Long-period trend analysis of annual and seasonal rainfall in West Bengal, India (1901–2020)

Location-specific information on annual and seasonal rainfall trends has immense utility in devising crop planning as well as water resource management in West Bengal. We assessed long-period (1901–2020) trends and magnitudes of seasonal and annual rainfall across districts of West Bengal. The non-parametric Mann-Kendall (MK) test, sequential Mann-Kendall (SQMK) test, and Sen’s slope estimator were applied to the gridded (0.25° × 0.25°) rainfall dataset. Results revealed that both the annual and seasonal rainfall of West Bengal increased non-significantly (p>0.05), except for the winter season, which experienced a non-significant decrease. Annual rainfall across a majority of the districts in sub-Himalayan West Bengal (SHWB) declined non-significantly. On the contrary, a significant (p<0.05) increase in annual rainfall was observed across most of the districts of Gangetic West Bengal (GWB) at the rate of 1.8 mm year−1 to 2.9 mm year−1. Monsoon rainfall increased significantly over Gangetic West Bengal (GWB) at 1.4 mm year−1 to 2.1 mm year−1, while it declined significantly in Dakshin Dinajpur district at 3.2 mm year−1 of SHWB. Post-monsoon rainfall increased significantly over GWB at the rate of 0.5 mm year−1 to 0.9 mm year−1. The winter rainfall decreased non-significantly across all the districts. Normalized rainfall anomaly (NRA) revealed that 17% of the study period experienced surplus (NRA>1) rainfall, while another 17% received deficit (NRA>−1) rainfall. Nearly 70% year received normal monsoon rainfall (NRA = ±1) and 16% year deficit and 14% year surplus rainfall. The SQMK test for seasonal rainfall showed a general trend change point around 1960 and 1970 in both the district and state-level annual rainfall.


Introduction
In recent times, climate change is a serious environmental issue posing serious threats to human beings through a range of pathways.Climate change in reality has increased the frequency and magnitude of climatic events such as floods and droughts, cyclones, tornadoes, storm surges, glaciers melting, sea level rise, and thus land erosion and saline water intrusion.These changes can directly harm human lives or cause severe threats to the ecosystem, biodiversity, land resource, water, food, health, and lives (Pecl et al. 2017).Though the natural change of climatic parameters (e.g., rainfall, temperature, and humidity) follows a naturalistic rhythm, rapid anthropogenic greenhouse gas (GHGs) emissions since the post-industrial era in particular cause global warming as well as climate change (IPCC 2014;Sam and Chakma 2019).As a consequence, global surface temperature has increased nearly 0.6±0.2°C in the 20 th century since 1861 (Kumar et al. 2014).In association with global warming, rainfall changes have already been recorded across the globe.Several global studies (IPCC 2014;Adler et al. 2017) reported increasing rainfall trends with increasing inconsistency.However, such change may not be identical at the regional level, since both the increasing and decreasing trends have been reported from different parts of the globe (Das et al. 2015).A decreasing trend of rainfall was observed in Tanzania (Gebrechorkos et al. 2019), north and central Ethiopia (Asfaw et al. 2018), North China (Su et al. 2020), middle India (Duhan and Pandey 2013), Pakistan, and Bangladesh (Khan et al. 2019).On the contrary, increasing trends were reported from Southern and Central China (Akhter et al. 2018), Sri Lanka (Nisansala et al. 2020), and arid East-Central Asia (Hong et al. 2014).Such changes in rainfall adversely affected regional crop production systems as well as food security, biodiversity, livelihood, and human health (Connell 2015).For example, very heavy and rare rainfall events in the United States increased by 20% in magnitude and increased by 200% in frequency in the past 100 years, which led to an increase of 30-127% in the number of people at risk from floods (Swain et al. 2020).Nearly 540,000 deaths were registered worldwide due to floods during 1980-2009(Salvati et al. 2018)).Even in the single year 2016, flood (excluding landslides)-induced deaths were recorded as 4720 people and 74 million sufferers worldwide (Paterson et al. 2018).Besides, crop loss due to inconsonant rainfall has increased threefold in Europe during the past 50 years (from −2.2% during 1964-1990 to −7.3% during 1991-2015) (Brás et al. 2021).
Rainfall directly affects runoff and freshwater availability as well as water demand in various sectors (drinking, domestic, irrigation, industry, hydropower generation) of a region (Padrón et al. 2020).Voudouris et al. (2012) estimated that a decrease in rainfall by 20% will reduce runoff by 29% to 32% in the Crete region of Greece and the subsequent dearth of freshwater availability in the region.Any abrupt change in annual rainfall affects the spatiotemporal allocation of runoff, moisture content in the soil, groundwater storage, stream flow, and water quality (Das et al. 2014).Besides, anomalies in rainfall distribution bring a series of environmental consequences such as soil erosion, landslide, flood, and drought (Gupta et al. 2014).Owing to low resiliency and adaptive capacity, developing countries are the worst hit by climate change, since a majority of the population relies on climate-sensitive economic activities like agriculture, fishing, and tourism (Mandal et al. 2018).
The agrarian economy of India largely depends on the normal distribution of annual rainfall, more than 80% of which occurs during monsoon months (June to September).Spatiotemporal anomalies in southwest monsoon (SWM) rainfall pose serious threats to the agricultural production system of India.The SWM rainfall was in decreasing trend during the beginning of the 21 st century, while pre and post-monsoon rainfall showed an increasing trend (Ghosh and Dutta 2020).Aggarwal et al. (2010) reported a 23% deficit of SWM rainfall in 2010, which adversely affected Kharif production; thus, agricultural GDP declined by 0.2% compared to the previous year.Another report warned that crop production will reduce by 31.3% with the reduction of rainfall by 2030 in India (Vyankatrao 2017).However, at a subregional scale, Das et al. (2014) reported an increasing trend in summer monsoon rainfall and rainy days over the east coast and Deccan Plateau, while decreasing trend in the west coast, eastern part, western desert region, and northeastern region of India during 1971 to 2005.Guhathakurta and Rajeevan (2008) reported a significant decrease in annual rainfall for the subdivisions of Konkan and Goa, Madhya Maharashtra, North Interior Karnataka, Rayalaseema, coastal Andhra Pradesh, Gangetic West Bengal, Assam, Meghalaya, and Jammu and Kashmir during 1901 to 2003.However, for the country as a whole, annual and monsoon rainfall decreased and winter rainfall increased from 1871 to 2005 (Kumar et al. 2010).In a study on 236 districts ' rainfall data (1901-2000), Bera (2017) showed that half of the Ganga basin experienced a decrease in annual rainfall, while a significant declining trend in annual, pre-monsoon, and post-monsoon rainfall over Kosi, Gandak, and Sone subbasins.Basistha et al. (2009) reported that the annual rainfall over the Indian Himalayan region increased during 1902-1964while decreasing in-between 1965and 1980. Narayanan et al. (2016) ) reported a rise in pre-monsoon rain over Ajmer, Bikaner, Indore, and Kolkata and a fall in Minicoy and Belgaum during 1949-2009. Kamal and Pachauri (2019) observed a negative trend in annual rainfall over northeast India from 1901 to 2015, though the state of Meghalaya and Mizoram experienced a significant positive trend in SWM rainfall, and Arunachal Pradesh, Assam, Nagaland, and Sikkim felt significant decrease.
Likewise, in West Bengal, wide variations of annual as well as seasonal rainfall occurrences are likely to be observed, and any abrupt change in rainfall distribution affected the predominant agricultural system.Thus, the proper knowledge of interannual and seasonal rainfall variability, their trends, and anomalies through the sound analysis of long-period rainfall datasets would be of immense utility in devising agricultural planning and water resource management.However, literature available in the public domain for the lower Gangetic plains (Chatterjee et al. 2016;Mukhopadhyay et al. 2016;Kundu and Mondal 2019;Ghosh and Dutta 2020) did not include recent years' data, while rainfall has changed a lot in past few decades-for example, heavy rainfall event has increased over the coastal West Bengal during the recent year (Datta and Das 2019).Despite the inclusion of recent years' data in the work of Datta and Das (2019), Nandargi and Barman (2018), and Nandargi and Barman (2018b), there is a dearth of rainfall trend analysis across seasons and districts of West Bengal.Though the knowledge of seasonal rainfall trends is imperative in devising district-level planning.Therefore, realizing the need for current consciousness on the spatial pattern of rainfall occurrences across districts and seasons, we emphasized the study of spatiotemporal anomalies in rainfall occurrences, annual and seasonal trends, and magnitude of rainfall distribution in West Bengal, India.We used long period gridded (0.25°× 0.25°) rainfall dataset  and employed Mann-Kendall (Mann 1945;Kendall 1975) non-parametric trend test, sequential Mann-Kendall test (Sneyers 1990), and Sen's slope estimator (Sen 1968).

Study area
West Bengal is one of the 28 states of India, located in the eastern part of the country (21° 25′ 02″ to 27° 13′ 15″ N latitudes and 85° 49′ 20″ to 89° 53′ 04″ E longitudes) by occupying nearly 88Th km 2 land area (Fig. 1).Altitude varies from 3636 meters (Sandakphu at Singa lila range) in the north to <3 meters (at Sagar Island) in the south, with an average of 44 meters from mean sea level (MSL).Due to wide altitudinal variation and diverse physiographic settings, West Bengal experiences varied climatic conditions from tropical wet-dry in the south to humid subtropical in the north (Kundu and Mondal 2019).The India Meteorological Department (IMD) has categorized the state into two homogeneous climatic regions, i.e., the sub-Himalayan West Bengal (SHWB) and the Gangetic West Bengal (GWB) (Parthasarathy et al. 1995), and four seasons, e.g., summer or pre-monsoon (March-May), southwest monsoon (June-September), post-monsoon (October-December), and winter (January-February) (Mandal et al. 2013).The SHWB consists of 6 northern districts, namely, Darjeeling, Jalpaiguri, Cooch Behar, Uttar Dinajpur, Dakshin Dinajpur, and Malda, while the rest falls into GWB.The average maximum temperature goes up to 43 °C during summer months, while in winter average minimum temperature goes down to 10 °C.The Rarh Bengal in the west experiences heat wave (>45 °C) in the summer months, while cold waves and snowfall (<0 °C) are observed during winter months in the SHWB region.Southwest monsoon (SWM) contributes >76% of the annual rainfall (1825 mm).Frequent occurrences of severe cyclonic storms along with heavy downpours during pre-monsoon and post-monsoon months cause flooding, inundation, and livelihood devastation in the districts of GWB.Predominant Kharif (rice) cultivation solely depends on the sufficient and timely occurrence of SWM rainfall, though in recent times early and/ or delayed onset and/ or recession including wide anomalies cause frequent crop failure vis-à-vis livelihood insecurity to the resource-poor farming community of Bengal (Mandal et al. 2015;Mandal et al. 2018).

Dataset
We used long-term (1901-2020) gridded (0.25° × 0.25°) rainfall dataset covering 19 districts of West Bengal.The dataset was sourced from the India Meteorological Department (IMD), Pune, through the Water Resource Information System (WRIS) interface (https:// india wris.gov.in/ wris/#/ rainf all).The IMD generated gridded data at 0.25° spatial resolution from the observed data of 6955 rain gauge stations covering the entire India using Shepard's technique.In West Bengal, the IMD has 23 major rain gauge stations and innumerable minor observatories maintained by several state government organizations (e.g., the Agricultural Department, the Agricultural Meteorological Office, the Water Resources Department, and the Disaster Management Department) (Pai et al. 2014).Generally, the IMD converts station data to regular space-time gridded data after removing all kinds of errors by validating and multi-stage quality control of the observed data.Such errors include suspicious values, repeated values, location errors, ambiguity in recorded data, and duplication of monthly or submonthly record that is affected by the correlation coefficient, outliers, unknown errors, and human errors arising at various levels from field measurement.The IMD used the inverse distance weighting interpolation (IDW) method to obtain gridded data (Rajeevan et al. 2006).

Data analysis
We estimated the long-period  trend and magnitude of both the annual and seasonal rainfall time series across districts as well as for the state as a whole by employing the non-parametric Mann-Kendall test (Mann 1945;Kendall 1975).Magnitudes of such trends were estimated using Sen's slope estimator (Sen 1968).We followed the entire computational procedure path as (i) testing of autocorrelation effects in the rainfall data series, (ii) removal of positive serial correlation if any by pre-whitening method, (iii) detection of the Mann-Kendall trend, (iv) sequential Mann-Kendall test (SQMK), (v) Sen's slope estimation, and (vi) computation of relative change (%).

Testing autocorrelation
The major problem in trend detection of rainfall time series is the effect of autocorrelation or serial correlation.The existence of any positive or negative serial correlation underestimates the trend result (Yue et al. 2002).The nonparametric test generally detects a significant trend if there exists positive autocorrelation; however, there may exist no actual trend at all.Rainfall time series data often shows a tendency to be correlated automatically, which strengthens the probability of trend detection in the non-parametric test.Therefore, it is essential to remove the serial correlation effect from the data series.In the rainfall time series datasets, we tested serial correlation using lag-1 autocorrelation coefficient (r 1 ) at p<0.05 significant level using a two-tailed test (Table 1).We computed the lag-1 serial correlation coefficient following Kendall and Stuart (1968) and Salas (1980).
where E x(i) is the mean of sample data and n is the sample size.
To check the significance of the serial correlation, the autocorrelation coefficient (r 1 ) was tested against the null hypothesis at a 95% confidence interval using two-tailed tests.
The data is considered serially independent if r 1 is concentrated within the confidence interval; otherwise, the prewhitening approach is applied to remove serial correlations by a non-parametric test proposed by Yue et al. (2002).

Trend-free pre-whitening
To minimize the effects of serial correlations in the dataset, trend-free pre-whitening (TFPW) method was applied before the non-parametric test following Yue et al. (2002).The following are the steps of the TFPW method applied in this study.
(i) At first, we calculated the lag-1 autocorrelation coefficient (r 1 ).If the r 1 value exceeded the upper and lower limits of the confidence level, then the trendfree pre-whitening approach was applied before the Mann-Kendall (MK) test (as mentioned earlier).(ii) The slope of n pairs of data points was computed by using Eq. 12, and then, the trend was removed from the series to acquire a detrended series using Eq. 4.
(iii) We computed the lag-1 serial correlation coefficient for the detrended series (r 1 ) by using Eq. 2. (1) from the detrended series to get a residual series as given below (Eq.5).
(v) Again, the value of the trend (Q ×i) was added to the residual series to get a new data series as described below.
The new Y i series was then considered for the Mann-Kendall (MK) trend analysis.

Mann-Kendall test
The non-parametric Mann-Kendall (MK) test (Mann 1945;Kendall 1975) is extensively used to detect significant monotonic trends in hydro-meteorological time series.In recent times, researchers across the globe extensively used the method to detect trends in rainfall datasets.In this study, we used the non-parametric Mann-Kendall trend test to detect a statistically significant (p<0.05)trend in the long-term  annual and seasonal rainfall data series following the standard method. (5)

Sequential Mann-Kendall test
We used the sequential Mann-Kendall test (SQMK ;Sneyers 1990) to detect the potential trend change points in long-term data series.This test was computed using ranked values (x i ) of the original values x 1 , x 2 , … , x n .The magnitude of x i (i= 1, 2, 3, … , n) was compared with x j (j= 1, 2, … , i−1).For every comparison, the cases where x i > x j were counted and denoted by n i .A statistic can therefore be defined as The distribution of the test statistic has a mean and a variance as The forward sequential statistic U(t) values of a standardized variable were computed.Using the original time series, values of the backward sequential statistic U′(t) were estimated.
When the progressive series U(t) and backward series U′(t) were plotted as curves, the intersection point of this duo provides an approximate potential trend change point in a time series.If they intersected within ±1.96 (95% confidence limit) of the standardized statistics Z, a change might detect at that point, but if they intersected beyond the confidence limit then that change point was considered a statistically significant turning point.The separation point of the upward and downward series indicated the change point where the trend begins.Besides, if at least one value of the progressive series was greater than a chosen significance level of the normal distribution, the null hypothesis (H0: sample under investigation showed no beginning of a new trend) was rejected.Therefore, the significant trend year was considered the trend turning point or trend change year from where a new trend started (Bisai et al. 2014).

Sen's slope estimation
We used Sen's slope estimator to estimate the true slope (change per unit of time) of a linear trend (Sen 1968).The method was widely used in magnitude estimation in hydro-meteorological time series trends (Mandal et al. 2013;Kumar et al. 2014).The slope (Q) of N pairs data was obtained from Eq. 12.
where x i and x k represent data values at times j and k, respectively, and obviously j>k.Now, the median of N values of Q i is represented as Sen's slope (Q), which determined the magnitude of the trend and was calculated following Eq.13.
The positive value of Q i indicated an increasing trend and the negative value expressed decreasing trend.( 10)

Relative change
We computed the relative change of annual and seasonal rainfall over mean rainfall during 1901-2020 following Eq.14 (Some'e et al. 2012;Kumar et al. 2016).
where n = length of trend period, Q = magnitude of the trend slope of the time series which was determined by Sen's median estimator, and |x| = absolute average value of the time series.

Persistency in rainfall series
All the long-term (1901 to 2020) annual and seasonal rainfall time series across different districts of West Bengal were checked for autocorrelation coefficient (r 1 ) at p<0.05 significant level (Table 1).Results revealed that the annual (r 1 : 0.3728) and monsoon (r 1 : 0.2867) rainfall series of Dakshin Dinajpur district and the annual (r 1 : 0.3339) and monsoon (r 1 : 0.3012) rainfall series of Malda district showed significant lag-1 autocorrelation as their value fell outside the critical limit (−0.1873<r 1 >0.1873).Therefore, the trend-free pre-whitening test was applied in the monsoon and annual rainfall series of Dakshin Dinajpur and Malda districts, to eliminate the effect of autocorrelation from the data series.Either the annual or seasonal time series of other districts showed no serial or autocorrelation.This indicated no successive value in the time series and they were not influenced by their antecedent values, rather they were independent data values.

Descriptive statistics of seasonal and annual rainfall
West Bengal received nearly 1825 ± 211 mm rainfall annually during the past century , though the spatial distribution widely varied among districts and followed the north-south altitudinal gradient.As a result, comparatively higher mean annual rainfall was recorded in the districts of SHWB and lower in the districts of GWB.Average annual rainfall varied from 3772 ± 636 mm in the Jalpaiguri district followed by Darjeeling (3238 ± 431 mm) in the SHWB to as low as 1331 ± 224 mm in the Purulia district followed by Bankura (1371 ± 229 mm) in the western plateau region (Table 2).The median of annual rainfall remained between 2000 mm and 3000 mm in most of the districts in the SHWB, while in the GWB it ranged from 1500 to 2000 mm (Fig. 2a).
In general, the annual rainfall in GWB was more variable (CV: 16.5% in West Midnapore to 24.6% in Kolkata) than SHWB (CV: 13.3% in Darjeeling to 16.9% in Jalpaiguri).Most of the districts showed positive skewness (Sk) with low kurtosis (Ku) value, which affirmed that the annual rainfall is distributed asymmetrically and located to the right of the mean with lack or minimum outliers (Fig. 2a).The Sk and Ku of Kolkata (1.06, 5.01), South 24 Parganas (1.08, 4.56), and Howrah (1.09, 4.79) showed a highly positive skewed distribution with a heavy tail compared to other districts (Table 2).Normalized rainfall anomaly (NRA) revealed that 17% of the years experienced surplus (NRA>1) rainfall, while another 17% received deficit (NRA>−1) rainfall during the study period (Fig. 3a).
Likewise, seasonal rainfall varied widely across districts.Pre-monsoon rainfall was recorded as low as 126 ± 53 mm in the Purulia district of the western plateau fringe to a maximum of 606 ± 184 mm in the Jalpaiguri district of SHWB (Table 2).Rainfall during the pre-monsoon months highly varied in Malda district (CV: 52.1%) and was most consistent in Darjeeling district (CV: 28.4%).The median of pre-monsoon rainfall was higher in the SHWB (200 to 600 mm), while it was lower (50 to 200 mm) in the western and southern part of the GWB (Fig. 2b).West Bengal as a whole received 254 ± 70 mm pre-monsoon rainfall with 27.5% variability and 13% year received deficit (NRA<−1) rainfall (Fig. 3b).Monsoon month (June-September) rainfall highly accumulated over the sub-Himalayan region (1358 ±357 mm in Dakshin Dinajpur to 2940 ±525 mm in Jalpaiguri district) (Table 2).On the contrary, GWB received comparatively lower monsoon rainfall 987±232 mm (Nadia district) to 1242 ± 250 mm (East Midnapore) during 1901-2020 (Table 2 and Fig. 2c).Apart from this, the median of monsoon rainfall remained higher over SHWB (2000-3000 mm), which was closer to 1000 mm in GWB (Fig. 2c).The occurrence of monsoon rainfall over the state as a whole was 1392 ± 166 mm with the variability of 11.9%.Nearly 70% year received normal monsoon rainfall (RAI=±1), while 16% year deficit and 14% year surplus rainfall (Fig. 3c).
The lowest accumulation of post-monsoon rainfall was recorded in the western plateau fringe area (Purulia: 108 ± 75 mm) and highest in the Jalpaiguri district (194 ± 108 mm) of SHWB (Fig. 2d).Post-monsoon rainfall was more consistent in Jalpaiguri (CV: 55.4%) district and highly variable in Malda district (CV: 83.6%).The median of postmonsoon rainfall remained closer to 150 mm in every district, though considerable numbers of outliers exist (Fig. 2d).During the study period , East Midnapore district experienced the highest winter rainfall (42 ± 38 mm), while Uttar Dinajpur (22 ± 19 mm) received the lowest.Similar to post-monsoon rainfall, considerable numbers of outliers exist in winter rainfall (Fig. 2e).Occurrence of winter rainfall (33 ± 25 mm) was found to be highly variable (75%) compared to all seasons of the state (Table 2).

Trend and magnitude of seasonal and annual rainfall
Mann-Kendall trend statistics revealed that in the past century, annual rainfall across the districts of SHWB declined (Table 3).A significant (p<0.05)decrease occurred in the district of Dakshin Dinajpur at 3.6 mm year −1 .Darjeeling is the exception among SHWB districts where a significant increase (3.3 mm year −1 ) was observed.On the contrary, a significant increase in annual rainfall was observed in most of the districts of GWB (North 24 Parganas, Howrah, Kolkata, South 24 Parganas, and East Midnapore) at the rate of 1.8 mm year −1 to 2.9 mm year −1 (Table 3, Fig. 4a).Though the annual rainfall of the state as a whole increased nonsignificantly at 0.5 mm year −1 .Pre-monsoon rainfall significantly increased in the districts of Darjeeling and Purulia at the rate of 0.3 mm year −1 to 0.7 mm year −1 , while a significant decline occurred in Nadia district at 0.6 mm year −1 (Fig. 4b).Monsoon rainfall contributed nearly 76% of the annual rainfall of West Bengal.Monsoon rainfall in most of the districts of GWB increased significantly (e.g., North 24 Parganas, Howrah, Kolkata, South 24 Parganas, and East Midnapore) at 1.4 mm year −1 to 2.4 mm year −1 , while declining significantly in Dakshin Dinajpur district of SHW at 3.2 mm year −1 (Fig. 4c).Post-monsoon rainfall increased significantly over GWB (e.g., North 24 Parganas, Kolkata, and South 24 Parganas) at the rate of 0.5 mm year −1 to 0.9 mm year −1 (Fig. 4d).The winter rainfall decreased nonsignificantly across all the districts.During the past century , seasonal rainfall of West Bengal as a whole increased (at 0.02 mm year −1 to 0.4 mm year −1 ) non-significantly (p>0.05)except winter rainfall, which decreased at 0.01 mm year −1 (Table 3).

Abrupt trend change in annual and seasonal rainfall
The abrupt change in the long-term trend of annual and seasonal rainfall was detected using the SQMK test.Significant (p<0.05)intersection point between the forward series U(t) and backward series (U′t) of annual and seasonal rainfall if any across districts and in the state as a whole is depicted in Fig. 5a-e 5b).The significant trend years in monsoon rainfall were found in 1990 (2.00), 1991 (2.19), 1993 (2.12), and 1995 to 2010 (1.98 to 2.71), but 2000 is the significant trend change year (Fig. 5c).Abrupt change point in post-monsoon rainfall occurred in 1910; however, significant trend turning point was observed mainly in 1952 (2.08) and in 2005 (2.15) (Fig. 5d).The winter rainfall of the state did not show any significant results (Fig. 5e).

Relative change in rainfall
Relative change of annual rainfall in the long-period (1901-2020) average was found to be positive across districts of GWB ranging from 7.7% (West Midnapore) to 22.7% (North 24 Parganas).Conversely, across SHWB districts, negative deviation was observed from −38% (Dakshin Dinajpur) to −1.9% (Birbhum) (Table 3).Pre-monsoon rainfall deviated from −33.7% (Nadia) to 27.7% (Purulia); however, for the entire state, it increased by 1.1%.Percentage change in both the monsoon and post-monsoon rainfall across GWB deviated positively from 6.1% (Bankura) to 25.4% (North 24 Parganas) and 9.6% (Murshidabad) to 69.7% (North 24 Parganas).Conversely, it showed negative deviation across districts of SHWB for both the monsoon and post-monsoon seasons.Post-monsoon rainfall for the state as a whole showed maximum positive change (15.6%) from the rest of the seasons, while the winter season showed negative change during the study period (23.8%).Besides, all the districts experienced a declining change in winter rainfall from 10.8% (Birbhum) to 48.0% (Dakshin Dinajpur) (Table 3).
Besides, a trough of retreating monsoon over the SHWB forms a convergence zone between the western disturbances and easterly wind from the Bay of Bengal.Due to the shifting of the trough towards the Bay of Bengal (BOB) it gains moist air from the ocean which causes heavy rain and thundershower over the coastal regions of Bengal (Attri and Tyagi 2010).At the same time, the SHWB gets precipitation from the western disturbance in the form of snowfall (Chatterjee et al. 2016).
Most of the districts of GWB exhibited decreasing trend in pre-monsoon rainfall, while districts of SHWB and the western part of West Bengal (Rarh Bengal: Purulia, Bankura, and West Midnapore) revealed a non-significant increasing trend.This corroborated with the findings of Choudhury et al. (2012) from mid-altitude Meghalaya.Based on 1454 rain gauge station data  across India, Rathore et al. (2013) also reported an increase in premonsoon rainfall across different sub-Himalayan states of northeast India, e.g., Manipur, Mizoram, Nagaland, Meghalaya, Tripura, and West Bengal.Extrapolated results from the analysis of long-period  data based on 32 meteorological subdivisions covering the entire country, Jain and Kumar (2012) reported an increasing trend in the pre-monsoon rainfall in SHWB.Our findings contradicted with Datta and Das (2019) and Mandal et al. (2013) but corroborated with Kundu and Mondal (2019), who reported decreasing pre-monsoon rainfall in all parts of GWB and increasing in all districts of SHWB.Besides, our findings of the increasing trend in Rarh Bengal were supported by Mukhopadhyay et al. (2016).
The trend of annual rainfall declined in the SHWB and the northern part of GWB (Bardhaman, Birbhum, Nadia, and Murshidabad).Annual rainfall in the lower Gangetic plain or coastal Bengal and two districts of SHWB (Darjeeling and Cooch Behar) experienced increased annual rainfall.Likewise, the monsoon rainfall trend followed a similar pattern as annual rainfall.Jhajharia et al. (2012) also reported a decreasing trend of monsoon rainfall from Assam in northeast India (NEI).Researchers also reported a decreasing trend in monsoon rainfalls from different parts of India (Choudhury et al. 2012;Dash et al. 2015).Similarly, Nair et al. (2018) using the high-resolution IMD and Global Rainfall Climatology Project (GPCP) dataset also revealed comparable trends with our findings in pre-monsoon and monsoon rainfalls for the SHWB region.The declining trend in monsoon rainfall might be partially due to the decrease in vertically integrated moisture transport (VIMT) over the BOB (Konwar et al. 2012).Apart from that, the weakening of monsoon might be because of the warmer tropical ocean, especially the central-eastern Pacific and the western Indian Ocean (Soraisam et al. 2018).Our findings corroborated with Datta and Das (2019) who reported a positive trend of monsoon and annual rainfall for the coastal districts of GWB and a negative trend for SHWB.However, our trends of pre-monsoon and monsoon rainfall for GWB contradicted the findings of Mandal et al. (2013).This might be because of their single point and short period  of data analysis.
In the case of post-monsoon rainfall, the districts of SHWB except Darjeeling experienced a declining trend, while GWB revealed an increasing trend.The finding contradicted Datta and Das (2019) and Kundu and Mondal (2019); however, it supported by Mukhopadhyay et al. (2016).The winter rainfall was non-significantly decreased over the entire state, which was supported by several researchers (Mukhopadhyay et al. 2016).
Our findings showed that the pre-monsoon, monsoon, and post-monsoon rainfall in the Darjeeling district increased significantly.This might be associated with the complex hilly terrain that led to orographic rainstorms.Moreover, the dense forest cover of the district allowed a higher volume of evapotranspiration, which might favor increasing rainfall.Mukhopadhyay et al. (2016) reported a similar increasing trend of seasonal rainfall from the region by analyzing the dataset from 1901 to 2000.Similar to our findings, significant decreasing trend in monsoon rainfall in Dakshin Dinajpur district was observed by Datta and Das (2019).In addition to this, the non-significant negative trend of annual rainfall and winter rainfall in the district was documented by Kundu and Mondal (2019).
An increasing trend of pre-monsoon rainfall over SHWB might be associated with the higher amount of aerosol concentration in this season, which is largely responsible for heating the regional atmosphere and thereby enhancing premonsoon rainfall by intensifying moisture gaining mechanism (Lau and Kim 2006).Similarly, a decrease in aerosol concentration in the SHWB during monsoon season might be responsible for the declining trend in monsoon rainfall (Sarkar et al. 2015).
In reverse, increasing events of severe cyclonic storms (SCS) as a consequence of global warming over the north Indian Ocean increased rainfall during the pre-monsoon and post-monsoon seasons in different parts of West Bengal (Dong et al. 2016).The number of cyclones occurring in the Bay of Bengal (BOB) was five times higher than that of the Arabian Sea (Sahoo and Bhaskaran 2016).An increasing trend of tropical cyclonic events was observed by 26 percent over BOB in the last century (Singh 2007;Ghosh and Mistri 2021).Tropical cyclones that originated over the BOB mostly made landfall along the coast of Odisha and West Bengal.In their recent study, Kantamaneni et al. (2022) showed that the Indian coastal districts were affected by 61 cyclonic disturbances from 2006 to 2020, most of which made landfall along the coast of Odisha (20 cyclones) and West Bengal coast (14 cyclones).Many researchers manifested that global climate change has altered the frequency and intensity of tropical cyclones and associated rainfall events (Irvine et al. 2019).Therefore, the rising trend of precipitation is perhaps associated with the incremental cyclonic activities over the BOB and their landfall along the West Bengal coast.The coastal part of West Bengal received rainfall extremes due to cyclonic depressions mainly in the post-monsoon season (Singh et al. 2020).The seasonal cyclonic activities and increased precipitation extremes contributed a significant quantum of rainfall in seasonal as well as annual rainfall.By analyzing the long-period  record of cyclonic depressions in India, Singh et al. (2020) reported that the state of West Bengal experienced heavy rainfall associated with cyclonic depressions.Besides, the state has received an average rainfall of up to 50 mm year −1 due to cyclonic depressions during the study period.Because of the proximity to the BOB, there were higher chances of experiencing cyclonic precipitation which might contribute to the rising trend of seasonal and annual rainfall particularly in the GWB.On the contrary, insufficient moisture supply in SCS at the post-landfall stage is owed to the decreasing trend in post-monsoon rainfall over SHWB compared to GWB.Again, the declining sea surface temperature and southward shifting of the Intertropical Convergence Zone (ITCZ) are accompanied by decreasing frequency of cyclones during the winter months in Bengal, which may be responsible for the insignificant decline of winter rainfall (Khullar 2011).
The SQMK test revealed an independent short-term trend within the long-period trend of rainfall over time.Both the district and state-level annual and seasonal rainfall showed a general trend change point around 1960 and 1970.Districts of SHWB (Jalpaiguri, Uttar Dinajpur, and Dakshin Dinajpur) showed decreasing trend just after the change point; however, rainfall over the state and GWB increased after the change point.The short-term trends occurred before and after the change point might have counterbalanced the long-term trend.Our results of the short-term trend in annual rainfall corroborated the findings of Kundu and Mondal (2019).Likewise, the shortterm independent trend in monsoon rainfall was similar to the report of Chatterjee et al. (2016) for the state of West Bengal.The ongoing warming period which started around 1950 could be the possible reason for trend changes around 1960 and 1970.Warming of the Indian Ocean in recent periods might have influence on the increase in rainfall over GWB after the change point.The decreasing trend of rainfall over SHWB during the post-change period might be due to local factors such as micro-level topographical variations, massive deforestation, urbanization, and the associated change in the atmosphere.

Conclusions
The trend analysis of seasonal and annual rainfall by Mann-Kendall test statistics and Sen's slope estimator concluded that the spatiotemporal distribution of rainfall was drastically changed in West Bengal over the last 120 years.The significant increasing trend in annual and seasonal rainfall in the coastal districts of Gangetic West Bengal (annual: 1.8 mm year −1 to 2.9 mm year −1 , monsoon: 1.4 mm year −1 to 2.1 mm year −1 , and post-monsoon: 0.2 mm year −1 to 0.6 mm year −1 ) and western drier region (although non-significant) of West Bengal would be beneficial for rainwater harvesting and would help to overcome the water crisis and crop water stress in the regions.Moreover, the increasing trend over the coastal districts further raised the probability of flood, inundation, land erosion, water stagnation, and thus crop failure.The decreasing trend in pre-monsoon rainfall and increasing trend in post-monsoon rainfall over the districts of GWB indirectly indicated that the monsoon is being delayed on its arrival as well as its withdrawal, which has subsequent impacts on cropping cycles as well as the agricultural economy.An increase in the post-monsoon rainfall in every district of GWB might be detrimental to Kharif crop harvesting.On the other hand, most of the districts of SHWB showed a non-significant declining trend in annual as well as seasonal rainfall.The winter rainfall showed a clear reduction (0.1 mm year −1 ) over the entire state during the study period, which alarmed the water crisis during winter crop cultivation.Overall, a decrease in annual and seasonal rainfall across the districts increased the possibility of drier conditions and water scarcity.As a result, the agrarian economies as well as the livelihood of the resource-poor farming communities need to cope with the changing rainfall pattern vis-à-vis changing climate.The findings of this study will help in understanding the seasonal water budget, which is essential for devising crop planning, water security, and overall livelihood security of the resource-poor farmers of the state.

Fig. 5
Fig. 5 a-e Detection of change points in annual and seasonal rainfall of West Bengal during 1901-2020.Red line showed the forward U(t) and green line showed the backward U′(t) series of sequential Mann-Kendall test.Test done at significance level p<0.05

Fig. 6
Fig. 6 a-h Detection of change points in annual and seasonal rainfall of selected districts of West Bengal during 1901-2020.Red line showed the forward U(t) and green line showed the backward U′(t) series of sequential Mann-Kendall test.Test done at p<0.05 significance level

Table 1
Autocorrelation tests of both the annual and seasonal rainfall time series across the districts of West Bengal Critical limit of autocorrelation test is −0.1873<r 1 >0.1873 at p<0.05.Values beyond the critical limit marked in bold

Table 2
Descriptive statistics of rainfall distribution across the districts of West Bengal during 1901-2020