The Indira Sagar Region (ISR) is situated within three districts of Madhya Pradesh: Barwani, East Nimar (Khandwa), and West Nimar (Khargone) (Figure 1). In the Indira Sagar Region, construction of the canal (Indira Sagar Pariyojana) began in April 2002. The low seasonal rainfall due to the geographic location and climate characteristics of the ISR and the lack of an adequate quantity of rainwater for irrigation purposes have led to the construction of a canal in this region. Hence, a lined canal was created to remove water from the reservoirthrough the Punasa tunnel. The study area is located between 74˚46' to 76˚29' East longitude and 21˚46' to 22˚19' North latitude and covers an area of approximately 3550 km². The elevation of the study area varies from 84 to 320 m above mean sea level. However, due to the construction of the Indira Sagar dam about

91,348 ha (land including 41,111 ha of forest) was submerged under water which contains 248 villages and one town (Harsud) and about 80,572 people in total 30,739 families (Desai et al., 2007) .

As per the World Meteorological Organization (WMO, 1986) , a minimum record length of 30 years is deemed sufficient for the statistical validity of trends in climate change research, a sentiment echoed by Kahya & Kalayci (2004) , Rudra et al. (2023) and Shukla et al. (2023) . In this study, monthly rainfall data of 3 stations covering a period of 110 years (1901-2010) were downloaded from the Indian Meteorological Department (IMD), site of India water portal website, (https://www.indiawaterportal.org/articles/district-wise-monthly-rainfall-data-list-raingauge-stations-india-meteorological) and (https://www.indiawaterportal.org/met_data) and location of meteorological stations is presented in spatial Figure 1 & Figure 8. The spatial representation in Figure 8 indicates the locations of meteorological stations through the use of red arrows and also depicts both upward and downward trends in annual and seasonal rainfall. Data quality control is a necessary step; however, non-parametric tests are robust against outliers. On the other hand, outliers play a key role in parametric tests and in assessing the magnitude of the possible changes by computing means (moments) and linear regression. However, rainfall in all series for the period of 110 years was complete, and no gap-filling method was used in this study. By contrast, parametric tests are susceptible to outliers, impacting the assessment of potential changes through mean and linear regression computations (Duhan & Pandey, 2013; Mishra et al., 2013) . The seasonal rainfall was computed by averaging monthly values for the following seasons: winter (December, January, and February), pre-monsoon (March, April, and May), monsoon (June, July, August, and September), and post-monsoon (October and November). For this study, rainfall data covering 110 years were analyzed for three stations in Madhya Pradesh. The analysis encompassed monthly, seasonal, and annual perspectives for rainfall. Figure 2 illustrates the data collection and trend analysis framework.

In this study, the investigation into spatial and temporal annual and seasonal trends in rainfall series involved the application of both parametric (Student-t) and non-parametric (Mann-Kendall and Sen’s slope estimator) methods. To mitigate the impact of serial correlation (autocorrelation), pre-whitening was initially applied, following the approach suggested by Von Storch & Navarra (1995) . Despite initial assertions by Lettenmaier et al. (1994) that serial correlation effects on trend tests could be considered negligible, concerns about potential impacts on trend analysis have gained momentum in the recent years. Yue & Hashino (2003) noted that persistent positive serial correlation in time series could elevate the risk of rejecting the null hypothesis, even if it is true that the time series has no trend.

Following the pre-whitening of data series, standard precipitation characteristics were calculated, including mean (µ), standard deviation (σ), and the coefficient of variation (C_v) for monthly scales across all three stations. Subsequently, the student-t parametric method was applied to detect trends in the pre-whitened rainfall data series. This parametric test involves considering the linear regression of the random variable Y on time X. The Pearson correlation coefficient (r) was computed using the equation provided by Haan (1977) (with detailed explanations available in the supplementary material).

Non-parametric rank-based tests, specifically the MK test, were then employed to identify trends in the time series data, offering robustness to extremes and suitability for skewed variables (Hamed, 2008) . Non-parametric trends are preferable in cases where the data is non-normally distributed and contains outliers (Helsel & Hirsch, 1992, 2002; Birsan et al., 2005) . Then, the Sen’s Slope Estimator was applied in the time series to calculate the true slope in the presence of a linear trend, utilizing a simple non-parametric procedure developed by Sen (1968) detailed explanation with equations are given in supplementary material.

Finally, the Cumulative Sum (CUSUM) test was implemented to determine the most probable year when a significant shift occurred in rainfall trends. This test involves comparing successive observations with the series median to detect changes in the mean of a time series after a specific number of observations (McGilchrist & Woodyer, 1975; Chiew & McMahon, 1993; Kundzewicz & Robson, 2004) .

Initially, the serial correlation (autocorrelation) test was applied to the all-time series to check the randomness available in the data. Then the pre-whitening method was employed to remove the effects of serial correlation from rainfall time series data before applying certain statistical tests. The outcome reveals that after removing randomness from the series by the pre-whitening method, serial correlation coefficients were found statistically insignificant (Table 1). In this study, removing randomness from a rainfall series typically refers to the process of identifying and eliminating or reducing the effects of random variability or noise in the data. Rainfall data often exhibit random fluctuations due to various factors such as atmospheric conditions, weather patterns, and measurement errors. By removing randomness, analysts aim to uncover underlying patterns, trends, or signals in the data that may be obscured by random noise (Von Storch & Navarra, 1995) . Further, an MK test with Sen’s slope estimator was applied for trend analysis. The results of the serial correlation coefficient after pre-whitening analysis for 1901 to 2010 are presented in Table 1.

Rainfall characteristics of the Indira Sagar Region for the period of 1901-2010 are presented in Table 2. The mean (µ) annual rainfall of the region is 781.4 mm with a standard deviation (σ) of 170 mm and the coefficient of Skewness of annual rainfall is −0.003. In addition, the coefficient (C_v) of variation for the mean annual rainfall is 21.8%. Monsoon contributes 88.3% of the annual rainfall in the region, whereas rainfall in the winter is the least (0.45%). During the monsoon season, the coefficient of variation is low (23.4%) as compared to other seasons, which shows a dependable monsoon rainfall. Monthly rainfall in June, July, and August can be considered as dependable. Also, the spatial and temporal distribution of daily precipitation during monsoon season and in these months is irregular at different parts of the region though showing a dependable nature when summed for the whole period. Here, dependable monsoon rainfall implies a level of reliability and predictability in the occurrence of monsoon rainfall, suggesting

Note: µ = Mean of the rainfall data series, σ = Standard Deviation, C_v = Coefficient of Variation, and CS = Coefficient of Skewness.

that it occurs consistently over time and can be counted upon for sustaining ecosystems and human activities. However, Spatial variations and fluctuations in monsoon patterns can impact the dependability of monsoon rainfall, leading to challenges such as droughts, floods, and agricultural losses. Therefore, understanding the factors influencing monsoon variability and improving forecasting capabilities are essential for ensuring the dependability of monsoon rainfall and mitigating its associated risks. Furthermore, an outcome of the parametric (student-t) test is presented for three stations namely, Barwani, East Nimar, and West Nimar (Table 3).

Annual

Results of the MK test and CUSUM test are presented for three stations namely, Barwani, East Nimar, and West Nimar (Table 4 and Table 5). The entire study region received high rainfall in the years 1973 for Barwani and West Nimar, with amounts exceeding 1376 mm, and 1123 mm, and year 1944, the regions of East Nimar experienced 1237 mm of rain, respectively, over the course of a century. However, the 5-year moving average for the region, considering all three stations, showed a significant decline in the trend of annual rainfall from 1900 to 1930 and 2000 to 2010 on a decadal basis (Figures 3(a)-(c)). A 5-year moving average to identifying and analyzing trends over 110 years, particularly if

there is a gradual or long-term decline or increase in the data. By averaging data over 5 years, the moving average can highlight underlying trends while reducing the influence of short-term fluctuations. However, Figure 3 also shows the inter-decadal variability and oscillations of the average annual rainfall time series for the period of 1901-2010. This observation can provide valuable insights into the complex dynamics of regional climate variability and inform adaptive responses to the changing environment of ISR. Additionally, the results of the MK test on the annual rainfall series for all three stations are shown in Figure 8(a). The test revealed that the trends in the annual rainfall time series for Barwani and West Nimar were consistently positive, while for East Nimar, the trend was negative.

While the annual trend in the region does not reach statistical significance at a 90% confidence level (α = 0.10). Furthermore, the Sen’s estimator of slope was employed to determine the rate of change of the observed trends in all the rainfall time series. The mean annual rainfall over the Indira Sagar Region showed a long-term insignificant trend. It is important to note that a statistically significant trend may not be practically significant and vice versa may also be true (Daniel, 1978) .

Seasonal rainfall trend

Pre-monsoon

In the Indira Sagar region, there is a noticeable upward trend in annual rainfall in Barwani from 1985 to 2005 in the pre-monsoon season (see Figure 4(a)). Similarly, stations in East and West Nimar exhibit increasing rainfall trends from 2000 to 2010 (refer to Figure 4(b) and Figure 4(c)). This rising trend is reflected in the overall analysis through regression analysis, attributed to the increase in moving averages. Nonetheless, when subjected to the MK test, the results for the pre-monsoon precipitation series at all three stations are depicted in Figure 8(b). These results indicate a positive monotonic trend in pre-monsoon rainfall time series at the East and West Nimar stations between 1901 and 2010. However, the statistical significance of the pre-monsoon trend in the region does not reach the 90% confidence level (α = 0.10). Sen’s estimates alongside corresponding residuals are presented in Figure 4.

Monsoon

Figure 5 illustrates the monsoon trend across the Indira Sagar Region from 1901 to 2010, focusing on the stations Barwani, East Nimar, and West Nimar. Analysis of rainfall data for the monsoon season revealed a decreasing trend observed from 2000 to 2008 at all three stations, as depicted in Figures 5(a)-(c). Regression analysis was conducted to assess this trend. Additionally, the Mann-Kendall (MK) test was performed on the monsoon time series, which contributes a significant percentage (88.33%) to the total annual precipitation. The results indicated that the monsoon trend in the region over the last century was statistically insignificant at the 90% confidence level. However, for the Barwani and West Nimar stations, the MK test statistics showed positive values, while for East Nimar, a negative value was obtained (Figure 8(c)). This suggests a monotonic upward trend for Barwani and West Nimar, whereas East Nimar exhibited

a slight downward trend over the century. Sen’s slope and estimates, along with corresponding residuals, are presented in Figure 5 for all the selected stations. These findings provide valuable insights into the long-term rainfall trends in the region, offering important implications for water canal management and conservation planning initiatives.

Post-monsoon

For the past decades in this area, the three stations have exhibited a positive trend in rainfall from 1995 to 2004, during reservoir construction, but after construction shows a decreasing trend to the post-monsoon season (as depicted in Figures 6(a)-(c)). The results of the MK test for the regional basis for all the stations show insignificant (no trend) at a 90% confidence level (Figure 8(d)). Although Sen’s estimates and corresponding residuals are illustrated in Figure 6, it is noteworthy that Barwani and West Nimar display a positive trend (i.e., an upward trend), while East Nimar shows a decreasing trend over the course of the study.

Winter

The linear trend during the winter season exhibited a consistent downward

Existence of Shift Change in the Indira Sagar Region

The distribution-free CUSUM test was applied to test the hypothesis to check the existence of a step (shift) change in rainfall time series during the period of study. The results for annual and seasonal precipitation time series for all three stations of the region are shown in Table 5.

The serial correlation coefficient (r_k) of a discrete time series for lag-k is estimated as follows:

r k = ∑ k = 1 n − k ( X t − X ¯ t ) ( X t − k − X t + k ) [ ∑ k = 1 n − k ( X t − X ¯ t ) 2 ( X t + k − X ¯ t + k ) 2 ] 0.5 (1)

( r k ) t g = − 1 ± t g ( n − k − 1 ) 1 / 2 n − k (2)

where, ( r k ) t g is the normally distributed value of r_k, t_g is the normally distributed statistic at g level of significance. The value of t_g are 1.645, 1.965 and 2.326 at a significance level of 0.10, 0.05 and 0.01 respectively. If | r k | ≥ ( r k ) t g , the null hypothesis about serial independence is rejected at the significance level α (here 0.05). For the non-normal series, MK test is an appropriate choice for the trend analysis (Yue & Pilon, 2004; Basistha et al., 2008). Therefore, the MK test has been used wherever the serial correlation is not significant at 5% significance level.

The method of pre-whitening was applied to remove the effect of serial correlation and autocorrelation on the non-parametric test. Lettenmaier et al. (1994) suggested that the effects of serial correlation upon trend tests in such applications could be assumed negligible; concern about the potential impacts of autoregressive processes upon trend analysis nevertheless appears to be gaining momentum. For e.g., assessments of the potential effects of urbanization and climate change upon river behavior undertaken by Leith & Whitfield (2000) and Zhang et al. (2001) , respectively, applied the prewhitening or deserialization scheme of Von Storch & Navarra (1995) to deal with serial correlation:

x p w i = x i − c x i − 1 (3)

where ^PWX is the pre-whitened data to be used in the subsequent trend analysis and c is the lag-1 serial correlation coefficient as determined directly from the data using Equation (3). Pre-whitening is utilized only if observed r is greater than some critical value, C_criti taken to be 0.1 by Von Storch & Navarra (1995) .

There are many parametric methods, which have been applied for detection of trends. The parametric test considers the linear regression of the random variable Y on time X.

The regression coefficient b1 (or the Pearson correlation coefficient r) was computed from the data. It is known (Haan, 1977) that the statistic.

t = r n − 2 n − r 2 = b 1 s / s s x (4)

Follows Student’s t distribution with degrees of freedom n − 2, where n is the sample size, s is the standard deviation of residuals, and SS_x is the sums of squares of the independent variable (time in trend analysis). The hypothesis H₀: ρ = 0 (or β₁ = 0) is tested against the hypothesis H_1: ρ≠ 0 (or β₁ ≠ 0) at a chosen level of significance α, where ρ and β₁ are the population values, respectively, of the correlation coefficient and regression coefficient. The hypothesis that there is no trend is rejected when the t value computed by Equation (4) is greater in absolute value than the critical value t_α/2 (Onoz & Bayazit, 2003) .

Non-parametric trends can be adopted in the case with the required data to be non-normally distributed and containing outliers in the data (Helsel & Hirsch, 1992; Birsan et al., 2005) .

This non-parametric rank-based method was used to identify in which year an abrupt change has occurred in the precipitation time series. In particular, successive observations were compared with the median of the series to detect a change in the mean of a time series after a number of observations (McGilchrist & Woodyer, 1975; Chiew & McMahon, 1993; Kundzewicz & Robson, 2004) . The Cusum is computed as follows (Kiely, 1999) :

S i = ∑ i = 1 i x i − x ¯ (10)

where x ¯ is the average value of the time series. A possible change has occurred when S_i is a maximum. In this study, the magnitude of S_i was calculated for the time series with significant changes.

In 17^th century, De Moivre introduced the concept of moving averages in his work on probability theory. Later, Jeffreys (1939) discussed the use of moving averages in statistics and their relevance in analyzing time series data. The moving average computation, a series of averages of different subsets were generated from the full data set. Given a series of numbers and a fixed subset size, the moving average was obtained by first taking the average of the first subset. The fixed subset size was then shifted forward, creating a new subset of numbers, which is averaged. This process was repeated for the entire data series. The plotline connecting all the (fixed) averages is the moving average. Thus, a moving average is not a single number, but it is a set of numbers, each of which is the average of the corresponding subset of a larger set of data points.

2 MK Test Monthly trend analysis results:

The trend in monthly rainfall series (1901-2010) for all three stations of a region was evaluated using the non-parametric test (Table S1). The trend was decreasing in most of the months for all three stations. Only the month of August showed the statistically significant increasing trend at the 95% and 99% confidence level for all 3 stations. An upward trend can be seen in the month of May and October whereas there is a significant downwards trend in April, July, and December. Consequently, it would be expected that increasing rainfall in the month of May and decreasing in July. The same phenomena would happen in the months of October and December. The distribution-free CUSUM test was applied to test the hypothesis to check the existence of a step (shift) change in precipitation time series during the period of study. The results for annual and seasonal precipitation time series for all three stations of the region are shown in Table S1.

where, r k is the lag-k serial correlation coefficient of the series. The hypothesis of serial independence is then tested by the lag-1 autocorrelation coefficient as H₀: r 1 = 0 against H₁: | r 1 | > 0 using the test of significance of serial correlation (Yevjevich, 1971) following Rai et al. (2010) ,

trajectory across all three stations, as depicted in Figures 7(a)-(c). Sen’s estimates, along with the corresponding residuals, are visible in the same figure. Furthermore, Figure 8(e) displays the results of the MK test. For the winter season, the monotonic trend reveals statistically significant findings at the 90% confidence level (α = 0.10), with the Z statistics indicating negative values for all stations within the region. These results underscore a notable decline in winter rainfall trends, suggesting potential implications for regional water resource management and ecosystem dynamics.