Evaluating temporal trends and variability of rainfall in Bundelkhand region of Madhya Pradesh using Mann-Kendall test

Introduction

The Bundelkhand region of central India, encompassing key districts in Madhya Pradesh such as Chhatarpur, Tikamgarh, Damoh, Sagar, Datia, and Panna, is historically known for its unique geographical and climatic characteristics. Situated on a semi-arid plateau, this region experiences highly variable annual rainfall patterns, predominantly influenced by the monsoon season (Fanai et al., 2022) [2] . The economy of Bundelkhand remains heavily dependent on rain-fed agriculture, making the availability and distribution of precipitation critical for the livelihoods of its predominantly rural population. Multiple studies indicate that Bundelkhand receives mean annual rainfall ranging from about 650mm in the north to over 1,200mm in the southern districts, with approximately 85-90% of precipitation concentrated in the Southwest Monsoon season (June-September) (Singh, et al., 2023) [7] . However, rainfall across the region is marked by considerable year-to-year variability, frequent droughts, and occasional floods, all of which collectively threaten agricultural productivity and water resource security (Yadav et al., 2025; Jatav, 2024) [9,4] . This variability is reflected in significant spatial gradients as well: southern districts such as Sagar, Damoh, and Panna tend to receive more rainfall and show greater variability compared to more drought-prone northern districts like Datia and Tikamgarh (Singh, et al., 2023) [7] . Trend analyses employing nonparametric methods such as the Mann-Kendall test and Sen's slope estimations consistently reveal either declining or stagnant rainfall trends over multidecadal periods, though these changes are typically not statistically significant at conventional confidence levels for most districts (Kumar et al., 2023; Fanai et al., 2022) [5,2] . Some locations, notably Sagar, show weak positive tendencies, but overall, there is little robust evidence for systematic increases or decreases in annual rainfall. Moreover, tests for autocorrelation suggest rainfall events in the region are largely random and independent from year to year, illuminating the stochastic nature of precipitation in Bundelkhand (Fanai et al., 2022; Yadav et al., 2025) [2,9] . The region's agriculture is therefore intricately tied to this climatic unpredictability and faces increasing challenges in adapting to both current variability and projected climate changes (Jatav, 2024; Vishwakarma et al., 2024) [4,8] . Given the critical challenges posed by rainfall variability and its profound impact on agriculture and water resources in Bundelkhand, this study undertakes a rigorous analysis of annual precipitation patterns across the major districts of Madhya Pradesh from 2008 to 2022. Employing robust statistical methods such as the Mann-Kendall trend test and autocorrelation function (ACF) analysis, the study aims to detect any significant trends or persistent patterns in rainfall. The primary objective is to determine whether the rainfall regime in Bundelkhand exhibits definitive long-term changes or is predominantly governed by natural inter-annual variability. The insights gained will provide valuable evidence to inform sustainable agricultural planning, effective water resource management, and targeted climate adaptation strategies, thereby supporting policymakers and stakeholders in enhancing the region's resilience against climatic uncertainties.

Methodology

This study employed non-parametric statistical techniques to analyze the temporal trends in rainfall data, focusing on detecting the presence, direction, and magnitude of trends over the study period. Trend analysis will be done by using non-parametric Man-Kendall test. This is a statistical method which is being used for studying the spatial variation and temporal trends of rainfall.

Mann-Kendall Test:

The Mann-Kendall statistic S is given as

𝑖=1

Each of the data point x i is taken as a reference point which is compared with the rest of the data point's x j so that,

It has been documented that when n ≥ 8, the statistic S is approximately normally distributed with the mean.

E(S) = 0

The variance statistic is given as

Where t i is considered as the number of ties up to sample i. The test statistics Z c is computed as

, 𝑆 < 0 Z c here follows a standard normal distribution. A positive (negative) value of Z signifies an upward (downward) trend.

A significance level α is also utilised for testing either an upward or downward monotone trend (a two-tailed test). If Z c appears greater than Z α/2 where α depicts the significance level, then the trend is considered as significant.

Sen's Slope Estimator Test

The magnitude of trend is predicted by the Sen's estimator.

Here, the slope (T i ) of all data pairs is computed as (Sen, 1968)

𝑇 𝑖 = 𝑥 𝑗 -𝑥 𝑘 𝑗 -𝑘 For i = 1,2,……,N Where x j and x k are considered as data values at time j and k (j>k) correspondingly. The median of these N values of T i is represented as Sen's estimator of slope which is given as:

If n appears odd, and it is considered as Q med =[T N/2 +T (N+2)/2 ]/2 if N appears even. Positive value of Q i indicates an upward or increasing trend and a negative value of Q i gives a downward or decreasing trend in the time series.

Results and discussion

The Bundelkhand region is a historically and geographically important area in central India, spanning primarily across northern Madhya Pradesh and lower Uttar Pradesh. The larger part of Bundelkhand lies within Madhya Pradesh, specifically covering key districts such as Chhatarpur, Tikamgarh, Damoh, Sagar, Datia, and Panna (Jain, 2002) [] . This region forms a distinct plateau, recognized for its semi-arid climate, characterized by low to moderate rainfall, hot summers, and dry conditions outside the monsoon period (Scott and Divakar, 2024). Geographically, Bundelkhand sits between the fertile Gangetic plains to the north and the rugged Vindhyan highlands to the south, making it a transitional zone between two significant landscapes. It is roughly positioned between 23°20′N to 26°20′N latitude and 78°20′E to 81°40′E longitude, reinforcing its identity as a bridge between plains and uplands. Agriculture dominates the regional economy, but farming is mostly rain-fed, making communities highly vulnerable to erratic monsoon rains and recurring droughts. As a result, crop failures are a persistent challenge affecting rural livelihoods. Despite climatic and economic challenges, Bundelkhand boasts several major rivers: Sindh, Betwa, Ken, Bagahin, Tons, Pahuj, Dhasan, and Chambal. These rivers are crucial lifelines, supporting drinking water supplies, irrigation, and domestic needs not only for Bundelkhand but also for neighboring areas in Uttar Pradesh.

Overall, Bundelkhand's landscape, water resources, and economic dependence on rain-fed agriculture play a pivotal role in shaping the lives and environment of its population.

The base map of the study area is shown in Figure 1. suggests a gradual increase in rainfall over time. However, statistical results from the Mann-Kendall test (with a high pvalue of 0.766) confirm that this apparent increase is not statistically significant, meaning the trend could be due to natural variability rather than a consistent long-term change. shows that, aside from lag 0, most autocorrelation values fall within the 95% confidence limits, indicating they are not statistically significant. This suggests that the rainfall data lacks strong autocorrelation, meaning there is little to no predictable pattern or dependency between rainfall values over time. Such a pattern is typical of natural processes like rainfall, which often behave randomly. Therefore, the rainfall in Datia appears to follow a weakly correlated or near-random pattern, with limited influence from previous time periods. ) and Kendall's tau (0.2297), with an estimated increase of about 9.37 mm per year according to Sen's slope. However, the p-value of 0.2545 suggests that this increasing trend is not statistically significant, meaning there is insufficient evidence to confidently conclude that rainfall has been changing over the 15-year period. Overall, while rainfall appears to be gradually increasing, the observed variations could be due to natural fluctuations rather than a clear long-term trend. Figure 15, The ACF (Autocorrelation Function) plot for Sagar's rainfall data from 2008 to 2022 shows that the autocorrelation at lag 0 is 1, which is expected as it's perfectly correlated with itself. At other lags up to 10, the autocorrelation values fluctuate around zero and mostly lie within the significance bounds (dashed lines at approximately ±0.5), indicating that there is no strong or statistically significant autocorrelation in the rainfall data at these lags. This suggests that the annual rainfall in Sagar during this period is largely randomly distributed over time, with no clear pattern of dependence or persistence from one year to the next. Although the results suggest a weak increasing trend, the pvalue exceeds the 0.05 threshold, indicating that the trend is not statistically significant. The Z-value also lies within the non-significant range (-1.96 to +1.96), reinforcing this conclusion. There is no clear consistent upward or downward trend, as some years exhibit high rainfall followed by sharp drops in the next years. This pattern suggests considerable variability in annual rainfall in Tikamgarh during this time frame. Figure 18, the Autocorrelation Function (ACF) plot for Tikamgarh rainfall data from 2008 to 2022 at lag 10 shows that the strongest correlation occurs at lag 0, as expected, with an autocorrelation of 1 (since any time series is perfectly correlated with itself at lag 0). Beyond lag 0, the autocorrelation values at other lags fluctuate around zero and mostly fall within the confidence bounds (the dashed blue lines). This indicates that there is no significant autocorrelation in the rainfall data beyond the immediate year, suggesting that the annual rainfall values are largely independent over time and there is no strong seasonal or lagged relationship in the data up to lag 10.

Conclusion

The comprehensive analysis of annual rainfall across the Bundelkhand region's districts-Chhatarpur, Damoh, Datia, Panna, Sagar, and Tikamgarh reveals substantial year-to-year fluctuations but no clear, statistically significant long-term trend between 2008 and 2022. The Mann-Kendall test and Sen's slope estimations consistently indicate only weak positive or negative trends in some districts, none of which are significant at the 95% confidence level. Autocorrelation function analyses further confirm the absence of persistent temporal patterns, demonstrating that rainfall in these districts behaves largely as a sequence of independent yearly events driven by natural variability. This variability dominates over any detectable signals of increasing or decreasing precipitation, suggesting that the region's climate has remained relatively stable in terms of annual rainfall over the study period. Consequently, water resource management and agricultural planning in Bundelkhand must continue to address the inherent unpredictability of rainfall rather than rely on expectations of consistent changes in precipitation.

The findings emphasize the critical need for adaptive strategies to cope with climate variability and mitigate impacts on rural livelihoods dependent on rain-fed agriculture.

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