Abstract

In this reply, the authors clarify the points made in the original paper in 2015 and show that issues raised in the comment by Li et al. are unsubstantiated. The main conclusions can be summarized as follows: 1) The time evolution of the anomalous low-level northwest Pacific anticyclone (NWP-AC) is largely caused by combination mode (C-mode) dynamics. 2) The theoretical C-mode index accurately captures the rapid development of the anomalous NWP-AC. 3) Thermodynamic air–sea coupling does not play a major role for the rapid phase transition of the NWP-AC and the meridionally antisymmetric atmospheric circulation response during the peak phase of El Niño events in boreal winter.

1. Introduction

We will demonstrate the following points in this reply to the comment by Li et al. (2016, hereafter L16): 1) the combination mode (C-mode) time scale (combination tones) is clearly evident in various indices of the anomalous low-level northwest Pacific anticyclone (NWP-AC); 2) C-mode dynamics are crucially important for the phase transition of the NWP-AC and explain a considerable amount of variance; and 3) thermodynamic air–sea coupling is of secondary importance for the rapid phase transition of the NWP-AC in boreal fall. However, as discussed in Stuecker et al. (2015b), air–sea coupling provides additional memory (persistence) in early boreal summer to the NWP-AC via the capacitor effect (Xie et al. 2009) and local air–sea interaction (Wang et al. 2000). In the following reply we will address each of the comments raised by L16.

In the following analysis we use three indices for the anomalous low-level NWP-AC: 1) our original NWP-AC index as used in Stuecker et al. (2015b), which is defined as the area averaged anomalous surface streamfunction in the northwest Pacific (NWP) region (5°–20°N, 120°–160°E,), referred to as NWP-AC surf in this paper; 2) the anomalous streamfunction at the 850-hPa pressure level (as used by L16) averaged in the same region, labeled NWP-AC 850 hPa; and 3) the anomalous sea level pressure (SLP) averaged in the same region (also used by L16), labeled NWP SLP. All indices are calculated using ERA-40 (Uppala et al. 2005). The anomalies are defined as the departure from the annual cycle for either the period 1980–2001 or 1958–2001, which will be explicitly stated in the following analysis. As in Stuecker et al. (2015b), the sea surface temperature (SST) anomaly (SSTA)-based Niño-3.4 (N3.4) index will be used to describe the direct linear ENSO signal, while the annual cycle modulated ENSO response is captured by our theoretical C-mode index equal to N3.4 index × cos(ωatϕ), where ωa denotes the angular frequency of the annual cycle and ϕ represents a 1-month phase shift (Stuecker et al. 2015b).

2. Is NWP-AC variability characterized by C-mode dynamics?

The first issue raised by L16 is the periodicity of the anomalous low-level NWP-AC. The authors claim that the NWP-AC does not exhibit near-annual combination tones and use this finding as an argument against the C-mode dynamics demonstrated in Stuecker et al. (2015b). We showed extensively using a wide range of advanced spectral methods (e.g., Ghil et al. 2002; Welch 1967) and on a variety of datasets that the near-annual combination tones are a nonspurious feature of the anomalous circulation in the NWP (Stuecker et al. 2013, 2015a,b). The near-annual time scale (combination tones) of the meridionally antisymmetric circulation (which the NWP-AC is part of) is even more apparent when analyzing a multicentury integration of a coupled general circulation model (CGCM) that simulates well both ENSO and the C-mode response [Fig. S9 in Stuecker et al. (2013) and Fig. 3 in Stuecker et al. (2015b)]. It is important to note that this near-annual time scale variability in the northwest Pacific region was previously discussed in Wang et al. (1999, p. 1)—“The tendency of thermocline displacement and local wind stress curl in the WNP exhibit a coherent, broad spectral peak on a 8–20 month time scale”—and in Wang et al. (2001, p. 4073)—“The WNP monsoon has leading spectral peaks at 50 and 16 months. . . .” However, it was only linked to C-mode dynamics much later in our recent work (Stuecker et al. 2013, 2015a,b).

While L16 use similar spectral methods to our previous work to examine three NWP-AC indices (NWP-AC surf, NWP-AC 850 hPa, and NWP SLP), their methodological choice results in several unjustified conclusions. The two most distinguishing choices made by L16 are discussed below.

First, L16 test against an arbitrarily chosen statistical (red noise) null hypothesis (Figs. 1 and 2 in L16). It is not explained from an atmospheric physics perspective why the authors would expect a red noise spectrum (Figs. 1 and 2 in L16) for tropical atmosphere dynamics. It is worth noting, however, that both L16 and Stuecker et al. (2015b) find that the lower-frequency difference tone (1 − fE) is statistically significant (when tested against a red noise null hypothesis) in the power spectrum [Fig. 3 in Stuecker et al. (2015b)]. Nevertheless, both statistical null hypotheses of either a white or red noise process [as used by us previously (e.g., Stuecker et al. 2013, 2015b) and also by L16] for the combination tone spectral peaks are arbitrary because they do not project onto a physical null hypothesis. The C-mode spectrum is neither white nor red due to the deterministic frequency cascade mechanism (Stuecker et al. 2015a). Instead, the correct test would be to falsify the following null hypothesis: The NWP-AC indices are not part of the C-mode response, which is essentially the claim of L16. This null hypothesis can be rejected statistically if we can demonstrate (i) that a significant linear correlation exists between our theoretical C-mode time series and the NWP-AC indices, and (ii) that significant spectral coherence exists between these time series on the near-annual time scale (combination tones). In the following subsections we demonstrate that the null hypothesis can be rejected with high confidence, which implies that a considerable fraction of the NWP-AC can indeed be attributed to C-mode dynamics.

Second, L16 use a 12-month low-pass filter and a subsequent 13–19-month bandpass filter (plus another time scale filter by calculating seasonal means) to isolate the C-mode time scale. However, this approach is unsuitable as the C-mode response is associated with a time scale from ~4 months up to ~2 yr [Fig. 5 in Stuecker et al. (2015a) and Fig. 9 in Stuecker et al. (2015b)]. A similar wide range of the C-mode time scale is also evident in the aforementioned multicentury CGCM integration [Fig. S9 in Stuecker et al. (2013)]. The broad spectral range of the C-mode response is a direct result of the broad spectral range of ENSO itself. The ENSO time scale of ~(2–7) yr results in deterministic variability on the aforementioned time scale of ~4 months to ~2 yr via a so-called frequency cascade mechanism (Stuecker et al. 2015a). It is important to reiterate that the variance on this time scale is potentially as predictable as ENSO itself due to its deterministic nature. Thus, using a very narrow bandpass filter (13–19 months) as done by L16 removes an important part of the variance associated with the C-mode.

a. Observed correlation between the NWP-AC indices and the theoretical C-mode

We composite the three aforementioned normalized NWP indices, as well as the N3.4 and theoretical C-mode indices, for the five major El Niño events (1965/66, 1972/73, 1982/83, 1991/92, 1997/98) during the period 1958–2001 (Fig. 1). As expected from our C-mode theory, we find very high linear correlations between the circulation based NWP-AC indices (NWP-AC surf and NWP-AC 850 hPa) and our theoretical C-mode index (R = 0.80 and R = 0.74 respectively; refer to Table 1 for all correlation coefficients and their respective p values) for the El Niño event composite. In contrast, no significant correlation is found between N3.4 and these indices (R = 0.16 and R = 0.04 respectively). For the NWP SLP index we find also a high correlation with the C-mode (R = 0.72, p = 0.000 07) and a smaller correlation with N3.4 (R = 0.60, p = 0.0008). The reason that the NWP SLP index exhibits both a correlation with ENSO and the C-mode will be discussed in section 3. Based on these correlations we are able to reject the null hypothesis that the observed NWP-AC time evolution is not related to the C-mode (confidence level >99%). This implies that indeed a close linear relationship exists between the C-mode and the NWP-AC, contrary to the claims in L16. Note that the observed high correlations between the NWP-AC and the theoretical C-mode are in full agreement with our results from a large number of model experiments [Tables 2–4 in Stuecker et al. (2015b)].

Fig. 1.

Observed time evolution of the following normalized indices for five major El Niño events (1965/66, 1972/73, 1982/83, 1991/92, and 1997/98) during the period 1958–2001: N3.4 (gray line), theoretical C-mode (red line), NWP-AC surf (solid blue line), NWP-AC 850 hPa (dashed blue line), and NWP SLP (cyan line). Also shown is the composite of these five events.

Fig. 1.

Observed time evolution of the following normalized indices for five major El Niño events (1965/66, 1972/73, 1982/83, 1991/92, and 1997/98) during the period 1958–2001: N3.4 (gray line), theoretical C-mode (red line), NWP-AC surf (solid blue line), NWP-AC 850 hPa (dashed blue line), and NWP SLP (cyan line). Also shown is the composite of these five events.

Table 1.

Correlation coefficient R between N3.4 and the theoretical C-mode with two NWP circulation indices and the NWP SLP index for the El Niño event composite (Fig. 1). The p values for each correlation coefficient are calculated using a nonparametric permutation method (n = 100 000) and given in parentheses. The p value measures the occurrences of a correlation coefficient larger than the observed in the permuted samples.

Correlation coefficient R between N3.4 and the theoretical C-mode with two NWP circulation indices and the NWP SLP index for the El Niño event composite (Fig. 1). The p values for each correlation coefficient are calculated using a nonparametric permutation method (n = 100 000) and given in parentheses. The p value measures the occurrences of a correlation coefficient larger than the observed in the permuted samples.
Correlation coefficient R between N3.4 and the theoretical C-mode with two NWP circulation indices and the NWP SLP index for the El Niño event composite (Fig. 1). The p values for each correlation coefficient are calculated using a nonparametric permutation method (n = 100 000) and given in parentheses. The p value measures the occurrences of a correlation coefficient larger than the observed in the permuted samples.

b. Observed spectral coherence between the NWP-AC indices and the theoretical C-mode

We calculate the power spectrum of the theoretical C-mode index using the Welch method (Welch 1967). As demonstrated previously (Stuecker et al. 2013, 2015a,b), the spectrum of the C-mode index (red line in Fig. 2) is characterized by near-annual combination tones at the 1 − fE and 1 + fE frequency bands (where 1 denotes the annual cycle frequency and fE the interannual ENSO frequency band; units: yr−1). To test the null hypothesis that the NWP-AC is unrelated to the C-mode in the spectral domain, we determine whether significant magnitude squared coherence exists at combination tone frequencies between the theoretical C-mode and the three NWP indices used previously. Indeed, we find significant coherence at the 99% confidence level between the C-mode and the three NWP indices respectively (solid blue, green, and cyan lines in Fig. 2). Thus, together with the high correlation of the indices in the time domain (previous subsection), we can again reject the null hypothesis that the observed NWP-AC time evolution is not caused by the C-mode (confidence level > 99%). These results are fully consistent with the spectral coherence analysis in Stuecker et al. (2015a). In conclusion, all evidence (spectral peaks, linear correlations, and spectral coherence) supports our hypothesis that the anomalous low-level circulation in the NWP region during ENSO-active periods is to a large extent governed by C-mode dynamics as initially proposed in Stuecker et al. (2015b).

Fig. 2.

Power spectral density of the theoretical C-mode (red line, arbitrary unit) as well as the magnitude squared coherence (both using the Welch method) between the C-mode and the three NWP indices. The near-annual C-mode frequency band [~(8–20) months] is highlighted by the gray shaded area, which includes the sum and difference tones (1 ± fE). The solid lines for the coherence (blue, green, and cyan) indicate statistical significance above the 99% confidence level estimated with a bootstrapping approach (n = 1000). Dashed lines indicate nonsignificant coherence. The monthly ERA-40 indices for the 1980–2001 period were used for consistency with Stuecker et al. (2015b) and Li et al. (2016).

Fig. 2.

Power spectral density of the theoretical C-mode (red line, arbitrary unit) as well as the magnitude squared coherence (both using the Welch method) between the C-mode and the three NWP indices. The near-annual C-mode frequency band [~(8–20) months] is highlighted by the gray shaded area, which includes the sum and difference tones (1 ± fE). The solid lines for the coherence (blue, green, and cyan) indicate statistical significance above the 99% confidence level estimated with a bootstrapping approach (n = 1000). Dashed lines indicate nonsignificant coherence. The monthly ERA-40 indices for the 1980–2001 period were used for consistency with Stuecker et al. (2015b) and Li et al. (2016).

3. Is the C-mode an important contributor to the NWP-AC?

Li et al. (2016) claim that our C-mode mechanism is not able to explain the rapid establishment process of the NWP-AC. We will refute this unsubstantiated claim in the following section. The El Niño event composite for the three NWP indices (Fig. 1) shows that the theoretical C-mode captures well the phase transition of the NWP indices (as indicated by the high correlations for El Niño events; Table 1). According to Fig. 1 (bottom right), the C-mode (red line) predicts the phase reversal to start in September(0) and exhibits a crossing of the zero line (transition from cyclonic to anticyclonic circulation) in November(0). It then reaches its maximum amplitude in January(1)–February(1). This rapid phase reversal is clearly seen for both streamfunction-based NWP indices (solid and dashed blue lines). The composite NWP SLP index (cyan line in Fig. 1) exhibits a very similar time evolution (R = 0.72 between C-mode and NWP SLP for the event composite); however, the phase reversal from cyclonic to anticyclonic circulation occurs slightly earlier (the reason for this will be explained in the following two paragraphs). After the El Niño peak phase in boreal winter, the subsequent time evolution of all three NWP indices is again well captured by the C-mode. As discussed in Stuecker et al. (2015b), local and remote thermodynamic air–sea coupling will enhance persistence of the NWP-AC especially during May(1)–June(1), thereby helping to sustain the NWP-AC until the emerging La Niña conditions in July(1) cause again a strong anticyclonic response in the NWP (Stuecker et al. 2015b). Note that the C-mode index is again a powerful predictor for the NWP-AC during July(1)–October(1) (Fig. 1).

The slight mismatch of the C-mode and the NWP SLP (cyan line in Fig. 1) during the initial phase reversal in boreal autumn can be explained when examining the spatial patterns associated with ENSO (as captured by N3.4) and the C-mode (as captured by the C-mode index) for the streamfunction and SLP anomaly fields (Fig. 3). Whereas the ENSO response of the anomalous streamfunction at the surface and 850 hPa (Figs. 3c,e) is quasi-symmetric with regard to the equator, the C-mode response is meridionally antisymmetric and captures well the anomalous NWP-AC (Figs. 3d,f). As discussed in Stuecker et al. (2015b), the full atmospheric response to the ENSO SSTA forcing under a seasonally varying background state can be succinctly captured by a superposition of the quasi-symmetric linear ENSO response (Figs. 3a,c,e,g) and the meridionally antisymmetric annual cycle modulated ENSO response (Figs. 3b,d,f,h). Note that the direct ENSO streamfunction response (Figs. 3a,c,e) exhibits a small spatial loading in the far western Pacific (Stuecker et al. 2015b), which is consistent with the feature described by L16 to occur during boreal autumn of the El Niño event (e.g., Fig. 5b in L16). However, this anomalous circulation is clearly part of the large-scale response with its center over the Indian Ocean [caused by the El Niño–induced subsidence over the Maritime Continent; e.g., Figs. 3a,c,e herein and also discussion in Stuecker et al. (2015b)]. In contrast, the large-scale NWP-AC (as captured by the NWP-AC surf and NWP-AC 850-hPa indices) is evidently more related to the C-mode response (Figs. 3b,d,f).

Fig. 3.

Explained variance (R2) of the anomalous surface streamfunction by (a) ENSO and (b) the theoretical C-mode. Also shown are linear regression coefficients (RC) between the (left) normalized N3.4 and (right) theoretical C-mode indices and the (c),(d) anomalous surface streamfunction, (e),(f) anomalous 850-hPa streamfunction, and (g),(h) anomalous SLP. The monthly ERA-40 anomaly fields and indices for the full 1980–2001 period were used for all plots. The nonstippled areas indicate where the RC are significant above the 95% confidence level using t statistics that account for the autocorrelation at each grid point.

Fig. 3.

Explained variance (R2) of the anomalous surface streamfunction by (a) ENSO and (b) the theoretical C-mode. Also shown are linear regression coefficients (RC) between the (left) normalized N3.4 and (right) theoretical C-mode indices and the (c),(d) anomalous surface streamfunction, (e),(f) anomalous 850-hPa streamfunction, and (g),(h) anomalous SLP. The monthly ERA-40 anomaly fields and indices for the full 1980–2001 period were used for all plots. The nonstippled areas indicate where the RC are significant above the 95% confidence level using t statistics that account for the autocorrelation at each grid point.

As mentioned earlier, the ENSO-composited NWP SLP index is correlated with both the C-mode (R = 0.72) and ENSO (R = 0.60). The reason for this becomes clear when analyzing the linear regression maps (for the whole 1980–2001 period) between the N3.4 and C-mode indices respectively and the SLP anomaly field (Figs. 3g,h). The two patterns are not orthogonal over the NWP region, which means that the NWP SLP index captures partly the C-mode and the direct ENSO signals. This significant spatial overlap between the C-mode and ENSO is observed for the SLP (Figs. 3g,h), but not for the surface (Figs. 3c,d) and the 850-hPa (Figs. 3e,f) streamfunctions. The ENSO SLP pattern (Fig. 3g) shows mostly the large-scale zonal shifts of the pressure field associated with the Walker circulation response to the ENSO SSTA forcing. The positive SLP anomaly pattern ranges from ~60°E to the date line, and all the way from the equator to the subtropics (from ~30°S to ~30°N). Thus, indices based on the SLP anomaly field (such as NWP SLP) are not very useful in differentiating the C-mode and ENSO contributions to the more localized circulation features as the NWP-AC. Furthermore, other phenomena [such as the Indian Ocean dipole (IOD), intraseasonal oscillations (ISO), and synoptic atmospheric variability] can cause some of the variability in the NWP SLP index (Fig. 1).

Our analysis so far unequivocally demonstrates that the C-mode is of crucial importance for the rapid phase transition of the NWP-AC in boreal fall during the developing phase of an El Niño event (Fig. 1, bottom right). A major contradiction in the argument by L16 is that on one hand the authors highlight the rapid onset of the NWP-AC by ISO, and on the other hand they essentially reject the existence of any time scales faster than the slow interannual ENSO signal in the NWP-AC evolution (as implied by their bandpass filtering method; e.g., Fig. 3 in L16).

Moreover (as discussed earlier), L16 assume a narrow 13–19-month time scale for the C-mode, which is inadequate according to our analysis [Fig. 2; see also discussion in Stuecker et al. (2015a)]. In fact, L16 perform a three-step filtering procedure, which is designed to remove nearly all variance except on the interannual ENSO time scale (Fig. 3 in L16). First, L16 low-pass filter the monthly anomalies above a 12-month period. Then, the authors perform a narrow and inadequate 13–19-month bandpass filter on this data to isolate the C-mode contribution. Last, L16 calculate 3-month seasonal means on this filtered data, which is yet another time scale filter. Not surprisingly, nearly all of the variance left after this procedure will be at low frequencies, which leads L16 to conclude that the C-mode is not important for the circulation anomalies during the 1997/98 El Niño event (Fig. 3 in L16).

Here we repeat their analysis but using more reasonable data (the C-mode frequency range is displayed in Fig. 2) and theory-based (Stuecker et al. 2015a) time scale separation: We bandpass filter the monthly ERA-40 anomalies from 24 to 84 months to isolate the typical ENSO time scale (Fig. 4, middle) and bandpass the monthly anomalies from 8 to 20 months [a conservative time scale estimate for the C-mode given the frequency range reported in Stuecker et al. (2015a)] to isolate the C-mode time scale (Fig. 4, right). It is clearly evident that a large fraction of the variance in the circulation is explained by the C-mode (which includes the NWP-AC). In fact, we find that the C-mode and ENSO time scales explain a similar fraction of the NWP variability variance when applying the same bandpass filter to our three NWP indices (Table 2). Therefore, the statement by L16 that the explained variance of the C-mode is small is unsubstantiated.

Fig. 4.

Monthly anomalous sea level pressure (shading; hPa) and surface winds (vectors; m s−1) for the development and peak time of the 1997/98 El Niño event (September 1997–February 1998) using the ERA-40 (anomalies relative to the 1958–2001 climatology). Shown are (from left to right) the original data, the low-frequency ENSO component (filtered with a 24–84 months Lanczos bandpass filter; Duchon 1979), and the high-frequency C-mode component (filtered with a 8–20-month Lanczos bandpass filter; Duchon 1979). Additionally, the anomalous surface streamfunction (purple contours; 0.5 × 106 m2 s−1) is shown for the filtered reanalysis data.

Fig. 4.

Monthly anomalous sea level pressure (shading; hPa) and surface winds (vectors; m s−1) for the development and peak time of the 1997/98 El Niño event (September 1997–February 1998) using the ERA-40 (anomalies relative to the 1958–2001 climatology). Shown are (from left to right) the original data, the low-frequency ENSO component (filtered with a 24–84 months Lanczos bandpass filter; Duchon 1979), and the high-frequency C-mode component (filtered with a 8–20-month Lanczos bandpass filter; Duchon 1979). Additionally, the anomalous surface streamfunction (purple contours; 0.5 × 106 m2 s−1) is shown for the filtered reanalysis data.

Table 2.

Explained variance [R2 (original data, filtered data)] of the ENSO time scale (24–84-month bandpass filtered) variability and the C-mode time scale (8–20 months bandpass filtered) variability for the three NWP indices (monthly anomalies based on the 1958–2001 period). The same Lanczos filter (Duchon 1979) as in Fig. 4 is used.

Explained variance [R2 (original data, filtered data)] of the ENSO time scale (24–84-month bandpass filtered) variability and the C-mode time scale (8–20 months bandpass filtered) variability for the three NWP indices (monthly anomalies based on the 1958–2001 period). The same Lanczos filter (Duchon 1979) as in Fig. 4 is used.
Explained variance [R2 (original data, filtered data)] of the ENSO time scale (24–84-month bandpass filtered) variability and the C-mode time scale (8–20 months bandpass filtered) variability for the three NWP indices (monthly anomalies based on the 1958–2001 period). The same Lanczos filter (Duchon 1979) as in Fig. 4 is used.

As discussed in Stuecker et al. (2015b), we can consider the observed ENSO-associated circulation anomalies as a linear superposition of both the direct ENSO response and the C-mode response (which is nothing else but the seasonal modulation of ENSO). Furthermore, it is nicely demonstrated that the slow ENSO component is not able to explain the month-to-month evolution or rapid transitions of the NWP-AC (Fig. 4, middle). In contrast, it is the C-mode response (Fig. 4, right) that drives most of the spatial and temporal variability of the NWP-AC. By using an inadequate bandpass filter frequency range (13–19 months, after already low-pass filtering the original data with a 12-month period) and further calculating 3-month seasonal means (Fig. 3 in L16; another time scale filter), L16 miss the important contribution of the C-mode to the observed circulation variance (of same order as ENSO; Table 2 and Figs. 3b and 4). The importance of the fast C-mode time scale becomes even more apparent when comparing the contribution of each time scale (ENSO vs C-mode time scales) to the total indices in the time domain (Fig. 5). Both the theoretical C-mode (yellow line in Fig. 5) and the NWP indices bandpass filtered in the C-mode time scale range (red line in Fig. 5) capture the rapid phase reversals of the NWP-AC due to the annually varying climate state. The slow ENSO component (blue line in Fig. 5) is evidently not able to explain these fast transitions (see also Fig. 1). These examples highlight the dangers of narrow bandpass filtering as we also discussed in our previous work (e.g., Stuecker et al. 2015a,b,c)

Fig. 5.

(from top to bottom) Time evolution of the three NWP indices for the original time series (gray line), the C-mode time scale component (red line; 8–20-month Lanczos bandpass filtered), and the ENSO time scale component (blue line; 24–84-month Lanczos bandpass filtered). For comparison, the theoretical C-mode index (yellow line) is included (scaled to the same variance as the C-mode time scale component), as well as the linear correlation coefficients (R) of each NWP index with both ENSO (measured by the N3.4 index, not displayed) and the theoretical C-mode index.

Fig. 5.

(from top to bottom) Time evolution of the three NWP indices for the original time series (gray line), the C-mode time scale component (red line; 8–20-month Lanczos bandpass filtered), and the ENSO time scale component (blue line; 24–84-month Lanczos bandpass filtered). For comparison, the theoretical C-mode index (yellow line) is included (scaled to the same variance as the C-mode time scale component), as well as the linear correlation coefficients (R) of each NWP index with both ENSO (measured by the N3.4 index, not displayed) and the theoretical C-mode index.

Concluding, we have demonstrated that the observed formation and time evolution (characterized by phase reversal in September and zero crossing in November) of the anomalous low-level NWP-AC (as described by several indices) is well captured by our theoretical C-mode formulation (Fig. 1) and is in full agreement with previous studies (Stuecker et al. 2013, 2015b). Minor differences between the indices are expected as discussed above and observed in the spatial regression patterns (Figs. 3c–h). Moreover, we clearly showed why the method by L16 to estimate the importance of the C-mode leads to a large spurious underestimation of the true C-mode variability. The variability at the C-mode time scale explains ~(22%–30%) of the variance in the NWP (depending on which index is used), while the ENSO time scale explains ~(27%–36%) (Table 2).

4. How important are air–sea interactions for the NWP-AC evolution during DJF to JJA?

Here we demonstrate again that thermodynamic air–sea interactions are not the main driver for the NWP-AC time evolution from boreal winter (DJF) to the following summer season (JJA). The C-mode (which is the seasonally modulated ENSO response) initiates a meridionally antisymmetric atmospheric circulation (which includes the NWP-AC) that results in a rapid termination of the El Niño event [Fig. 12 in Stuecker et al. (2015b)]. This feedback of the C-mode on the El Niño event evolution subsequently allows thermodynamic air–sea coupling to prolong the NWP-AC in early boreal summer (Stuecker et al. 2015b).

L16 claim that our AGCM experiment fails to realistically simulate the anomalous low-level NWP-AC during DJF of an El Niño event. The authors use Fig. 7b in Stuecker et al. (2015b) (Fig. 7b in L16 shows the DJF response in one of our idealized fixed frequency AGCM experiments) to make this invalid generalized statement. This figure shows the results of the idealized fixed frequency experiments, which were mainly conducted to unambiguously demonstrate the C-mode mechanism in the frequency domain [Fig. 9 in Stuecker et al. (2015b)]. These experiments were not indented to accurately reproduce the observed time evolution of, say, the 1997/98 event (Stuecker et al. 2015b). If we instead compare the composite of the observed DJF response during the 1997/98 El Niño event with our simulated uncoupled 1997–99 case [Fig. 11 in Stuecker et al. (2015b)], it clearly shows the correct timing of the NWP-AC, as pointed out in Stuecker et al. (2015b)—without air–sea coupling.

The 10-member ensemble of uncoupled 1997–99 simulations in Stuecker et al. (2015b), which is based on the observed SSTA forcing in the eastern equatorial Pacific, clearly demonstrates that the rapid phase transition [Fig. 11 in Stuecker et al. (2015b)] of the anomalous NWP circulation is generated by the atmospheric response (AGCM experiment) and does not necessarily require thermodynamic air–sea coupling [as included in the partially coupled (PARCP) experiment]. Here we show the spatial maps from the 1997–99 AGCM and PARCP experiments (Figs. 6b,c), which were not shown in Stuecker et al. (2015b), to make our point even more lucid. The DJF-average map of the anomalous low-level surface streamfunction (contours) for our AGCM experiment (Fig. 6b) shows that the observed (Fig. 6a) meridionally antisymmetric circulation response, which includes the NWP-AC, is qualitatively very well reproduced. This is in agreement with our C-mode hypothesis and demonstrates that thermodynamic air–sea coupling (Fig. 6c) is not required to set up the large-scale antisymmetric response during this season. In fact, all observed phase transitions of the anomalous NWP circulation during the period 1997–99 are very accurately reproduced by our AGCM experiment [Fig. 11 in Stuecker et al. (2015b)].

Fig. 6.

(a) Observed composite patterns of SST anomalies (shading, °C) and 1000-hPa streamfunction anomalies (thin contour interval: 0.2 × 106 m2 s−1 from −0.8 × 106 to 0.8 × 106 m2 s−1 with zero line omitted and thick contour interval: 106 m2 s−1) for the El Niño peak phase (DJF) for the following events: 1982/83, 1991/92, 1994/95, and 1997/98. This subplot was prepared by Li et al. (2016) (Fig. 4a in L16). (b) SST anomaly and anomalous surface streamfunction [both units as in (a)] response during the 1997/98 DJF season in our AGCM experiment with observed N3.4 time evolution. Some of the thick contour lines are labeled with their value to clarify the highly meridionally antisymmetric character of the response (marked by magenta arrows). (c) As in (b), but for our PARCP experiment. Areas where the circulation is statistically significant above the 95% confidence level [in (b) and (c)] are nonstippled [for details refer to Stuecker et al. (2015b)].

Fig. 6.

(a) Observed composite patterns of SST anomalies (shading, °C) and 1000-hPa streamfunction anomalies (thin contour interval: 0.2 × 106 m2 s−1 from −0.8 × 106 to 0.8 × 106 m2 s−1 with zero line omitted and thick contour interval: 106 m2 s−1) for the El Niño peak phase (DJF) for the following events: 1982/83, 1991/92, 1994/95, and 1997/98. This subplot was prepared by Li et al. (2016) (Fig. 4a in L16). (b) SST anomaly and anomalous surface streamfunction [both units as in (a)] response during the 1997/98 DJF season in our AGCM experiment with observed N3.4 time evolution. Some of the thick contour lines are labeled with their value to clarify the highly meridionally antisymmetric character of the response (marked by magenta arrows). (c) As in (b), but for our PARCP experiment. Areas where the circulation is statistically significant above the 95% confidence level [in (b) and (c)] are nonstippled [for details refer to Stuecker et al. (2015b)].

Small differences between the model simulation (Figs. 6b,c) and the observations (Fig. 6a) are expected due to biases in both mean state and annual cycle of simulated precipitation and circulation (resulting for instance in the slight westward shift of the NWP-AC in the simulations). Nevertheless, both the idealized fixed frequency AGCM experiment (Fig. 7b in L16) and our more realistic experiment (Fig. 6b in this article) show clearly a very strong antisymmetric circulation pattern with a much larger amplitude of the central Pacific cyclone in the Southern Hemisphere than in the Northern Hemisphere (note the nonlinear scale of our streamfunction contour lines).

We restate again our main point from Stuecker et al. (2015b): Thermodynamic air–sea coupling cannot explain the time scale and rapid phase reversals of the observed NWP-AC circulation. In contrast, the C-mode hypothesis is fully consistent with the observed features of the NWP-AC. The C-mode response results in a positive feedback loop [Fig. 12 in Stuecker et al. (2015b)], which increases the termination speed of the El Niño event (McGregor et al. 2012; Stuecker et al. 2013; Abellán and McGregor 2016) and effectively establishes La Niña conditions in the following summer (Stuecker et al. 2015b). In agreement with previous work, remote (Xie et al. 2009) and local (Wang et al. 2000) thermodynamic air–sea interactions result in additional persistence of the NWP-AC in the boreal summer season. However, our results suggest that coupled processes do not set the time scale, nor do they cause the rapid phase transitions (Stuecker et al. 2015b).

5. Summary and discussion

This reply to the comment by L16 shows that the points raised, with regard to the conclusions drawn in Stuecker et al. (2015b), are unsubstantiated. 1) With regard to the signal, we showed that both linear correlations and spectral characteristics clearly demonstrate that a statistically significant (>99%; Table 1 and Figs. 1 and 2) linear relationship exists between the observed anomalous low-level northwest Pacific anticyclone (NWP-AC) and the combination mode (C-mode). Thus, the C-mode time scale is clearly evident for the NWP-AC. 2) With regard to the rapid dynamics, we showed that the rapid onset of the NWP-AC is captured by the theoretical C-mode index (Fig. 1), which is explained by the fast near-annual time scale of the C-mode (Figs. 2 and 5). 3) Finally, with regard to the variance, the C-mode time scale [here: ~(8–20) months] explains a similar amount of variance (22%–30%) to the ENSO time scale (27%–36%; Figs. 3b, 4, and 5 and Table 2), contrary to the claims by L16. Hence, we were able to demonstrate the importance of the C-mode for the evolution of the NWP-AC, which does not contradict possible additional contributions of even faster time scale phenomena below 8 months [such as higher-order modes in the ENSO frequency cascade (Stuecker et al. 2015a) and ISO (Li et al. 2016)]. The inadequate choice of the bandpass filter range by L16 artificially removes a large fraction of the true near-annual C-mode signal (e.g., cf. Fig. 4 herein and Fig. 3 in L16), which leads the authors to make unsubstantiated conclusions regarding the role of the C-mode on the rapid phase reversals of the anomalous NWP circulation.

Finally, by comparing the atmospheric circulation response to El Niño SSTA forcing during boreal winter with (PARCP experiment) and without (AGCM experiment) thermodynamic air–sea coupling, we see that the meridionally antisymmetric circulation (which includes the NWP-AC) can be well reproduced, albeit with smaller amplitude, without the need for air–sea coupling (Fig. 6). As discussed in Stuecker et al. (2015b), thermodynamic air–sea coupling enhances the persistence of the NWP-AC [in agreement with Xie et al. (2009); Wang et al. 2000], but even without it, the simulations for the realistic 1997–99 case show that the rapid phase reversals of the NWP-AC are well captured in the uncoupled AGCM experiment [e.g., Fig. 11 in Stuecker et al. (2015b)].

In addition to the supporting evidence in this reply, the dynamics of the C-mode have been demonstrated thoroughly in a number of different studies with a variety of different methods (Stuecker et al. 2013; McGregor et al. 2012; Stein et al. 2014; Widlansky et al. 2014; Stuecker et al. 2015a,b; Zhang et al. 2015a,b; Ren et al. 2016). Whereas the atmospheric response in the NWP region for both the composite El Niño event (Fig. 1) as well as for La Niña events (Stuecker et al. 2015b) clearly exhibits the underlying C-mode dynamics, other factors also impact the observed circulation in this region. For instance, the zonal location of the ENSO SSTA forcing plays an important role in determining the spatial pattern of the C-mode response (McGregor et al. 2013; Zhang et al. 2015a), while also large unforced internal variability exists in the NWP region (Stuecker et al. 2015b). Furthermore, other climate modes, like intraseasonal oscillations (ISO) (Li et al. 2016) and the Indian Ocean dipole (IOD), generate variability in this area.

Here we have clearly demonstrated that the C-mode explains a large part of the variability in the NWP region and is of crucial importance for the rapid phase reversals of the anomalous circulation in this region. Summarizing, the following methodological choices of Li et al. (2016) lead to their vastly different conclusions compared to Stuecker et al. (2015b):

  1. A statistical red noise null hypothesis test was used, which is not appropriate for evaluating the existence of the C-mode–NWP-AC relationship. Instead, we need to test (a) whether a significant linear correlation exists between the theoretical C-mode time series and the NWP-AC indices, and (b) if significant spectral coherence exists between these time series at combination tone frequencies.

  2. A narrow 13–19-month bandpass filter (combined with 12-month low-pass filtering and subsequent seasonal mean calculations) was used, which is not an adequate choice to capture the C-mode variability. Because of this method L16 greatly underestimate the contribution of the C-mode to the explained variance of the anomalous NWP circulation.

  3. L16 are not able to explain the mismatch between the fast time scale evident for the NWP circulation and the slow ENSO time scale. In contrast, the C-mode and frequency cascade concepts can explain the deterministic ENSO-induced variability on this fast time scale.

  4. As reported in L16, the idealized uncoupled sinusoidal SST forcing experiment [Fig. 7b in Stuecker et al. (2015b)] does show only a weak NWP-AC in DJF. However, the realistic forced uncoupled 1997–99 case [Fig. 6b herein and Fig. 11 in Stuecker et al. (2015b)] simulates well a pronounced NWP-AC in this season. Hence, thermodynamic air–sea coupling is not crucial, even though it amplifies the NWP-AC and enhances its persistence (especially in May–June of the decaying El Niño year).

Acknowledgments

This study was partially supported by U.S. NSF Grant AGS-1406601 and U.S. Department of Energy Grant DE-SC0005110. AT additionally was supported by U.S. NSF Grant 1049219. Computing resources were provided by the University of Southern California HPCC and by NCAR CISL project UHWM0005. SM was supported by the Australian Research Council.

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Footnotes

*

International Pacific Research Center Publication Number 1181 and School of Ocean and Earth Science and Technology Contribution Number 9603.

The original article that was the subject of this comment/reply can be found at http://journals.ametsoc.org/doi/abs/10.1175/JCLI-D-14-00225.1.