# El Niño−Southern Oscillation frequency cascade

See allHide authors and affiliations

Edited by Mark A. Cane, Lamont Doherty Earth Observatory of Columbia University, Palisades, NY, and approved September 18, 2015 (received for review May 1, 2015)

## Significance

This study identifies a mechanism to generate atmospheric variability on near-annual and subannual timescales. Responding nonlinearly to both the El Niño−Southern Oscillation (ENSO) and the annual cycle in sea surface temperatures, the atmosphere develops a wide range of deterministic spectral peaks and corresponding spatial patterns. It is demonstrated that the resulting deterministic variability, which projects onto one of the major modes of East Asian Monsoon variability, exhibits similar predictability as ENSO.

## Abstract

The El Niño−Southern Oscillation (ENSO) phenomenon, the most pronounced feature of internally generated climate variability, occurs on interannual timescales and impacts the global climate system through an interaction with the annual cycle. The tight coupling between ENSO and the annual cycle is particularly pronounced over the tropical Western Pacific. Here we show that this nonlinear interaction results in a frequency cascade in the atmospheric circulation, which is characterized by deterministic high-frequency variability on near-annual and subannual timescales. Through climate model experiments and observational analysis, it is documented that a substantial fraction of the anomalous Northwest Pacific anticyclone variability, which is the main atmospheric link between ENSO and the East Asian Monsoon system, can be explained by these interactions and is thus deterministic and potentially predictable.

The El Niño−Southern Oscillation (ENSO) phenomenon is a coupled air−sea mode, and its irregular occurring extreme phases El Niño and La Niña alternate on timescales of several years (1⇓⇓⇓⇓⇓⇓–8). The global atmospheric response to the corresponding eastern tropical Pacific sea surface temperature (SST) anomalies (SSTA) causes large disruptions in weather, ecosystems, and human society (3, 5, 9).

One of the main properties of ENSO is its synchronization with the annual cycle: El Niño events tend to grow during boreal summer and fall and terminate quite rapidly in late boreal winter (9⇓⇓⇓⇓⇓⇓⇓⇓–18). The underlying dynamics of this seasonal pacemaking can be understood in terms of the El Niño/annual cycle combination mode (C-mode) concept (19), which interprets the Western Pacific wind response during the growth and termination phase of El Niño events as a seasonally modulated interannual phenomenon. This response includes a weakening of the equatorial wind anomalies, which causes the rapid termination of El Niño events after boreal winter and thus contributes to the seasonal synchronization of ENSO (17). Mathematically, the modulation corresponds to a product between the interannual ENSO phenomenon (ENSO frequency: ^{-1}), which generates near-annual frequencies at periods of

In nature, a wide variety of nonlinear processes exist in the climate system. Atmospheric examples include convection and low-level moisture advection (19). An example for a quadratic nonlinearity is the dissipation of momentum in the planetary boundary layer, which includes a product between ENSO (E) and the annual cycle (A) due to the windspeed nonlinearity: **v**_{E}⋅ v_{A} (17, 19). In the frequency domain, this product results in the near-annual sum (1 + *SI Appendix*, *SI Materials and Methods*) exhibits most power at interannual frequencies (Fig. 1*A*). In contrast, the near-annual combination tones (*B*).

Physically, the dominant near-annual combination mode comprises a meridionally antisymmetric circulation pattern (Fig. 1*D*). It features a strong cyclonic circulation in the South Pacific Convergence Zone, with a much weaker counterpart cyclone in the Northern Hemisphere Central Pacific. The most pronounced feature of the C-mode circulation pattern is the anomalous low-level Northwest Pacific anticyclone (NWP-AC). This important large-scale atmospheric feature links ENSO impacts to the Asian Monsoon systems (20⇓⇓⇓⇓–25) by shifting rainfall patterns (*SI Appendix*, Fig. S1*B*), and it drives sea level changes in the tropical Western Pacific that impact coastal systems (26). It has been demonstrated using spectral analysis methods and numerical model experiments that the C-mode is predominantly caused by nonlinear atmospheric interactions between ENSO and the warm pool annual cycle (19, 20). Local and remote thermodynamic air−sea coupling amplify the signal but are not the main drivers for the phase transition of the C-mode and its associated local phenomena (e.g., the NWP-AC) (20).

Even though ENSO and the C-mode are not independent, their patterns and spectral characteristics are fundamentally different, which has important implications when assessing the amplitude and timing of their regional climate impacts (Fig. 1). Here we set out to study the role of nonlinear interactions between ENSO and the annual cycle (10) in the context of C-mode dynamics. Such nonlinearities can, in principle, generate a suite of higher-order combination modes, which would contribute to the high-frequency variability of the atmosphere—in a deterministic and predictable way.

## Idealized Frequency Experiments

To investigate the nonlinear atmospheric response to interannual ENSO SSTA, in the presence of the annual cycle, we use a similar experimental setup as in ref. 20. The eastern tropical Pacific SSTA pattern (Fig. 2*A*) is multiplied by a sinusoidal interannual time series (e.g., Fig. 2*B* for one experiment example) to derive the spatiotemporal evolution of the anomalous boundary forcing for a suite of atmospheric general circulation model (AGCM) experiments using the Community Earth System Model (CESM) Community Atmosphere Model version 4 (CAM4) (27) in a T42 horizontal resolution with 26 vertical levels (details in *SI Appendix*, *SI Materials and Methods*). The total boundary forcing comprises the observed SST annual cycle additional to the aforementioned ENSO anomalies. In the following, the warm pool annual cycle time evolution is given the variable A(t), and the ENSO time evolution is given the variable E(t).

The aforementioned nonlinear processes are an essential part of general circulation models such as CESM CAM4. For an SST boundary forcing that includes only ENSO (E) and the annual cycle (A), the nonlinear interaction during these processes can be expanded with a Taylor expansion, as a sum of terms *f* = 1 y^{-1}) and 2 denotes the semiannual (SA) cycle frequency (*f* = 2 y^{-1}).

For our experiments, we chose five different discrete idealized ENSO SSTA forcing frequencies (*A*): 3/7 y^{-1}, 2/5 y^{-1}, 3/10 y^{-1}, 3/13 y^{-1}, and 3/16 y^{-1}. These choices were motivated by an intended separation of all ENSO forcing frequencies and the resulting ENSO/annual cycle nonlinear interaction frequencies (*SI Appendix*, Table S1). We also added additional sinusoidal frequency experiments that have some overlapping forcing and interaction frequencies, ^{-1}, 1/3 y^{-1}, and 1/4 y^{-1}, to investigate the role of frequency overlapping in estimating the functional form of the atmospheric response. The expected response frequencies for these experiments, as well as the respective number of ensemble members for each experiment, are listed in *SI Appendix*, Table S1. The cubic ENSO noninteraction term (frequency

When analyzing the nonlinear atmospheric response to the combined ENSO/annual cycle forcing, we focus here on the anomalous low-level NWP-AC because it acts as the crucial bridge between ENSO variability and the East Asian Monsoon system (20). To characterize this anomalous circulation, we define the anomalous surface wind stream function averaged over the NWP region (120°E−160°E, 5°N−20°N, Fig. 2) as our circulation index NWP-AC(t) for each experiment (as in ref. 20). To remove the noise (unforced internal atmospheric variability), the ensemble mean indices are calculated and reduplicated to give a time series of the same length as the original indices, which is labeled

## Higher-Order Combination Modes

The power spectra for the *SI Appendix*, Figs. S2*A*, S3*A*, and S4*A*) show that most of the variance can be attributed to the quadratic combination tone peaks (

Distinctively different anomalous low-level atmospheric circulation patterns (Fig. 3 *G*−*K*) are associated with the individual frequency components (Fig. 3 *A*−*E*), adding together to the full response pattern (Fig. 3*L*). Most of the meridionally antisymmetric response can be attributed to the ENSO interactions with either the annual or semiannual cycle. These distinct pattern and associated timescales demonstrate that ENSO’s impact extends far beyond its interannual timescale and canonical response pattern (Fig. 1 *A* and *C*).

The very clearly identifiable peaks (*SI Appendix*, Figs. S2*A*, S3*A*, and S4*A*) at the theoretically expected frequencies (*SI Appendix*, Table S1) motivate us to use a least square optimization approach to determine the following amplitude (

where

We find that for the cases with nonoverlapping response frequencies, the estimated regression coefficients agree very well (*SI Appendix*, Table S2). We use these five experiments to calculate the averaged coefficients. The estimates clearly diverge for the experiments with 1/2 y^{-1} and 1/3 y^{-1} forcing frequencies, as the frequencies from different terms overlap (*SI Appendix*, Table S1). Using the averaged coefficients *SI Appendix*, Table S2), we now reconstruct our theoretical index time series for each experiment, which includes all of the terms (linear, quadratic, and cubic) listed in the equations above. We find very high correlations (R*Materials and Methods* for the reconstruction nomenclature) and the ensemble mean indices (*SI Appendix*, Figs. S2, S3, and S4 and Table S3), with the largest contribution to the correlation coming from the quadratic combination tones. Furthermore, we see that the full reconstruction captures well the *F*).

## Application of the Concept

These results motivate us to test if we are also able to identify these higher-order combination tones in (*i*) an AGCM experiment with observed nonsinusoidal (broad spectral peak) ENSO forcing and (*ii*) the Japanese 55-year reanalysis (JRA-55) for the period 1958–2013 (28).

Consistent with the previous idealized frequency experiments, we find that the linear correlation coefficient (R) between the AGCM ensemble mean

The JRA-55 index comprises, in addition to the fixed pattern ENSO response, attributions from different SSTA patterns as well as internal unforced variability that is not accounted for in our idealized AGCM experiments. Using a multiple linear regression approach, we calculate the amplitude regression coefficients *SI Appendix*, Table S4). The contribution of the quadratic C-mode term is larger in the reanalysis than in the model experiments, most likely because of the C-mode amplification due to thermodynamic air−sea coupling (20). Furthermore, the estimated coefficients agree very well with our previous estimates (from the individual frequency experiments) for both the linear ENSO term and the ENSO interaction term with the semiannual cycle. It is important to note that the JRA-55 reanalysis exhibits a different skewness (caused mostly by the quadratic noninteraction ENSO term) in the NWP circulation than estimated from the AGCM experiments. This is explained by model biases, specifically by a too-strong cyclonic response in the NWP region during the El Niño developing phase.

Using the linear ENSO term alone, we find a correlation coefficient of only 0.04 between the filtered JRA-55 NWP-AC(t) index and our reconstruction (

Our spectral analysis (*SI Appendix*, Fig. S5) shows a clear cross-spectral coherence between reanalysis, model experiment, and the theoretical reconstruction at the near-annual quadratic combination tone frequencies (*SI Appendix*, Fig. S5*C*). Furthermore, the phase estimation for the quadratic interaction term between model and theoretical reconstruction is well captured (red line in *SI Appendix*, Fig. S5*B*). Additionally, we find significant coherence and phase relationships when comparing the JRA-55 reanalysis with both our model experiment (green line) and the reconstruction *SI Appendix*, Fig. S5).

## Predictability of the NWP Circulation During ENSO

To demonstrate the predictability of the NWP-AC, we use the National Centers for Environmental Prediction coupled forecast system model version 2 (CFSv2) (29) to hindcast the onset (*SI Appendix*, Fig. S6) and termination (Fig. 4) phases of major ENSO events. All selected termination phase hindcasts begin during the event peak phases in December. As expected from previous studies (17, 19), we see that the N3.4 prediction (thick magenta line for the ensemble mean and thin magenta lines for the 1 SD error) captures the observed evolution of the index (dashed black line) reasonably well. A hindcast of the NWP-AC is performed (thick solid orange line for the mean and thin orange lines for the 1 STD error) using the

For instance, for the hindcast starting in December 1982, we accurately predicted the NWP-AC in the following boreal summer. Persistence due to thermodynamic air−sea coupling, which is not included in our idealized AGCM experiments, plays a role in sustaining the C-mode response in boreal spring during some El Niño events (e.g., 1982–1983) (20). However, it is the atmospheric response (as captured by our AGCM experiments) that drives the crucial phase reversal of the anomalous NWP circulation and is responsible for the fast near-annual and subannual timescales in this region. For instance, these phase reversals include the rapid transition from cyclonic to anticyclonic circulation starting in October 1982 and the subsequent decay of the anticyclonic anomalies after the peak of the warm pool annual cycle in February 1983 (Fig. 4).

## Discussion

Our results reveal a nonlinear combination mode frequency cascade in the seasonally modulated atmospheric response to ENSO: The nonlinear interaction between interannual ENSO variability and the seasonal cycle results in a wide range of high-frequency variability, with peaks, for instance, at *SI Appendix*, Table S5). We conclude that the atmosphere uses the annual cycle as a carrier frequency to effectively transfer power from the interannual ENSO band to higher frequencies.

We outlined a general way to determine the coefficients of this atmospheric response function and to assess the regional importance of the individual frequency components (Fig. 3). Despite evident model biases, we found a remarkable agreement of many of these coefficients between our AGCM and the reanalysis. Further model improvements will allow us to estimate the nonlinear functions with even more confidence. Internal unforced variability and different SSTA forcing pattern play an additional role for the observed anomalous circulation in the NWP region. For instance, the zonal location of the SSTA forcing plays a crucial role in determining the combination mode response (30, 31). The fact that the estimated regression coefficients are largely independent of the forcing frequency indicates a robust atmospheric response to SSTA forcing. This gives us confidence that the proposed methodology can be applied for other climate combination modes. We outlined a very powerful, yet simple, framework to identify any interactions of climate phenomena occurring on different timescales, and showed that a significant part of the atmospheric spectrum in the tropical Western Pacific is due to ENSO/annual cycle interactions and thus is deterministic.

## Materials and Methods

To reduce the noise in the JRA-55 index, we first low-pass filtered the index with a 4-mo cutoff Lanczos filter (32). The choice of 4 mo does not interfere with the quadratic and cubic combination tone timescales. Our reconstruction using only the linear ENSO term, labeled *A*) with different forcing frequencies and time evolution (e.g., Fig. 2*B*). The detailed methods can be found in *SI Appendix*, *SI Materials and Methods*.

## Acknowledgments

We thank two anonymous reviewers for a very thorough and constructive review process that helped considerably in clarifying our manuscript. Matthew J. Widlansky provided assistance with the coupled forecast system model version 2 data processing. M.F.S acknowledges discussions with Masahiro Watanabe and financial support during a research visit at the University of Tokyo. This study was partially supported by US National Science Foundation (NSF) Grant AGS-1406601 and US Department of Energy Grant DE-SC0005110. A.T. was additionally supported by US NSF Grant 1049219. Computing resources were provided by the University of Southern California Center for High-Performance Computing (HPCC) and by the National Center for Atmospheric Research (NCAR) Computational and Information Systems Lab (CISL) Project UHWM0005. This is International Pacific Research Center (IPRC) Publication 1154 and School of Ocean and Earth Science and Technology (SOEST) Contribution 9513.

## Footnotes

- ↵
^{1}To whom correspondence should be addressed. Email: stuecker{at}soest.hawaii.edu.

Author contributions: M.F.S., F.-F.J., and A.T. designed research; M.F.S. performed research; M.F.S. analyzed data; and M.F.S., F.-F.J., and A.T. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1508622112/-/DCSupplemental.

## References

- ↵
- ↵
- ↵.
- Philander SG

- ↵
- ↵.
- McPhaden MJ,
- Zebiak SE,
- Glantz MH

- ↵
- ↵
- ↵
- ↵
- ↵.
- Jin FF,
- Neelin JD,
- Ghil M

- ↵.
- Tziperman E,
- Stone L,
- Cane MA,
- Jarosh H

- ↵
- ↵
- ↵.
- Tziperman E,
- Zebiak SE,
- Cane MA

- ↵
- ↵
- ↵
- ↵
- ↵
- ↵
- ↵
- ↵
- ↵
- ↵.
- Wang B,
- Xiang B,
- Lee JY

- ↵.
- Kosaka Y,
- Xie SP,
- Lau NC,
- Vecchi GA

- ↵
- ↵
- ↵
- ↵
- ↵
- ↵
- ↵

## Citation Manager Formats

## Article Classifications

- Physical Sciences
- Earth, Atmospheric, and Planetary Sciences