Comparative analysis of indices in capturing the onset and withdrawal of the South Asian Summer Monsoon

The South Asian summer monsoon (SASM) exerts a profound influence on South Asia and the southern Tibetan Plateau. The timing of its onset and withdrawal significantly impacts regional rainfall, a critical water source for agriculture and the economy. Various SASM indices, employing different variables, have been employed to gauge monsoon onset and withdrawal, each demonstrating distinct characteristics. This study provides a comprehensive comparison of prominent SASM indices related to onset and withdrawal, revealing similar timing but varying magnitudes. Across nearly all indices, a consistent pattern emerges, indicating a trend towards earlier onset and delayed retreat during 1979–2018, marked by pronounced interdecadal variability, with a notable turning point around 1997. The earlier onset and later retreat are likely to enhance rainfall and potential water resources for South Asia and the Tibetan Plateau. Delving into the mechanisms revealed a delayed connection between the SASM onset to the large-scale sea surface temperature (SST) anomalies characterized by the Oceanic Niño Index (ONI) in the preceding spring, but a simultaneous connection between SASM withdrawl and ONI in autumn. Current index definitions, relying on single or dual variables, may fall short in accurately depicting monsoon onset and withdrawal. To address this, we introduce a novel monsoon index derived from multiple large-scale circulation variables, offering improved trend capture and enhanced representation of interannual variability in SASM onset and withdrawal. This study advances our understanding of SASM indices and their correlation with monsoon rainfall, providing insights into the dynamics of SASM onset and withdrawal.


Introduction
The onset of the South Asian Summer Monsoon (SASM) at the southern tip of India marks the commencement of the rainy season, with over 90% of the region's annual rainfall occurring during this period (Li et al 2023).The SASM has a significant influence on the socioeconomic development of South Asian and neighboring regions.Understanding the precise timing of the onset and retreat of SASM is an active area of research due to their farreaching impacts on agriculture and water resource management decisions (Sperber et al 2013, Misra et al 2017).While the SASM onset has garnered considerable attention, research on its withdrawal, although less prevalent, remains crucial.This is because the total seasonal rainfall is predominantly determined by the variability in the withdrawal phase (Raju and Bhatla 2014).Consequently, the accurate determination and forecasting of both the onset and withdrawal dates become of utmost importance, given their critical roles in agricultural and economic planning.Previous studies have delved into the connection between the SASM onset or intensity and monsoon rainfall in the Indian subcontinent (e.g.Wang and Lin 2002).In general, there exists a positive correlation between SASM intensity and rainfall levels across the Indian subcontinent.The weakening SASM has been linked to reduced summer monsoon rainfall in this region (Roxy et al 2015).Furthermore, an early onset of the SASM tends to be associated with a higher seasonal rainfall anomaly, while a late onset corresponds to a lower anomaly within the Indian subcontinent.Similarly, the timing of SASM withdrawal exhibits a positive influence on seasonal rainfall (Syroka and Toumi 2004, Noska and Misra 2016, Misra et al 2017).
The SASM exerts a profound influence on the Tibetan Plateau, which lies to the north of South Asia, primarily through land-atmosphere-ocean interactions (Liu et al 2020).Notably, the intensity of the SASM exhibits a negative correlation with rainfall along the Himalayas (Yao et al 2012) and a positive connection with rainfall in the southeastern regions (Jiang and Ting 2017).Given the strong interplay between precipitation and surface water resources, alterations in the SASM have notable repercussions for various water systems.The decline in precipitation has, for instance, contributed to the shrinking of lakes in the southern Tibetan Plateau ( Lei et al 2018).Moreover, the timing of the SASM onset plays a pivotal role in this context, with an earlier onset accelerating lake expansion (Liu et al 2019).This, in turn, enhances the wetting and greening of the Tibetan Plateau (Zhang et al 2017).
Due to the profound impact of the SASM on climate dynamics, numerous studies have developed or examined indices associated with its onset and intensity.These indices fall into two main categories.The first type examines the abrupt increase in local-scale rainfall, particularly over Kerala at the southwestern tip of India (Raju et al 2005, Misra et al 2018).The second, labeled as dynamical, focuses on regional-scale circulation changes over the Arabian Sea (Moron and Robertson 2014).This approach incorporates various climate variables such as atmospheric circulation (Taniguchi and Koike 2006), rainfall patterns (Ananthakrishnan and Soman 1988), convection dynamics (Wang and Fan 1999), moisture transport patterns (Fasullo and Webster 2003), and temperature trends (Prasad and Hayashi 2005).Fasullo and Webster (2003) (hereinafter referred to as FW03), defined the SASM's onset and withdrawal by vertically integrated moisturetransportation over the Arabian Sea.Syroka and Toumi (2004) pointed that the HWSI index, defined by low-level zonal wind for describing the withdrawal of the monsoon, is both a physically sensible and a practical tool to study the withdrawal of the monsoon.The integrated water vapor cannot detect the beginning of the monsoon (Taniguchi and Koike 2006).Ailikun and Yasunari (1998) showed that the WY index is more closely associated with the convective activity over the western Pacific and not with the convective activity over theIndian monsoon region.Although onset or withdrawal of the SASM has been defined by various methods, it is uncertain which definition is most adequate.All lie in their reliance on dynamic and thermodynamic principles, but each index has its unique strengths and limitations due to the use of a limited set of variables.
Previous research has compared the predictive ability of several SASM indices, and pointed out that the existing indices showd unsatisfactory prediction (Zhang et al 2022).In our study, we seek to deepen our comprehension of SASM indices in capturing the onset and withdrawal by undertaking a thorough comparison of existing indices from 1979 to 2018.The definition of an index is somewhat arbitrary.To quantify complex large-scale monsoon characteristics using a single index is often difficult.In addition, to avoid the 'Bogus' due to the rapid development of the single variable continuing over short periods, then we introduce a novel index based on a multivariable approach.Section 2 provides detailed information on the datasets and methodologies employed.In section 3, we present the results of our comparative analysis of SASM indices, focusing on their effectiveness in delineating onset and withdrawal dates, and introduce the new index tailored for the 1979-2018 period.Finally, section 4 succinctly summarizes the principal findings and conclusions derived from our study, contributing to the broader understanding of SASM dynamics.

Datasets
The data in this study include daily reanalysis data from the U.S. National Centers for Environmental Prediction-Department of Energy (NCEP-DOE) reanalysis 2 project (NCEP2) (Kanamitsu et al 2002) and daily mean precipitation data from the second Modern-Era Retrospective Analysis for Research and Applications (MERRA-2) (GMAO: Global Modeling and Assimilation Office 2015).Additionally, monthly precipitation were derived from the Global Precipitation Climatology Project (GPCP) (Adler et al 2003, Huffman andBolvin 2012).To enhance our dataset, we incorporated Outgoing Longwave Radiation (OLR) data from the U.S. National Oceanic and Atmospheric Administration (NOAA) and the Oceanic Niño Index (ONI) (Huang et al 2017).A summary of these datasets is presented in table 1.

SASM index
Nine indices from the literature are employed to assess SASM onset and withdrawal dates.Figure 1 illustrates the defined regions for these nine SASM indices, each with distinct characteristics.Notably, certain indices encompass a broader geographical domain (e.g.FW03), while others focus on a more confined area (e.g.PH05).These indices differ not only in their defined regions but also in the variables considered (table 2).Despite some indices originally designed for either onset or withdrawal, our analysis calculates both onset and withdrawal dates using each index.Detailed definitions for each index are provided in table 2 and elaborated upon below.
(1) EIMR: The arrival of the SASM always brings an abrupt increase in rainfall.Goswami et al (1999)   (2) MHI: Given that the SASM rainfall is predominantly influenced by the regional monsoon Hadley circulation, Goswami et al (1999) additionally established the Monsoon Hadley Circulation Index (MHI), defined as the meridional wind difference between 850 hPa and 200 hPa over the region (10°N-30°N, 70°E-110°E).The transition from negative to positive signifies the onset of the SASM, while the shift from positive to negative indicates its conclusion.
(3) HWSI: In contrast to the onset, the withdrawal of the SASM exhibits greater variability, and limited attention has been directed toward its study.Recognizing its significance, Syroda and Toumi (2004) introduced a withdrawal index based on characteristic low-level circulation patterns.This daily circulation index is defined as the difference in the 850 hPa zonal winds between the southern region (5°N-15°N, 50°E -80°E) and the northern region (20°N-30°N, 60°E-90°E), termed the Horizontal Wind Shear Index (HWSI).The withdrawal date of the SASM is identified as the first occurrence of seven consecutive days when the HWSI is negative.On the other hand, when the HWSI is positive for seven consecutive days, this marks the initiation of the SASM.(4) OCI: Wang et al (2009) introduced the Onset Circulation Index (OCI), which involves the sustained 850 hPa zonal wind averaged over the southern Arabian Sea (5°N-15°N, 40°E-80°E).The onset date is identified as the first day when the OCI surpasses 6.2 m s −1 for six consecutive days, while the transition of the OCI from positive to negative signifies the withdrawal of the monsoon.The selection of 6.2 m s −1 as the critical value aligns with the climatological mean onset date at Kerala on June 1st, where the mean 850 hPa zonal wind over the southern Arabian Sea reaches 6.2 m s −1 .
(5) TT: In the context of the meridional gradient of tropospheric temperature, Goswami et al (2006) introduced the Tropospheric Temperature (TT) as the temperature difference between 200 hPa and 600 hPa over two defined regions: the northern region (TTN: 5°N-35°N, 40°E-100°E) and the southern region (TTS: 7.5°N-20°N, 62.5°E-75°E).The SASM onset is identified when the difference between TTN and TTS exceeds 0, and the SASM concludes when this difference becomes negative.
(6) TK06: Taniguchi and Koike (2006) observed that the abrupt increase in integrated water vapor and moisture transport, indicative of a sudden transition in circulations, was insufficient to determine the onset of the SASM.Consequently, they defined the onset as the point when the low-level wind speed at 850 hPa exceeds 8 m s −1 for seven consecutive days over the region (7.5°N-20°N, 62.5°E-75°E).Our assessment demonstrated that this definition aligns well with the abrupt increases in rainfall and the distinct transition in atmospheric circulations.
(7) PH05: Prasad and Hayashi (2005) established the onset and withdrawal criteria for the SASM based on a circulation index and the formation of a deep convective zone off the coast of India.The onset is defined using the zonal asymmetric temperature anomaly (ZATA) between 850 hPa and 600 hPa over the region (10°N-17.5°N,65°E-75°E).Specifically, the onset is identified when the ZATA becomes negative for more than three consecutive days, accompanied by a minimum vertical wind shear index (VWSI) of 10 m s −1 over the region (5°N-20°N, 40°E-80°E).The withdrawal date is determined by the onset of negative VWSI.
(8) CI: Acknowledging the pivotal influence of convective latent heat release in propelling the summer monsoon, Wang and Fan (1999) introduced a Convection Index (CI) specifically for the Bay of Bengal-India region.The CI is delineated by OLR anomalies within the region (10°N-25°N, 70°E-100°E).
(9) FW03: Fasullo and Webster (2003) recognized the direct correlation between large-scale hydrological cycles and fundamental monsoon dynamics.Consequently, they opted to utilize hydrological cycles as a key physical foundation for monitoring the monsoon transition, leveraging large-scale and relatively well-measured parameters such as wind and humidity.In this study, we defined the onset and withdrawal dates of the SASM based on vertically integrated moisture transport over the Arabian Sea (20°S-30°N, 40°E-100°E).The alteration in the sign of the index value from negative to positive (and vice versa) serves as an indicator of the onset (withdrawal) of the SASM.

Methods
To discern evolving trends in onset and withdrawal dates, we employ the cumulative anomaly method.Firstly, the anomaly values are obtained by subtracting the climatological values .Then the cumulative anomaly time series are cumulatively summed, which represents the long-term departure of the variable from its 'normal' cycle.From the obvious ups and downs of the time series, the long-term evolution trend and sustained changes can be detected.The correlation coefficient is then determined using the least-squares method, with statistical significance assessed through Student's t-test.Linear regression analysis is conducted separately for the onset date and related June rainfall, as well as 850-hPa wind, and for the withdrawal date and associated September rainfall, along with 850-hPa wind.
To unveil key features of rainfall patterns during the onset period (June) and withdrawal period (September), we conduct Empirical Orthogonal Function (EOF) analysis on South Asian regions' rainfall.This analysis yields distinct modes, each accompanied by its temporal variation.The eigenvalue associated with each mode represents the total variance along a specific EOF mode, and the percentage of variance explained by each mode is determined by the ratio of the squared eigenvalue of that mode to the sum of squared eigenvalues across all modes, diminishing with the mode's order.

A multivariable monsoon index
Different criteris and definitions have been posed to determine the monsoon onset, but these difinitions are diverse to be used to understand the monsoon variability on various time scales.Try to reproduce the sudden changes of the general circulation fields from the low level to the high level as much as possible, we employ a multivariate EOF analysis to detect the onset and withdrawal dates, encompassing a combined consideration of multiple variables.Seven variables outlined in table 2, including precipitation, air temperature, 850-hPa zonal wind, 200-hPa zonal wind, temperature at 600 hPa, temperature at 200 hPa, and Outgoing Longwave Radiation, are incorporated to enhance the representation of large-scale circulation information.Normalized anomaly series are initially created for each variable to facilitate the analysis of coherent variables across all fields.Subsequently, a combined normalized anomaly data matrix is formulated, mirroring the approach in singlevariable EOF analyses.
The common EOF method is then applied to this data matrix, spanning the domain from 5°N to 35°N and 65°E to 85°E, that is a core monsoon region.The onset and withdrawal dates are determined by the time series of the first mode of EOF (hereafter called as CEOF).Specifically, the onset is identified as the date when the value of EOF1 transitions from negative to positive values, while the withdrawal date corresponds to the transition from positive to negative values.

Comparison of SASM onset and withdrawal dates
While all SASM indices exhibit similar interannual variability during 1979-2018, noticeable differences in amplitudes, particularly for withdrawal dates, are evident among the indices (figure 3).The box plots for onset dates reveal a mean onset date ranging from Julian day 143 to 157 (23 May to 6 June) across the nine indices.Most indices exhibit withdrawal dates between Julian day 280 and 294 (7 September to 21 October), except for FW03.In comparison to withdrawal dates, onset dates among the nine indices demonstrate larger dispersion, indicated by higher box.
The calculated correlation coefficients among onset dates range from 0.33 to 0.79 consistently with significant confidence (figure 4).Withdrawal dates, however, are more diverge, with correlation coefficients ranging from 0.12 to 0.83.Notably, HWSI, OCI, and TT have the largest correlation coefficients.Eight out of nine indices display increasing trends with comparable magnitudes, suggesting an early onset of SASM during 1979-2018 (figure 5).The advanced onset is most likely to be attributed to the heat contrast between the Asian landmass and the tropical Indian Ocean (Kajikawa et al 2012).Withdrawal dates also exhibit increasing trends   (PDO) from a predominantly warm phase since the mid-1970s to a cold phase since the late 1990s.Several indices (EIMR, HWSI, FW03, and PH05) shows an opposite trend pattern for onset, while others display different variability, such as TT and MHI.In short, the estimated onset and withdrawal dates exhibit a relatively consistent pattern among the indices, although there is a larger spread among the indices for withdrawal dates.

Relationship between SASM's onset and withdrawal with rainfall
SASM typically initiates in June and retreats in September.An EOF analysis conducted on the precipitation patterns across South Asia finds that the first mode, represents 92.56% of the total squared variance in June (figure 7(a)) and 90.59% in September (figure 7(b)).During the monsoon onset, two distinct rainfall belts manifest along the west coast of the Indian subcontinent and the east coast of the Bay of Bengal, extending to the southern Tibetan Plateau.As the monsoon weakens in September, the primary rainfall belt is situated along the east coast of the Bay of Bengal, covering most South Asian regions with reduced precipitation compared to June.
The spatial regression patterns of onset indices with rainfall and lower-level (850 hPa) circulation reveal that positive rainfall anomalies are evident in June along the west coast of the Indian subcontinent and the east coast of the Bay of Bengal, extending to the southeastern Tibetan Plateau (figure 8).Low-level southwest winds prevail across South Asia and the southern Tibetan Plateau.A prominent high-value center is observed along the east coast of the Bay of Bengal and the west coast of the Indian subcontinent, consistent across all onset indices.This spatial pattern of two maximum centers is mainly caused by a northwest-southeast low pressure extending from Rajasthan, India to the BOB and the interaction between low-level winds and terrain, respectively (Zhang et al 2022).The rainfall anomalies associated with the onset indices mirror the first mode of EOF.A similar regression for withdrawal indices finds that positive rainfall anomalies appear north of the Bay of Bengal and in the southeastern Tibetan Plateau, with variations in the positive and high values among different indices (figure 9).The rainfall anomalies associated with withdrawal indices align with the first mode of EOF.

Linkage between SASM onset and withdrawal with SST signals
The interannual variability of the SASM has been associated with ENSO boundary forcing (Webster et al 1998).The onset dates from all nine indices exhibit significant connections with the ONI index in the preceding spring, while withdrawal dates are closely associated with the ONI index in the simultaneous autumn (figure 10).All onset dates exhibit positive correlations with the ONI index, with coefficients exceeding 0.3.Delayed onsets often correspond to an anomaly pattern resembling El Niño, whereas La Niña status is observed in early onsets (Joseph et al 1994, Liu et al 2015).Among the indices, OCI, TT, and TK06 demonstrate higher correlation coefficients compared to others.
For withdrawal dates, all indices display significantly negative correlations with SST signals in the simultaneous autumn, except for MHI.TT, PH05, and HWSI outperform other indices in this regard.The ONI SST anomalies exhibit a weak positive correlation before the monsoon season (up to several months before).As the monsoon onsets, the correlation gradually becomes negative, intensifying during the withdrawal period compared to the summer months (figure 10(b)), as also observed by Syroka and Toumi (2004).The mid-late summer monsoon is notably linked to the anomalous state of ENSO in the following rather than the previous winter (Ailikun and Yasunari 2001).In addition to large-scale processes (e.g.ENSO (Joseph et al 1994; PDO (Watanabe and Yamazaki 2014)), SASM's onset and withdrawal dates are modulated by sea surface temperature anomalies (SSTA) in the Indian Ocean (Misra et al 2018) because they are believed to be a localized synoptic process.

A multivariance monsoon index and its impacts on rainfall and runoff
The existing indices are defined by either a single or two large-scale circulation variables, each having its own set of advantages and disadvantages.To account for the complex large-scale characteristics and their temporal variations during the onset and withdrawal of the monsoon, a multivariate monsoon index is introduced through a multivariate EOF analysis, encompassing a combined consideration of multiple variables.The first EOF mode, explaining about 36% of the total variance, is utilized to derive the onset and withdrawal dates (figure 11).Clear interannual variability is evident, superimposed on a trend towards an earlier onset and later withdrawal.The correlation results (figure 12(a)) reveal that the EOF-based index exhibits significant correlations with the other nine indices, all exceeding 0.30, except for the withdrawal date in EIMR.The mean onset date from EOF is 148 Julian days, positioned in the middle when compared with previous indices.The withdrawal date from EOF-based index is 283 Julian days, comparable to previous indices with a smaller difference.A criterion from Ghanekar et al (2019) is used to evaluate the performance of this new index.This criterion is based on rainfall, wind field and Outgoing Longwave Radiation (OLR) and is used in operational mode for the India Meteorological Department (IMD) since 2006.The correlation coefficients are calculated between this criterion and all ten indices in our study (shown in figure 12(b)).From the figure, we can find that the new index (CEOF) shows the higher correlation coefficient (0.72) with this criterion than other nine indices (0.36-0.68).This new index shows better performance compared to existing indices and can effectively reproduces the interannual variability of monsoon onset.
To reveal the interdecadal changes of index, further evaluation (figure 13) finds that over the past four decades, the mean values of onset dates display a slight decrease, with a standard deviation ranging from 4 to 7 days, demonstrating moderate variability (13-25 days).The mean values of withdrawal dates exhibit an increasing trend, particularly in recent years, accompanied by a larger standard deviation and amplitude, notably in the period 1989-1998, collectively greater than the onset date.In summary, while the onset and withdrawal dates show significant interdecadal variability, the overall variation is relatively small.
We computed climatological composites centered on the onset date (figure 14) and withdrawal date (figure 15) to assess the efficacy of seasonal monsoon transitions.A gradual seasonal variation precedes the onset, followed by an abrupt transition at day 0, reaching a mature stage approximately two weeks later.The entire mature monsoon stage persists for about three months.Before monsoon onset, an evident latitude of maximum precipitation, representing the Intertropical Convergence Zone (ITCZ), shifts across the equator (figure 14(a)).A corresponding transition in upper-level circulation is observed.The 200-hPa meridional wind (V200) and zonal wind (U200) depict the upper-level flow of large-scale circulation in the SASM region.Upon monsoon onset, the southern hemisphere cell expands into the northern hemisphere and strengthens, while the  northern hemisphere cell contracts and weakens (figure 14(b)).The upper-level westerly jet in the northern hemisphere weakens, migrates northward, and a subtropical westerly jet begins to develop in the southern hemisphere (figure 14(c)).In the lower level (850 hPa), the northern hemisphere tropical trade winds develop and prevail over the entire SASM region (figure 14(d)).In contrast, monsoon withdrawal is much more gradual, with a slow retreat of the rain belt and a transition in winds (figure 15).In summary, our index effectively represents the transition of large-scale SASM circulation and characterizes the sudden onset of the monsoon.
The timing of monsoon onset, whether earlier or later, undoubtedly impacts rainfall patterns across South Asia and its surroundings.While numerous studies have investigated the onset of the SASM, crucial for regional agriculture (Bollasina et al 2013), fewer have explored the implications of SASM withdrawal dates on precipitation.The correlation results (figure 16(a)) reveal the new index negatively correlats well with the rainfall along the east coast of the Bay of Bengal, the west coast of the Indian subcontinent and the southeastern part of the Tibetan Plateau, where obvious more rainfall appears in figure 8.An earlier onset may bring more rainfall to these regions.Similarly, withdrawal dates negatively influence September rainfall (figure 16(b)) around the southeastern Tibetan Plateau and the northern Bay of Bengal, signifying that a delayed retreat can result in less rainfall during the monsoon retreat period.Around the southeastern Tibetan Plateau, both onset and withdrawal dates exert the same (negative) effect on rainfall.The earlier onset and delayed retreat of the monsoon may potentially yield heterogeneous influences on rainfall for the southeastern Tibetan Plateau.
The further synthetic analysis of monsoon precipitation finds that a substantial reduction in precipitation appears over a large area, particularly around the southern Tibetan Plateau and Indian subcontinent, in positive onset years, indicative of a delayed monsoon onset (figure 17(a)).Negative or earlier onset years exhibit the opposite phenomenon.In comparison with onset, the effects of withdrawal dates on monsoon rainfall appear weaker.When the monsoon retreat is delayed, increased precipitation is observed along the Himalayas and in   Similar to rainfall, we examined the influence of SASM onset and withdrawal on potential water availability reflected in runoff, given the close connection between rainfall and runoff in monsoon seasons (Liu et al 2018).A delayed monsoon outbreak (figure 18(a)) leads to a substantial reduction in runoff across the Indian subcontinent, north of the Bay of Bengal, and the inner Tibetan Plateau, consistent with precipitation distribution (figure 17(a)).Conversely, an early monsoon onset (figure 18(b)) results in a positive runoff anomaly across most regions.During the monsoon retreat period in September, delayed monsoon withdrawal potentially brings more runoff along the Himalayas and the Indian subcontinent (figure 18(c)).An early monsoon retreat leads to a contraction in regions with a positive runoff anomaly (figure 18(d)).Clearly, both early onset (figure 18(e)) and delayed retreat (figure 18(f)) generate more rainfall and subsequently increase runoff, with the former exhibiting a stronger effect than the latter.

Summary and conclusions
SASM is an important component of the global monsoon system and acts on a significant influence on South Asia and its surrounding areas in agriculture, life and socio sconomy.Numerous indices have been raised to study the SASM.In this study, we firstly choose the existing nine indices to compare their performance in capturing the onset and withdrawal of the SASM during 1979-2018.The existing nine monsoon indices exhibit similar and comparable onset and withdrawal dates for the SASM, despite variations in their definitions.Among the existing indices, some are more empirical and largely based on precipitation amounts, some rely on the low-level circulations, and some are connected to the changes of the total column water vapor.These indices are generally derived from the orginal datasets, and are easy to be affected by synoptic signals hidden in data.Consequently, we bring forward a simple and yet reliable method to examine the onset and withdrawal of the SASM.A multivariate monsoon index is introduced, incorporating multiple standardized variables to comprehensively capture large-scale circulation characteristics from low to high levels.This method preserves large-scale information as much as possible and eliminates the interference of synotic information, which may have existed in previous indices before.Due to include more variables, the new index takes into account the dynamic and thermodynamic principles for the best possible.The index demonstrates efficacy in depicting the  1979, 1983, 1992, 1996, 1997, 2012, and 1984, 1985, 1994, 1999, 2002, 2006, 2009, 2018 for the negative onset years.The positive withdrawal years are 1983, 1984, 1985, 1995, 1998, 2001, 2010, 2017 and 1982, 1987, 1994, 1997, 2002 for negative withdrawal years.seasonal evolution of large-scale circulation with evident interannual variability.Earlier onset and delayed retreat are identified as favorable conditions for increased rainfall and potential water resources across South Asia and the Tibetan Plateau.

Figure 1 .
Figure 1.Study regions defined by nine indices of South Asian summer monsoon.

Figure 3 .
Figure 3.Time series of South Asian summer monsoon's onset dates (a) and withdrawal dates (b) and the corresponding box diagram derived from nine indices during 1979-2018.

Figure 5 .
Figure 5. Linear trend (days decade −1 ) of South Asian summer monsoon's onset dates and withdrawal dates from nine indices during 1979-2018.

Figure 4 .
Figure 4. Correlation coefficients among all indices based on onset date (a) and withdrawal date (b) during 1979-2018 (values greater than 0.30 are significant at the 95% confidence level).

Figure 6 .
Figure 6.Time series of cumulative anomaly of South Asian summer monsoon's onset dates and withdrawal dates from nine indices during 1979-2018.The climatological mean is calculated during 1981-2010.

Figure 7 .
Figure 7. Spatial distribution and time-series of the first mode of precipitation in June (a) and September (b) during 1979-2018.

Figure 8 .
Figure 8. Spatial patterns of 850-hPa wind and rainfall regressed against the onset dates derived from South Asian summer monsoon indices.The black dots represents the significant values between the onset dates and precipitation at the 95% confidence level.

Figure 9 .
Figure 9. Similar to figure 7, but for withdrawal dates.

Figure 10 .
Figure 10.Correlation coefficients between the Oceanic Niño Index (ONI) and onset dates (a) and withdrawal dates (b) .The dashed line represents the significance at the 95% confidence level.Shading in figures 10(a) and 10(b) represents spring period and autumn period, respectively.

Figure 11 .
Figure 11.Time-series of onset and withdrawal dates derived from the multivariable EOF method during 1979-2018.The linear regression equations and significant test are shown in figure.

Figure 12 .
Figure 12.Correlation coefficients between the index from CEOF and previous nine indices (a) and between all ten indices and a criterion from Ghanekar et al (2019) (b) during 1979-2018.The dashed line represents the significance at the 95% confidence level.

Figure 13 .
Figure13.The mean, standard deviation and range of SASM onset and withdrawal dates derived from the multivariable EOF method in different period.

Figure 14 .
Figure 14.Seasonal variation of precipitation (mm day −1 ) (a), 200 hPa meridional wind (m s −1 ) (b), 200 hPa zonal wind (m s −1 ) (c) and 850 hPa zonal wind (m s −1 ) (d) climatological composite centered on onset date averaged at 65 °E −85 o E. Vertical dashed line is the onset date.The blue arrow indicates the location of South Asia.

Figure 15 .
Figure 15.Same to figure 13, but for withdrawal date.

Figure 16 .
Figure16.Spatial distribution of correlation coefficients between onset date and rainfall at June (a), withdrawal date and rainfall at September (b), respectively.The vector arrow is the mean wind at 850 hPa.The plus sign represents the significant values at the 95% confidence level.

Table 1 .
Summary of datasets used in this study.
developed an Extended Indian Monsoon Rainfall (EIMR) index averaged over the region (10°N-30°N, 70°E-110°E), which effectively captrues the variation in convective heating associated with the SASM.The mean value of 4.83 mm day −1 on June 1st (the mean onset date) during 1980-2018 is the threshold for the beginning of the