On the Surface Independent Signals Within the ENSO Events

By analyzing the two types of El Niño Southern-Oscillation (ENSO) indices, i.e., the Central Pacific (CP) type index and the Eastern Pacific (EP) type index by Ren and Jin (2011), this study finds that the low correlation between the two types of indices by some previous studies should be reconsidered. Then based on previous ideas of the unified Niño index systems, the new ocean surface regions for the CP and EP El Niño indices’ calculation are defined. The features of the new CP and EP El Niño indices are consistent with sea surface temperature anomaly (SSTA) evolution along the Pacific equator. This study suggests that, concerning the El Niño characteristics, the CP and EP El Niño indices are not necessarily independent of each other; but their differences are almost absolutely independent of the unified Niño region SSTA. The results quantitatively confirm the relationship between the Trans-Niño Index (TNI) and Niño 3.4 indices (which are nearly independent of each other and provide different flavors for each El Niño event). Results presented here contribute to a better understanding of the nature of the El Niño events.


Introduction
Traditionally, it is suggested that an El Niño event occurs when 5-month running means of SST anomalies in the Niño 3.4 region (5°N-5°S, 120°-170°W) exceed 0.4°C or SST anomalies in the Niño 3 region (5°N-5°S, 90°-150°W) exceed 0.5°C for more than a certain number of months (Trenberth, 1997;Trenberth et. al, 2001). Most of currently existing Niño indices are based on the region coverage of the Niño 3, Niño 4, Niño 3.4, Niño 1+2 (Trenberth, 1997;Trenberth et. al, 2001;Trenberth and Stepaniak, 2001;Trenberth and Smith, 2006) and even recently merging indices such as the CP and EP indices are also strongly related to these Niño regions (Ashok et al., 2007;Kug et al., 2009;Yeh et al., 2009;Ren and Jin, 2011). Trenberth and Stepaniak (2001) suggested the Trans-Niño index (TNI), which is based on the difference between normalized SST anomalies averaged in the Niño-1+2 and Niño-4 regions, to describe the character and evolution of the El Niño events. At the same time, they found that the Niño 3. According to the facts that the ocean surface areas with maximum temperature anomaly are different for El Niño events, Fang et al. (2013) suggested a unified Niño region (UNR) outlined by the 0.7°C contour line of the temporal SSTA standard deviation along the Pacific equator and showed that all the traditional Niño indices can be well rebuilt by simple linear combination of the mean SST anomaly and the zonal thermal centroid (ZTC) anomaly of the UNR with highly linear correlation. The ZTC anomaly agrees quite well with the EP/CP El Niño classification by Yeh et al., 2009 or Kug et al., 2009 and the TNI index by Trenberth and Stepaniak (2001).
The Niño-3 index and Niño-4 index are often concerned in the EP/CP El Niño classification Yeh et al., 2009;Ren and Jin, 2011). The differences between these two indices are often considered in the EP/CP El Niño classification Yeh et al., 2009). Although the Niño-3 index and Niño-4 index are used to describe the different types of CP or EP El Niño events, they are actually highly correlated to each other (Ren and Jin, 2011). Trenberth and Stepaniak (2001) proposed the TNI index (regarded approximately as the SSTA gradient along the Pacific equator) and demonstrated the capabilities of the TNI index in describing different characters of each El Niño event.
The TNI index shows that the SSTA gradient along the Pacific equator during the El Niño events is a fundamental feature of the El Niño events. The SSTA differences between the different Niño regions along the Pacific equator during the El Niño events, to a great extent, show the different flavors of El Niño events.
However, to decrease the correlation between the CP or EP indices, Ren and Jin (2011) proposed a new way of defining the CP and EP indices (see Equ. (1)). Their CP and EP indices are little correlated, which could lead to the implication that the CP Niño index and the EP Niño index are almost independent of each other. As mentioned above, Trenberth and Stepaniak (2001) found that the Niño 3.4 index and TNI are nearly orthogonal. The sensitivity of the eastern-western SSTA gradient needs to be further examined to ascertain if it is consistent with the physical nature of the CP/EP indices proposed by Ren and Jin (2011). And what are truly the independent factors associated with El Niño events need to be object of further investigations.
This study firstly investigates the background of the CP and EP indices' definitions of Ren and Jin (2011) and the calculation shows that their index system is, in nature, a result of searching for a zero correlation between CP and EP indices by linearly fitting CP and EP indices to Niño-3 and Niño-4 indices. Then, based on the work by Fang et al. (2013), this study shows that the differences between our new CP/EP indices and the mean SSTA within the UNR are nearly absolutely independent of each other. Results suggest that the fundamental independent features of the El Niño events are the group features of the Niño region mean SSTA and the zonal SSTA gradient, which were already similarly established by Trenberth and Stepaniak (2001) with their TNI and Niño-3.4 indices. The new CP and EP index system represents an improved version of the traditional systems associated with the TNI and Niño-3.4 group by Trenberth and Stepaniak (2001). The CP and EP region warming rates are also examined.

Data
The Optimum Interpolation Sea Surface Temperature Analysis (OISST) by NOAA is used here for the Niño indices' calculation, signal analysis and the new CP and EP region definition test. This SST analysis is mapped on a 1x1-degree grid monthly from Nov.1981 to Sept. 2014. Data between Oct.2014 to Feb.2017 were used to validate the new CP and EP region definitions. Satellite SST data, incorporated in the dataset, are adjusted for biases by using the methods of Reynolds (1988) and Reynolds and Marsico (1993) [(for further details see also Reynolds and Smith (1994)]. The indices presented here are not standardized.

Statistical Analysis of the EP/CP Indices by Ren and Jin (2011)
Previous studies show that the CP and EP types of El Niño events can co-exist, and this feature contributes to the high correlation detected between the CP and EP indices (Bejarano and

EP CP
R J R J + (also 3 4 0.6 N N + ( )) and Niño-3.4 index is close to 0.99 (see Figure 4) and then one almost has (N 3.4 denotes Niño-3.4 index): Equ. (3) and Equ. (4) together can give Equ. (6) (both correlations higher than 0.99): CP R J indices results from the low correlation between the right sides of Equ. (6) (simultaneous correlation in between is near 0.14).
The simultaneous correlation between the TNI and Niño-3.4 is about -0.25 (Trenberth and Stepaniak, 2001) and that between the . .
CP R J is about 0.14. These two values are indicative of key features associated with El Niño events. In detail, the correlation (-0.25) between the TNI and Niño-3.4 suggests that the SSTA gradient along the Pacific equator is nearly independent of the mean SSTA of the Pacific equator and the correlation (0.14) between the . . EP R J and . . CP R J suggests that the CP and EP El Niño events are almost independent between them. In physics, the independence of the CP and EP El Niño events results in the independence of the TNI/Niño-3.4 indices but the independence of the TNI/Niño-3.4 indices could not necessarily result in a complete independence of CP and EP El Niño events. For example, the co-existence of the CP and EP El Niño events but with independent strength can also cause the independence of the TNI/ Niño-3.4 indices. The low correlation between the . . EP R J and . . CP R J indices indicates that the CP and EP type El Niño events are not coherent. Therefore, further investigations are required on the independent features among El Niño events. In other words, no pair of truly orthogonal indices is able to provide independent features associated with El Niño events. Here, this study defines new CP and EP regions, arguing that the lack of truly orthogonal indices is because that, up to now, not-so-naturally defined rectangular traditional Niño regions have always been investigated.

Experimental Definitions of the Spatial Coverage for the New EP/CP Indices
The standard deviation distribution of the equatorial SSTA is shown in Figure 5  Niño Index(t)= Coeff1+Coeff2×the mean SST anomaly(t) +Coeff3×the ZTC anomaly(t) (7) where where SST i stands for the grid temperature within the UNR. The ZTC anomaly time series are calculated by removing the monthly climatology.
This study further tries to linearly regress the SSTA monthly time series (spanning from 1982 to 2014) of each grid along the Equatorial Pacific regions from the same two time series of the mean SST anomaly and the ZTC anomaly of the UNR, as outlined by Equ. (9): SST anomaly(lon, lat, t)= Coeff1(lon, lat)+Coeff2(lon, lat)×the mean SST anomaly(t) +Coeff3(lon, lat) × the ZTC anomaly(t) (9) For each grid location (lon, lat), there is a specific set of Coeff1 (lon, lat), Coeff2 (lon, lat) and Coeff3 (lon, lat).
The correlation information between the time series of the SSTA of each grid within the UNR and its regression outputs from Equ.9 can be found in Figure 6 and Figure 7. The distribution of the regression correlation coefficients are shown in Figure 6. The regression coefficient distributions of Coeff1, Coeff2 and Coeff3 in Equ. (9) are shown in Figures 7a,  b, and c respectively. As expected, Figure 6 shows that the SSTA time series of each grid within the UNR can be well described by the simple linear fittings of Equ. (9).
The Coeff1 (lon, lat) is the constant component of the grid SSTA. The Coeff2(lon, lat) shows how much the grid SSTA changes resulted by a 1℃ change of the mean SSTA of the UNR. The Coeff3 (lon, lat) shows how much the grid SSTA changes resulted by a 1º change (in longitude) of the ZTC anomaly of the UNR. The Coeff2 (lon, lat) and Coeff3 (lon, lat) reflect the sensitivity of the grid SSTA to the changes of the mean SSTA and the ZTC anomaly of the UNR, respectively. Figure 7a suggests that Coeff1 (lon, lat) is somewhat small and can be neglected. Figure 7b suggests that nearly all the SSTA time series within the UNR are positively correlated to the mean SSTA of the UNR. Figure 7c indicates that the SSTA time series of different grid within the UNR are differently correlated with the ZTC anomaly of the UNR. Furthermore, the maximum values of Coeff2 (lon, lat) are mainly within the Niño-3.4 region where the grid SSTA is most sensitive to the mean SSTA change of the UNR. It's also observed that the maximum values of Coeff3 (lon, lat) are mainly within the Niño-1+2 region where the grid SSTA is most sensitive (positively correlated) to the ZTC anomaly change of the UNR. The minimum values of Coeff3 (lon, lat) are mainly within the Niño-4 region where the grid SSTA is most sensitive (negatively correlated) to the ZTC anomaly change of the UNR. This feature is consistent with the TNI/Niño-3.4 definition adopted by Trenberth and Stepaniak (2001) to track the El Niño flavors. In Figure 7, the simply acquired distribution patterns of Coeff2(lon, lat) and Coeff3(lon, lat) are very similar to those of the EOF1 and EOF2 modes of Takahashi et al. (2011) and Cai et al. (2015), and these features point out that the methodology used here is versatile and consistent with previous results.
Because the coeff3(lon, lat) in Figure 7c shows the sensitivities of the grid temperature anomaly to the ZTC anomaly of the UNR and the ZTC anomaly reflects the surface thermal distribution changes along the Pacific Equator (Fang et al., 2013), the coeff3(lon, lat) distribution patterns could provide guidelines for the new definitions of the CP or EP regions. In Figure 8 Figure 9a shows the mean SSTA time series of the new CP and EP regions as the new CP and EP indices by this study. In Figure 9, the simultaneous correlation between the new CP index and the . . EP R J indices is only 0.14. Figure 9a suggests that the new CP and EP Niño indices are not independent of each other, and this is a result somewhat different from those presented by Ren   New indices by this study in Figure 9a agree quite well with previous findings. As a whole, one can find that in the recent more than 30years, the CP type of El Niño events have happened much more frequently than the EP type El Niño events, a feature consistent with previous studies (Yeh et al., 2009;McPhaden et al., 2011;Xiang et al., 2012). The Jan.-Jun.1982 period was classified as CP type and the late stage of 1982-1983 El Niño was classified as EP type by Kao and Yu (2009). This transition can be seen clearly from Figure  9a. Before Jun. 1982, the CP index was higher than the EP index and after Jun. 1982, the relationship between these indices appears reversed. Kao and Yu (2009) also pointed out that a cold CP stage began after Apr. 1983, a feature in agreement with results displayed in Figure 9a. Nevertheless, Figure 9b shows that the cold CP came too early. One can also find that the cold CP of 1997-1998 by Ren  A detailed comparison between the classification results of the CP and EP type El Niño events by Yu and Kim (2013) and by this study shows the two results agree perfectly with each other and hints that the CP and EP Niño region definition by this study is one of the proper choices. Those El Niño events (1986-1987; 2006-2007; 2015-2016) classified as "Mix" by Yu and Kim (2013) or Paek et. al. (2017) have the similar magnitudes of CP and EP indices; those El Niño events (1982-1983; 1997-1998) Figure 9a) suggests that the CP type and the EP type indices are of comparable magnitudes, which indicate that both the CP type and EP type co-existed, which is also clearly shown by Figure 10. Statistics in a detailed El Niño classification by Yu and Kim (2013) showed that, from 1867 to 2010, there were 15 EP/CP mixed events out of total 39 events during that period; and that there were only 13 El Niño events out of the total 39 events could be agreed to be of the same type with different methods. These facts suggest again that the very low correlation between the CP and EP indices should be reconsidered. Actually, Figure 9a and Figure 10 show that the CP and EP types of El Niño events happened with a relatively high possibility of co-occurrence which causes a high correlation between the CP and EP indices.

Comparison Between the New EP/CP Indices and the EP R.J and CP R.J Indices
The new CP and EP indices formulated in this study give a more detailed description on the El Niño events. Although the correlation between the new CP and EP indices by this study is higher than that of Ren and Jin (2011), it could result from the frequent co-existence (sometimes with leads and lags) of these two types of El Niño events (Yu and Kim, 2013;Ren et al., 2013). The low correlation between these two types of El Niño indices is not necessarily physical as suggested by Ren and Jin (2011). However, it is very difficult to ascertain the total independence between these two types of El Niño events and further studies are required on this topic ( Figure 11 shows the correlation between the TNI index and the EP/CP index difference. It's should be noted that the difference between the new CP and EP indices by this study is much more correlated to the TNI index than the difference between the . . EP R J and . . CP R J indices. Figure 11 also shows that difference between the . . EP R J and . . CP R J is unable to clearly depict the temperature gradient along the Pacific equator. On the contrary, the difference between the new CP and EP indices by this study is highly correlated with the TNI index, reflecting quite well the temperature gradient along the Pacific equator and thus bearing more physical significance than the . . EP R J and . . CP R J indices. In Figure 12, the black line shows the lead-lag correlation between the new EP/CP difference (EP index minus CP index) and the mean SSTA of the UNR (with a 0.0 simultaneous correlation). The red line shows the correlation between the TNI index and the Niño 3.4 (with a -0.25 simultaneous correlation). The blue line shows the correlation between the . . EP R J and . . CP R J indices by Ren and Jin (with a 0.14 simultaneous correlation). Figure 12 suggests that the difference between the new CP and EP indices and the mean SSTA of the UNR are truly independent of each other. This finding is consistent with that presented by Trenberth and Stepaniak (2001) concerning the relationship between the Niño 3.4 and TNI indices. The author regards the relation between the mean SSTA of the UNR and the new CP and EP index difference as an improved version of that between the Niño 3.4 index and TNI index group. This study confirms that the mean SSTA of the Niño regions and the SSTA gradient across the Pacific equator are truly independent measurements for the El Niño features, which hints that even if the strength of the El Niño event can be predicted, the SSTA distribution feature prediction across the equatorial Pacific will be a great challenge. Recently Guckenheimer et. al. (2017) suggests that the timing of strong El Ni ño events on decadal time scales is unpredictable because the weak seasonal forcing or noise in the"recharge oscillator" model of ENSO can induce irregular switching between an oscillatory state that has strong El Ni ño events and a chaotic state that lacks strong events. Their conclusions agree well with the results of this study.

Important Features of the New EP/CP Indices
The variation of the CP and EP index differences is dynamically induced by the different warming rates of the EP and CP region mean SSTA. Figure 13a shows the CP index, the EP index and the warming rate difference between the CP indices and the EP indices. The CP/EP classification results by Yu and Kim (2013) are also shown in Figure 13a. Figure 13b shows the continuous wavelet spectrum(in magnitudes) patterns of the warming rate difference between the CP and EP regions, which, in physics, indicates that the CP warming rate and EP warming rate are always competing semi-periodically. It's noted that, the warming rate difference between the CP and EP regions gives rise to an unstable ENSO-like oscillation (Figure 13b). Figure 13 shows that, an EP warming faster (or cooling slower) event is often followed by a CP warming faster (or cooling slower) event, and vice versa, although in only a few cases, the CP or EP warming rate differences were very weak. Figure 13 shows clearly that within the Niño regions, there also exists an internal see-saw like oscillation. As the CP and EP indices are the result of the temporal accumulation of the CP and EP warming rate respectively, the CP/EP warming rate competition in these two regions, as an intrinsic oscillation mode, has important influences on the final stages of the Niño events. Figure 13 also suggests that although the CP warming and the EP warming may have different driving forcings (Capotondi et. al, 2014), these forcings certainly have interactions. This feature suggests that the CP and EP El Niño events should not be isolated.
It can be found in Figure 13a that, before the red line (CP index) rises up to cross the zero line, such as around Feb. 1982, Jun. 1986, Dec. 1989, Oct. 1992, Jun. 2001, May 2006, Apr. 2009, May 2012, Feb. 2014, the CP warming rates were higher than EP warming rates. Only around Feb.1997 when the CP line was rising up across the zero line, the CP warming rate was lower than EP warming rate. However, even for the 1997-98 case, there was also a short period during which the CP warming rate was higher than EP warming rate (as also can be seen in Figure 10). It shows that most of the CP warming cases (transitioning from negative SSTA to positive SSTA) were originated from its own CP regions. Another interesting point is that, in most cases (before 2007 and after 2014), when the black lines (EP index) transitioned from negative SSTA to positive SSTA, all the red lines (CP index) were already (or almost simultaneously) positive. There were only two exceptional cases: Apr. 2008 and Feb. 2012 (both of which were very weak EP warm events). This feature leads to the implication that most of the El Niño events began with a high CP warming rate, although sometimes the CP warming was very weak. It is noted that, in Figure 13a (and in Figure 9a), when the El Niño events happen, most of the CP peaks happen around the end of the calendar year (with only a few exceptions). For those strong ENSO events (1982-1983, 1997-1998, 2015-2016), the EP peaks arose no later than the CP peaks and the EP peak magnitudes were stronger than the CP peak magnitudes. For other weaker ENSO events, CP peaks arose no later than EP peaks and the CP peak magnitudes were stronger than the EP peak magnitudes (only the 2010 event was an exception). This study suggests that the temporal phases of the CP/EP events are highly and mechanically correlated, although further investigations are required to better ascertain this relationship.
The CP warming events (whose warming rate is higher than that of the EP warming) happened during different seasons and last for different months. For example, the 1982-83 CP warming case began in the early 1982 and last for about 3 months, but the 1986-87 CP warming began in the end of the year and last for about 7 months. This feature suggests that the differences between the CP/EP warming rates largely contribute to the El Niño characteristics. As for the two strong El Niño events, i.e., the 1982-1983 and 1997-1998 cases (Figure 13), both events showed larger EP index magnitudes than those associated with the CP index. This study also suggests that these two events both have two EP warming rate peaks within the EP warm episodes. These peaks agree with those displayed in Figure 10, in which there were twice of the maximum cores of the SSTA in both events (it should be noted that the time when the maximum SSTA occurred was not the time when the EP and CP warming rate difference peak occurred). The similarity between results presented in Figure  10 and Figure 13 also suggests that the CP and EP region definition by this study is physical and thus reasonable.
Analysis above suggests that the new CP and EP index differences are truly independent of the mean SSTA of the UNR, quantitatively confirming and improving the relationship between the traditional group indices of TNI and Niño-3.4. This study suggests that the fundamental independent factors of the El Niño events are the SSTA gradient along the Pacific equator and the mean SSTA within the Niño regions, not the CP and EP indices.  Yu and Kim (2013) and by this study. Yellow shade means the EP warming rate is higher than CP warming rate and the blue shade means the CP warming rate is higher than the EP warming rate. The warming rate is calculated by ∆CP/∆months or ∆EP/∆months and the difference is ∆EP/∆months -∆CP/∆months. (b) shows the continuous wavelet (Morlet) spectrum(in magnitudes) patterns of the blue lines (the warming rate difference) in (a).

Conclusions
The nature of the . . EP R J and . . CP R J indices from Ren and Jin's scheme was studied and results show that the low correlation between them reflects the low correlation between the right sides of Equ. (6). This feature indicates that this low correlation is not indicative of the total independence between the CP and EP type El Niño events. Actually the . . EP R J and . . CP R J indices could not correctly represent the physical details of the Niño events' evolution or transitioning, and therefore their scheme needs further improvements.
This study proposes a new version of the CP and EP Niño region definition according to the SSTA fitting coefficient distributions to the thermal centroid anomaly of the UNR. The UNR are separated into two parts: the central Pacific part and the eastern Pacific part. The new CP and EP indices based on the new Niño regions show that these two types of El Niño events are highly correlated. However, their differences are somewhat independent from the mean SSTA of the UNR. The record of data used here shows that the independent feature group about the El Niño events is between the mean SSTA of the Niño regions and the CP/EP difference (the SSTA gradient along the equator), and not between the CP and EP indices themselves. The CP and EP region warming rate competition in these two regions has great effects on the El Niño evolutions and characteristics. Actually, the warming rate competition between the CP and EP regions can be also regarded as an intrinsic oscillation mode of the El Niño events. It is found that, most of the El Niño events began with a high CP warming rate, which partly explains the high correlation between the CP/EP events and their co-existence.
The UNR show the greatest SSTA variability across the global ocean, which also covers most of the traditional Niño regions. The CP and EP regions in UNR suggested by this study are not necessarily the best choice. Since the literature lacks an accurate and natural definition of the Niño regions, the author believes that discussions presented on the independence or interaction about the two types of El Niño events could contribute to our scientific knowledge.
Because the UNR is defined based on the SST variations along the Pacific Ocean equator, the UNR could be subject to variations when a different period is analyzed, even though this region appeared quite stable in the past sixty years (this result was checked by other data sets and it is not shown here). As a consequence, the CP and EP region definitions appear somewhat independent from the timing selections. Sensitivity tests (not shown here) suggest that, by using the method proposed here, the separating boundaries between the CP region and the EP region could always be found and stay almost fixed for the past sixty years with only slight variation. The slight variation of the separating boundaries of the CP and EP regions may reflect the constantly changing nature of the El Niño events. Similarly, the fixedness of the traditional rectangular Niño regions may also need a "change". The CP and EP types of ENSO events have been long discussed so far, and they should have their own specific regions properly defined, similar to or different from this study.