Introduction

The water availability in any area is largely determined by the amount of precipitation that occurs in that area (Gadgil 2003). This reflects the significance of rainfall in countries like India which is based on rain-fed farming. This fact intrigued us to study spatiotemporally seasonal rainfall variation, related to the monsoon classification (Gadgil 2003). This study has a significant impact on agriculture and in turn the economy of India. Agriculture occupies a significant place in the economy of India (Rajeevan et al. 2006). The summer monsoon rainfall in India occurs from June to September and is based on the average weightage of 306 well-distributed rain gauge stations throughout the country (Parthasarathy et al. 1992, 1995) except the rainfall occurring in the east coast of the southern peninsula during October–November (Kothawale and Rajeevan 2017). The Indian monsoon rainfall largely gets effected by jet streams, cyclonic storms, Indian Ocean Dipole, Tibetan Plateau, El Niño, monsoon trough, and mid troposphere cyclones (Krishnamurthy and Kinter III 2002).

Temperature, as one of the factors, changes throughout the vertical as well as across the horizontal surface of the earth, which further affects the climatic conditions throughout the globe (Basist and Chelliah 1997; Esau et al. 2013; Alexeev et al. 2011). This varying temperature of the Earth’s atmosphere is also believed to be the primary cause for climatic variations and another major factor for determining precipitation rate (Krishnamurthy and Kinter III 2002). Emission of greenhouse gasses with increasing population is causing global warming which increases the Earth temperature by ~ 1 °C (from 1880 to 2005); this results in a rise in sea level and hence the extermination of species (Hansen et al. 2006; Mann and Jones 2003; Jones et al. 1999). Vertical status of temperature particularly at the stratosphere and troposphere along with ozone condition highly regulates the phenomenon of weather. Sometimes this negatively influences the Indian climate, by increasing floods, hurricanes, and storms.

The changing environmental condition is fluctuating even the horizontal temperature. By the end of the 1940s, there was a warming of about 0.48 to 0.13 °C at a 95% confidence interval which has cooled down by 0.24 to 0.12 °C until 1975. This again was followed by large warming of 0.8 to 0.16 °C from 1975 (Hansen et al. 2010). The monthly temperature data (from ERA-40), based on the three-dimensional structure (Trenberth and Smith 2006) studied the Tropics core region from 30° N to 30° S. The tropical troposphere showed a highly coherent zonal mean warming. This increases in magnitude with height to 300 hPa, drops to zero about 100 hPa at the tropopause, and has a reverse sign to 30 hPa with peak negative values at 70 hPa.

Researches are being carried out investigating the interannual variability in the Indian rainfall. The studies show the significant associations with the regional and global climate variables in the system of epochs: below or above normal rainfall activity (Sikka and Gadgil 1980; Krishnamurthy and Shukla 2000; Goswami 2007; Yadav 2009; Kripalani et al. 1997). Fluctuation in the sea surface temperature, the wind patterns, the tropospheric geopotential height, and the mean sea level pressure across the globe are considered as they may regulate the interannual variation in the Indian monsoon. The results lead to a weak relationship of ENSO over the Indian monsoon, although the sea surface temperature in the North-western of North Atlantic showed a good relationship with the Indian monsoon (Yadav 2009).

A major hurdle for agriculture is the extremities of rainfall at both ends which can cause either drought or flood. Researchers are working actively to eradicate this challenge with proper assistance disaster risk management experts and climate scientists. The comprehensive analysis of rainfall variation at definite periods, trends, factors affecting rainfall will help in decision-making. While major changes have been observed in the tropospheric thermal structure, there is a large asymmetry that exists throughout the globe. The rainfall trend is not uniform across India. So, it required an in-depth analysis of extreme wet and dry periods over different parts of the country, correspondingly its relation to the intra-seasonal fluctuations in the tropospheric thermal, moisture, and wind fields of dry and high lands of Asia as well as across the whole globe.

The need which enforces to study the Indian monsoon is the country’s economy, as it depends upon the agricultural sector. Plus this agricultural value in the country (India) is highly dependent on the monsoon. This will help to overcome the challenges in ensuring food security. The hydro-meteorological parameters (like temperature, rainfall, wind velocity) make a great impact on groundwater quality and the hydrologic cycle. So, the detailed climatological analysis will help in planning a well-organized water resource.

The outcomes may be useful in the long-range prediction of rainfall on sub-divisional scales. Accordingly, these results can be beneficial in the agro-sector, for the prediction of extreme events, such as floods and droughts and water resource planning. Different global regions and meteorological parameters will help to know the variation of the Indian monsoon in an improved manner.

Materials and methods

Scientists regard the Mann-Kendall test as an outstanding tool for trend recognition (Addisu et al. 2015). It helps in assessing the implication of trends in hydro-climatic time series like temperature, water quality, precipitation, and streamflow (Somsubhra and Edwards 2016; Azam et al. 2018). Sen’s estimator is commonly used to determine the trend magnitude for time series of hydro-meteorological data (Jain and Kumar 2012; Ambun et al. 2013). The basic statistical parameters like correlation, mean, and median are also used to examine meteorological data. The most useful method to analyze the long-term variables is the correlation technique with the help of the “Monte Carlo simulation” (Raychaudhuri 2008; Neng et al. 2005) and the confidence interval with the help of the “bootstrapping” method (Wood 2004).

Moving average

The first step in trend analysis is to smooth the data and is defined as regularization in data (Raudys et al. 2013). The simplest method is the process of moving average (Rajasekhar and Kanth 2014). Equal weights are assigned, i.e., (1/N) to all N data points, and the equation is given below:

$$ Y(n)=\frac{1}{N}\left[\sum \limits_{k=0}^{N-1}x\left(n-k\right)\right] $$

To obtain one period ahead forecast, the method uses a mean or average of past k observations.

Basic statistics

The climatology which is the monthly averages of the atmospheric parameters is prepared for the specified region. Mean and standard deviation help to calculate the climatological and fluctuation features of the regions.

$$ \mathrm{Mean}=\frac{\sum x}{N} $$

where x = data set required and N = total observations.

$$ \mathrm{Standard}\ \mathrm{Deviation}=\sqrt{\frac{\sum {\left(x-\overline{x}\right)}^2}{N}} $$

where x = required data set,\( \overline{x} \)= mean data set, and N = total number of observations.

The basic anomaly method

To observe the interannual variations of the atmospheric parameters, the basic “anomaly method” is used. Anomaly method is the average of the data set minus the actual data point of the required data set. It helps to set a benchmark for easier interpretation (Hafez and Almazroui 2014).

The Student t test for the analyses of recent changes

It is used to comprehend the possibility of the link between two variables. This test is beneficial for a numerical variable and comparing the averages of two data groups. A null hypothesis is stated as H0: U1 − U2 = 0, where U1 is the mean of the first group and U2 is the mean of the second group. The null hypothesis states that the difference between the two populations is zero. According to Akhoury and Avishek (2019a, b), the two populations taken are the two sub-periods 1949–1978 and 1979–2013 and the equation used is as below:

$$ {\left\{\frac{\mathrm{X}1\left(\mathrm{mean}\right)-\mathrm{X}2\left(\mathrm{mean}\right)}{\left(\frac{\left(\mathrm{N}1-1\right)\mathrm{S}{1}^2+\left(\mathrm{N}2-1\right)\mathrm{S}{2}^2}{\mathrm{N}1+\mathrm{N}2-2}\right)\left(\frac{1}{\mathrm{N}1}+\frac{1}{\mathrm{N}2}\right)}\right\}}^{1/2} $$
(1)

Trend analysis

Researchers found Mann-Kendall’s trend test to be an excellent tool to measure the implication of trends in hydro-climatic time series. Each data is compared with all successive data points. The initial value “S” is supposed to be “0,” i.e., no trend. The “S” is incremented by “1” if the data point from a later period is larger than a data point from an earlier period, else is decremented by “1.” The final result of “S” is the net result of all the increments and decrements. The comparison is made by the mathematical equation as below:

$$ \operatorname{sign}\left({x}_j-{x}_i\right)=\left\{\begin{array}{c}1,\kern0.5em \mathrm{if}\ \left({x}_j-{x}_i\right)>0\\ {}0,\kern0.5em \mathrm{if}\ \left({x}_j-{x}_i\right)=0\\ {}-1,\kern0.5em \mathrm{if}\ \left({x}_j-{x}_i\right)<0\end{array}\right. $$

where xi is the time series (i = 1, 2...n – 1), xj ranked from j = i + 1, 2...n, and then comparing each data point xi (reference point) with other data points xj.

The Mann-Kendall test statistics “S” is given by

$$ S=\sum \limits_{k=1}^{n-1}\sum \limits_{j=k+1}^n\operatorname{sign}\left({x}_{\mathrm{j}}-{x}_{\mathrm{k}}\right) $$

where sign(xj − xk) is the signum function.

The statistic variance is given as

$$ \mathrm{Var}(S)=\frac{\left[n\left(n-1\right)\left(2n+5\right)-{\sum}_tt\left(t-1\right)\left(2t+5\right)\right]}{18} $$

where “t” is the figure of ties up to sample “i.” The zmk (statistics of the standardized Mann-Kendall test) is assessed as below:

$$ {Z}_{\mathrm{mk}}=\left\{\begin{array}{c}\frac{S-1}{\sqrt{\mathrm{Var}(S)}}\ \mathrm{if}\ S>0\\ {}0\kern4em \mathrm{if}\ S=0\\ {}\frac{S+1}{\sqrt{\mathrm{Var}(S)}}\ \mathrm{if}\ S<0\end{array}\right\} $$

The value Zmk helps to evaluate the presence of a statistical trend. The upward (downward) trend is quantified by the positive (negative) value of Zmk. It (Zmk) has a normal distribution to test at α level of significance (usually 5% with Z0.025 = 1.96), if the absolute value of Zmk is greater than Z1 − α/2 H0 is rejected. The α is the significant level and Z1 − α/2 is the standard normal deviates for the test (Ambun et al. 2013).

Sen’s slope estimator

The purpose of Sen’s slope estimator is to assess the true slope of the prevailing trend (as a change per year). It is generally used where the trend can be expected to be linear.

$$ f(t)= Qt+B $$

Here, Q is the slope, t is time, and B is a constant.

The equation below helps to derive an estimate slope of Q:

$$ {Q}_i=\frac{x_j-{x}_k}{j-k} $$

where xj and xk denote the data points at period j and k (j > k) respectively. If there are n values xj in the time series, the slope estimates Qi will be N = n(n − 1)/2. The median of these N values of Qi is Sen’s estimator of the slope. The rank of the N values of Qi is from the smallest to the largest. Sen’s estimator is given as below:

$$ Q=\left\{\begin{array}{c}{Q}_{\frac{N+1}{2}},\kern0.75em \mathrm{if}\ N\ \mathrm{is}\ \mathrm{odd}\\ {}\frac{1}{2}\left({Q}_{\frac{N}{2}}+{Q}_{\frac{N+2}{2}}\right),\kern0.75em \mathrm{if}\ N\ \mathrm{is}\ \mathrm{even}\end{array}\right. $$

For the estimate of B in the equation f(t), the n values of differences xi − Qti are measured and the median helps to give an estimate of B (Ambun et al. 2013). In time series, the positive Q points depict an upward (increasing) trend and vice versa. The sign and slope (magnitude) of increasing or decreasing trend are given by the Mann-Kendall test and Sen’s slope respectively (Yadav et al. 2015).

Regime shift analysis

This is the method used by Rodionov and Overland (2005), and the investigation is built on the sequential t test analysis of regime shifts (STARS). In this process, a new observation (data) is checked to decide whether the data is diverged (statistically significant) from the mean values of the current regime or not. The potential change point “c” is the year of significant deviation. To test the hypothesis calculated for each c, the regime shift index is used:

$$ {\mathrm{RSI}}_c=\sum \limits_{i=c}^{c+m}\frac{x_i^{\ast }}{{l\sigma}_1} $$

where the number of years since the start of a new regime is m = 0….l − 1, the cut-off length of the regimes = l, σ1 = the average standard deviation, and RSI is the cumulative sum of normalized deviations \( {x}_i^{\ast } \) from the hypothetical mean level for \( {\overline{x}}_{\mathrm{new}} \) (new regime), for which the alteration from the mean level for \( {\overline{x}}_{\mathrm{cur}} \) (current regime) is statistically significant according to Student’s t test:

$$ \mathrm{diff}={\overline{x}}_{\mathrm{new}}-{\overline{x}}_{\mathrm{Cur}}=t\sqrt{2{\sigma}_1^2}/l $$

Here, t is the value of the t-distribution at p, the given probability level.

The test is failed for the negative value of RSI, and then the value assigned is zero. Though, if the RSI values remain positive throughout l − 1, c at level ≤ p is stated to be the time of the regime shift.

There are two parameters which control the magnitude, the shift detection, and scale of the detected regime. The first one is the change between the mean values of the old and new regimes. It is statistically significant every time when a regime shift is detected; the larger the magnitude of the shift detected, the lower the significance level. Second, the longer the cut-off length, the longer the regime detected and vice versa (Keevallik 2011).

Table 1 shows the detail of the various datasets used in different analyses.

Table 1 Detail of the datasets used
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Global temperature variations and the interannual Indian rainfall variations

Even a small change in global temperature affects the meteorological state, agricultural conditions, and also the water resources which directly or indirectly influence the society and economy of the country. So, it is essential to study global temperature variations. Esau et al. (2013) found that the Arctic region is facing a robust warming condition. The surface temperature trends were observed to be stronger than the tropospheric temperature for every latitude band north of 50° N for all month except for the season of ice melting. Trenberth and Smith (2006) focused on the Tropics region from 30° N to 30° S to analyze the three-dimensional structure of monthly temperature. A highly coherent zonal mean warming was observed throughout the region.

Lindzen and Giannitsis (2002) compared the surface temperature record and radiosonde record of vertical temperature over 850–300 mb. This leads to a conclusion that there was a rise in tropospheric temperature due to greenhouse warming around the year 1976. The Northern Hemisphere (region Alaska) faced a large increase in temperature during 1988 while a substantial decrease was seen in the North-Pacific Ocean (Trenberth 1990).

With this respect, we studied the three-dimensional global atmospheric temperature (paper is communicated concerning this analysis). It was perceived that climatologically the annual tropospheric temperature declines from the equator to the pole in lower, middle, and upper troposphere; however, the gradient reverses in the upper troposphere-lower stratosphere (UTLS). The mean annual inter-hemispheric temperature difference (Northern Hemisphere (NH)-Southern Hemisphere (SH)) across the globe rises poleward away from the equator. Temperature is positive throughout the year in the lower, middle, and upper troposphere but is negative for tropics and subtropics in the UTLS layer. It specifies that troposphere across NH is warmer than SH on an annual basis, although there is a non-uniform upsurge in the temperature in the troposphere through the globe. The asymmetry in the rise in temperature reflected in the significant decrease in inter-hemispheric temperature contrasts over most of the climatic zones.

Now, as the Indian summer monsoon rainfall (ISMR) is considered and characterized by strong intra-seasonal rainfall variability, many researchers focused on the ISMR (Sikka and Gadgil 1980; Krishnamurthy and Shukla 2000; Goswami 2007; Kumar et al. 2010;  Jain and Kumar 2012). Along with India as a whole, the subdivision and regional scale too were analyzed on the monthly, seasonal, and annual rainfall trends (Arora et al. 2005; Jain and Kumar 2012; Addisu et al. 2015; Khavse et al. 2015; Jain et al. 2013). Azmi and Sarmadi (2016) used simple linear regression techniques to analyze the summer monsoon data from 1871 to 2005. Further different time segments were analyzed and it was observed that there were a systematic increase and decrease in rainfall trends (Naidu et al. 2009). The late 1950s witnessed the wet monsoon condition for the Indian subcontinent, but in the early 1900s, it faced a dry condition. In the era of global warming, during the period 1970–2005, a negative pattern in the summer monsoon rainfall was acknowledged in 19 out of 30 meteorological subdivisions (Naidu et al. 2009).

The link between the interannual and decadal changeability in ISMR and the northern hemisphere surface temperature and Eurasian snow was deliberate by Kripalani et al. (2003). They observed a random fluctuation in the interannual variations while the decadal differences expose distinct alternate epochs of above and below standard rainfall. The period 1871–2005 witnessed none of the significant trends for annual, monthly, or seasonal rainfall for the Indian subcontinent. The trends found to be decreasing in annual and monsoon (June–September) rainfall, whereas it elevated in post-monsoon (October–November), winter (December–February), and pre-monsoon (March–May) rainfall. The monthly rain analysis verifies that June, July, and September experienced a downward trend while August exhibited an upward trend (Kumar et al. 1999).

The northeast region (NER) of India is the utmost rain receiving region and hence favorable for huge water and hydropower potential (Jain et al. 2013). For the regions Central India (CI) and the Western Ghats (WG), Krishnamurthy (2011) executed a rainfall trend analysis based upon low-pressure systems (LPSs). The total LPS days exists with an increasing rainfall trend, observed for the period 1930–2003, whereas a decline in rainfall trend was detected during the period 1951–2004. The trend analysis of temperature is yet another key factor to analyze rainfall variation (Arora et al. 2005). An increasing trend during different seasons over different regions of the Indian subcontinent was perceived (Dash and Hunt 2007). The period 1881–1997 noticed an increasing trend for the annual and seasonal air temperature at the rate of 0.57 °C per 100 years (Pant and Kumar 1997). The yearly average temperature and mean maximum and minimum temperature increased at the rate of 0.42 °C, 0.92 °C, and 0.09 °C per 100 years, respectively (Arora et al. 2005).

In view of the above-reviewed paper, an analysis (1949 to 2016) of the interannual variations in the Indian rainfall was carried out by Akhoury and Avishek (2019a, b). The rainfall regions of India were taken as the All India Rainfall (AIR), the West Central India Rainfall (WCIR), the North East India Rainfall (NEIR), the Central North East India Rainfall (CNEIR), the Northwest India rainfall (NWIR), and the Peninsular India Rainfall (PIR). The main objectives of the paper were (a) to analyze Indian rainfall on a sub-divisional scale and (b) to define relationships between rainfall and SOI for three different sub-periods (1949–1965, 1966–1990, and 1991–2016). Table 2 shows the rainfall trends for all the subdivisions for the period 1949–2016.

Table 2 Rainfall trends (1949–2016)
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A downward trend in Indian monsoon rainfall along with subdivisions was seen for the period 1949–2016. The regime shift analysis method was used to detect the rainfall shifts which leads to a conclusion that during the periods 1949–1965 and 1972–1990, 6 and 7 shifts were detected respectively.

Figure 1a, b, and c show the relationship between rainfall (JJAS) and SOI. A robust direct relationship was observed for the sub-periods 1949–1965 and 1966–1990, which deteriorated in the sub-period 1991–2016. A weak correlation was seen for all the subdivisions during the season MAM. However, during 1966–1990, the region NWIR showed a strong correlation with the SOI. The subdivisions during the post-monsoon months (OND) rainfall showed a robust direct relationship with the SOI for the sub-period 1949–1965, though the other two sub-periods exhibit a weak relationship (Akhoury and Avishek 2019a, b).

Fig. 1
figure 1

a–c A link between rainfall (JJAS) and SOI (Akhoury and Avishek 2019a, b)

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The Indian rainfall and its relation to different global parameters

The Indian monsoon rainfall variation is restricted to not only the wind, but also a macro variation, ENSO, namely geopotential height, temperature, etc. According to Sir Gilbert Walker, the monsoon rainfall in India is a global occurrence which is linked to various global climatic variables observed at various global locations (Krishnamurthy and Kinter III 2002). Even the major socio-political progress of the Vedic civilizations and the Indus Valley indicates a probable role of climate change in deciding the major chapters of human civilization history, as there has been a close relationship between the large hydro-climatic changes (Kathayat et al. 2017).

Yadav (2009) considered the interannual variability of the Indian summer monsoon rainfall (ISMR) (1949–2005) on the large-scale features. It was alleged that the relationship between the northwest of North Atlantic sea surface temperatures and ISMR has increased. As well, during the excess years of ISMR, the sea surface temperature was beyond normal. A connection between the outgoing longwave radiation over tropical Asia and Indian summer monsoon (June to September) was analyzed by Prasad and Bansod (2000) using data from June 1974 to September 1993.

Global warming directly influences precipitation. Heating is directly proportional to evaporation resulting in a dry surface which inclines towards the drought condition. As well, the water holding capacity of air rises roughly by 7% per 1 °C warming. This leads to an increase in water vapor in the atmosphere. Hence, extratropical rain, storms, or tropical cyclones, or snowstorms, abounded with full moisture content produce more intense rain events (Trenberth 2011). ISMR’s dependence on the sea surface temperature over the tropical Indian Ocean and the surface (India) air temperature has been proposed by Vittal et al. (2016).

A robust relationship was seen between the strength of the ISMR to the upper troposphere-lower stratosphere zonal wind over India and other regions of the globe (Madhu 2014). The Tibetan Plateau temperature anomaly was associated with the ISMR for the period 1957–1989 by Bansod et al. (2003). A dependable and robust relationship between the temperature anomaly and the Indian rainfall was observed. This relationship with the north-eastern Tibetan Plateau during January may be beneficial in predicting the drought and flood situations over the monsoon trough regions of India.

The geopotential heights at the middle and upper troposphere in the Northern hemisphere play an important role in studying the Indian rainfall variations (Keshavamurty and Awade 1974; Bhalme and Mooley 1980; Rajeevan 1993; Kripalani et al. 1999; Krishnan and Mujumdar 1999; Krishnamurthy and Goswami 2000; Sahai et al. 2003). A relationship was studied between the mid-tropospheric geopotential height (at 500 hPa) over the band of the Northern Hemisphere (20°–90° N) and the ISMR for the period 1958–2003 (Bansod 2005). Applying correlation technique, Kripalani et al. (1997) established a connection between the geopotential height of the Northern Hemisphere (30°–60° N and 0°–180° E at 5° latitude by 10° longitude) and the ISMR for the period 1974–1984. The ISMR shows a positive correlation with the mid-latitudes, the Algerian region, the Manchurian region, and the Caspian Sea.

Kripalani et al. (1999) established a link between the northern hemisphere low stratospheric geopotential height at 50 hPa and ISMR for the period 1958–1990. The decadal and interannual variability in the ISMR and its teleconnections were studied using 131-year (1871–2001) data in view of IPCC global warming projections on the Asian monsoon. It was observed that there was a changeability in interannual variation, but the decadal differences disclose the distinct alternate epochs of below and above normal rainfall (Kripalani et al. 2003). A statistical relationship was observed over the warming Tibetan highlands with that of the monthly rainfall from May to October over five homogenous zones (as described above) and the country as a whole (Paper Submitted). The results showed that there was a significant change in the tropospheric thermal structure of Tibetan Plateau. Besides, the trends in the rainfall characteristics across India were not uniform.

Indian monsoon and its link with ENSO

According to Sir Gilbert Walker, El Niño Southern Oscillation (ENSO) is one of the key factors in the variation of the Indian rainfall. Researchers say that during El Niño the Indian monsoon gets weaken, whereas La Niña strengthens the same (Kripalani et al. 2003; Krishnamurthy and Goswami 2000; Kripalani and Kulkarni 1997). Due to the large spatial and temporary unevenness of monsoon rains, it is challenging to rule any single relationship of ISMR to ENSO (Singh 2001). India’s maximum droughts are linked with El Niño events, though only less than half of El Niño events are linked with deficient rainfall over India. The Indian summer monsoon rainfall was either normal or excess during the El Niño years (Rajeevan and Pai 2007). The hypothesis was made that the El Niño actions with the warmest SST anomalies in the central Pacific are more efficient in aiming drought generating subsidence over India than events with the warmest SST anomalies in the eastern equatorial Pacific. The SST data were analyzed for the period 1880–2004.

A climate shift took place in 1976 (Qian et al. 2002). Earlier in 1976, El Niño events propagated westward, with moderate amplitude and a period of 2–4 years, but, after 1976, it propagated eastward with a larger amplitude and time scale of about 3–7 years. It is noteworthy that the Indian monsoon and the interdecadal changes in ENSO have gone through coherency and invariance over the last 125 years (Torrence and Webster 1999). They applied the technique of wavelet coherency to the Indian monsoon and ENSO indexes. Krishnamurthy and Goswami (2000) focused on the relation between the various indices of ENSO and the interdecadal variations of the ISMR and found a strong correlation between the two. The inter-annual variances of both ISMR and ENSO indices change in phase and follow mutual interdecadal variations.

Based on the reviewed paper, the following analysis of the interannual variations in the Indian rainfall was carried out concerning the Arabian Peninsula by Akhoury and Avishek 2019a, b. Table 3 shows the climatology and fluctuation features of the Arabian Peninsula of different parameters

Table 3 Climatological and fluctuation features of Arabian Peninsula
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The subdivisions of the Indian subcontinent experienced low rainfall during the period 1979–2013. The lower, middle, and whole tropospheric temperature and the tropospheric thickness of the Arabian Peninsula showed an increase in temperature during 1979–2013 as compared with those during 1949–1978. The tropospheric thickness is a function of the normal virtual temperature between 1000 hPa and 250 hPa; thickness will rise if the average virtual temperature rises and vice versa. Figure 2 shows the correlation comparison of rainfall with WTT, TT, and MSLP. The regions NWIR, WCIR, and CNEIR revealed a positive correlation with the tropospheric thickness and temperature in June and September. This relationship grows stronger during the period 1979 to 2013. A weak association was witnessed with the tropospheric thickness and temperature of the Arabian Peninsula with the rainfall regions NEIR and PIR. The Arabian Peninsula MSLP showed a robust negative correlation with the sub-divisional rainfall (except NEIR) for the period (1979–2013) (during June, July, August, and September). The correlation gets weaker during the La Niña years. Figure 3 shows the relationship during El Niño and La Niña years.

Fig. 2
figure 2

Correlation comparison: rainfall with WTT, TT, and MSLP (Akhoury and Avishek (2019a, b))

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Fig. 3
figure 3

Relationship during El Niño and La Niña years (Akhoury and Avishek (2019a, b))

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Correlation between the Northern Atlantic Oscillation and the Indian rainfall

A correlation was recognized between the Northern Atlantic Oscillation (NAO) in addition to the Indian sub-divisional rainfall. Figure 4 displays the correlation between NAO and the Indian sub-divisional rainfall (AIR, all India region; HIR, homogeneous India region; CNEIR, central northeast India region; NEIR, northeast India region; PIR, peninsular India region).

Fig. 4
figure 4

Correlation: NAO and rainfall

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The sub-divisional rainfall regions show a direct connection with the NAO for the season JF. All the regions except CNEIR show a negative correlation with the NAO during Mar–Apr–May. The possible physical reason perhaps during the negative phase of NAO is that the Azores High and the Icelandic Low shift poleward which reduces the Eurasian snow cover (Gutzler and Roses 1992). This has been linked with earlier and strong warming of the Eurasian continent, which makes large land-ocean temperature contrast, hence leading to an earlier and stronger Asian summer monsoon (Hahn and Shukla 1976). However, the monsoon season (JJAS) shows a good positive relationship among the NAO and the regions AIR and HIR. A weak relationship was seen between the NAO and the rainfall regions PIR and NEIR. The months from May to November show a positive correlation.

The long term from the year 1871 to 2005, summer monsoon rainfall data were used to study over 30 meteorological subdivisions of India. The simple linear regression technique was used for trend analysis. Maximum subdivisions showed a systematic increase and decrease in trends through various fragments of the time series. During the late 1950s, the country experienced (especially west Uttar Pradesh, Bihar, Haryana, the west-central, Telangana, and north interior Karnataka, Assam, Meghalaya, Nagaland, Manipur, Mizoram, and Tripura) wet monsoon conditions. During the early 1900s, dry monsoon conditions were seen especially over North India and Goa and Konka (Naidu et al. 2009).

Daily rainfall data (1907–2012) was analyzed to observe a difference in rainfall and its frequency of intensity. It was observed that the northeast monsoon (NEM) contributes 50.3% to the annual rainfall and showed an increasing trend every 30 years. The southwest monsoon contributes 26.3% to the annual rainfall. There was a decrease in the total number of rainy days in all the seasons. Nevertheless, during the northeast monsoon, there was an intensification in the number of rainy days. Hence, it is determined that in the long term there was no change in annual, monthly, and seasonal rain and frequency of rainy days (Rani et al. 2014). Central India challenged a fall in the total rainfall with a simultaneous increase in the frequency and magnitude of extreme rain events. During 1950–2015, Central India faced an upsurge in the extreme rain events and this was due to a growth in the variability of the low-level monsoon westerlies over the Arabian Sea (Roxy et al. 2017).

Precipitation concentration index, standardized rainfall anomaly index, and coefficient of variation were used to study monthly rainfall variation (1901–2016) over West Bengal. A rise in dry years percentage (75% to 97%) in Gangetic West Bengal and southern districts of Sub-Himalayan West Bengal (69% to 84%) was perceived especially 1990 onwards (Nandargi and Barman 2018). A link between ISMR and the Iran surface pressure was studied with the help of correlations, regressions, and trend analysis. There was a decreasing trend in surface pressure over Iran, and this was related to the unusual cyclonic circulation with westerlies and northerlies across the north Arabian Sea and the Persian Gulf, respectively, hence leading to an increase in rainfall over NW India as these reinforce the climatological background cross-equatorial flow over the Arabian Sea and further converge towards NW India with abundant moisture supply (Yadav 2018).

Conclusions

The central idea of the research review is to focus upon the variations in the Indian rainfall owing to global atmospheric changes. Different global atmospheric parameters influence the Indian rainfall. The first and basic parameter was the global atmospheric temperature taken at different pressure levels and regions. As the Indian monsoon is a global phenomenon, the temperature analysis will help to understand the variability in the Indian monsoon. The results have shown that the period 1979–2013 was the warming period for the regions in both the hemispheres. Even the lower, middle, and upper tropospheric temperatures showed a significant increase in most of the climatic zones during the period of 1979–2013. The tropic, sub-tropics, and equator regions showed a significant temperature increase in the upper troposphere-lower stratosphere. It was also observed that in spite of temperature increase, the rate of increase was not uniform across the globe. The asymmetry in the temperature rise reflected in the significant decline in inter-hemispheric temperature contrast over most of the climatic zones. This could be one of the reasons for the weakening of thermally directed Asia-Pacific Monsoon circulation.

The Arabian Peninsula tropospheric temperature indicated an increase in the period 1979–2013. Some of the Indian subdivision (CNEIR, NWIR, and WCIR) displayed a positive and strong correlation with the tropospheric thickness and temperature (of AP) for June and September (1979–2013), whereas the MSLP and OLR (of AP) showed a negative correlation with the sub-divisional rainfall for all the months during 1979–2013. The above association gets weakened during the La Niña and El Niño years, excluding June and September.

The lower tropospheric temperature has shown a significant rising trend in the Iranian plateau (all months) and Central Tibet (May–June), while West Tibet (June–July) and East Tibet (June–October) have shown a decrease during 1949–2013. In MTT, Central Tibet (May–June) has shown a significant increasing trend and East Tibet (June–October) has shown a significant decreasing trend. A significant increasing trend in WTT has been observed in the Iranian Plateau (August) and Central Tibet (May–June) while East Tibet (June–Oct) shows a significant decreasing long-term trend. The tropospheric thickness of Iranian Plateau in June has shown an increasing trend while that of Central Tibet during October and East Tibet from June to October has shown a significant decreasing trend. The thermal properties of the Iranian Plateau and West Tibet has significantly correlated with the monsoon month (JJAS) rainfall of the West Central, North West, and Central North East India. For India, tropospheric temperature and geopotential thickness show strong positive anomalies over Iranian Plateau and West Tibet during high rainfall events and negative anomalies during low rainfall events for all months.

The weak Indian monsoon is related to El Niño years, whereas the good monsoon is linked to La Niña years. Although India’s maximum droughts are linked with El Niño years, less than half of El Niño events are linked with deficient Indian rainfall but, during other El Niño years, ISMR shows either normal or excess rain. Thus, the Indian rainfall (especially monsoon rain) shows a large variation owing to global climatic parameters. The analysis of the Indian rainfall with the global phenomenon is important from the point of view that India is an agriculturally based country, highly dependent on the monsoon, and needs a thorough study. This will help to overcome the challenges of food security, planning a well- organized water resource, disaster risk management, etc.