The local and global climate forcings induced inhomogeneity of Indian rainfall

India is home for more than a billion people and its economy is largely based on agrarian society. Therefore, rainfall received not only decides its livelihood, but also influences its water security and economy. This situation warrants continuous surveillance and analysis of Indian rainfall. These kinds of studies would also help forecasters to better tune their models for accurate weather prediction. Here, we introduce a new method for estimating variability and trends in rainfall over different climate regions of India. The method based on multiple linear regression helps to assess contributions of different remote and local climate forcings to seasonal and regional inhomogeneity in rainfall. We show that the Indian Summer Monsoon Rainfall (ISMR) variability is governed by Eastern and Central Pacific El Niño Southern Oscillation, equatorial zonal winds, Atlantic zonal mode and surface temperatures of the Arabian Sea and Bay of Bengal, and the North East Monsoon Rainfall variability is controlled by the sea surface temperature of the North Atlantic and extratropial oceans. Also, our analyses reveal significant positive trends (0.43 mm/day/dec) in the North West for ISMR in the 1979–2017 period. This study cautions against the significant changes in Indian rainfall in a perspective of global climate change.

Seasonal variability: role of local and global climate forcings. Figure 4 illustrates the variability of proxies (regression coefficient × standard deviation of proxies) contributing to the rainfall for various seasons in different regions, where high values indicate dominating contribution from the respective climate indices. Our analysis reveals that: (i) the interannual variability of ISMR is mainly driven by the remote forcings such as MEI and EQWIN and the local forcing SSTA in all regions. In addition to these parameters, EMI and AZM also influence the ISMR in the West Central, and SSTB, and AZM affect ISMR in the North West India. In the North East India, ISMR is also controlled by EMI, AMO, SSTB and AZM. (ii) The NEMR variability is mostly controlled by the remote signals of AMO and ESST in most regions. In the Peninsular region, NEMR is also affected by EMI and AZM. In the North East, NEMR is influenced by MEI, EMI, AMO, SSTB and AZM. (iii) The pre-monsoon variability is mostly driven by SSTB in the Peninsular region and by EMI, AMO, and SSTA in the North East. In other regions, rainfall in this season is mainly affected by MEI and AZM index. (iv) The changes in winter rainfall are governed by EQWIN or DMI, and AZM index in the Peninsular India and by the local forcings SSTA and SSTB in the North Central and North East.   Drivers of rainfall variability estimated using the MLR method. The contributions of different climate processes to the rainfall in different regions as analysed from the average data (average of GPCP and CMAP) for the period 1979-2017 are shown in Figs 5 and 6 for the ISMR and NEMR months, respectively. The top panels represent rainfall anomalies computed (rainfall-climatology) from the observations (thick solid line) and regressed data (thin solid line). The bottom panels (second to ninth) show contributions of climate modes (as noted in the figures) to the rainfall changes. The contributions of the climate forcings to the rainfall from the IMD data at 0.25° × 0.25° latitude × longitude horizontal grids are also analysed for ISMR and NEMR and are shown in the Supplementary Figs S1 and S2, respectively.
ISMR. The regressed data clearly replicate the observed rainfall in all regions. The contributions of proxies show large interannual and regional changes. For instance, (i) EP and CP ENSO, EQUINOO and SST of Arabian Sea and Bay of Bengal largely affect the ISMR, about ±0.5 mm/day, in all regions as observed from the respective indices of MEI, EMI, EQWIN, SSTA and SSTB. (ii) The response of EP ENSO is large compared to that of CP ENSO in all regions and the impact of ESST is small compared to other modes. (iii) The ocean component of IOD (DMI) is poorly correlated to the ISMR compared to its atmospheric counterpart (EQWIN). (iv) The peak rainfall in the North East occurs always opposite to that in other regions and all forcings contribute significantly to the rainfall there. In general, during ISMR, winds from the Indian Ocean have two arms when they reach Indian land mass, in which one arm passes through the Arabian Sea to the Western Ghats and the second arm crosses the Bay of Bengal and reaches the Himalayas through a part of North East region. Therefore, the influence of SST of Bay of Bengal is mostly restricted to the Peninsular and North East regions in this season, as demonstrated in the analyses (Fig. 5).
In general, El Niño suppresses and La Niña enhances rainfall and the warm phase of AMO induces rainfall 21 in India. Similarly, positive IOD phase leads to more rainfall while negative IOD phase leads to less rainfall. Several studies on ISMR 22,23 state that 1979, 1982, 1985, 1986, 1987, 2002, 2004 and 2009 were drought years and 1983, 1988, 1994 and 2007 were excess rainfall years in India. (v) Among these, 1982, 1987 and 2009 droughts were followed by the positive phase of EP ENSO, and the heavy rainfall in 1988 was due to the occurrence of EP La Niña. (vi) Our anlysis shows that heavy rainfall in 1983 is contributed by the CP La Niña in all regions, but also by AZM in the western regions. (vii) The normal rainfall received in 1997 could be attributed to the positive phase of EQUINOO, although it was a strong El Niño year. (viii) While the extremes in the interannual variation of the ISMR (excess/drought seasons) are explained rather well by ENSO individually or jointly with other climate processes, the spatial variation in the rainfall during these extremes and its links to the climate modes as well as other forcings, such as SST of nearby oceans, were not explored yet, as mentioned previously. The positive IOD These suggest that the anomalous and regional differences in rainfall can better be interpreted with multiple climate proxies, and the local forcings play a vital role in regional rainfall differences or spatial inhomogeneity.
NEMR. Figure 6 depicts the response of various climate processes to the NEMR. Pre-monsoon and winter seasons. The rainfall is very limited and sporadic in the pre-monsoon and winter seasons. The analysis was carried out for these too (see Supplementary Figs S3 and S4). The peak rainfall occurs in the Peninsular and North East India and the regressed data capture most features very well during these seasons.
In the pre-monsoon season, contributions of CP ENSO, AMO, AZM, and SSTA are large in the North East in agreement with the heavy rainfall there, but SSTB contributes to much of the variability in the Peninsular region. In winter, rainfall is very small and is mainly dominated by AZM and the local forcing SSTA in most regions. The largest rainfall occurs in the Peninsular India compared to other regions and is also contributed by EQWIN and Trends in Indian rainfall. MLR method. The long-term trends in rainfall are calculated using the MLR method and results with twice the standard deviation (95% confidence level) are shown in Table 1. In general, all data sets show similar trends during the 1979-2017 period in all seasons, indicating the consistency of measurements from different instruments. The trends are also estimated from the average of GPCP and CMAP data for the period 1998-2017 to compare with those from TRMM and the results are very similar. The trends are largest (in absolute value) for the ISMR and smallest for winter. Although most estimates are not statistically significant at the 95% confidence level, the NEMR trends estimated from the TRMM data show a significant negative trend (−1.10 ± 1.00 mm/day/dec) in the Peninsular region. All other data sets show significant positive trends (0.43 ± 0.30 mm/day/dec) for the ISMR in the North West India. The GPCP data show a significant positive trend (0.26 ± 0.25 mm/day/dec) for the pre-monsoon season in the North East India. The trend analysis with all four data sets in 1979-2017 shows that the ISMR is decreasing and NEMR is increasing in the Peninsular, North Central and North East regions, whereas opposite trends are observed in the West Central and North West India. The pre-monsoon rainfall is increasing in the Peninsular, West Central and North East India and decreasing in other regions while the winter rainfall is decreasing in all regions. None of these trends mentioned are significant at 95% confidence level.
The results are consistent with the analyses of Kumar et al. 24 , who also showed an insignificant negative trend in the ISMR (−0.43 mm/yr), positive trends in the NEMR (0.11 mm/yr) and pre-monsoon season (0.04 mm/yr) over different regions of India in the 1871-2005 period. They also showed insignificant negative trends in rainfall (−0.01 mm/yr) in the North East and North West India and positive trends (0.01 to 0.05 mm/yr) in other regions during winter. Similarly, Das et al. 25 found insignificant negative trend (−0.62 mm/yr) in the ISMR over North East in 1961-2010, as estimated in our study for the 1979-2017 period. However, they estimated significant positive trends for other seasons. Our study also shows significant positive trends for pre-monsoon season, but insignificant positive trends for NEMR. The slight differences in the computed trends among different studies can be due to the differences in the periods of estimates.

Conclusions
This study introduces multiple linear regression technique for the evaluation of the contribution of different local and remote drivers of climate change and to estimate trends in rainfall over different regions across four seasons in India. The importance of this method is that it uses a time-variant parameter for determining trends in rainfall and provides quantitative evaluation of trends in rainfall. Also, trends in climate modes are removed before applying in the regression model and hence, the computed trends would be apparently free from the trends of proxies used in the regression model. This study assesses combined relationship between Indian rainfall and different local and global climate processes. Our study finds that (i) changes in the Arabian Sea and Bay of Bengal surface temperatures, equatorial zonal winds, Atlantic zonal mode, EP ENSO and CP ENSO control the variability of ISMR in all regions. (ii) The CP ENSO and the changes in SST of North Atlantic and extratropical oceans decide the variability of NEMR. (iii) The pre-monsoon rainfall variability is controlled by CP ENSO, AMO and SSTA, whereas the winter rainfall  variability is dominated by EQWIN or DMI, AZM and the local forcings SSTA and SSTB. (iv) The Bay of Bengal surface temperature is the major driver of rainfall variability in the North East in all seasons. (v) These results unravel the role of a number of climate modes including the local forcings, in addition to the commonly used global climate forcings, in determining the variability of rainfall distribution over India. (vi) An insignificant negative trend is estimated for ISMR and positive trend for NEMR in the Peninsular, North Central and North East regions, and the trends are opposite in other regions. Statistically significant positive trend (0.43 mm/day/ dec) at 95% confidence level is found in the North West India for ISMR, as estimated from the IMD, GPCP and CMAP data. We have introduced a multiple linear regression model for the variability and trend analyses of rainfall, and the model with nine detrended and lagged climate parameters fits well with the observed rainfall in all seasons. Since similar statistical techniques are used for predicting weather and extreme weather events, the method presented in this study can be applied to improve the existing prediction models or weather forecasting models of Indian monsoon. Henceforth, our study unveils some interesting facts on the variability of Indian rainfall, both in terms of contributing factors and long-term trends. The observed changes in rainfall also have signatures of the impact of regional and global climate change, and hence, corroborate the importance of continued monitoring and long-term analyses of rainfall, as these kinds of studies have great significance in the context of climate impact assessments and government level decisions.

Methods
The gridded rainfall data compiled from rain gauges deployed at different places in India by . The negative of this wind anomaly, normalized by its standard deviation is used as the index of EQUINOO, termed as Equatorial zonal Wind Index (EQWIN) 27 . However, the positive IOD events are associated with EQUINOO, but is not true for negative IODs. In fact, IOD and EQUINOO are loosely coupled. Therefore, the correlation between EQWIN and ISMR is better than that between DMI and ISMR 28,29 although these two indices represent IOD. The extratropical SST is considered as the area-averaged SST anomaly of the extratropical oceanic region of 15°N − 75°N and 100°E − 5°W.
Apart from these, two new proxies are constructed to study the influences of SSTs of Arabian Sea and Bay of Bengal on Indian rainfall. The large SST variability region is determined from the spatial variance computed for the JJAS months in 1979-2017, and the regions considered are 10°N − 15°N and 51°E − 60°E for Arabian Sea and 6°N − 10°N and 78°E − 82°E for Bay of Bengal. Then, corresponding indices are computed for each month (January to December) using area-averaged SST for those regions. The monthly Extended Reconstructed SST (ERSST) version 5 data 30 are used for making these indices. All these climate modes are detrended, and are normalized to unity to be used in the regression model. The lagged combination of these parameters is used in the model and the considered lag is zero month for CP ENSO and one month for other proxies.
The analysis is carried out using monthly mean rainfall anomaly (mm/day) averaged for the winter season (January-February), pre-monsoon season (March-April-May), ISMR (June-July-August-September) and NEMR (October-November-December), as defined by IMD. The North West region takes October-November as the NEMR months and December-January-February as winter. Also, region-wise analysis is performed to investigate the spatial inhomogeneity of rainfall in relation to the climate modes.
The MLR model used to fit the rainfall data in terms of explanatory variables is: where Y is the rainfall data, z is years, A is a constant level term (taken as value 1), C z is linear trend, C A , C MEI , C EMI , C AMO , C AZM , C DMI , C EQWIN , C ESST , C SSTA and C SSTB are the regression coefficients of the time series of constant term, EP ENSO, CP ENSO, AMO, AZM, DMI, EQWIN, ESST, SSTA, and SSTB, respectively, that determines the contribution of each variable given the other variables are held constant and ε is the residual. This model can be expressed in vector form as ε = + Y CX (2) where X (z × p) is the proxy data and C (p × 1) holds the regression coefficient of each proxy. p is the number of proxy terms including the constant used in the regression model and is eleven in this study. The standard error of the regression coefficient is calculated by minimising the model using the generalised least squares method 31 by setting The residual is computed as The error standard deviation is The standard deviation of the regression coefficient is dependent on the variance and autocorrelation (φ) of the residual. Therefore, autocorrelation is also incorporated in the estimation of standard deviation without which a precise trend estimate is not possible and would falsely estimate the 95% confidence level.
The trend is said to be statistically significant if it is greater than twice its standard deviation (approximately 95% confidence level) in this study.
There are certain assumptions in using MLR model that (i) the explanatory parameters are not highly correlated each other. (ii) The residuals are normally distributed. (iii) The error term is not auto-correlated as it affects the error estimation. Therefore, the presented model is made by verifying all these factors. The multicollinearity among the climate indices is checked using the tolerance and variance inflation factor 32 and found that model is free from multicollinearity among the variables. Also, existence of autocorrelation of residuals is evaluated using Durbin-Watson test and is inside the limits as stated in 33 . Therefore, the considered MLR model satisfies the conditions of goodness of fit of the models.
A study by Krishnaswamy et al. 34 reported that there exists nonstationarity and nonlinearity among the climate processes, especially between ENSO and IOD. This nonlinear relationship among the climate modes can also be studied using multiple non-linear regression model as done by Esha and Imteaz 35 .