Previous studies have identified a reversal in the phase propagation characteristics (from westward to eastward propagation) of the El Niño–Southern Oscillation (ENSO) during the 1976 climate shift. These studies relied on the assumption of a stationary seasonal cycle in Sea Surface Temperature (SST), ignoring the possible effect of ENSO and decadal variability on the seasonal cycle strength. Here we demonstrate using complex empirical orthogonal functions combined with Radon transform methods that mutidecadal amplitude modulations of the seasonal cycle, the semiannual cycle, and the El Niño Modoki mode played an important role in determining the phase propagation characteristics of equatorial SST anomalies in past decades. We find very little evidence for changes in the propagation characteristics of the Cold Tongue ENSO mode.
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 The El Niño–Southern Oscillation (ENSO) is an oscillatory instability of the climate background state [Neelin et al., 1998]. As such, we expect ENSO properties to change, when the mean state changes. A prominent and well-studied climate transition, responsible for a rapid background warming in the equatorial Pacific, occurred around 1976 [Guilderson and Schrag, 1998; Urban et al., 2000]. This shift has been made responsible for numerous changes in ENSO characteristics, including a change in amplitude and instability [Li et al., 2011; Wang and An, 2001], periodicity [An and Wang, 2000], skewness [An, 2004], and propagation [An and Jin, 2000; Fedorov and Philander, 2000, 2001; Wang and An, 2002]. Prior to 1976, El Niño events, as identified by the Sea Surface Temperature Anomalies (SSTA), propagated westward along the equator. Things changed after 1976, and the major subsequent El Niño events were either stationary or exhibited a tendency for eastward propagation. The aforementioned studies attributed the shift in ENSO propagation characteristics to changes in the climate background state and then in ENSO mode stability. According to their analysis, ENSO switched from a westward propagating SST mode to a more stationary mixed SST/thermocline mode [Jin and Neelin, 1993a, 1993b; Neelin and Jin, 1993, series of articles referred to as JN93 hereafter].
 Another important element in the Eastern Equatorial Pacific (EEP) is the annual cycle of SST. It has amplitudes comparable to ENSO-related SSTA. The annual cycle is an air-sea coupled mode, largely driven by the seasonal cycle of meridional SST gradients across the equator [Xie, 1994]. It relies on the existence of a mean meridional SST gradient and is hence subject to changes in amplitude [Timmermann et al., 2007]. If such changes occur, the reference state for calculating ENSO SSTA needs to be adjusted. An illustrative example was the classification of the 1993 El Niño event. Using the mean seasonal cycle from 1950 to 1979, Trenberth and Hoar  classified the 1993 anomaly as an El Niño, in contrast to the Climate Prediction Center that used the 1971–2000 climatology [Qian et al., 2011]. Another remarkable feature of this annual mode is its westward equatorial propagation at a speed near 0.5 m/s [Horel, 1982].
 Superimposed on this slow evolution of the annual mode amplitude are other statistical SST modes that may influence equatorial propagation characteristics, such as the semiannual cycle and SST variability often referred to as El Niño Modoki [Ashok et al., 2007; Kug et al., 2009]. With a center of activity shifted toward the central Pacific, Modoki events contrast the Cold Tongue (CT) events. Observational data suggest that El Niño Modoki have become more frequent in recent decades [Kao and Yu, 2009; Lee and McPhaden, 2010]. How this shift may have affected propagation features of equatorial SSTA has not been studied yet. With these considerations in mind, we turn back to the simple question, “What is an SST anomaly?” Following the World Meteorological Organization guidelines, an anomaly is calculated by subtracting a fixed monthly mean climatology (based on a period of 30 years) from the original data. Whereas the notion of a fixed annual cycle is meaningful in a statistical sense, it is oftentimes not very useful for an in-depth understanding of the physical changes of the system.
 Here we will revisit the issue of conventional SSTA phase speed by projecting the equatorial SST signal onto statistically orthogonal modes of variability in the tropical Pacific to assess the effects of these modes on propagation characteristics. Our primary goal is to test the hypothesis that physically occurring long-term changes in the amplitude of the annual cycle of equatorial Pacific SST along with the hidden effect of other climate modes are responsible for the previously reported changes in ENSO propagation. In this study, we combine Complex Empirical Orthogonal Functions analysis (CEOF) [Barnett, 1983] that effectively captures propagating signals and the Radon Transform (RT) method [Radon, 1917], first to separate ENSO from other modes of tropical variability and their spatiotemporal behaviors and second to properly quantify the equatorial propagation of these modes. Section 2 provides an overview of the dataset and methodology. Section 3 describes the main results of the CEOF and RT analysis and re-assesses the propagation characteristics of SSTA before and after the 1976 climate shift. A summary and discussion conclude the paper.
2 Data Sets and Methods
2.1 CEOF Analyses
 The objective of this paper is to study changes in the amplitude and phase characteristics of tropical climate modes of variability. As shown by Stein et al. , CEOF is an efficient tool to disentangle the spatiotemporal signals of the equatorial annual cycle and ENSO dynamics from SST data sets. By providing amplitude and phase information, CEOF is also well suited to capture propagating features [Barnett1983]. We conduct a CEOF analysis of the UK Met Office Hadley Centre's 1° gridded monthly SST analyses (HadISST) [Rayner et al., 2003], covering the period 1870–2010. The analysis is restricted to the spatial domain from 110°E to 290°E and 15°N to 15°S. The results for the first four modes are presented in Figures 1 and 2. The first mode captures the annual mode and is characterized by strong amplitude in the EEP and weak amplitude in the western Pacific (Figure 1a). The phase decreases from the EEP to the western equatorial Pacific (Figure 1c), indicating a westward propagation of the annual mode (Figure 1e). Note that the phase information inferred from the CEOF analysis must be interpreted modulo 2π. The complex PC can be decomposed into a magnitude and phase time series (Figure 1g). The former exhibits a strong interannual to multidecadal modulation whereas the latter shows a relatively linear phase evolution (indicative of a weak frequency modulation). The second mode captures the Cold Tongue (CT) ENSO mode (sometimes simply referred to as ENSO) and is characterized by equatorially confined amplitude displaying large values in the Central to Eastern Pacific (Figure 1b). The phase is constant along the equator indicating an almost stationary CT ENSO mode (Figures 1d and 1f). The third mode displays stronger amplitude in the central Pacific, EEP, and along the coastal upwelling regions (Figure 2a). It strongly propagates eastward at a speed near 1.5 m/s (Figures 2c and 2e). Spectral analysis reveals a strong semiannual SST signal, which has not been studied in great detail yet. Finally, the amplitude pattern of the fourth mode suggests that it is related to the El Niño Modoki regime (Figure 2b). The phase information indicates a dominant westward propagation in the central equatorial Pacific (Figure 2f) that may be indicative of SST mode dynamics (JN93). Together, these four CEOF modes explain up to 92% of the total variance of SST in the tropical Pacific and hence provide an excellent basis to study the propagation features of equatorial SSTA. By taking the real part of the CEOF modes, we can reconstruct SST Hovmöller diagrams along the equator (2°S–2°N average) for the period 1950–2008 for the annual mode, CT ENSO, semiannual mode, and Modoki ENSO and then infer their effects on SSTA propagation characteristics. To determine the residual effects of the CEOF modes on classic SSTA, we examine the departure of each mode from its long-term mean climatology. These residuals represent the time-varying contributions of the modes to the conventionally calculated SSTA.
2.2 Radon Transform
 A number of 2-D data signal processing techniques can be applied to space-time Hovmöller diagrams to determine probability distributions of zonal phase speeds. The RT method, first introduced by Radon  is a well-established method that accomplishes this task. A recent study by Challenor et al.  provides more mathematical details that are summarized in the supporting material. In practice, we project the Hovmöller diagram onto a series of lines at various angles θ from 0° (the time axis) to 180° and for different times t′. When the line (t′ cos θ − x′ sin θ; t′ sin θ − x′ cos θ) in the 2-D space of t and x is perpendicular to crests in the data (positive El Niño SST anomalies) and troughs (negative La Niña SST anomalies), the projection will have the maximum so-called “radon energy.” Subsequently, we can identify the angles (i.e., phase speed) for which maximum radon energy is attained. In the next section, we apply a temporal and longitudinal running RT (RRT) to the different SSTA fields that were reconstructed according to the aforementioned methodology.
 To determine the evolution of propagation characteristics of the main climate modes in the tropical Pacific, we apply the RRT to the 3 months smoothed equatorial Hovmöller diagrams from the CEOF mode residuals. Such a residual is obtained here by subtracting any remaining long-term mean annual cycle from the CEOF mode reconstruction under consideration. We calculate the spatial average of the most energetic angles over the central to EEP [170°W–110°W] and apply a 7 year running mean to the resulting time series. Figure 3a displays the phase speed of each CEOF mode residual (color lines) and of the classic SSTA (absolute SST minus long-term mean monthly climatology, thick black line). The latter exhibits a well-marked decadal modulation and the expected change from negative (westward) to positive (eastward) SSTA propagation in the early 1980s. CEOF1 residual (Figure 3a, red line) displays decadal variability in phase speed similar to the classic SSTA. The CEOF2 residual (CT ENSO mode) exhibits distinct anomalous westward propagation from 1950 to 1970 and 2000 to 2008 and an eastward tendency from 1985 to 1995. A pronounced phase speed shift around 1976 is not apparent. Figure 3a clearly documents that changes in the residual of CEOF2 are not sufficient to account for the variations of phase speed estimated from conventional SSTA. Our results and, in particular, the important role of the residual annual cycle demonstrate that changes in the propagation characteristics of classical EEP SSTA can occur without underlying changes in the CT ENSO mode. Figure 3b further corroborates this statement since the phase speed of the combined residual from CEOF modes 1 and 2 compares considerably better with the classic SSTA phase speed than with the one from CEOF2 residual only. The annual mode and its multidecadal amplitude modulation are the main contributors to changes in equatorial SSTA propagation. The time series of the CEOF1 + 2 residual is similar to that of the |PC1| variation (i.e., amplitude of the annual mode PC, dashed blue line in Figure 3b), suggesting again that the identified shift in propagation direction in equatorial SSTA is due to the anomalous annual cycle rather than to the CT ENSO mode. Indeed, with a strong (weak) annual cycle amplitude, such as during the decades prior (after) to the 1976 climate shift, classic SSTA would be biased toward westward (eastward) propagation, because of a stronger (opposite) residual annual cycle. Compared to the shift in propagation direction in the early 1980s obtained from the classic SSTA (Figure 3a), the zero crossing for the combined CEOF1 + 2 occurred about 5 years later, thus suggesting that higher-order CEOF modes may play an additional role in determining multidecadal changes in phase speed.
 We now investigate the effect of the residual semiannual (CEOF3) and Modoki (CEOF4) modes on equatorial SSTA propagation characteristics. As previously observed (Figures 2c and 2e), the semiannual mode strongly propagates eastward and so does its residual (Figure 3a, grey line). The latter exhibits strong multidecadal variability superimposed on a slow trend toward reduced phase speed. Analyzing the RRT of the residual of the first three modes combined, we find similar behavior than for the conventional SSTA but with a bias toward eastward propagation. Compared to the CEOF1 + 2 reconstruction (Figure 3b), the extended reconstruction based on CEOF1 + 2 + 3 now captures the timing of the shift in propagation direction much more accurately. The CEOF4 residual phase speed is westward (Figure 3a, cyan line) but notably slower than the full Modoki mode (not shown). The latter seems to have a compensating effect over the semiannual mode, considerably reducing the eastward phase speed bias associated with CEOF1 + 2 + 3. We observe a clear reduction of the residual Modoki westward propagation around the late 1970s, assisting the annual mode in promoting the change of SSTA phase speed toward eastward propagation. Calculating the RRT from the equatorial SST reconstruction based on CEOF1–4 residuals, we find a similar propagation behavior than for the classical SSTA. Thus, the analysis of Figure 3 is a way of disentangling the changes in SSTA propagation characteristics in changes of individual CEOF modes, corresponding to the physical modes of the annual cycle, CT ENSO, semiannual cycle, and El Niño Modoki. Our results indicate that all modes contribute to the SSTA propagation to some extent. The CEOF results show that the shift of propagation direction in the early 1980s can be mainly attributed to the annual and Modoki modes, while the semiannual mode seems to play a role in determining the timing of this change. We find that the canonical CT ENSO mode has very little influence in this low-frequency variation of SSTA propagation.
4 Summary and Discussion
 The aim of this study was to revisit the issue of changes in ENSO propagation characteristics following the “1976 climate shift.” Previous studies linked such changes in ENSO properties to long-term variations in the climate background state [Fedorov and Philander, 2000, 2001]. Using stability analysis of simplified ocean-atmosphere coupled models, it was found that background states characterized by a shallower thermocline, such as prior to 1976, would have favored the westward propagating SST mode (JN93), whereas the post-1976 conditions might explain the emergence of higher amplitude, lower frequency, and standing to eastward propagating SSTA, associated with thermocline dynamics.
 Irrespective of the results of these simplified modeling studies, there is an even more fundamental question to address: How much of the observed SSTA can be attributed to interannual variability (or in other terms, to classic ENSO physics) and how much can be explained by the nonstationarity of the westward propagating annual cycle in equatorial SST [Horel, 1982; Xie, 1994] and by the residual effect of other propagating modes of variability in the tropical Pacific? Evidence for the high level of variability of the seasonal cycle on decadal to multidecadal time scales comes from numerous observational studies [Gu and Philander, 1995; Gu et al., 1997; Pezzulli et al., 2005; Qian et al., 2011; Wu et al., 2008]. The issue is further complicated by the fact that ENSO strongly interacts with the annual cycle [Jin et al., 1994; Stein et al., 2010; Tziperman et al., 1994], giving rise to seasonal variance modulation of SSTA, possibly ENSO irregularity and an interannual modulation of the annual cycle strength.
 Our CEOF analysis of the tropical Pacific SST reveals a westward propagating annual SST mode in the EEP, a stationary CT mode, an eastward propagating semiannual mode, and a westward propagating Modoki mode. While all exhibit a well-marked amplitude modulation at interannual to multidecadal time scales, the time-varying phase information is more difficult to interpret. The results from our RT analysis performed on each of these modes confirm that the CT mode has been mostly stationary over the last 50 years. Classical SSTA contain “clandestine” residuals from other statistical climate modes that may distort the interpretation of phase propagation. For instance, stronger (weaker) annual cycle amplitudes before (after) the early 1980s compared to the long-term mean generate a westward (eastward) propagating residual SSTA signal, which is in fact unrelated to the physical CT ENSO mode. While the annual mode appears to be the main contributor of this propagation change, other modes also play significant roles in this low-frequency modulation of SSTA phase speed. The Modoki mode displays reduced westward characteristics around the late 1970s, which then promotes similar changes on SSTA propagation than the annual mode. The semiannual mode propagation undergoes a strong modulation along with a steady decline since 1950 but is always associated with eastward phase speed. This tendency toward a much damped phase speed starts in the mid-1960s and acts as an earlier trigger of the shift in SSTA propagation, which occurs later (early 1980s) when accounting only for the two first CEOF modes.
 These results raise an interesting question: What mechanisms determine the low-frequency variability of the annual cycle strength? A recent study [Timmermann et al., 2007] showed that the amplitudes of the annual cycle and ENSO appear to be anticorrelated on multidecadal time scales. The authors proposed that changes in the Atlantic Multidecadal Oscillation might have affected the magnitude of the meridional temperature gradient in the EEP, which in turn determined the annual cycle strength. To explain the out-of-phase relation between ENSO and annual cycle amplitudes, Liu  suggested the frequency entrainment mechanism. Another possibility was proposed in An et al.  who found in a Coupled General Circulation Model simulation that long-term background state changes in the EEP trigger opposite responses in ENSO and annual cycle amplitude.
 While there is no consensus yet on the processes that modulate the amplitude of the annual cycle on decadal time scales, we provided evidence that this modulation needs to be accounted for, when describing decadal changes in ENSO properties. Whereas the separation into a long-term climatological mean and an anomaly may be a useful concept for climate impact studies (after all we are interested in the deviations from the norm), it may be a less optimal choice to study the physical behavior of climate modes.
 This study was supported by U.S. NSF grant ATM1034798, U.S. DOE grant DESC005110, U.S. NOAA grant NA10OAR4310200, the 973 Program of China (2010CB950404), and the China Meteorological Special Project (GYHY201206033). A.T. additionally was supported by U.S. NSF grant 1049219 and through the Japan Agency for Marine-Earth Science and Technology (JAMSTEC) through its sponsorship of the International Pacific Research Center (IPRC). This is IPRC publication 989 and SOEST contribution 8953.
 The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.