Change analysis of All India and regional rainfall data series at annual and monsoon scales

Recent times have seen significant warming of the atmosphere. The Intergovernmental Panel on Climate Change (IPCC) has recently released the Report of Working Group I covering the physical science basis for the sixth Assessment Report (AR6). This report categorically states that the atmosphere, ocean, and land have warmed up. As per the IPCC report, the human-caused increase in global surface temperature from 1850–1900 to 2010–2019 is about 1.07 °C (IPCC 2021).

Among the different climatic variables, for hydrologists and water professionals, precipitation/rainfall is perhaps the most important variable. Rainfall initiates and directly influences almost all the water-related processes in a watershed. Due to this reason, analysis of properties and trends in rainfall data is of immense interest to hydrologists, meteorologists, and all those who would like to know how climate change impacts water availability and management.

Many studies have tried to determine trends in rainfall (RF) data for India at the country and smaller spatial scales by using the data for individual/groups of stations on annual and seasonal levels. Depending on the data used, spatial coverage, and methodology, the conclusions have been quite different. The studies that had used the data up to the year 2000 are not much relevant now and hence, are not reported here. Jain & Kumar (2012) provided a detailed review of studies till about 2010, related to trend analysis of rainfall and temperature data with reference to India.

Table 1 summarizes the major conclusions of past trend analysis studies. Broadly, studies had used the data for about 50–100 years, for the whole of India or a part thereof (river basins or states). In most cases, a simple trend analysis was carried out. As can be seen, the results are somewhat different and not always consistent. Inconsistency in the outcomes of the various studies could arise due to several reasons. Different studies may have used different data or the data that may have been compiled differently. The study area and its geographical coverage might have been different. Furthermore, due to changes in climate, land use/cover, and other causes, the statistical properties of meteorological data series may undergo changes. Such changes can be detected by statistical tests. In case the series has some statistically significant change points, trend analysis by using the whole series is not very useful as the statistical properties of the series before and after the change point will be different. Results of the statistical analysis presented in subsequent sections show the presence of change points which are significant at a 5% significance level. Some studies listed in Table 1 may not have tested the data series for the presence of change points and the results of such studies may not be consistent with others.

The outcomes of some studies have been mentioned only in terms of rising and falling trends and their magnitude; some authors had also commented on the statistical significance of the trend. In most cases, Mann–Kendall (MK) test and Sen's slope method have been employed. A few studies have also tried to detect change points. In general, no consistent and statistically significant trends were detected for the whole nation or larger regions. This is not surprising because when the average rainfall values are computed for a larger region, the fluctuations tend to even out and trends are seen only when the underlying processes have changed substantially. Regarding the rainfalls in individual river basins or months, no consistent change in pattern (spatial or temporal) is emerging but broadly the studies report that rainfall in the months of July and August appears to be declining and that in September is rising.

Regarding extreme rainfalls, the outcomes of the various studies are more or less in agreement. The frequency of extreme rainfalls and their contribution to rainfalls have shown an increasing trend which is significant in many cases. Furthermore, the trend in low rainfall events has also been reported. Duan et al. (2016) studied spatiotemporal evaluation of the changes in floods and associated socioeconomic damage in China over the last century. In China, the Yangtze River basin accounted for about 27% of all floods, followed by the Huaihe River basin (13% of the floods) in the 20th century. Floods with small return periods (5–10 years) have caused most flood damages in recent times. Agriculture areas affected by floods exhibited a significant uptrend from 1950 to 2013 and due to the combined effects of climate change and rapid urbanization, the risks of flooding had increased.

The Gini coefficient is a measure of statistical dispersion. It is used in economics to represent the wealth inequality within a group. A Gini coefficient of 0 reflects perfect equality, where everyone has the same income. In contrast, a Gini coefficient of 1 shows maximal inequality, or within a group, a single individual has all the income. Duan et al. (2022) presented an analysis of the impacts of anthropogenic forcing on the temporal increase in the unevenness of precipitation amount, intensity, and extremes at national and regional scales in China. The anthropogenic influence was found to increase the temporal variation of precipitation extremes, especially in southern China. Projections of most future precipitation indices show an increasing trend in precipitation variability with time in most regions of China under most future scenarios. Except for Southern China and Yunnan Province, the R95p index (the index showing the total rainfall per year from days with rainfall above the 95th percentile daily rainfall total) has a significant decrease in the future, and the largest decrease is up to about 30% in North-West China under the SSP370 scenario (Duan et al. 2022).

The IPCC (Arias et al. 2021) has concluded that in many cases, the future changes in frequency and intensity of extreme events can be linked with the magnitude of future projected warming. They noted that since the 1950s, changes in climate extremes have been widespread; global-scale extreme precipitation is likely to have intensified. The IPCC suggests that it is extremely likely that human influence is the main contributor to the observed increase (decrease) in the likelihood and severity of hot (cold) extremes. Furthermore, the IPCC notes ‘the frequency of extreme precipitation events in the current climate will change with warming, with warm extremes becoming more frequent (virtually certain), cold extremes becoming less frequent (extremely likely) and precipitation extremes becoming more frequent in most locations’. The trends are likely to intensify in the future.

The association between El Niño Southern Oscillation (ENSO) and rainfall over India in the monsoon season has also drawn the attention of Indian researchers. Kothawale et al. (2010) found a strong correlation between ENSO events and deficiency in monsoon rainfall. Around 60% of major droughts in India have taken place in the years when ENSO took place. In contrast, La Niña events have been found to be associated with higher monsoon rainfall and cooling.

IPCC (2007), in the fourth assessment report, remarked about a ‘notable lack of geographical balance in the data and literature on observed changes, with marked scarcity in developing countries’. Data availability in developing countries has improved over time and the number of studies has also risen. However, much more progress is needed on both fronts to overcome the lack of data and the absence of more critical analysis.

With the above background, the aim of the present study was to analyze changes in observed long-term rainfall data series for the whole of India, for five homogenous regions, and for selected sub-divisions by using conventional and emerging statistical tools. We have subdivided change detection into several components: (a) identification of change points in the data series, (b) trend analysis to detect the presence of a trend, its magnitude, and statistical significance, (c) study of variabilities and trends in various components of the data series by using the wavelet analysis, and (d) attribution to find the reason behind the changes.

The present study has used long-term precipitation data for India. India is a large country with a high population. The country has huge variations in land use and cover, soil, vegetation, water resources, climate and so on. A range of actions are being taken by Indian water managers to manage water and land resources to meet ever-increasing water and food demands and mitigate disasters. These actions are causing widespread changes in land use and hydrology of the country. These changes along with the changes in climate are inducing changes in climatic variables. Climatic processes have teleconnections and the changes taking place over a large region do affect the climate at near and far places. Due to this reason, the global scientific community would be interested in knowing what is happening to the climate in India and what are its implications on the global climate. The present work aims to fulfill this need.

The data used in this study were taken from a report published by Kothawale & Rajeevan (2017). This report documented area-weighted rainfall time series for the whole of India and for its five homogeneous regions in units of 10th of mm. The data were picked from India Meteorological Department (IMD) database and other sources. After screening the available data, 306 rain gauge stations, one from each district in the plain regions of India and distributed fairly uniformly over the country, were selected and the data of these rain gauges were used by Kothawale & Rajeevan (2017). It was ensured that the non-homogeneous records were excluded and data of only those stations that are reliable were used. These data were then used to construct area-averaged rainfall series. Kothawale & Rajeevan (2017) noted that four sub-divisions fall in the hilly Himalayan regions and the rain gauge network in these sub-divisions was inadequate. Hence, data for these sub-divisions were not considered further. Thus, the contiguous area is considered to cover about 90% of India's total area. The data series had some gaps and attempts were made to fill these by using the information from other data-collecting agencies. The remaining data gaps were filled by multiplying the sub-division rainfall by the ratio of station mean rainfall and sub-division mean rainfall for the month. The spatial pattern of the mean summer monsoon rainfall map based on data for 306 stations was in good agreement with the map of normal rainfall prepared by IMD on the basis of about 3,000 rain gauge stations.

Kothawale & Rajeevan (2017) have described a quality control procedure wherein suspicious values were checked and corrected, if necessary. Weighted average monthly rainfalls for a sub-division were computed by using the areas of each district as weights. Likewise, to compute weighted average monthly rainfalls for a homogeneous region, the areas of each sub-division were used as weights. Finally, to compute the weighted average monthly rainfalls for the whole of India, the areas of each sub-division (total 30) were used as weights.

Here, the results of the analysis carried out for the average rainfall for the whole of India and for five homogeneous regions are presented. Analysis was carried out for the annual series and the summer monsoon season, the season that receives the highest rainfall. Data from homogeneous regions and sub-divisions that showed significant trends were also analyzed closely.

Table 2 gives key statistical parameters for rainfall series for All India and five homogenous regions. It is noted that the NE region receives the highest rainfall followed by Central NE India. The depth of average rainfall for the NE region is nearly double compared to the average rainfall for the whole of India whereas the depth of rainfall for North-West India is nearly 50% of the same for the whole of India. North-West India also has the highest variability (in terms of the coefficient of variation) among all the regions, nearly 2.7 times that for All India. It is noted from Table 2 that none of the annual data series had any significant lag-1 correlation.

Trend lines were fitted to the plotted data of annual and monsoon season (also called JJAS, using the initial letters of the months of monsoon season: June–July–August–September) series to identify the linear trends. Among the annual data series, the series for All India, West Central region, Central NE region, and NE region, showed declining trends whereas the series for the North-West region and Peninsular region showed rising trends. The NE India region has shown the highest declining trend, followed by Central NE India. Regression analysis showed that the trends in the annual and monsoon series for these two regions are statistically significant at 5% significance level. The time series for Peninsular India shows a small rising trend. However, besides the NE and Central NE regions, no statistically significant trend at 5% significance level was detected in the annual series for All India or any other region.

Change analysis of time series of hydro-meteorological data aims at finding many features: the magnitude of trend in a data series and its statistical significance, change points in the mean, variance, and distribution of the data. Trend analysis helps understand the historical variations and predicts the future values of the variables. It also helps in preparing plans to check the impacts of adverse changes or to exploit the opportunities arising due to the changes that are likely to be beneficial, e.g., increased rainfall in drought-prone areas. This topic has attracted the attention of a large number of researchers and numerous publications have described the results of various studies. Kundzewicz & Robson (2004) and Sonali & Nagesh Kumar (2013) have discussed in detail the trend detection methods for hydro-meteorologic data.

Changes in a precipitation data series can manifest in different ways – overall rising and falling trends in the data series, changes in mean and other statistical properties, change points in the series, and changes in the components of the data series. Since most trend detection methods try to find the changes in only one property of the data series, it is necessary to apply different methods to detect changes in the properties.

Statistical methods have been used with different variants, for the sake of clarity and completeness the various methods used in this study are briefly discussed next.

The Pettitt (1979) method is a rank-based nonparametric test, which is used to detect abrupt changes in a time series of data. The Pettitt test uses the Mann–Whitney statistic to check if the two samples (before and after the change point) have indeed come from the same distribution. It tries to identify the change point that maximizes the test statistic. In the Pettitt test, serial correlation in the series is ignored. The magnitude of the change is the median difference between all the pairs of observations where the first sample pertains to pre-change data and the second is after the occurrence of change point. The computational procedure has been described by, among others, Pettitt (1979) and Jaiswal et al. (2015). Many studies have applied the Pettitt change for change point detection. Zarenistanak et al. (2014) used the Pettitt test for change point detection in annual and seasonal precipitation and temperature series over southwest Iran. Jaiswal et al. (2015) used the Pettitt test for monthly, seasonal, and annual historical series of different climatic variables of a city. Mallakpour & Villarini (2016) examined the sensitivity of the Pettitt test to detect abrupt changes in mean.

The variance-based nonstationarity methods attempt to detect the place(s) where a significant change in the standard deviation or variance of the data has taken place. The Mood and Lombard Mood tests fall in this category. Distribution-based nonstationarity methods attempt to detect the location(s) where a significant change in the underlying distribution of the data has taken place. Two types of changes can take place: the distribution remains the same but the parameters change, or the probability distribution itself changes. The Kolmogorov–Smirnov and Cramer-Von-Mises test come in this category. Zhou et al. (2022) have applied many of these tests to perform detailed change detection of the rainfall data of Norway.

We suggest that change point detection should be carried out at the beginning of any trend/change detection study and if a significant change point is found, the data series (of sufficient length) after the change point should be used to detect trends. The trends in the data series before the change would not have much relevance for future projections.

To calculate the magnitude of the trend in a time series, two groups of methods are used: parametric and nonparametric. The parametric methods assume that the data follows a normal distribution. Nonparametric tests are employed in trend analysis when parametric tests are not suitable. Most nonparametric tests rank the data and check the distribution for unusual behavior. A parametric test has greater statistical power which means that the test is more likely to detect significant differences if they truly exist. Some situations when a nonparametric test is employed include when the distribution is not normal or is not known or the sample size is small.

If the time series has an increasing trend, β will have a positive value and a falling trend in the time series will yield a negative value of β.

In addition to magnitude, it is also necessary to determine if the detected trend is significant or not. To find out the statistical significance of the trend, the MK test (a nonparametric test) is commonly employed (Douglas et al. 2000; Burn et al. 2004).

The MK test checks the validity of the null hypothesis of no trend against the alternative hypothesis that the time series has a rising or falling trend. The MK test is helpful in detecting deterministic trends and this test makes only a few assumptions: the likely trend in the data may be linear or nonlinear. The MK test does not assume the underlying statistical distribution. However, the MK test is not robust when the series has high autocorrelation. Yue et al. (2002) reported that the existence of serial correlation alters the variance of the estimate of the Mann–Kendall (MK) statistic, and the presence of a trend alters the estimate of the magnitude of serial correlation. If the data has positive autocorrelation, the probability of detecting trends by the MK method when actually none exist increases. Hamed & Rao (1998) presented a variance correction approach for autocorrelated data. A modified equation was proposed to compute the variance of S and it was shown that the accuracy of the modified test was superior to that of the original MK test without any loss of power. Wang et al. (2020) noted that the power of the MK test is a monotonically increasing function of the sample length. In autocorrelated series, pre-whitening is often suggested to remove autocorrelation. However, Razavi & Vogel (2018) noted that if the attention is focused on the pre-whitened hydroclimatic series, it can be misleading because it leads to a loss of important information contained in the time series.

Sen (2012) presented a trend detection method based on the concept that if two time series that have identical statistical properties are plotted against each other, the data will fall on a straight line with 45° slope or 1:1 line and this will be the case independent of their underlying distributions, serial correlation and data length. If all the data fall on the 45° line, it indicates that the time series does not have a trend. While plotting the graphs, the data are sorted in order of their magnitude and accordingly fall along the 45° line. One way to implement this concept is by dividing a time series of data into two equal parts and the first half of the data are plotted against the second half. If the points are scattered on either side of the 45° line, it indicates that a non-monotonic increasing or decreasing trend is present in the time series at different temporal scales.

Sen (2012) noted that if the cluster of data points is closer to the 45° line, it shows the presence of a weaker trend magnitude. If the plot of data points appears along a line that is parallel to the 1:1 line, the time series is likely to have a monotonic trend. This method has been used in some studies, e.g., Kişi et al. (2018). However, Serinaldi et al. (2020) have raised concerns about this method noting that the graphs drawn in this method are equivalent to well-known two-sample quantile–quantile plots. They conclude that overall, this method suffers from a number of theoretical inconsistencies affecting its derivation, formulas, and interpretation.

In view of the concerns about the theoretical soundness of this method, it was not pursued in this study.

The wavelet technique is very useful to analyze a series of data at different time and frequency resolutions. It is used to decompose data series into various components. However, the wavelet cannot directly identify trend significance. Wavelets have become an effective and widely used tool in a range of applications including time series analysis. A wave is a real-valued function and this function is defined over the complete real range. A wavelet can be visualized as a wave-like oscillation which is localized in time. As the name suggests, a wavelet is a smaller version of a wave; it has finite magnitude over some defined finite interval; beyond this interval, the value of a wavelet is (very close to) zero. The value of a wavelet function oscillates about zero and the amplitudes of the oscillations do not vary much over the entire range.

A function ψ(.) will be called a wavelet if it satisfies three conditions: (a) ψ(.) must integrate to 0; (b) ψ²(.) must integrate to 1; and (c) ψ(.) must be ‘admissible’; this condition rules out certain functions from its domain (Percival et al. 2004).

Here, ψ is the mother wavelet. Coefficients a and b indicate the amount of dilation (scale factor) and translation of the wavelet, respectively.

After decomposing the series into various components, statistical tests were employed to detect the presence of trends and Sen's slope for the various components of the rainfall data series.

Researchers have developed a wide variety of wavelet forms which are used in different problems. These wavelet forms include the Daubechies wavelet, the Haar wavelet, and the Legendre wavelet. Here, the Daubechies (db) wavelet was employed since it is one of the most commonly used mother wavelets for analysis of hydro-meteorological data (Pandey et al. 2017) and is said to be ‘smooth’. Smooth wavelets were employed here since the trends in rainfall series are expected to be moderate. Among the different forms of the Daubechies wavelet, db5–db10 (Pandey et al. 2017) were used in this study. To select among the best Daubechies wavelet from the group db5–db10, the mean relative error (MRE) criterion (de Artigas et al. 2006; Joshi et al. 2016) was employed. MRE can be computed by Equation (6).

Taking into consideration the above-mentioned advantages and limitations of various methods in analyzing the characteristics of a time series, a combination of the method was used in this study. The regression lines were fit to the data to determine the overall trend. The Pettitt test was applied to detect change points in the series. We applied the MK test and Sen's slope method to identify the trend and its magnitude and the Mood test to detect changes in variance. The Change Point Method (CPM) package in R language, developed by Ross (2015) and Friedman et al. (2016) was used for the Pettitt test, MK test, and to compute Sen's slope. More details about the tests and CPM have been given by Ross (2015) and Friedman et al. (2016). For wavelet analysis, Matlab (https://matlab.mathworks.com/) routines were used.

The results are presented corresponding to the framework of the methods used (described in Section 3).

First, change points in the data series for All India and Homogenous regions at annual and monsoon season scales were identified by using the Pettitt test and the results are given in Table 3. Change points were found to be significant in three cases only – Central NE India – monsoon season and NE India for both annual and monsoon. For most regions, the year of change corresponds to 1957 to 1965; for the data series of North-West India region, the change year corresponds to 1942. It is conjectured that the period 1950 to 1965 was the time when many large industries were set up in India and many water resources projects (dams and diversions) were constructed. In order to feed the rising population, much emphasis was given to increasing agricultural production by expanding agricultural areas and irrigation. Such changes might be one of the reasons behind the changes in the processes that impact rainfall. Of course, the rainfall in a region also depends on teleconnections. More about this topic will be discussed in the attribution section.

Continuing the analysis, Table 3 also shows the average values of the series before and after the change points for all regions and for All India. The changes in average values can be easily noticed in the table. Except for two cases, the average values before the change points are higher than the average values after the change point. Subsequently, Sen's slope and MK test were applied to the series after the change point since the behavior of the series subsequent to change point is more important and relevant.

The annual data series and the monsoon season or JJAS series for the whole of India as well as for five homogenous regions were subjected to the MK test; Sen's slope values were also computed for all the series. Trends were examined in a two-tailed test at 5% significance level for which the standard Z-value is ±1.96. The results of the test are presented in Table 4.

It is noted from this table that there are rising and falling trends in various series during the annual and monsoon seasons. However, the falling trends dominate indicating that the decline in rainfalls is quite widespread. But none of these trends were found to be statistically significant at 5% significance level as the p-value in all cases was more than 0.05. Furthermore, Sen's slope values for the annual data series were found to vary over the range from −12.231 to 3.29. Specifically, annual data for the NE region and the Central NE region showed high Sen's slope, meaning thereby large declining trends in the rainfalls for these regions. For the monsoon season, the Sen's slope varied from −14.427 to 3.707. Sen's slope values for the monsoon data series for the NE and the Central NE regions are quite high, indicating that the declining trends in the annual rainfall series are largely due to a reduction in the monsoon rainfalls.

Each homogenous region is composed of several sub-divisions whose rainfall data at annual and seasonal scales were available. Based on the Sen's slope, 14 sub-divisions having a high value of Sen's slope were identified and their annual and monsoon season data were used for change point and trend analysis in the similar fashion as for the homogenous regions. Results of the Pettitt change point test, MK test and Sen's slope are presented in Table 5. It is noted from Table 5 that out of 14 sub-divisions, only four sub-divisions have a positive value of Sen's slope which indicates rising rainfalls. Sen's slope values for 10 sub-divisions are negative, meaning thereby that the rainfalls are falling and this behavior is pervasive. The magnitude of positive values of Sen's slope for the annual data varied from 3.92 to 27.8; the negative values ranged from −1.83 to −45.6; for the monsoon season, the negative values ranged from −3.0 to −44.0.

As mentioned earlier, smooth wavelets were employed in this study to model the data series since the trends in rainfall series are expected to be moderate. Among the different forms of the Daubechies wavelet, db5–db10 (Pandey et al. 2017) were used in this study. To select among the best Daubechies wavelet from the group db5–db10, the mean relative error (MRE) criterion (de Artigas et al. 2006; Joshi et al. 2016) was employed. MRE was computed by Equation (6).

The computed values of MRE for the data of various regions are given in Table 6; minimum values of MRE for a particular data set are shown in bold numbers. The computed values of MRE show that the db9 wavelet had the lowest value of MRE for annual RF for All India and two other regions and db5, db6, and db10 had the lowest MRE values for one region each. However, the MRE values for db9 for these regions were only marginally inferior to the best value and hence db9 wavelet was used for all the regions.

Next, the annual and monsoon time series were decomposed into one approximate (A3) component and three detailed components (D1, D2, and D3) by use of wavelet transformation. A detailed component represents dyadic fluctuations at the 2ⁿ level; here n represents the level of the detailed component. For annual or seasonal series, components D1, D2, and D3 represent 2¹ year (or 2 year), 2² year (or 4 year), and 2³ year (or 8 year) period, respectively. Furthermore, the approximate component of transformation represents the low-frequency part of the series. It is the high-scale component of the series, and it shows the key points of the series to lose minimum potential information (He et al. 2016). Note that the approximate component has less variability as the high-frequency information has been filtered away from the signal.

Examination of the wavelet components helps in better appreciation of variabilities and trends. For example, the periods of high and low variabilities can be easily demarcated in the approximate series A3. In Figure 5, A3 series displays low variability between years 50 and 90. Components D1 and D2 have rapid fluctuations over a narrow range and D3 shows slightly slower fluctuations over a still narrow range. Detailed D1 series shows high variabilities almost throughout and extreme fluctuations are seen around year 48. Fluctuations are progressively damped moving from D1 to D2, and then to D3. Note that in the D1, D2 and D3 series, the values vary over a small range. Thus, MRA enables to identify some localized features of data that are of interest in water resources management.

Next, for the detailed and approximate components of annual and monsoon season data series from two homogenous regions (NE India and Central NE India), Sen's slopes were computed and the MK test was performed. The results of these are summarized in Table 7. It can be seen that all four approximate components had a declining trend. Furthermore, the A3 + D1 and A3 + D1 + D2 series also showed a statistically significant (all but one case) declining trend. In all the cases, Sen's slope had a high negative value.

An improved insight can be obtained from the statistical analysis of wavelet decomposed components. Since A3 series has a relatively large magnitude compared to the detailed components, the falling trend in A3 could be a precursor to the overall falling trend in the data series in the future. Roughly, the approximate component can be visualized as ‘climate’ and the detailed components as ‘weather’. Decomposition also helps in identifying time spans for which the series had small or high variability; this information can be gainfully employed for better understanding or prediction of the series.

Trend analysis deals with hydroclimatic variables and thus, it is subjected to uncertainties that arise due to many reasons. First, the data series itself is likely to have some errors due to the inherent variability of the underlying phenomenon and the inability to correctly and completely capture this variability. In the case of rainfall, spatial average values are used, and errors may have been introduced while computing these. Finally, underlying assumptions of various trend analysis methods may not hold good.

One of the possible follow-up of change detection is attribution. Attribution is defined as the process of evaluating the relative contributions of multiple causal factors to a change or event with an assessment of confidence (IPCC AR6 Glossary 2021). It is the process by which the contribution of one or more causal factors to such observed changes or events are evaluated.

Attribution seeks to find out the underlying causes of changes in the properties of climatic data series. It thus helps in deciding the future courses of action, both at the policy front as well as research and development fronts. However, there are gaps in the knowledge of the physics of climatic processes and the requisite data at the desired temporal and spatial granularity. Hence, beyond some generalized understanding, an attribution at present is more a topic of research that is gradually developing to provide inputs to policy-making. There are large uncertainties in the future climate forcings and climate response at various scales.

An approach frequently followed in attribution studies is to run a climate model under two different input scenarios. In the first, concentrations of greenhouse gases are kept at the levels observed in the past before humans started burning fossil fuels at a high rate. This scenario is called the ‘counterfactual world’ – the world that might have existed in the absence of large-scale changes. In the second scenario, the concentrations of greenhouse gases input to the model are exactly as they have increased with time in the past. By comparing the outputs from the climate models under the two scenarios, it is possible to determine the impact of changed concentrations of greenhouse gases. Statistical methods are then used to quantify the differences in severity and frequency of the event.

Depending upon the region (All India, homogenous region, or sub-division) under consideration, precipitation in India has shown both increasing and decreasing trends in various seasons although most regions/seasons show declining trends. A number of factors have been identified to be important in determining the precipitation in India and its regions. India Meteorological Department (IMD) had developed a power regression model to issue long-range rainfall forecasts over India. This model had 16 parameters (Rajeevan 2001) including El Nino (same and the previous year), South Indian Ocean SST (Feb. and March), East coast India temperature (March), Central India temperature (March), Arabian Sea SST (Nov. to Jan.), Darwin pressure tendency (April–Jan.), Southern Oscillation Index (March to May), Himalayan snow cover (Jan. to March), and Eurasian snow cover (Dec.). Forecasts produced by this model were reasonably correct. However, Rajeevan (2001) noted that the predictability of the Indian Summer Monsoon (ISM) exhibits ‘epochal variations’. Furthermore, the predictand–predictor relationship is found to be changing with time (Rajeevan et al. 2007). Due to this, in the models to predict rainfall, it becomes necessary to change the predictors in use or their combination. Pal & Al-Tabbaa (2011) hypothesized that the trends in precipitation could be due to changes in a number of factors, viz., number of rainy days, rainfall intensity and extremes, convective phenomena, sea surface temperature changes, and ENSO. Sonali & Nagesh Kumar (2020) presented a review of various processes and advances made in climate change detection and attribution in the recent past.

According to the Clausius–Clapeyron equation, due to warming, low-altitude specific humidity increases by about 7%/°C of warming. The IPCC AR6 has reported the likelihood of an increase in monsoon precipitation in South Asia. Warming over the land region in Asia will be higher compared to the ocean and this will contribute to the intensification of the monsoon low-level southwesterly winds and precipitation (Endo et al. 2018). Chevuturi et al. (2018) report that at global warming levels of 1.5 and 2 °C, mean precipitation and monsoon extremes are likely to intensify over India and South Asia in the summer season; a 0.5 °C difference would result in a 3% rise in precipitation.

Detailed results of many attribution studies are now becoming available. AR6 of the IPCC contains a detailed treatment of this topic (see, for example, Seneviratne et al. 2021). Roxy et al. (2017) report that in recent times, the monsoon circulation over central India is weakening along with reducing locally available moisture and the frequency of moisture-containing depressions that originate in the Bay of Bengal. In spite of these, extreme rain events over central India have shown a threefold increase during 1950–2015. The rise in these events is attributed to the rising variability of low-level monsoon westerlies over the Arabian Sea. Devanand et al. (2019) found that increases in irrigation is responsible for the rise in rainfall intensity over Central India. Greater warming in the Arabian Sea is projected in CMIP5 simulation and this might further increase the occurrence of such extreme events in future. Devanand et al. (2019) tried to study the impact of increased irrigation on the Indian Summer Monsoon by using a climate model and found that the excess application of irrigation in northern India is responsible for shifting the monsoon rainfall towards the northwestern part of the Indian subcontinent in September. Results of recent research suggest that it is important to better represent irrigation practices in climate models. Dong et al. (2020) tried to evaluate the human influence on extreme precipitation by using percentile-based extreme indices which were computed from the simulations results from the Coupled Model Intercomparison Project (CMIP6) models. They report that a fingerprinting (see Bindoff et al. 2013) analysis could detect signals of greenhouse gases but not the signals of anthropogenic aerosols and natural forcings. Chug et al. (2020) found that during 1980–2003, the frequency of extreme flow events in the Western Himalayan rivers has doubled and the increasing trend in annual maximum streamflow is statistically significant. This behavior is attributed to increased extreme precipitation events. Based on CMIP5 and CMIP6 model projections, IPCC AR6 also indicates the likelihood of an increase in short intense active days and a decrease in long active days.

Performing attribution analysis for rainfall data series poses many challenges because the natural variability in the rainfall series for a given region from one year to the other is quite high. Hence, it is hard to correctly capture the climate change signal in presence of the noise of variability. Considering all the factors, the attribution of precipitation trends for India has considerable uncertainty as of now. Understanding of the processes likely to be impacted due to global warming and the GCMs results project an increase in precipitation whereas such signals are missing in the observed data series so far. Scientists need to periodically analyze the updated data.

This paper presents the results of trend analysis of observed long-term rainfall data series for the whole of India as well as different homogenous regions and sub-divisions. The study reveals that the use of multiple methods can give useful information about the different trend-related features of rainfall time series. Results of MK and linear regression test showed no statistically significant trend in the rainfall series of All India and three regions for the annual and monsoon seasons. Data from the NE region (annual and monsoon) and Central NE (annual and monsoon) series displayed statistically significant falling trends. Change points in the various series were explored by using the Pettitt test. Results of this test showed that most rainfall series show the presence of change points around the years 1957–1965. A possible explanation could be that many new water resources projects were constructed in this period, giant industries were established, and large tracts of land were brought under cultivation and irrigation. Finally, multi-resolution analysis of the wavelet decomposed series highlighted periods of high variabilities in the approximate and detailed series. It also showed that the approximate data series for the NE region (annual and monsoon) and for the Central NE region had declining trends. Furthermore, A3 + D1 and A3 + D1 + D2 data series for NE also showed statistically significant declining trends. Data from two sub-divisions having large declining trends were also analyzed.

This paper has used long-term rainfall data series that were carefully compiled after detailed scrutiny of available data and this is, perhaps, the best available long-term data for India. Hence, much confidence can be placed in the outcome. Keeping in view of the findings of the study, it is necessary to collect and analyze rainfall data for all the regions/sub-divisions at various temporal scales and the findings should be used to update water management plans, design flood practices, and flood/low flow management in these regions. Furthermore, detailed modeling studies are needed to more carefully understand and predict the roles of global warming (including warming of oceans), land use changes, and widespread irrigation in changes in rainfalls in various regions of India.

This paper has focused on the magnitude of rainfalls. In water resources management, rainfall intensities also have critical importance. Trend analysis of rainfall intensities requires data at finer time intervals and the geographical extent of such events is not very large. Hence, it would be helpful to establish denser networks of instruments to collect (multi)hourly data and analyze them to understand the trends as well as identify spatial and temporal hotspots. The results of the studies should also be corroborated with the results of climate models.

The authors would like to thank IIT Roorkee for making available the facilities to conduct the study reported in this paper. This study is (partially) financially supported by the National Key Research and Development Program of China (2021YFC3200303) and the Research Council of Norway (FRINATEK Project No. 274310).

All relevant data are available from an online repository or repositories (https://www.tropmet.res.in/~lip/Publication/RR-pdf/RR-138.pdf).

The authors declare there is no conflict.