1 Introduction

Using widely available long-term monthly time series data, a great deal of effort has been done in the last three decades evaluating changes in monthly precipitation and mean maximum, minimum, and average temperature for so many parts of the world (e.g. Easterling et al. 1997; Peterson and Vose 1997; Hansen et al. 2001; New et al. 2001; Jones and Moberg 2003). Changes in monthly values, on the other hand, address only a small fraction of issues related to climate variability and climate change. Frequent changes in weather extremes have substantial impacts than alterations in average value. Moreover, shifts in anomalies can be potent markers of climate change, as it has been postulated that the hydrological cycle will be more active in a warming world in which the atmosphere can retain more water vapour (Folland et al. 2001). A “world—wide” evaluation of shifting climatic extremes published in 2002 (Frich et al. 2002) did not use data from Central or South America and only a tiny quantity from Africa and southern Asia. Different studies were conducted in all over the world by using monthly and daily data of both rainfall and temperature which revealed interesting results. Researchers conducted studies based on a set of parameters showing the increase in both precipitation and temperature in different parts of the world, e.g. central and northern South America (Aguilar et al. 2005), central and south Asia (Klein Tank et al. 2006), South America (Vincent et al. 2005), Canada (Vincent and Mekis 2006), southeast Asia and south Pacific (Manton et al. 2001), Western US (Hamlet et al. 2005), India (Pal and Al-Tabbaa 2010), South America (Haylock et al. 2006), Australia (Haylock and Nicholls 2000), Argentina (Rusticucci and Barrucand 2004), China (Zhai et al. 2005), South Asia (Gunnell 1997), and Caribbean region (Peterson et al. 2002). Furthermore, different patterns are observed in the study of Europe by Klein Tank and Konnen (2003). They investigated precipitation and temperature trends from 1946 to 1999 and divided the time period in two halves, i.e. 1946–1975 and 1976–1999. In the case of temperature, decrease in warm extremes was observed in first half but, in the second half, the increase in the rate of temperature doubled. Throughout the time period, precipitation showed an increasing trend over Europe. In his study, Frich et al. (2002) evaluated daily data and found that throughout the second half of the twentieth century, the worldwide land area was more affected by a major change in climatic extremes. Also, world patterns of precipitation and temperature were studied by Alexander et al. (2006) and found that over 70% of the land in the world exhibited a significant drop in annual cold night occurrence and a substantial increase in yearly warm nights. He also observed changes in precipitation and demonstrated widespread and dramatic increase in precipitation, but the changes were significantly less spatially coherent than the changes in temperature.

Apart from the above studies, several studies were also conducted on different coastal and mega cities all around the world. These studies measure the impact of rainfall variability on climate change. Some studies conducted by different scholars are Emery and Aubrey (1991), Roth (2000), Buytaert et al. (2006), Carrera-Hernandez and Gaskin (2007), McGranahan et al. (2007), Nicholls et al. (2008), World Bank (2010), and Hanson et al. (2011). Emery and Aubrey (1991) conducted the study by taking into account the parameters of glacial rebound and relative Sea Levels in Europe from Tide-Gauge records. The results of his study find that rise in sea level in different parts of the European coast due to melting of ice sheets as a result of atmospheric warming. Roth (2000) investigated more than fifty studies in his review of atmospheric turbulence over cities and reported that increasing tendencies in climatic extremes were observed in most of the studies. Also, Buytaert et al. (2006) and Carrera-Hernandez and Gaskin (2007) studied the spatio-temporal patterns of rainfall and temperature over south Ecuadorian Andes and Mexico Basin. The results of both the studies reveal that rainfall variability is extremely high especially in the case of mountain environment over Ecuadorian Andes. Apart from that, Nicholls et al. (2008), Hanson et al. (2011), and World Bank (2010) investigated the estimate exposure of the world’s large port cities with reference to climatic extremes. The results revealed that the most significant global drivers of the total rise in exposure, particularly in emerging nations where low-lying areas are urbanized, are population expansion, socio-economic growth, and urbanization. Furthermore, McGranahan et al. (2007) signify the assessment of the Impacts of Climate Change and Human Settlements in Low Elevation Coastal Zones. This study reveals that they carry out the first global analysis of the population and urban settlement patterns in the Low Elevation Coastal Zone (LECZ), which is here defined as the continuous area along the coast that is less than 10 m above sea level. This region is home to 10% of the world’s population and 13% of the world’s urban population, although only making up 2% of the world’s land area. Also, different researchers analyze the spatio-temporal patterns of precipitation. For example, Liuzzo et al. (2015) conducted a deep investigation of rainfall patterns over Sicily from 1921 to 2012. Data on precipitation showed that Sicily experienced a general decline in precipitation from 1921 to 2012. During the fall and winter, downward trends were prevalent. However, between 1981 and 2012, there was a discernible rise in the amount of precipitation that fell annually. Recent temporal trends of precipitation and temperature over Langat River Basin, Selangor, Malaysia, is studied by Amirabadizadeh et al. (2015). The analytical findings showed that, while there were increasing and decreasing trends in the annual and seasonal precipitation and temperature, only the increasing trends were significant at the 95% confidence level. The relationship of rainfall and river discharge variations over Southwestern Iran from 1956 to 2012 was studied by Sabzevari et al. (2015). The results of the precipitation time series showed that the majority of the stations had insignificant trends in both the annual and monthly series. When discharge trends were analyzed, it was discovered that both the annual and the October through April series had a significant rise. Interestingly, monthly precipitation trends over Iran (Khalili et al. 2015; Asakereh 2016) and modelling of monthly rainfall and runoff relationship over Urmia Lake Basin, Iran, were studied by Farajzadeh et al. (2014) and Fathian et al. (2016). The results of the PCI index showed a significant increasing trend in the data, indicating significant increase of precipitation concentration abnormalities all over Iran. Whereas the amount of annual precipitation declined from southwest to northeast, it was concentrated in the southwest and in mountainous areas. However, the temporal trends in precipitation over Urmia Lake Basin demonstrated that over the basin, both increasing and decreasing patterns were apparent at all-time scales. Also, spatial patterns of rainfall over Bangladesh and Greece were studied by Bari et al. (2016) and Markonis et al. (2016) respectively. Spatio-temporal trends of rainfall over Bangladesh exhibited declining trend in annual rainfall values over western, north-western, south-central, south-western, north-eastern, and northern part of northern region whereas rising trend is found only in south-eastern region. In the case of Greece, trends in rainfall exhibit an increasing trend.

Heavy rainfall has serious ramifications for modern civilization. Changes in the severity and frequency of weather extremes will most likely be felt as a result of climate change (Sarker 1966; Venkatesh and Jose 2007; Dhorde et al. 2009; Ratna 2012). As per studies, anthropogenic activities have contributed to a rise in atmospheric greenhouse gas concentrations, which has resulted in the strengthening of heavy rainfall events (Bussières and Hogg 1989; Kulkarni and Reddy 1994; Narkhedkar et al. 2006; Kothawale et al. 2010). Across different locations round the world, the severity of heavy rainfall events is poised to increase as a result of global warming (Ashrit et al. 2001), even in locations where average rainfall is decreasing (e.g. Semenov and Bengtsson 2002; Wilby and Wigley 2002). Thus, as a result of these high rainfall events, it is imperative to understand the associated hydrological risk that helps in building of urban infrastructure designs (Ramachandran and Banerjee 1983; Korade and Dhorde 2016). Indian economy is primarily based on agriculture. Therefore, assessing the variability of rainfall across India is really a significant task. Many studies in this regard are conducted by different researchers, particularly dealing with spatio-temporal patterns of rainfall and temperature in different states across India (Mondal et al. 2015, 2018; Chandniha et al. 2016; Jin and Wang 2017; Prabhakar et al. 2017; Nema et al. 2018; Warwade et al. 2018; Pal et al. 2019; Pillai et al. 2019). These studies basically address the trends and patterns of precipitation with reference to climate change. Since majority of the population lives in cities, a change in extreme storm events might have a significant influence on India’s booming economy. Since the turn of the twentieth century, several researchers have examined rainfall trends in India. Parthasarathy et al. (1993), Roy and Balling (2004), and Rana et al. (2012), among several others, have explored the long-term tendencies in southwest monsoon over India. Long-term trends show a significant decline in the probability of moderate-to-heavy rainfall events in most parts of India (e.g. Naidu et al. 1999; Dash et al. 2009). This is endorsed by a considerable rise in the incidence and intensity of monsoon breaks over India in past few decades (Kripalani et al. 2003; Ramesh Kumar et al. 2009; Turner and Hannachi 2010), and perhaps an increased prevalence of heavy rainfall events (100 mm/day) in certain parts of the state (Gadgil 1986; Goswami et al. 2006). Scientific research for India based on climatic model simulations implies that greenhouse gas–induced climate change will substantially boost monsoon rainfall across a vast region spanning South Asia (e.g. Lal et al. 2000; May 2002, 2004, 2011; Rupakumar et al. 2006). However, due to substantial discrepancies in model projections, accurate projection of future developments in regional monsoon rainfall has raised questions (e.g. Kumar et al. 2011; Sabade et al. 2011). Models based on climate show that the reaction of rainfall to global warming is coupled with a reduction in southwest monsoon (e.g. Kripalani et al. 2003; Ueda et al. 2006; Sabade et al. 2011; Krishnan et al. 2013; Stowasser et al. 2009). Nevertheless, Rupakumar et al. (2006) evaluated the consequences of climate change in India by reviewing the PRECIS climate model by using present-day simulation (1961–1990) and found that a slight increase in intense rainfall events along the west coast (Patwardhan and Asnani 2000; Tawde and Singh 2015) and western regions of central India.

Multiple researchers have examined Mumbai’s vulnerability to long-term climate scenarios. Increase in anthropogenic activities and greenhouse gases may exacerbate the problem of urbanization pressures in the coming decades. Bohra et al. (2006), Ranger et al. (2011), and Hallegatte et al. (2013) painted a bleak image of Mumbai flooding and the associated financial damage during the floods of 26 July 2005, and then went on to examine the problem in possible conditions. The interplay of multispectral weather systems with macro-scale coastal land-surface features, as well as inadequate rainfall size, extent, and intensity predictions by existing weather-forecast models, may be the root causes of such rainfall vagaries (Jenamani et al. 2006; Shyamala and Bhadram 2006; Lei et al. 2008; Chang et al. 2009; Zope et al. 2015). They hypothesized that the development of a macro level vortex over Mumbai and the interplay of multi-temporal weather systems with meso-scale coastal land-surface features contributed to the intensification of this extremely confined rain event. Following the occurrence of the heavy rain event on 26 July, IMD in Mumbai realized how inadequate it was to have only two rainfall-recording meteorological stations (at Santacruz and Colaba). In order to record the spatial pattern of rainfall in Mumbai, the Municipal Corporation of Greater Mumbai (here after uses as MCGM) planned to establish 26 rain gauging stations in the city in 2006 which later increased to 60 (MCGM 2007; Lokanadham et al. 2009).

For rainfall events exceeding 25 mm/h, Nikam and Gupta (2013) developed a forecasting methodology that combined the probabilistic global search-Lausanne (PGSL) and least-squares support vector machine (LS-SVM) techniques. However, this method was unable to clearly capture spatio-temporal variability. Furthermore, efforts have been made to estimate the rainfall design for Mumbai along with such studies on rainfall forecasting. Sen et al. (2013) used 43 years (1969–2012) of rainfall data in Mumbai to perform at-site design storm estimation for two rain gauge stations (Santacruz and Colaba) in order to quantify its spatio-temporal variability. Using the same dataset, Sherly et al. (2015) proposed a methodology for rainfall design and estimation using a multivariate semi-parametric approach. The present research work is one of the few studies that use data from Indian Meteorological Department (IMD), disaster department, and MCGM to evaluate the rainfall variability and possible impacts of heavy storm events in the study area. Such potential consequences might have major ramifications for Mumbai, i.e. India’s financial capital. Throughout this investigation, it was examined that how in the metropolis of Greater Mumbai (consists of city and sub-urban district), deviations in rainfall dataset have changed as a result of climate change. Therefore, the main objective of the present research work is to apply various statistical tests in order to understand the behaviour of rainfall trends and extreme events.

2 Study area

In Western Ghats, Mumbai is among the most prominent megacity and a big coastline (Fig. 1). It spans from 18°53′N to 19°160′N latitude, and from 72°E to 72°59′E longitude, covering an area of 471.9 sq. km. Mumbai is the world’s fifth most populous megacity, with a population density of 4445 people per square kilometer (Census of India 2011; United Nations 2012). In the metropolitan city of Mumbai, prominent geomorphological features are also found like rivers, water bodies, canals, creeks, linear ridges, terrestrial harbours, and coastal lowlands. Peninsular Mumbai is known for its numerous medium and small islands, reclamation sites, and drainage features. The Creek of Thane in the east and the Arabian Sea in the west define the city of Mumbai on India’s western coast. During the southwest monsoon, the area receives an average rainfall of about 253.3 cm of rain per year (1990–2015), with July and August accounting for almost 90% of this total. The annual mean temperature remains between 27.2 and 28.8° C and the city’s relative humidity ranges from 54.5 to 85.5% (IMD 2007). The Mumbai city’s tidal height ranges around 1.8 to 3.5 m. Tidal flushing in the city’s lower reaches is a sign of rising sea levels (GRB Report 2006, 2013). Forests, mangroves, wetlands, and lakes are all part of the city’s natural landscape. In the study area, coastal mangroves and wetlands have a key role in preventing coastal erosion (Dahdouh-Guebas et al. 2005; GRB Report 2006; Pacione 2006).

Fig. 1
figure 1

Locational map of the study area along with its rain gauge stations

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3 Database and methodology

3.1 Data collection and composition

Hourly data of rainfall and temperature for 2 stations, i.e. Colaba and Santacruz setup by IMD, which represent the city district and sub-urban district respectively, are used in the present study (1985–2020). Later, a dense network of rain gauge stations (60 stations at present) was set up by Disaster Department, MCGM after the heavy storm event of 26 Jul, 2005. The current study selects a total of 23 stations out of 60 (MCGM 2007) and use data that was obtained from MCGM (2006–2020). The stations are selected by using a distance matrix tool in ARC GIS 10.9. The dense network of selected stations is shown in Fig. 1.

General information of each selected station like coordinates, mean annual rainfall, annual maximum, and minimum rainfall with their respective years is shown in Table 1. Also, station-wise general information based on daily statistics like daily maximum rainfall with their respective year, SD, and CV is shown in Table 2. The climate data were subjected to trend analysis after homogeneity and homogenization were checked. Monthly, seasonal, and annual time series are created by averaging daily values. The IMD has designated four seasons: (a) winter (January–February), (b) pre-monsoon (March–May), (c) monsoon (June–September), and (d) post-monsoon (October–December). Though this paper primarily focuses on rainfall variability and extreme events, analysis of temperature has also been carried out as both rainfall and temperature are co-related to each other.

Table 1 General information of Selected Stations in the study area based on annual statistics (2006–2020)
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Table 2 General information of selected stations in the study area based on daily statistic of monsoon season (2006–2020)
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3.2 Methodology

For each station, appropriate statistical methodologies such as summation, average, percentage, standard deviation (SD), coefficient of variation (CV), skewness (Cs), kurtosis (Ck), and moving average were performed. The extreme storm event was then estimated using the procedure outlined below.

3.2.1 Identification of heavy and extreme heavy rainfall events

To examine rainfall climatology and analyze various categories of extreme rainfall events, criteria given by IMD were used, which are as follows: very light rainfall (VLR), light rainfall (LR), moderate rainfall (MR), heavy rainfall (HR), very heavy rainfall (VHR), and extremely heavy rainfall (EHR). Table 3 depicts different rainfall intensity ranges for various IMD-classified rainfall events. In this study, extreme rainfall event is categorized as very heavy (115.6–204.4 mm/day) and extremely heavy (> 204.5 mm/day) based on the rainfall intensity and IMD criteria of defining heavy rainfall events. Very heavy and extremely heavy rainfall events are calculated by taking into account the highest rainfall in a year on a certain day. The list of very heavy and extremely heavy rainfall events is calculated manually by the authors.

Table 3 Various categories of rainfall events and respective rainfall intensity ranges as defined by India Meteorological Department (IMD)
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3.2.2 Trend detection

To discover the trends in rainfall and temperature datasets, statistical approaches such as the Mann–Kendall test (Mann 1945; Kendall 1948), Sen’s slope estimator (Sen 1968), and simple linear regression were applied. The non-parametric rank-based Mann–Kendall is an outstanding tool for determining trends in time series data at various meaningful intervals (Singh et al. 2015). The trend and its significance level are determined using the standard normal variable Z. Positive Z values indicate an upward trend, whereas negative ones indicate downward trend. The value of Z for a 95% confidence level of 1.96 was used in the current study. When the value of Z in both the rainfall time series is greater than 1.96, it indicates a substantial increasing or decreasing trend. The current study uses Sen’s slope estimator to determine the trend’s intensity. If a dataset has a linear trend, the slope of the trend (change per unit time) can be correctly predicted (Sen 1968). The trend in a temporal dataset is also detected by using parametric simple linear regression. The approaches outlined above are commonly utilized in hydro-meteorological investigations to discover trends.

3.2.3 Homogeneity analysis

There are different ways to evaluate the inhomogeneity or abrupt change point in a data series. These techniques can be broadly divided into relative and absolute (Yang et al. 2018). The inhomogeneity of the dataset is separately evaluated using the absolute methods across each station without taking data from neighbouring stations into account. Through the use of neighbouring station data, inhomogeneity within a time series is found by using relative approach (Ahmed et al. 2018; Ahmed et al. 2021). Comparing the spatial and temporal variation of chosen series to the nearby series reveals that the relative approach is more trustworthy. Despite the fact that relative approach is the more effective, Yozgatligil and Yazici (2016) suggested that their effectiveness is highly dependent on the caliber of the data from the nearby stations. Additionally, relative techniques are inappropriate for the region where stations are spaced. However, each station has a different topography and environment, making it challenging to identify a strong relationship with other stations. So, wherever possible, absolute procedures are preferred against relative ones. Finding the best absolute homogeneity strategy for a given situation is never easy because there are so many different options available. Since each approach has merits and demerits. Therefore, using a variety of techniques to check the homogeneity or abrupt change point of data for a particular area is generally advised (Singh et al. 2019). Detecting abrupt change point in a time series is critical for determining the period during which significant change occurred. The next sections go through the specifics of many abrupt change point detection tests used in the study.

Pettitt’s test

The non-parametric Pettitt’s test is helpful in detecting sudden change in a time series dataset (Winingaard et al. 2003). It also detects a big shift in the mean of a time series when the period of the alteration is uncertain. If x1, x2, x3,…, xn is actually a series of observable data with a deviation at t, then x1, x2, x3,…, xt have a distribution function F1(x) that differs from the distribution function F2(x) of the second segment of the series xt +1, xt+2, xt+3,…, xn, then Pettitt’s (1979) test is true. The mathematical expression for this test statistic (Ut) is:

$${U}_{t}=\sum_{i=1}^{t}\sum_{j=t+1}^{n}\mathrm{sgn}({x}_{i}-{x}_{j})$$
(1)
$$\mathrm{sgn}\left({x}_{i}-{x}_{j}\right)=\left\{\begin{array}{ccc}+1, \mathrm{if}& {(x}_{i}{-x}_{j})& >0\\ 0, \mathrm{if}& {(x}_{i}-{x}_{j})& =0\\ -1, \mathrm{if} & {(x}_{i}-{x}_{j})& <0\end{array}\right\}$$
(2)

where xi signifies date value at time i.

For the sample length (n), the test statistic K and the accompanying confidence level (q) can be defined as:

$$K=\mathrm{Max}\left|{U}_{t}\right|$$
(3)
$$p=\mathrm{exp}(\frac{-K}{{n}^{2}- {n}^{3}})$$
(4)

Whenever q is below the specified confidence threshold, null hypothesis is rejected. The projected significance probability (P) for a change point is defined as:

$$P=1-p$$
(5)

where there is a significant dramatic change point, the series is clearly separated into two sub-series at that time. At various confidence levels, the test statistic K can be compared to the corresponding statistic for detecting a transition point in a time series. This test is commonly used to detect changes in hydrological and climatological investigations (Zhang et al. 2008; Guerreiro et al. 2014).

Standard normal homogeneity (SNH) test

The time series (Tt) is separated into two portions for the SNH test (Alexandersson 1986), one from 1 to t years (z1) and the second from t to n—t years (z2). Then, by using following mathematical statement, the averages of these two series are compared:

$${T}_{t}=t{z}_{1}^{2}+(n-1){z}_{2}^{2}$$
(6)

where z1 and z2 are calculated as follows:

$${z}_{1}=\frac{1}{t}\sum_{i=1}^{t}\frac{{(x}_{i}-\overline{x })}{\sigma x}$$
(7)
$${z}_{2}=\frac{1}{n-1}\sum_{i=t+1}^{n}\frac{{(x}_{i}-\overline{x })}{\sigma x}$$
(8)

where the standard deviation and mean of the time series are \(\sigma x\) and \(\overline{x }\) respectively. The year t is a turning point, with a break where the value of Tt reaches its highest peak. The test statistic must be greater than the crucial value to reject the null hypothesis, which is determined by the sample size (n).

Buishand range test

This is indeed a non-parametric test that can be used with variables of any distribution (Buishand 1982). The observed time series are thought to be distinct of one another. The test statistic Bt is calculated as follows:

$${B}_{t}=\sum_{i=1}^{t}({x}_{i}-\overline{x })$$
(9)

Even though the time series is evenly distributed around its average value on both sides of the mean series, it can be homogenous without any change points if Bt = 0. The rescaled adjusted range (R) can be used to determine the importance of the shift.

$$R=\frac{\mathrm{Max}\left({B}_{t}\right)-\mathrm{Min}({B}_{t})}{\overline{x} }$$
(10)

Von Neumann ratio test

This test detects heterogeneity in any time series that is not expressed as a tight stepwise shift. Furthermore, Jaiswal et al. (2015) found that this test is highly related to the first-order serial correlation coefficient. The parameter Ne of the test is expressed as the time series variance divided by the mean square successive difference and is denoted as:-

$${N}_{e}=\frac{\sum_{i=1}^{n-1}({x}_{i}-{x}_{i-1})}{\sum_{i=1}^{n}({x}_{i}-\overline{x })}$$
(11)

Following the Winingaard et al. (2003) technique, rainfall and temperature data series of a station are classified as homogenous (no change point) if none or one of the four tests contradicts the null hypothesis at a 5% significant level. If two out of four tests reject the null hypothesis at a 5% significant level, a station’s rainfall and temperature time series is considered heterogeneous (doubtful), and if more than two tests reject the null hypothesis at a 5% significant level, the rainfall all over Mumbai is considered heterogeneous. Various research papers suggest that Pettitt’s test is more reliable in detection of abrupt change point in a data series.

4 Results and discussion

4.1 Annual analysis

For the entire duration of time-series data, Table 1 shows the distribution of climatological mean, maximum, and minimum rainfall. Dataset exhibits the maximum rainfall (2306.55 mm) over Santacruz and the minimum rainfall (1717.55 mm) over Gowalia, with SD values ranging from 388.05 to 564.61 mm. Furthermore, the year 2020 has recorded the highest rainfall (3721.99 mm) and the least in 2015 (1005.46 mm). It was observed, the years 2007, 2011, and 2020 are the years of maximum rainfall and 1986, 2002, 2015, and 2018 were the years of minimum rainfall. It is clearly seen from the analysis that the rainfall deficit years coincide with the El Nino years. Both CS and CK are the indicators of data flatness, unevenness, distortedness, symmetry (or, more correctly, lack of symmetry), and their values for a normal data distribution are close to zero. In a normal distribution, CK determines whether data is heavy-tailed or light-tailed, whereas CS determines whether a dataset is symmetric or asymmetric. Santacruz and Colaba stations in the study area have high CK, but Mulund has a low CK. Except for Colaba and Santacruz, all of the stations show a negative CS, indicating that rainfall is falling over the rest of the stations while increasing over Colaba and Santacruz.

The spatial distribution of normal annual rainfall and CV from 1985 to 2020 is constructed (Fig. 2a, b). The map shows that rainfall has little variations in its spatial distribution. It is high over Santacruz and BMC stations and low over Bandra, Dharavi, Dadar, Worli, Byculla, Memonwada, and Gowalia (Fig. 2a). In the case of CV, the values are high in city and northern part and low over Colaba, Santacruz, and BMC stations (Fig. 2b). As per Hare (2003), CV is being used to categorize rainfall occurrences into three categories: low (CV < 20), moderate (20 < CV < 30), and high (CV > 30). According to the above-cited paper, the study area falls in the moderate variability zone. The CV values in the study area decrease around Santacruz and BMC station, indicating that variability is high in the rest of Mumbai. Its proportions drop from 27.91% in Dahisar to 21.25% in BMC (Fig. 2b). Figures 3 and 4 show the distribution of rainfall and average annual temperature over the stations that are setup by BMC. From the bar and line graphs, it is clearly seen that rainfall has decreased in all stations, whereas it has increased over Santacruz and Colaba (Fig. 5). Apart from this, the temperature values have also increased. This differential behaviour of monsoon around Mumbai is influenced by variety of factors like the impact of Western Ghats or Sahyadri Mountains (which stretch across the states of Maharashtra, Karnataka, and Kerala) on monsoon winds around Mumbai. When the Somali Jet, which are powerful winds of the southwest monsoon, carrying moist air from the Arabian Sea collides with the Western Ghats, they are orographically lifted (Jenamani et al. 2006). A number of other phenomena, such as the existence of a meso-scale offshore vortex over the northeast Arabian Sea and the north-westward passage of low-pressure systems from the Bay of Bengal via the monsoon trough, also contribute to this erratic behaviour of monsoon in and area around Mumbai. The heavy rainfall event on July 26, 2005, in Mumbai clearly proves that variability in rainfall is high as rainfall values across different stations are highly variable. This intensely localized rainfall event that occurred over a 24-h period in several parts of Mumbai suburbs {Santacruz (94 cm), Bhandup (81 cm), Dharavi (49), Vihar Lake (104 cm), Malabar Hill (7 cm), and Colaba (7 cm)} clearly demonstrated great spatial variability (Bohra et al. 2006). Also, the interplay of synoptic-scale weather systems with meso-scale coastal land-surface features, as well as inadequate rainfall size, extent, and intensity predictions by current weather-forecast models, may be the root causes of such rainfall vagaries. Furthermore, Nayak and Ghosh (2013) discovered that the high-speed wind flowing from the Arabian Sea brings surplus moisture which reduces away from the coastline was one of the important causes for the occurrence of this differential behaviour of excessive rainfall on the west coast. Also, normal annual rainfall and temperature over Santacruz and Colaba are shown in Fig. 5. Normal annual rainfall over the study area follows the cyclic pattern of 5-year moving average over both the stations. Also, temperature shows rising trend over the time period (1985–2020). The detection of trends in the study area is computed by employing MK test and Sen’s slope estimator. The test shows that rainfall is increasing at the rate of 22.081 mm/year at 95% confidence level (Table 4). Also, it is clearly seen from the slope value (R = 0.22) calculated by using regression analysis that rainfall is increasing all over the study area. Furthermore, the value of Ck is 0.64 which also suggests that the rainfall over the study area as a whole has increased. The detection of trends in annual rainfall by using simple linear regression is shown in Fig. 6. Thus, from the above analysis, it was observed that though the rainfall over the study is highly erratic it has registered an increasing trend over the time period (1985–2020).

Fig. 2
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Spatial distribution of a normal annual rainfall and b coefficient of variation over the study area (1985–2020)

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Fig. 3
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Station-wise trends of average annual rainfall over the study area (2006–2020)

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Fig. 4
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Station-wise trends of average annual temperature over the study area (2006–2020)

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Fig. 5
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Average annual rainfall and temperature over a Santacruz and c Colaba (1985–2020)

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Table 4 Mean (M), standard deviation (SD), coefficient of variation (CV), kurtosis (CK), skewness (CS), Mann–Kendall test (Z), Sen’s slope estimator (Q), and regression (R) of monthly, seasonal, and annual rainfall over Mumbai based on the combined rainfall data of Colaba and Santacruz (1985–2020)
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Fig. 6
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Trends in average annual rainfall and temperature over the study area using regression analysis (1985–2020)

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4.1.1 Extreme rainfall events

The events of annual maximum rainfall of different intensities over the study area are categorized using the scheme of IMD mentioned in Table 3. In the present study, events only under two categories are considered that are very heavy and extremely heavy. A heavy rainfall event is defined when rainfall values range between 115.6 and 204.4 mm/day and extremely heavy for rainfall that exceeds 204.05 mm/day in accordance with the rainfall patterns over the study area. The intensities of both the categories of events over Santacruz and Colaba are shown in Fig. 7. From the bar graphs of the said station, it is clearly seen that the intensities of both the categories of events increased after 1994 in the case of Santacruz and in the case of Colaba after 2005. However, rainfall events of immensely high intensity are observed over Santacruz in 2005 having rainfall over 944 mm/day and in 2011 over Colaba having rainfall over 1058 mm/day. The events of 2005 are responsible for the flood havoc over Mumbai. The 2005 flood event caused extensive damage to Mumbai and surrounding areas. Mumbai Metropolitan Region (MMR) authorities reported 700 deaths, 244,110 houses destroyed or partially damaged, 97 collapsed school buildings, 5667 damaged electricity transformers, together with vehicular losses to national highways and transportation systems (52 broken local trains, 41,000 taxi cabs, 900 buses, 10,000 trucks). Trade and commerce suffered losses of 50 billion U.S. dollars (5000 cores) (Government of Maharashtra 2005; FFCMF 2006).

Fig. 7
figure 7

Heavy and extreme heavy rainfall events over Santacruz and Colaba (1985–2020)

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4.1.2 Change point detection

As it is difficult to determine which strategy is best for a given area and as each method has upsides and downsides, it is usually advised to use a variety of techniques to check the homogeneity and change points of data for a certain area. Therefore, four distinct tests, i.e. Pettitt’s, SNH, Buishand range, and von Neumann ratio, have been used in this section to detect the abrupt change points in rainfall and temperature datasets. Table 5 illustrates the test statistics for these tests, as well as the null hypothesis acceptance or rejection in rainfall and temperature data series. Figures 8 and 9 depict the graphical representations of rainfall and temperature time series over Colaba and Santacruz with the most important positive (increasing) trends from 1985 to 2020 with their respective change points. The current variations in rainfall trend, major mechanisms, and inter-annual variability of Indian summer monsoon rainfall (ISMR) are explored in this study during the period 1985–2020. Rainfall data revealed a downward tendency from 1985 to 2005 (period 1), then a strong upward trend from 2006 to 2020 (period 2). The abrupt change point in rainfall time series is observed only over Santacruz station and the change point in the data series starts from 2005 whereas at the rest of the stations, no change point was detected in the data series. In the case of temperature dataset, change point detection is observed from 2001 onwards over Colaba and Santacruz (Fig. 9). The study reveals that two significant changes in the second period are likely to be the cause of ISMR’s current upward trend. The first is increasing easterly wind anomalies from the equatorial Pacific, which are linked to recent cooling in the eastern Pacific; the second is enhanced cross-equatorial flow in the Indian Ocean, which is linked to increased land-sea thermal contrast. The main mode of ISMR variability and temperature increase during the second period, and the relationship with boundary forcing became stronger. After 2000, the first mode of ISMR became substantially linked to central and east Pacific SST anomalies (El-nino Southern Oscillation (ENSO)), but its relationship with key SST indices was weak before. Significant warming in the temperature record after the year 2001 was observed in the second phase, which is strongly linked to the Indian Ocean Dipole mode. During both periods, these modes represent the inter-annual variability of ISMR, which increases significantly in the second. Another noteworthy difference between the two periods is that many of the severe monsoon events during period 1 were not related to ENSO, but many during period 2 were (Devika and Pillai 2020). The result of all the three tests in the case of temperature time series shows change in the dataset from 2001 onwards. Both for rainfall and temperature, the study findings of change points from three distinct tests of homogeneity detection closely confirm each other at 99 and 95% significance levels. It is discovered that the von Neumann ratio test findings cannot be evaluated because it provides results for both positive and negative change points.

Table 5 Results of abrupt change point analysis for rainfall and temperature over Mumbai 1985–2020
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Fig. 8
figure 8

Abrupt change point detection in rainfall time series data over Santacruz by using different tests (1985–2020)

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Fig. 9
figure 9

Abrupt change point detection in temperature time series data over Santacruz and Colaba by using different tests (1985–2020)

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4.2 Seasonal analysis

The seasonal description of different determinants is given in Table 4. For that, rainfall data of two stations (Colaba and Santacruz) are merged and analyses are performed. It is done because of the discontinuity (or later setup of rain gauge stations by MCGM after the flood event of 2005) of the dataset of remaining 23 stations. Average annual rainfall in the monsoon season is about 2081.53 mm having SD values ranging from 20.95 to 123.96 mm. The value of R (regression) is also high in the month of monsoon which shows that the rate of increase in rainfall is high. The graphical representation of rainfall by using linear regression is shown in Fig. 10. It shows that the rainfall in all seasons is increasing but the gradient or slope of change is high in monsoon season only. Furthermore, spatial distribution of seasonal rainfall all over the study area is shown in Fig. 11. It shows that in the winter season, rainfall is high over Santacruz station and low over the southern tip of Mumbai city, i.e. Colaba. The contrasting nature of ISMR is clearly seen in the rainfall distribution map of monsoon season, i.e. high rainfall over Colaba, Bandra, and Santacruz station and low over Mulund and Bhandup camp. A different trend in rainfall is observed in pre- and post-monsoon seasons. In post-monsoon season, rainfall all over the study area is high except over Colaba and Santacruz, i.e. areas of high rainfall in monsoon are the areas of low rainfall in post-monsoon season. An opposite trend is observed in pre-monsoon season. The values of CV are highest in the month.

Fig. 10
figure 10

Seasonal rainfall trend over the study area using regression analysis (1985–2020)

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Fig. 11
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Spatial distribution of seasonal rainfall over the study area (1985–2020)

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of winter (481.97%) because winter season is not a rainfall season whereas CV in monsoon season is 23.82%. Thus, we can say that the study area lies in moderate variability zone. Interestingly, about 95% of total rainfall occurs in monsoon season and rest of the seasons only receives about 5% of total rainfall. The change in rainfall trends is calculated using MK statistic and the value of Z signifies the level of significant change in the data series. The Z statistic shows that rainfall shows an increasing trend only in monsoon season which is at the rate of 5.177 mm/year at 99% significance level (Table 4).

4.3 Monthly analysis

In this section also, only two stations (Colaba and Santacruz) are included in the analyses because of the discontinuity of the dataset. CV was calculated and reported in Table 4 to better understand the variability of mean monthly rainfall over the study area. (Standard deviation/mean) * 100 were used to determine the CV. CV during different months is depicted in this table. Rainfall seems to be highly variable over the entire study area, having CV values ranging from 42.43% in July to 574.5% (in February). This illustrates the complexities of rainfall patterns in the studied area. The average monthly rainfall ranges from 0.56 mm in January to 752.75 mm in July. Thus, it is clearly seen from the discussion that July is the month of heavy rainfall over the entire study area. Similarly, the value of CV is high in the active monsoon month of September which is 66.68%. The rainfall behaviour is highly erratic as we look at the SD value that ranges between 1.47 and 319.37 mm. Furthermore, it is clearly seen in the table that about 80% of annual rainfall has occurred only in 3 months, i.e. June, July, and August. The value of Z statistic or MK test signifies that change in rainfall was observed only in the months of July and November. It is increasing at the rate of 14.95 mm/year in July (at 99% confidence level) and 0.018 mm/year in November (at 95% confidence level). Furthermore, the spatial distribution pattern of monthly rainfall is shown in Fig. 12. It clearly shows that the distribution of monthly rainfall is furcating, as one moves from northeast to southwest.

Fig. 12
figure 12

Spatial distribution of monthly rainfall over the study area (1985–2020)

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5 Conclusion

A detailed assessment of hourly rainfall at 2 rain gauge stations spread through two districts of Maharashtra (Mumbai city and sub-urban), India, spanning for 36-year period between 1985 and 2020 was carried out. Distance matrix tool in ArcGIS is used to pick distinct stations. Many rainfall datasets have been accessible in recent years, but in this study, an hourly rainfall analysis across Greater Mumbai utilizing a dense network of 23 rain gauge stations from MCGM for the last 15 years (2006–2020) is also performed. The aspects examined are rainfall’s climatological behaviour, its variability, and extreme events over Mumbai, as well as a detailed analysis of different severe event intensities. Using datasets for rainfall amounts, CV, maximum daily rainfall, rainfall intensity, abrupt change point detection in rainfall and temperature time series, monthly and seasonal climatology for each rain gauge station have been derived.

The spatial patterns of rainfall revealed that the rainfall is primarily concentrated near Colaba and Santacruz stations. Total rainfall over central Mumbai is high, and it falls across a vast area from June to September. The rainfall is high during the active monsoon months and is low during the onset and retreating phase of the monsoon. Rainfall distribution of annual rainfall over the study area shows more than 2600 mm over Santacruz and 2000–2400 mm in rest of the stations of the study area. This suggests that rainfall patterns are highly variable in terms of both geographical and temporal variability across the whole study area. Rainfall is steadily decreasing from central Mumbai to eastern Mumbai (areas near Mulund, Tulsi, BMC, Vikhroli, and other stations). The Arabian Sea branch of the monsoon influences the entire study region, which receives 2208.82 mm of rainfall. The spatial distribution of climatological rainfall suggests that the southern and western areas of Mumbai receive higher rainfall. The eastern and northern parts of Mumbai get less rain than rest of the city. The rainfall is highly variable across the entire study area, demonstrating the complexities of rainfall occurrence across Mumbai. The study area falls in the moderate variability zone. CV values in the study area decrease around Santacruz and BMC station, indicating high variability in rest of Mumbai. Its proportions drop from 27.91% in Dahisar to 21.25% in BMC. The results of abrupt change point detection indicate that rainfall has been increasing significantly after 2005 only over Santacruz station (in accordance with Pettitt’s and Buishand test) whereas, in the case of temperature, the point of change in data series is observed after 2001 over Colaba and Santacruz in all four tests. The rest of the stations show no significant changes in the time series data. Santacruz station has the highest number and intensity of extreme incidents, followed by Colaba. The rest of the stations, on the other hand, have not seen much rain in the study area. In comparison to July and August, extreme events are lower in June and September because June is the onset month, September is the withdrawal month, and July and August are the active monsoon months over the study area. Moreover, it is observed that rainfall has increased over Santacruz and Colaba during July and August. Both heavy and extremely heavy rainfall events have also increased in the study area. In the case of Santacruz, increase has been observed after 1994 while over Colaba it has been observed after 2005.

It is usually observed that the rains cripple the daily activities of people in Mumbai city hampering the industrial and tertiary services. The lifeline of Mumbai city, the local trains, their services are also affected with greater intensity during a wet spell. Increase in the heavy and extremely heavy events over Mumbai has thrown a greater challenge for the city administration. The work further calls upon demarcation of low-lying area with respect to their vulnerability of floods during heavy rains so as to identify areas for better management of flood waters, particularly during Monsoon season. Despite the fact that this work is limited to 15 years of data from 23 stations and 36 years of data from two stations from the recent time, it throws light on the spatial variation of rainfall over the area. As the length of datasets from these new stations will increase, more details of the rainfall climatology will be available to the administrators.

The findings of this study strongly imply that extreme weather events and variability of rainfall have an impact on the surrogate observations that are the subject of this investigation. Furthermore, considering that temperature trends have the greatest impact on rainfall trends, we should anticipate that these trends will persist given the predictions of further increase in extreme rainfall events in the near future. The use of rainfall variability in accordance with scenarios of extreme events may currently be the best strategy for understanding the overall effects of climate change on the rainfall behaviour along the west coast of India because rainfall variability seems most strongly associated with decadal variability rather than long-term trends. Such a strategy also means that “rainfall variability” and “extreme events” are likely to happen in the future at different locations, and MCGM authorities must take these possibilities into account when testing alternate management plans for Mumbai.