El Niño-Southern Oscillation frequency cascade Malte F. Stuecker a,1 , Fei-Fei Jin a , and Axel Timmermann b a Department of Atmospheric Sciences, University of Hawai‘i at M anoa, Honolulu, HI 96822; and b International Pacific Research Center, University of Hawai‘i at M anoa, Honolulu, HI 96822 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) 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 pro- nounced over the tropical Western Pacific. Here we show that this nonlinear interaction results in a frequency cascade in the atmo- spheric 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 North- west 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. ENSO | frequency cascade | combination mode | annual cycle | monsoon T he 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 combi- nation 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 phenome- non. 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 synchro- nization of ENSO (17). Mathematically, the modulation corre- sponds to a product between the interannual ENSO phenomenon (ENSO frequency: f E ) and the annual cycle (annual frequency: 1 y -1 ), which generates near-annual frequencies at periods of ∼ 10 mo (1 + f E ) and ∼ 15 mo (1 - f E ) (19). 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 + f E ) and difference (1 - f E ) tones (19). The com- monly used Niño 3.4 (N3.4) SSTA index (details in SI Appendix, SI Materials and Methods) exhibits most power at interannual fre- quencies (Fig. 1A). In contrast, the near-annual combination tones (1 ± f E ) are the defining characteristic of the C-mode (Fig. 1B). Physically, the dominant near-annual combination mode comprises a meridionally antisymmetric circulation pattern (Fig. 1D). 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. S1B), 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 be- tween 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. 2A) is multiplied by a sinusoidal interannual time series (e.g., Fig. 2B 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 Appen- dix, 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 Significance This study identifies a mechanism to generate atmospheric variability on near-annual and subannual timescales. Re- sponding 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. 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. 1 To whom correspondence should be addressed. Email: stuecker@soest.hawaii.edu. This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. 1073/pnas.1508622112/-/DCSupplemental. www.pnas.org/cgi/doi/10.1073/pnas.1508622112 PNAS Early Edition | 1 of 6 EARTH, ATMOSPHERIC, AND PLANETARY SCIENCES