A novel index for depicting ENSO transition with application in ENSO-East Asian summer monsoon relationship

The monthly mean data analyzed in this paper, for the period of 1979–2019, are from the following: (1) the European Centre for Medium-range Weather Forecasts 5 reanalysis (ERA5) in a 0.75° × 0.75° spatial resolution (Hersbach et al 2019), (2) the Global Precipitation Climatology Project (GPCP) in a 2.5° × 2.5° resolution (Adler et al 2003), (3) the Hadley Centre SST in a 1° × 1° resolution (Rayner et al 2003), and (4) sea surface height relative to geoid from Global Ocean Data Assimilation System in a 0.333° × 1.0° horizontal resolution from the National Centers for Environmental Prediction (Behringer and Xue 2004). Correlation analysis is applied to evaluate relationship features, and the two-tailed Student's t-test is used to evaluate the statistical confidence levels for all results obtained. The long-term linear trends are removed before any further analysis to attain more apparent signals on the interannual timescale.

The EASM strengthens and moves northward with the western Pacific subtropical high during June and July but retreats and moves southward in August (Yang et al 2022), and different physical mechanisms are responsible for the strengthening and retreating processes of the monsoon. Here, we focus on the early summer from June to July when the EASM intensifies. The Niño-3.4 index, defined as the area-averaged SST anomalies in the equatorial Pacific (170° W–120° W, 5° S–5° N), is used to measure ENSO conditions (Trenberth and Stepaniak 2001).

Previous studies have quantified the SPB intensity on interdecadal timescale by computing the gradients on autocorrelation coefficients of Niño-3.4 index for a specific period of time, such as the SPB index by Fang et al (2019) and Liu et al (2019). Fang et al (2019) computed the difference between the autocorrelation values of February and May, for autocorrelation curves starting from each month. The SPB intensity index was finally defined as the average of these February-to-May gradients for all 12 curves. Besides, Liu et al (2019) proposed a similar method, but instead of considering the difference between February and May, a band of maximum decline in autocorrelation coefficients in monthly Niño-3.4 SST index was used to represent the SPB intensity (see detailed description in text S1 in the supplementary information).

In fact, the results from Fang's method are consistent with those from Liu's method (figure S1(b) in the supplementary information). The autocorrelation coefficient values in February are always higher while those values in May have a larger variance. Therefore, the SPB intensity depends on the autocorrelation coefficients in May. During the transitive El Niño (La Niña) events, the warm (cold) SST over the central Pacific in the preceding winter changes to cold (warm) SST in the following summer, which implies a negative autocorrelation coefficient in May, resulting in a large SPB intensity. In contrast, during the persistent El Niño (La Niña) events, a warm (cold) SST over the central Pacific in summer follows the warm (cold) SST in the preceding winter, which implies a positive autocorrelation coefficient in May, resulting in a smaller SPB intensity. In short, the SPB intensity is mainly contributed by the autocorrelation coefficients in May, which depend on the transitive or persistent nature. In this way, ENSO transition can be linked to the SPB.

One of the main interests of this study is to quantify and analyze the SPB intensity and ENSO persistence on the interannual timescale. Weise and Weise (1999) have performed this kind of task by using two sine waves to describe the evolutions of the Niño-3 index and the Southern Oscillation index. Yet, their results depend on the prescribed form of the waves and cannot match those in models very well. In this study, we use the method from Liu et al (2019, SPB_L) to quantify the contribution of each specific year to the full-period SPB intensity, by taking the difference between the SPB_L index for the whole period and that resulting from leaving out the year 't' (i.e. leave-one-out cross validation, Gelfand and Dey 1994). Specifically, the autocorrelation coefficients of the monthly Niño-3.4 SST index ${R_I}\left( {i,j} \right)$ are calculated as a function of starting month and lagging time, where$\,i$ is the starting months ($i = 1,\,2,\, \ldots ,\,12$) the leading time ($j = 0,\,1,\,2,\, \ldots ,\,12$) and $I$ refer to a specific window period of years, encompassing 1979–2019. Starting month $i$ represents the calendar month from January to December. For each month within the dataset ($i$) and for the 12 different possible lags ($j$), we drop out the samples from the subsequent $j$ months if the month is before or equal to May ($i \le 5$), and drop out the samples from the preceding $j$ months if it is after May ($i > 5$). To be specified, in the case where the month is before or equal to May ($i \le 5$), for example, dropping out the samples during 198 101–198 107 is used to calculate$\,{R_I}\left( {1,6} \right)$ after removing the year 1981. That is, for the Niño-3.4 SST index in January and July, (1979/01, 1980/01, 1982/01,..., and 2019/01) and (1979/07, 1980/07, 1982/07,..., and 2019/07) are used to calculate the corresponding correlation coefficient (namely ${R_I}\left( {1,6} \right)$). In addition, in the case where the month is after May ($i > 5$), for instance, dropping out the samples during 198 012–198 108 is used to calculate ${R_I}\left( {9,8} \right)$ after removing the year 1981. In other words, for the Niño-3.4 SST index in September and following May, (1979/09, 1981/09, 1982/09,..., and 2018/09) and (1980/05, 1982/05, 1983/05..., and 2019/05) are used to calculate the corresponding correlation coefficient (namely ${R_I}\left( {9,8} \right)$). This method guarantees that all the data points are relevant and the same SPB of year for ${R_I}\left( {i,j} \right)$ is removed. Since the SPB index represents ENSO transition/persistence as mentioned in the introduction, we call this new index as 'ENSO transition index'. For each year '$t$', it is computed as follows (see detailed equations in text S2 in the supplementary information):$ENSO{ }transition{ }index{ }\left( t \right) = SP{B_L}[ \text{for autocorrelation coefficients for the whole}$ $\text{period}] - SP{B_L}[ \text{for autocorrelation coefficients}$ $\text{for the whole period but with year}^{^{\prime}}t^{^{\prime}}{\text{ removed}}]$, as shown in equation (1):

$$\begin{align}& {\text{ENSO}}{\mkern 1mu} \;{\text{transition}}\;{\mkern 1mu} {\text{index}}{\mkern 1mu} \left( t \right) \nonumber\\ & = {\text{SP}}{{\text{B}}_L}\left[ {1979 - 2019} \right] - {\text{SP}}{{\text{B}}_L}\nonumber\\ & \quad \left[ {1979,{\mkern 1mu} \ldots ,t - 1,t + 1, \ldots ,{\mkern 1mu} 2019} \right].\end{align} \tag{ 1 }$$

Then, we can obtain the SPB index on the interannual timescale. For all ENSO events, the lagged autocorrelation coefficients of the preceding winter are always significantly positive while those of the following summer are close to zero, which implies that some ENSO events transition in spring but others do not. The SPB intensity primarily reflects the different phases of SST during summer. Fast-decaying ENSO events tend to show negative autocorrelation coefficients between SST anomalies of the preceding winter and the following summer due to the opposite signs of the anomalies, while slow-decaying events exhibit positive autocorrelation coefficients. Therefore, SPB intensity, which captures the varying decaying pace of ENSO events, can be used to quantify ENSO transition.

During the transitive (persistent) events, the negative (positive) autocorrelation coefficient of the Niño-3.4 SST index in summer corresponds to the high (low) value of the ENSO transition index. This analysis suggests that a positive (negative) ENSO transition index represents a transitive (persistent) ENSO event. The higher (lower) ENSO transition index, the stronger (weaker) ENSO transition. It is worth noting that a zero value of ENSO transition index indicates an inconspicuous feature of ENSO transition/persistence, rather than an absence of the SPB, indicating that some ENSO events are followed by neutral conditions (Yu and Fang 2018, Fang and Yu 2020b). Compared with the previous methods that quantify ENSO transition by calculating the SST gradient between the preceding winter and summer (Wang et al 2013, 2015, Liang et al 2023), this method using autocorrelation coefficients offers two advantages. (1) The dimensionless correlation coefficient prevents the features of higher magnitude data from polluting the features of lower magnitude data. (2) Autocorrelation coefficients imply the influence of previous SST on the following SST, which represents the link of ENSO among different seasons.

As shown in figure 1(a), the ENSO transition index (red solid line) shows a significant interannual variability from 1980 to 2019. For example, it exhibits a large positive value in 2016, meaning that the ENSO event displays a prominent transitive feature from June 2015 to May 2016. Similarly, the ENSO transition index is largely negative in 1987, representing the prominent persistent feature from June 1986 to May 1987. Previous studies use the SST gradient between the preceding winter and summer to describe ENSO transition (Wang et al 2013, 2015, Liang et al 2023). Here, the absolute values of Niño-3.4 SST gradient between the preceding winter and summer are defined as a traditional ENSO transition index. The absolute values make the traditional ENSO transition index more comparable to our new index because we neglect whether the ENSO transitions from a warm phase to a cold one (or from a cold phase to a warm one). To be specific, the traditional ENSO transition index is close to zero, which represents almost no seasonal variation of the ENSO SST anomalies and thus a persistent ENSO event. After normalization, it becomes the minimum value of the time series of traditional index. On the contrary, the large Niño-3.4 gradient between the preceding winter and summer denotes a transitive ENSO event. The higher traditional ENSO transition index, the more transitive the ENSO event is. The maximum, zero, and minimum values represent transitive, neutral, and persistent conditions respectively, in both new and normalized traditional indices. Then, we compare our new ENSO transition index with the standardized traditional ENSO index. Overall, the strong correlation ($R = 0.64$) between the normalized traditional ENSO transition index and our new index further proves the validity of ENSO transition index.

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Although the traditional index can capture the variability of ENSO transition, we find that the new index can quantify ENSO transition more accurately than the traditional one by examining the transitions of historical El Niño and La Niña episodes on a case-by-case basis. Table S1 shows the historical ENSO events identified by the Oceanic Niño Index with the criterion of the Climate Prediction Center (Huang et al 2017). Here, we focus on the ENSO evolution cycle, namely from preceding May–June–July to June–July–August. During 1999, a strong persistent La Niña event was shown in our index but not in the traditional index (table S1). The years 1990 and 2014 were ENSO neutral, which should not be interpreted as the persistent years, as shown in our index. For the ENSO event in 2015, the significant El Niño was persistent most of the time, which should be interpreted as a persistent event as our new index indicates. The El Niño events in 1983 maintained until early summer and did not experience significant decaying most of the time, which should not be interpreted as strong persistent years by the traditional ENSO transition index. Therefore, our new index can quantify ENSO transition more precisely than the traditional index using the seasonal SST gradient. Given that ENSO characteristics underwent decadal changes by the end of the 20th century, we also use a different reference period to calculate the index (figure S1(a)). Although the magnitude of the index becomes smaller due to the changed reference value, its variability remains nearly unchanged, suggesting that ENSO transition identified by the index is not sensitive to the reference period. We also validate the above transition feature by using different lengths of time series (figure S2(a)), and the results clearly demonstrate the validity of the ENSO transition index.

In this section, we further testify the validity of the ENSO transition index by examining its relationship with the factors that affect ENSO transition. As shown in figure 1(b), the correlation coefficient between the Niño-3.4 index in the previous winter (blue dashed line) and the ENSO transition index ($R\, = \,0.47$) is significantly above the 99% confidence level, indicating that the ENSO transition in the following year is positively correlated with ENSO intensity. A positive Niño-3.4 index represents the occurrence of an El Niño event, and most El Niño events possess a strong transitive characteristic, which can be explained by the charged-discharged mechanism (Fang and Yu 2020b). If the El Niño SST anomalies are much stronger, the related westerly wind anomalies over the equatorial Pacific become stronger, resulting in a more active discharged process via stronger poleward Sverdrup transport (Jin 1997a, 1997b). Therefore, the value of ENSO transition index is high. On the contrary, a negative Niño-3.4 index indicates the occurrence of La Niña events, and most La Niña events exhibit a strong persistence (DiNezio and Deser 2014, Geng et al 2023, Wang et al 2023, Li et al 2024), consistent with the lower value of the ENSO transition index.

Figure 2 shows the correlations of ENSO transition index with the SST and 850 hPa horizontal wind in previous seasons. The most prominent signal is the warm SST in the central-eastern Pacific, consistent with the high correlation coefficient between the Niño-3.4 index and the ENSO transition index as shown in figure 1(b). Note that the positive correlation pattern between the ENSO transition index and Pacific SST anomalies becomes more significant from summer to winter, with westerly wind anomalies moving to the eastern equatorial Pacific from the western Pacific. The Bjerknes feedback is one of the vital mechanisms for the development of El Niño events, by amplifying warm SST anomalies in the central-eastern Pacific. This amplification occurs due to a decrease in the SST gradient and associated decreasing longitudinal pressure gradient. Consequently, anomalous westerly winds develop and move eastward in the equatorial Pacific, reducing wind stress and exciting oceanic downwelling Kelvin waves propagating eastward. Therefore, the westerlies deepen the thermocline (i.e. positive sea surface height anomaly) in the eastern Pacific while shallow it in the western Pacific (figures S3(a)−(c)), which is conducive to El Niño development. Furthermore, the westerly wind anomalies are strongest at the equator and diminish away from the equator, resulting in positive anomalies of wind stress curl. This, in turn, leads to poleward Sverdrup transport and a stronger discharge process in the upper ocean. Therefore, in the post-ENSO spring and summer, the thermocline depth becomes shallower along the equatorial Pacific and deeper in the off-equatorial regions (Jin 1997a, 1997b, Clarke et al 2007, Geng et al 2022) (figures S3(d) and (e)). This result is consistent with the previous studies, which suggest that the warm SST in the central-eastern Pacific is favorable for transitive ENSO events (Jin et al 2021, Jin and Liu 2021b). Generally, El Niño events are more likely to be transitive (Fang and Yu 2020a, 2020b). The westerlies over the western Pacific favor the occurrence and development of El Niño events (figures 2(a)−(c)). Previous studies have also proposed that the rapid growth of warm SST favors a reduction of SST persistency in the Niño 3.4 region, thereby strengthening ENSO transition (Fang et al 2019, Fang and Zheng 2021). By contrast, La Niña events tend to be persistent (Fang and Yu 2020a, 2020b). The southeasterlies associated with the cold SST anomalies over the off-equatorial Pacific (180°–150° W, 30° S–0° N) in winter and spring (figures 2(c) and (d)) are favorable for the persistence of La Niña events (Fang et al 2022). This process is driven by a zonal Bjerknes feedback and various meridional physical mechanisms, such as the incursion of off-equatorial subsurface cold water, which prolongs the life of La Niña and thus large persistence (Zheng et al 2016).

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Note that the DJF-mean Niño-3.4 series explains only about 22% of the variance of the ENSO transition index (figure 1(b)), indicating that ENSO transition is not solely determined by previous ENSO conditions. To explore other potential factors, we exclude the ENSO signal using a partial correlation analysis. The SST signals outside the equatorial Pacific exhibit their own variabilities independent of ENSO. Positive SST anomalies in the tropical North Atlantic during spring can favor an El Niño event transfer to a La Niña event in the following season. One of the mechanisms is generating easterly wind anomalies over the western equatorial Pacific (figures 3(c)–(d)) that cools the equatorial Pacific (Ham et al 2013) and the other is stimulating mid-latitude atmospheric teleconnections (Yu et al 2023). The Pacific meridional mode (PMM) in spring can also modulate ENSO (Fan et al 2021, Lee et al 2023), which is proven in figure 3(d). The negative phase of PMM increases the decaying speed of El Niño by strengthening equatorial easterly winds, while positive PMM favors the prolonged lifetime by reinforcing tropical westerly wind anomalies and then suppresses the evaporation cooling (Lee et al 2023). In short, the ENSO transition index can capture the main factors governing ENSO transition, suggesting that this index is physically reasonable.

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Given the significant influences of ENSO transition on the relationship between ENSO and EASM, the application of the new ENSO transition index in this field can further validate the index. We select all the years when the index varies above 0.5 standard deviations from its climatological mean state. By this criterion, the years with index values greater than 0.5 are classified as transitive ENSO years (totally 5 yr) while the years with index values less than −0.5 are classified as persistent ENSO years (totally 9 yr), as shown in table S2. To analyze the relationship between transitive or persistent ENSO and monsoon, we calculate the correlation between the Niño-3.4 index in boreal winter and the atmospheric circulation from the subsequent spring to summer.

During the transitive ENSO events (figure 4(a)), the cold SST anomalies in the central Pacific in summer follow the warm SSTs in the preceding winter. The SST anomalies shift the Walker circulation westward and reinforce it, especially in its descending region, which strengthens the upward motions over the south of the Maritime Continent (figures S4(a) and (c)). As a result, the descending motions (figure S4(c)) and the anticyclone over the western North Pacific are strengthened by the enhanced local Hadley circulation, thereby inducing intensified rainfall and strong EASM circulation. This strengthening of the WNPAC during transitive ENSO events is consistent with the previous studies (Chen et al 2012, Jiang et al 2019). In contrast, during the persistent ENSO events (figure 4(b)), the warm SST anomalies persist in the central Pacific during summer, moving the Walker circulation eastward and weakening it, which causes downward motions over the Maritime Continent (figures S4(b) and (d)). Thus, the WNPAC and the associated descending motions are suppressed due to the adjustment of the local Hadley circulation, exerting a weaker impact on the EASM. This result is consistent with the mechanism proposed by Wang et al (2017). That is, cold SSTs in the central Pacific directly reinforce the Walker circulation and precipitation over the Maritime Continent, modulating the Hadley circulation and affecting the WNPAC. Thus, the linkage between transitive ENSO and EASM is stronger than that between persistent ENSO and the monsoon, which is further validated by a case analysis (text S3 and figures S5–S6 in the supplementary information). In general, the new index can capture the impacts of ENSO transition on the relationship between ENSO and EASM, suggesting that it may serve as a useful tool for predicting the monsoon anomalies in the following year by monitoring preceding ENSO transition signals.

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Given that the ENSO-induced anomalous WNPAC persists into the spring and early summer following the ENSO peak, we have also conducted the same analysis as in figure 4, except for the post-ENSO spring, to further examine the different impact of ENSO transition on the WNPAC in this season, as identified by the new index. There are stronger warm SST anomalies in the western-central Pacific during the persistent ENSO events compared with the transitive events (figures S7(c) and (d)), leading to more pronounced and westward precipitation anomalies over the western equatorial Pacific (160°–180° E). As a result, a stronger cyclonic circulation exists to the west of rainfall anomalies, confining the WNPAC over the South China Sea (figures S7(a) and (b)). This result indicates that the new index also effectively captures the different ENSO transitions during the spring and their distinct impacts on the WNPAC.

The thermal condition over the Indian Ocean also plays a role in the relationship between ENSO transition and monsoon. During the transitive ENSO events (figure 4(a)), warm SST anomalies in the Indian Ocean induce positive precipitation anomalies (figure 4(c)), which strengthen the EASM and the WNPAC by exciting eastward propagating atmospheric Kelvin waves (Kug et al 2006, Yang et al 2007, Xie et al 2009, Izumo et al 2010). By contrast, during the persistent ENSO events (figure 4(b)), warmer SST (figure 4(d)) also exists in the Indian Ocean but it does not increase precipitation significantly (figure 4(b)) because the eastward Walker circulation induces downward motions over the Indian Ocean. As a result, the Indian Ocean warm SST only exerts a weaker impact on the EASM and the WNPAC.