Recharge Oscillator Model Research Articles

Widening of wind-stress anomalies amplifies ENSO in a warming climate

Abstract Climate change simulations generally indicate the strengthening of El Niño Southern Oscillation (ENSO) sea surface temperature (SST) variability through the 21st century, yet a robust physical mechanism explaining this change across different models is still lacking, and the projections for ENSO amplitude exhibit a large spread. Most commonly, changes in the background state of the tropical Pacific are invoked to explain these changes of ENSO. Here we show that changes in the structure of wind-stress anomalies associated with ENSO are potentially as important as these background state changes. Specifically, changes in the magnitude, meridional width, and zonal structure of wind-stress anomalies can explain approximately 53% of the inter-model variance in the projected change of ENSO magnitude through the 21st century as well as 43% in ENSO periodicity changes. Among these changes in the wind structure, the meridional widening of wind anomalies plays the most important role. To demonstrate that these changes are indeed critical, we develop a hybrid model of ENSO based on the Community Earth System Model version 2, which incorporates a dynamical ocean coupled to a simplified statistical atmosphere within the tropical Pacific. In the absence of external forcing and corresponding mean-state changes, the imposed changes in wind stress anomalies in this hybrid model result in an increase of ENSO amplitudes of nearly 10% along the equator. Our results are also theoretically supported by a recharge-oscillator model that incorporates the meridional wind structure. Thus, changes in the structure of wind-stress anomalies, together with changes in the mean state, likely play a critical role in the projected strengthening of ENSO.

The dynamics of the El Niño–Southern Oscillation diversity in the recharge oscillator framework

This study investigates the observed El Niño-Southern Oscillation (ENSO) dynamics for the eastern Pacific (EP) and central Pacific (CP) events in reference to the canonical ENSO (T). We use the recharge oscillator (ReOsc) model concept to describe the ENSO phase space and polar coordinate statistics, based on the interaction of sea surface temperature (T) and thermocline depth (h), for the different types of ENSO events. We further look at some important statistical characteristics, such as power spectrum and cross-correlation as essential parameters for understanding the dynamics of ENSO. The results show that the dynamics of the EP and CP events are very different from each other and from the canonical ENSO events. The canonical ENSO (T) events fit closest to the idealised ReOsc model and has the most clearly oscillating ENSO phase space, suggesting it is the most predictable ENSO index. The EP phase space evolution is similar to the canonical ENSO, but the phase transitions are less clear, suggesting less of an oscillatory nature and that the index is more focussed on extreme El Niño and discharge states. The CP phase space, in turn, does not have a clear propagation through all phases and are strongly skewed towards the La Niña state. The interaction between CP and h are much weaker, making the mode less predictable. Wind forced shallow water model simulations show that the CP winds spatial pattern do not force significant h tendencies, strongly reducing the delayed negative feedback, which is essential for the ENSO cycle.

The El Niño Southern Oscillation Recharge Oscillator with the Stochastic Forcing of Long-Term Memory

The influence of the fast-varying variables that have a long-term memory on the El Niño Southern Oscillation (ENSO) is investigated by adding a fractional Ornstein–Uhlenbeck (FOU) process stochastic noise on the simple recharge oscillator (RO) model. The FOU process noise converges to zero very slowly with a negative power law. The corresponding non-zero ensemble mean during the integration period can exert a pronounced influence on the ensemble-mean dynamics of the RO model. The state-dependent noise, also called the multiplicative noise, can present its influence by reducing the relaxation coefficient and by introducing periodic external forcing. The decreasing relaxation coefficient can enhance the oscillation amplitude and shorten the oscillation period. The forced frequency is close to the natural frequency. The two mechanisms together can further amplify the amplitude and shorten the period, compared with the state-independent noise or additive noise, which only exhibits its influence by introducing non-periodic external forcing. These two mechanisms explicitly elucidate the influence of the stochastic forcing on the ensemble-mean dynamics of the RO model. It provides comprehensive knowledge to better understand the interaction between the fast-varying stochastic forcing and the slow-varying deterministic system and deserves further investigation.

The Indian Ocean Weakens the ENSO Spring Predictability Barrier: Role of the Indian Ocean Basin and Dipole Modes

Abstract Prediction of El Niño–Southern Oscillation (ENSO) is hindered by a spring predictability barrier (SPB). In this paper, we investigate the effects of the Indian Ocean (IO) on the SPB. Using a seasonally varying extended IO–ENSO recharge oscillator model, we find that the SPB is much weakened when IO is coupled with ENSO. To gauge the relative role of the Indian Ocean dipole (IOD) and the Indian Ocean Basin (IOB) modes in weakening ENSO SPB, we develop an empirical dynamical model, the linear inverse model (LIM). By coupling/decoupling the IOB or IOD mode with ENSO, we show that the IOB significantly weakens eastern Pacific and central Pacific ENSO SPBs, while the IOD plays a weaker role. The evolution of the optimum initial structures also illustrates the importance of the IOB in ENSO SPB. Moreover, the IOB strongly influences the forecast skill of La Niña SPB rather than El Niño SPB. This point is also identified through six coupled models from the North American multimodel ensemble. It may be related to the role of the IO in the asymmetry in the duration of El Niño and La Niña. The IOB-induced easterly wind anomalies are conducive to the development of La Niña and thus the prediction of La Niña events, whereas these anomalous easterlies are less important during the development of El Niño and the related forecast of El Niño events.

El Niño and La Niña asymmetry in short-term predictability on springtime initial condition

El Niño-Southern Oscillation (ENSO) asymmetry in predictability on springtime initial condition remains unclear. From the perspective of the spring predictability barrier (SPB), this paper investigates the ENSO asymmetry in SPB and explores the potential factors that may lead to this asymmetry. Both the observation and 29 Coupled Model Intercomparison Project Phase 6 (CMIP6) models show that the spring sea surface temperature (SST) persistence is significantly higher in El Niño years than that in La Niña years, and the SPB intensity is stronger in La Niña years than that in El Niño years. Through the recharge oscillator model, observation and CMIP6 models, we demonstrate that the nonlinear wind stress response to SST anomalies in spring is the main cause of the asymmetric SPB intensity. By the mixed-layer heat budget of the tropical Pacific in the spring, we further identify that a stronger response of zonal wind stress in El Niño events can cause a stronger zonal advection feedback, which finally leads to a weaker SPB and enhances the predictability of El Niño. In contrast, the cooling SST in the spring only leads to weak easterly anomalies, the zonal advection feedback is relatively weaker, thus SPB is stronger and the predictability of La Niña is lower. From the perspective of SPB, we suggest that El Niño is more predictable than La Niña.

ENSO phase space dynamics with an improved estimate of the thermocline depth

The recharge oscillator model of the El Niño Southern Oscillation (ENSO) describes the ENSO dynamics as an interaction between the eastern tropical Pacific sea surface temperatures (T) and subsurface heat content (thermocline depth; h), defining a dynamical cycle with different phases. h is often approximated on the basis of the depth of the 20 °C isotherm (Z20). In this study we will address how the estimation of h affects the representation of ENSO dynamics. We will compare the ENSO phase space with h estimated based on Z20 and based on the maximum gradient in the temperature profile (Zmxg). The results illustrate that the ENSO phase space is much closer to the idealised recharge oscillator model if based on Zmxg than if based on Z20. Using linear and non-linear recharge oscillator models fitted to the observed data illustrates that the Z20 estimate leads to artificial phase dependent structures in the ENSO phase space, which result from an in-phase correlation between h and T. Based on the Zmxg estimate the ENSO phase space diagram show very clear non-linear aspects in growth rates and phase speeds. Based on this estimate we can describe the ENSO cycle dynamics as a non-linear cycle that grows during the recharge and El Nino state, and decays during the La Nina states. The most extreme ENSO states are during the El Nino and discharge states, while the La Nina and recharge states do not have extreme states. It further has faster phase speeds after the El Nino state and slower phase speeds during and after the La Nina states. The analysis suggests that the ENSO phase speed is significantly positive in all phases, suggesting that ENSO is indeed a cycle. However, the phase speeds are closest to zero during and after the La Nina state, indicating that the ENSO cycle is most likely to stall in these states.

Equatorial Submesoscale Eddies Contribute to the Asymmetry in ENSO Amplitude

AbstractEl Niño/Southern Oscillation (ENSO) exhibits evident amplitude asymmetry with stronger El Niño than La Niña events. Equatorial submesoscale eddies act as an important damper of ENSO via their induced upward heat flux () from the subsurface to the surface ocean. Yet their effect on ENSO amplitude asymmetry remains unexplored. Using a high‐resolution global climate simulation, we found that strengthening of in the Niño3.4 region during La Niña is more evident than weakening of during El Niño, resulting in stronger damping of La Niña than El Niño events. This asymmetric response of to ENSO is primarily ascribed to that of the temperature fronts associated with larger‐scale processes. Using a recharge oscillator model modified to include the effects of , we show that the asymmetric damping of ENSO by contributes importantly to the ENSO amplitude asymmetry.

ENSO coupling to the equatorial Atlantic: Analysis with an extended improved recharge oscillator model

IntroductionObservational and modeling studies have examined the interactions between El Niño-Southern Oscillation (ENSO) and the equatorial Atlantic variability as incorporated into the classical charge-recharge oscillator model of ENSO. These studies included the role of the Atlantic in the predictability of ENSO but assumed stationarity in the relationships, i.e., that models’ coefficients do not change over time. A recent work by the authors has challenged the stationarity assumption in the ENSO framework but without considering the equatorial Atlantic influence on ENSO.MethodsThe present paper addresses the changing relationship between ENSO and the Atlantic El Niño using an extended version of the recharge oscillator model. The classical two-variable model of ENSO is extended by adding a linear coupling on the SST anomalies in the equatorial Atlantic. The model’s coefficients are computed for different periods. This calculation is done using two methods to fit the model to the data: (1) the traditional method (ReOsc), and (2) a novel method (ReOsc+) based on fitting the Fisher’s Z transform of the auto and cross-correlation functions.ResultsWe show that, during the 20th century, the characteristic damping rate of the SST and thermocline depth anomalies in the Pacific have decreased in time by a factor of 2 and 3, respectively. Moreover, the damping time of the ENSO fluctuations has doubled from 10 to 20 months, and the oscillation period of ENSO has decreased from 60-70 months before the 1960s to 50 months afterward. These two changes have contributed to enhancing ENSO amplitude. The results also show that correlations between ENSO and the Atlantic SST strengthened after the 70s and the way in which the impact of the equatorial Atlantic is added to the internal ENSO variability.ConclusionsThe remote effects of the equatorial Atlantic on ENSO must be considered in studies of ENSO dynamics and predictability during specific time-periods. Our results provide further insight into the evolution of the ENSO dynamics and its coupling to the equatorial Atlantic, as well as an improved tool to study the coupling of climatic and ecological variables.

Multiyear ENSO Dynamics as Revealed in Observations, Climate Model Simulations, and the Linear Recharge Oscillator

Abstract El Niño–Southern Oscillation (ENSO) events occasionally recur one after the other in the same polarity, called multiyear ENSO. However, the dynamical processes are not well understood. This study aims to elucidate the unified mechanisms of multiyear ENSO using observations, phase 6 of the Coupled Model Intercomparison Project (CMIP6) models, and the theoretical linear recharge oscillator (RO) model. We found that multiyear El Niño and La Niña events are roughly symmetric except for cases of multiyear La Niña following strong El Niño. The composite multiyear ENSO reveals that anomalous ocean heat content (OHC) in the equatorial Pacific persists beyond the first peak, stimulating another event. This prolonged OHC anomaly is caused by meridional Ekman heat transport counteracting geostrophic transport-induced recharge–discharge process that otherwise acts to change the OHC anomaly. A meridionally wide pattern of sea surface temperature anomalies observed during multiyear ENSO is responsible for the Ekman heat transport and multiple factors such as decadal variability, subtropical processes, and ENSO diversity modulate the ENSO meridional structure. CMIP6 multimodel ensemble shows a significant correlation between the ENSO meridional width and the occurrence ratio of multiyear ENSO, supporting the aforementioned mechanism. A multiyear ENSO-like oscillation was simulated using the linear RO model that incorporates a seasonally varying Bjerknes growth rate and a weak recharge efficiency representing the effect of Ekman transport. When the recharge efficiency parameter was estimated using reanalysis data based on geostrophic transport alone, a multiyear ENSO rarely occurred, confirming the importance of Ekman transport in retarding the recharge–discharge process.

The Different Relationships between the ENSO Spring Persistence Barrier and Predictability Barrier

Abstract In this paper, we investigate the relationship between the El Niño–Southern Oscillation (ENSO) spring persistence barrier (PB) and predictability barrier (PD) and apply it to explain the interdecadal modulation of ENSO prediction skill using the anomaly correlation coefficient (ACC). Previous studies showed that a longer persistence (i.e., autocorrelation) tends to produce a higher prediction skill. Using the recharge oscillator model of ENSO, both analytical and numerical solutions suggest that the predictability (i.e., ACC) is related to the persistence of sea surface temperature (SST) and cross correlation between SST and subsurface ocean heat content in the tropical Pacific. In particular, a larger damping rate in SST anomalies will lead to a lower persistence and ACC and a stronger PD. However, a shortened ENSO period, which controls the cross correlation, will lead to a lower persistence but a higher ACC associated with a weaker PD. Finally, we apply our solutions to observations and suggest that a higher ACC associated with a weaker PD after 1960 is caused by the shortened ENSO period.

Asymmetries in the ENSO phase space

El Niño Southern Oscillation (ENSO) dynamics are best described by the recharge oscillator model, in which the eastern tropical Pacific sea surface temperatures (T) and subsurface heat content (thermocline depth; h) have an out-of-phase relationship. This defines a 2-dimensional phase space diagram between T and h. In an idealized, stochastically forced damped oscillator, the mean phase space diagram should be a perfectly symmetrical circle with a clockwise propagation over time. However, the observed phase space shows strong asymmetries. In this study we illustrate how the ENSO phase space can be used to discuss the phase-dependency of ENSO dynamics. A normalized spherical coordinate system allows the definition of phase-depending ENSO growth rates and phase transition speeds. Based on these we discuss the implications of the observed asymmetries with regards to the dynamics and predictability of ENSO; with a particular focus on the variations in the growth rate and coupling of ENSO along the oscillation cycle. Using linear and non-linear recharge oscillator models we will show how dynamics and noise are driving ENSO at different phases of the ENSO cycles. The results illustrate that the ENSO cycle with positive phase transitions is present in all phases but has strong variations in its strength. Much of these variations result from presenting the ENSO phase space with estimates of h based on the iso-thermal depth, that is not ideal as it is not out-of-phase with T. Future work should address how h can be estimated better, including aspects such as the vertical temperature gradients and the meridional or zonal range. We further illustrated that a non-linear growth rate of T can explain most of the observed non-linear phase space characteristics.

The Signal‐to‐Noise Paradox in ENSO Prediction: Role of ENSO Growth Rate and Period

AbstractThis paper investigates the relationship between heterogeneous predictability and homogeneous predictability for El Niño‐Southern Oscillation (ENSO) prediction. Previous studies showed that a larger heterogeneous predictability than homogeneous predictability, referred as the signal‐to‐noise paradox, is caused by a higher persistence in the observations than in the model. By using the recharge oscillator model, it is found analytically and numerically that both ENSO growth rate and period contribute to this paradox. A larger ENSO growth rate in the observation can lead to a higher persistence and heterogeneous predictability. However, a larger ENSO growth rate associated with a shortened ENSO period can also lead to this paradox although the persistence of the observation is lower than forecast model. Finally, we apply it to explain the paradox after 1960 is caused by a larger ENSO growth rate and a shortened ENSO period.

Multidecadal variability of ENSO in a recharge oscillator framework

We use a conceptual recharge oscillator model to identify changes in El Niño and the Southern Oscillation (ENSO) statistics and dynamics during the observational record. The variability of ENSO has increased during the 20th century. The cross-correlation between sea surface temperature (SST) and warm water volume (WWV) has also changed during the observational record. From the 1970s onwards, the SST drives WWV anomalies with a lead-time of ten months and the WWV feedbacks onto the SST with a lead-time of eight months. This is reminiscent of a recharge-discharge mechanism of the upper ocean heat content. The full recharge-discharge mechanism is only observed from the 1970s onwards. This could be the result of the degradation of the quality of observations in the early part of the 20th century. However, it may also be a consequence of decadal changes in the coupling between WWV and SST. Additional analysis fitting the recharge oscillator model to the coupled state-of-the-art climate models indicates that ENSO properties show little decadal changes in the climate models. The disagreement in changes in ENSO properties between the reanalysis and the climate models can be due to errors in the available observational data or due to the models missing the low frequency variability and decadal wind trends. Longer and more reliable observational records would be required to validate our results.

Distinct Off-Equatorial Zonal Wind Stress and Oceanic Responses for EP- and CP-Type ENSO Events

Abstract This study utilizes observations and a series of idealized experiments to explore whether eastern Pacific (EP)- and central Pacific (CP)-type El Niño–Southern Oscillation (ENSO) events produce surface wind stress responses with distinct spatial structures. We find that the meridionally broader sea surface temperatures (SSTs) during CP events lead to zonal wind stresses that are also meridionally broader than those found during EP-type events, leading to differences in the near-equatorial wind stress curl. These wind spatial structure differences create differences in the associated pre- and post-ENSO event WWV response. For instance, the meridionally narrow winds found during EP events have (i) weaker wind stresses along 5°N and 5°S, leading to weaker Ekman-induced pre-event WWV changes; and (ii) stronger near-equatorial wind stress curls that lead to a much larger post-ENSO event WWV changes than during CP events. The latter suggests that, in the framework of the recharge oscillator model, the EP events have stronger coupling between sea surface temperatures (SST) and thermocline (WWV), supporting more clearly the phase transition of ENSO events, and therefore, the oscillating nature of ENSO than CP events. The results suggest that the spatial structure of the SST pattern and the related differences in the wind stress curl, are required along with equatorial wind stress to accurately model the WWV changes during EP- and CP-type ENSO events.

A Theory of the Spring Persistence Barrier on ENSO. Part III: The Role of Tropical Pacific Ocean Heat Content

AbstractIn this paper, we investigate the relationship between upper ocean heat content (OHC) and El Niño–Southern Oscillation (ENSO) sea surface temperature (SST) anomalies mainly using the neutral recharge oscillator (NRO) model both analytically and numerically. Previous studies showed that spring OHC, which leads SST by 6–12 months, represents a major source of predictability for ENSO. It is suggested that this seasonality is caused by the seasonally varying growth rate in SST anomalies. Moreover, a shortened ENSO period will lead to a reduced SST predictability from OHC, with the most significant decrease occurring in the latter half of the calendar year. The cross-correlation relationship between OHC and ENSO SST anomalies is further identified in the damped and self-excited version of the recharge oscillator model. Finally, we suggest that the seasonal growth rate of ENSO anomalies is the cause of the seasonality in the effectiveness of OHC as a predictor in ENSO forecasting, particularly as it relates to the boreal spring persistence barrier and associated spring predictability barrier. We also explain the shorter lead time between spring OHC and ENSO SST anomalies after the turn of the twenty-first century in terms of the apparent higher frequency of the ENSO period.

Seasonal Gap Theory for ENSO Phase Locking

Abstract The life cycle of El Niño-Southern Oscillation (ENSO) typically follows a seasonal march, onset in spring, developing during summer, maturing in boreal winter, and decaying over the following spring. This feature is referred to as ENSO phase locking. Recent studies have noted that seasonal modulation of the ENSO growth rate is essential for this process. This study investigates the fundamental effect of a seasonally varying growth rate on ENSO phase locking using a modified seasonally-dependent recharge oscillator model. There are two phase locking regimes associated with the strength of the seasonal modulation of growth rate: (1) a weak regime in which only a single peak occurs; and (2) a strong regime in which two types of events occur either with a single peak or double peak. Notably, there is a seasonal gap in the strong regime, during which the ENSO peak cannot occur because of large-scale ocean-atmosphere coupled processes. We also retrieve a simple analytical solution of the seasonal variance of ENSO, revealing that the variance is governed by the time-integral of seasonally varying growth rate. Based on this formulation, we propose a seasonal energy index (SEI) that allows explaining the seasonal gap, and provides an intuitive explanation for ENSO phase locking, potentially applicable to global climate model ENSO diagnostics.

A theory of Spring Persistence Barrier on ENSO. Part II: Persistence Barriers in SST and ocean heat content

AbstractIn this paper, we investigate the potential factors that control the relationship between the El Niño-Southern Oscillation (ENSO) persistence barriers (PB) in sea surface temperature (SST) and ocean heat content (OHC) and apply it to explain observational ENSO PBs. With the addition of seasonal growth rate in SST in the neutral recharge oscillator (NRO) model, approximate analytical solutions of autocorrelation functions for SST and OHC suggest strictly that the timing of PB for OHC leads that of SST by half a year and the strength of the two PBs are the same. The numerical solutions of the NRO model also show a similar relationship. The role of ENSO growth rate to PBs in SST and OHC is then identified in the damped and unstable ENSO regime. Therefore, it is suggested that for the observational ENSO, the seasonally varying ENSO growth rate in SST controls PBs in SST and OHC simultaneously.

A Theory of the Spring Persistence Barrier on ENSO. Part I: The Role of ENSO Period

AbstractIn this paper, we investigate the role of the period of El Niño–Southern Oscillation (ENSO) in the spring persistence barrier (SPB), mainly using the neutral recharge oscillator (NRO) model both analytically and numerically. It is suggested that a shorter ENSO period strengthens the SPB. Moreover, in contrast to the strict phase locking of the SPB in the Langevin equation, the phase of the SPB is no longer locked exactly to a particular time of the calendar year in the NRO model. Instead, the phases of the SPB for different initial months shift earlier with lag months of maximum persistence decline. In particular, the phase of the SPB will be shifted from the early summer to early spring, corresponding to the initial months of the early half year and later half year. This feature demonstrates that for the later half year, ENSO predictability decreases as the presence of ENSO period. For realistic parameters, the range of the phase change is modest, smaller than 2–3 months. A similar phase shift is also identified for the SPB in the damped ENSO regime, unstable ENSO regime, and observations. Our theory provides a null hypothesis for the role of ENSO period with regard to the SPB.

A Recharge Oscillator Model for Interannual Variability in Venus’ Clouds

AbstractSulfur dioxide is a radiatively and chemically important trace gas in the atmosphere of Venus and its abundance at the cloud tops has been observed to vary on interannual to decadal timescales. This variability is thought to come from changes in the strength of convection which transports sulfur dioxide to the cloud tops, although the dynamics behind such convective variability are unknown. Here, we propose a new conceptual model for convective variability that links the radiative effects of water abundance at the cloud‐base to convective strength within the clouds, which in turn affects water transport within the cloud. The model consists of two coupled equations which are identified as a recharge‐discharge oscillator. The solutions of the coupled equations are finite amplitude sustained oscillations in convective strength and cloud‐base water abundance on 3–9 years timescales. The characteristic oscillation timescale is given by the geometric mean of the radiative cooling time and the eddy mixing time near the base of the convective clouds.

Fokker\u2013Planck dynamics of the El Ni\xf1o-Southern Oscillation

The asymmetric nature of the El Niño-Southern Oscillation (ENSO) is explored by using a probabilistic model (PROM) for ENSO. Based on a Fokker–Planck Equation (FPE), PROM describes the dynamics of a nonlinear stochastic ENSO recharge oscillator model for eastern equatorial Pacific temperature anomalies and equatorial Pacific basin-averaged thermocline depth changes. Eigen analyses of PROM provide new insights into the stationary and oscillatory solutions of the stochastic dynamical system. The first probabilistic eigenmode represents a stationary mode, which exhibits the asymmetric features of ENSO, in case deterministic nonlinearities or multiplicative noises are included. The second mode is linked to the oscillatory nature of ENSO and represents a cyclic asymmetric probability distribution, which emerges from the key dynamical processes. Other eigenmodes are associated with the temporal evolution of higher order statistical moments of the ENSO system. The model solutions demonstrate that the deterministic nonlinearity plays a stronger role in establishing the observed asymmetry of ENSO as compared to the multiplicative stochastic part.