programa Nacional Hídrico [54], is essential for focusing efforts on the true drivers of the crisis—primarily unsustainable demand—ensuring long-term water security for the region.