El Nino-Southern Oscillation Model Research Articles

A review of progress in coupled ocean-atmosphere model developments for ENSO studies in China

El Nino-Southern Oscillation (ENSO) is the strongest interannual signal that is produced by basinscale processes in the tropical Pacific, with significant effects on weather and climate worldwide. In the past, extensive and intensive international efforts have been devoted to coupled model developments for ENSO studies. A hierarchy of coupled ocean-atmosphere models has been formulated; in terms of their complexity, they can be categorized into intermediate coupled models (ICMs), hybrid coupled models (HCMs), and fully coupled general circulation models (CGCMs). ENSO modeling has made signifiscant progress over the past decades, reaching a stage where coupled models can now be used to successfully predict ENSO events 6 months to one year in advance. Meanwhile, ENSO exhibits great diversity and complexity as observed in nature, which still cannot be adequately captured by current state-of-the-art coupled models, presenting a challenge to ENSO modeling. We primarily reviewed the long-term efforts in ENSO modeling continually and steadily made at different institutions in China; some selected representative examples are presented here to review the current status of ENSO model developments and applications, which have been actively pursued with noticeable progress being made recently. As ENSO simulations are very sensitive to model formulations and process representations etc., dedicated efforts have been devoted to ENSO model developments and improvements. Now, different ocean-atmosphere coupled models have been available in China, which exhibit good model performances and have already had a variety of applications to climate modeling, including the Coupled Model Intercomparison Project Phase 6 (CMIP6). Nevertheless, large biases and uncertainties still exist in ENSO simulations and predictions, and there are clear rooms for their improvements, which are still an active area of researches and applications. Here, model performances of ENSO simulations are assessed in terms of advantages and disadvantages with these differently formulated coupled models, pinpointing to the areas where they need to be further improved for ENSO studies. These analyses provide valuable guidance for future improvements in ENSO simulations and predictions.

Global Sensitivity Analysis of Parameters in the ENSO model Based on Sobol' Method

Cao, X.; Su, S.; Leng, H., and Liu, B., 2020. Global sensitivity analysis of parameters in the ENSO model based on Sobol' method. In: Zheng, C.W.; Wang, Q.; Zhan, C., and Yang, S.B. (eds.), Air-Sea Interaction and Coastal Environments of the Maritime and Polar Silk Roads. Journal of Coastal Research, Special Issue No. 99, pp. 340–345. Coconut Creek (Florida), ISSN 0749-0208.In this work, a global sensitivity analysis (GSA) is performed on physical parameters and initial values of a nonlinear El Nino Southern Oscillation (ENSO) model, to determine the influential parameters at different prediction times. The anomaly of sea surface temperature (SST) at each prediction time is viewed as the response quantity of interest in the sensitivity analysis by Sobol' method. And the Latin Hypercube Sampling technique is applied to all input parameters. Then, the first-order sensitivity indexes (FSI) and total sensitivity indexes (TSI) of physical parameters and initial values are calculated, respectively. The results of numerical simulations show that the proposed method is very effective and feasible for sensitivity analysis of nonlinear ENSO model. It is concluded that the sensitive parameters and relative ranking vary considerably at different prediction times. In the beginning period, initial values of the model have a great influence on the SST anomaly forecast, while for the long-term prediction, physical coefficients become main sensitive parameters, and the initial values have little effect on the output variable. In addition, the interaction between input parameters in the model increases with forecast time, which is indicated by that the difference between the TSI and FSI of each parameter becomes larger.

ENSO Asymmetry in the CAMS-CSM

This study presents an overview of El Nino-Southern Oscillation (ENSO) asymmetry using the Chinese Academy of Meteorological Sciences climate system model (CAMS-CSM). We discover that the coupled run of the CAMS-CSM has an obvious bias of ENSO opposite-sign asymmetry compared to observation, mainly in the eastern Pacific. Further analysis shows that the spatial distributions of sea surface temperature anomalies (SSTA) during both phases of the ENSO present individual biases, consisting of a warmer field during the warm phase and a colder field during the cold phase, in comparison with observation. The bias of ENSO asymmetry during both phases is partly due to the unrealistic simulation of shortwave (SW) radiation flux and the corresponding total cloud cover (TCC). The Atmospheric Model Intercomparison Project (AMIP) run demonstrates that biases of the SW radiation flux and the associated TCC originate in the atmospheric component of the model, which could be attributed to its unrealistic cloud microphysical scheme. Through air-sea interaction, these biases are amplified significantly during both ENSO phases of the coupled run. Moreover, another cause for the bias of ENSO asymmetry during the warm phase is the relatively slow decay of the ENSO in the simulation, with the thermocline anomalies propagating eastward more slowly. The bias of ENSO asymmetry in the cold phase is attributed to oceanic internal dynamic advection, mainly associated with zonal and meridional terms. Further analysis also highlights the essential role of reasonably representing the climatological mean state in ENSO model simulation.

Extension of sea surface temperature unpredictability

The sea surface temperature (SST) variability is clearly affected by global climate patterns, which involve large-scale ocean-atmosphere fluctuations similar to the El Nino-Southern Oscillation (ENSO). We give mathematical arguments for the SST to be unpredictable over oceans. Sensitivity (unpredictability) is the core ingredient of chaos. Several researches suggested that the ENSO might be chaotic. It was Vallis (Science 232:243–245, 1986) who revealed unpredictability in ENSO by reducing his model to the Lorenz equations. We discuss the unpredictability for SST as an extendable phenomenon through coupled Vallis ENSO models and advection equations by using theoretical as well as numerical analyses. To perform theoretical research, we apply our recent results on replication of chaos and unpredictable solutions of differential equations, while for numerical analysis, we combine results on unpredictable solutions with numerical analysis of chaos in the advection equation.

Linear dynamical modes as new variables for data-driven ENSO forecast

A new data-driven model for analysis and prediction of spatially distributed time series is proposed. The model is based on a linear dynamical mode (LDM) decomposition of the observed data which is derived from a recently developed nonlinear dimensionality reduction approach. The key point of this approach is its ability to take into account simple dynamical properties of the observed system by means of revealing the system’s dominant time scales. The LDMs are used as new variables for empirical construction of a nonlinear stochastic evolution operator. The method is applied to the sea surface temperature anomaly field in the tropical belt where the El Nino Southern Oscillation (ENSO) is the main mode of variability. The advantage of LDMs versus traditionally used empirical orthogonal function decomposition is demonstrated for this data. Specifically, it is shown that the new model has a competitive ENSO forecast skill in comparison with the other existing ENSO models.

Time-varying spectral characteristics of ENSO over the Last Millennium

The characteristics of El Nino–Southern Oscillation (ENSO) spectra over the Last Millennium are examined to characterise variability over past centuries. Seven published palaeo-ENSO reconstructions and Nino3.4 from six Coupled Model Intercomparison Project-Phase 5 and Paleoclimate Modelling Intercomparison Project-Phase 3 (CMIP5–PMIP3) Last Millennium simulations were analysed. The corresponding Historical and pre-industrial Control CMIP5–PMIP3 simulations were also considered. The post-1850 spectrum of each modelled or reconstructed ENSO series captures aspects of the observed spectrum to varying degrees. We note that no single model or ENSO reconstruction completely reproduces the instrumental spectral characteristics. The spectral power across the 2–3 years (near biennial), 3–8 years (classical ENSO) and 8–25 years (decadal) periodicity bands was calculated in a sliding 50 year window, revealing temporal variability in the spectra. There was strong temporal variability in the spectral power of each periodicity band in observed Nino3.4 and SOI and for all reconstructions and simulations of ENSO. Significant peaks in spectral power such as observed in recent decades also occur in some of the reconstructed palaeo-ENSO (around 1600, the early 1700s and 1900) and modelled series (around the major volcanic eruptions of 1258 and 1452). While the recent increase in spectral power might be in response to enhanced greenhouse gas levels, the increase lies within the range of variability across the suite of ENSO reconstructions and simulations examined here. This study demonstrates that the analysis of a suite of ENSO reconstructions and model simulations can build a broader understanding of the time-varying nature of ENSO spectra, and how the nature of the past spectra of ENSO is to some extent dependant on the climate model or palaeo-ENSO reconstruction chosen.

Predicting monthly precipitation along coastal Ecuador: ENSO and transfer function models

It is well known that El Nino-Southern Oscillation (ENSO) modifies precipitation patterns in several parts of the world. One of the most impacted areas is the western coast of South America, where Ecuador is located. El Nino events that occurred in 1982–1983, 1987–1988, 1991–1992, and 1997–1998 produced important positive rainfall anomalies in the coastal zone of Ecuador, bringing considerable damage to livelihoods, agriculture, and infrastructure. Operational climate forecasts in the region provide only seasonal scale (e.g., 3-month averages) information, but during ENSO events it is key for decision-makers to use reliable sub-seasonal scale forecasts, which at the present time are still non-existent in most parts of the world. This study analyzes the potential predictability of coastal Ecuador rainfall at monthly scale. Instead of the discrete approach that considers training models using only particular seasons, continuous (i.e., all available months are used) transfer function models are built using standard ENSO indices to explore rainfall forecast skill along the Ecuadorian coast and Galapagos Islands. The modeling approach considers a large-scale contribution, represented by the role of a sea-surface temperature index, and a local-scale contribution represented here via the use of previous precipitation observed in the same station. The study found that the Nino3 index is the best ENSO predictor of monthly coastal rainfall, with a lagged response varying from 0 months (simultaneous) for Galapagos up to 3 months for the continental locations considered. Model validation indicates that the skill is similar to the one obtained using principal component regression models for the same kind of experiments. It is suggested that the proposed approach could provide skillful rainfall forecasts at monthly scale for up to a few months in advance.

Analysis of the non-linearity in the pattern and time evolution of El Niño southern oscillation

In this study the observed non-linearity in the spatial pattern and time evolution of El Nino Southern Oscillation (ENSO) events is analyzed. It is shown that ENSO skewness is not only a characteristic of the amplitude of events (El Ninos being stronger than La Ninas) but also of the spatial pattern and time evolution. It is demonstrated that these non-linearities can be related to the non-linear response of the zonal winds to sea surface temperature (SST) anomalies. It is shown in observations as well as in coupled model simulations that significant differences in the spatial pattern between positive (El Nino) versus negative (La Nina) and strong versus weak events exist, which is mostly describing the difference between central and east Pacific events. Central Pacific events tend to be weak El Nino or strong La Nina events. In turn east Pacific events tend to be strong El Nino or weak La Nina events. A rotation of the two leading empirical orthogonal function modes illustrates that for both El Nino and La Nina extreme events are more likely than expected from a normal distribution. The Bjerknes feedbacks and time evolution of strong ENSO events in observations as well as in coupled model simulations also show strong asymmetries, with strong El Ninos being forced more strongly by zonal wind than by thermocline depth anomalies and are followed by La Nina events. In turn strong La Nina events are preceded by El Nino events and are more strongly forced by thermocline depth anomalies than by wind anomalies. Further, the zonal wind response to sea surface temperature anomalies during strong El Nino events is stronger and shifted to the east relative to strong La Nina events, supporting the eastward shifted El Nino pattern and the asymmetric time evolution. Based on the simplified hybrid coupled RECHOZ model of ENSO it can be shown that the non-linear zonal wind response to SST anomalies causes the asymmetric forcings of ENSO events. This also implies that strong El Ninos are mostly wind driven and less predictable and strong La Ninas are mostly thermocline depth driven and better predictable, which is demonstrated by a set of 100 perfect model forecast ensembles.

An empirical model of decadal ENSO variability

This paper assesses potential predictability of decadal variations in the El Nino/Southern Oscillation (ENSO) characteristics by constructing and performing simulations using an empirical nonlinear stochastic model of an ENSO index. The model employs decomposition of global sea-surface temperature (SST) anomalies into the modes that maximize the ratio of interdecadal-to-subdecadal SST variance to define low-frequency predictors called the canonical variates (CVs). When the whole available SST time series is so processed, the leading canonical variate (CV-1) is found to be well correlated with the area-averaged SST time series which exhibits a non-uniform warming trend, while the next two (CV-2 and CV-3) describe secular variability arguably associated with a combination of Atlantic Multidecadal Oscillation (AMO) and Pacific Decadal Oscillation (PDO) signals. The corresponding ENSO model that uses either all three (CVs 1–3) or only AMO/PDO-related (CVs 2 and 3) predictors captures well the observed autocorrelation function, probability density function, seasonal dependence of ENSO, and, most importantly, the observed interdecadal modulation of ENSO variance. The latter modulation, and its dependence on CVs, is shown to be inconsistent with the null hypothesis of random decadal ENSO variations simulated by multivariate linear inverse models. Cross-validated hindcasts of ENSO variance suggest a potential useful skill at decadal lead times. These findings thus argue that decadal modulations of ENSO variability may be predictable subject to our ability to forecast AMO/PDO-type climate modes; the latter forecasts may need to be based on simulations of dynamical models, rather than on a purely statistical scheme as in the present paper.

Perturbed solving method for interdecadal sea-air oscillator model

A coupled system of the interdecadal sea-air oscillator model is studied. The El Nino-southern oscillation (ENSO) atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The oscillator model is involved with the variations of both the eastern and western Pacific anomaly patterns. This paper proposes an ENSO atmospheric physics model using a method of the perturbation theory. The aim is to create an asymptotic solving method for the ENSO model. Employing the perturbed method, the asymptotic solution of corresponding problem is obtained, and the asymptotic behaviour of the solution is studied. Thus we can obtain the prognoses of the sea surface temperature anomaly and related physical quantities.

How dynamical models can learn from the data—an example with a simplified ENSO model

Most dynamical models of the natural system contain a number of empirical parameters which reflect our limited understanding of the simulated system or describe unresolved subgrid-scale processes. While the parameterizations basically introduce some uncertainty to the model results, they also hold the prospect of tuning the model. In general, a deterministic tuning is related to an inversion of the model which is often impossible or requires considerable computing effort for most climate models. Another way to adjust the model parameters to a specific observed process is stochastic fitting where a set of parameters and model output are taken as random variables. Here, we present a dynamical–statistical approach with a simplified model of the El Nino–Southern Oscillation (ENSO) cycle whose parameters are adjusted to simulated and observed data by means of Bayesian statistics. As ENSO model, we employ the Schop–Suarez delay oscillator model. Monte Carlo experiments highlight the large sensitivity of the model results to varied model parameters and initial values. The statistical adjustment is done by Bayesian model averaging of the Monte Carlo experiments. Applying the method to simulated data, the posterior ensemble mean is much closer to the reference data than the prior ensemble mean. The learning effect of the model is evident in the leading empirical orthogonal functions and statistically significant in the mean state. When the method is applied to the observed ENSO time series, the ENSO model in its classical setup is not able to account for the temporally varying periodicity of the observed ENSO phenomenon. An improved setup with continuous adjustment periods and extended parameter range is developed in order to allow the model to learn from the data gradually. The improved setup leads to promising results during the twentieth century and even a weak forecast skill over 6 months. Thus, the described method offers a promising tool for data assimilation in dynamical weather and climate models. However, the simplified ENSO model is barely appropriate for operational ENSO forecasts owing to its limited physical complexity.

Progress in predictability studies in China (2003–2006)

Since the last International Union of Geodesy and Geophysics General Assembly (2003), predictability studies in China have made significant progress. For dynamic forecasts, two novel approaches of conditional nonlinear optimal perturbation and nonlinear local Lyapunov exponents were proposed to cope with the predictability problems of weather and climate, which are superior to the corresponding linear theory. A possible mechanism for the “spring predictability barrier” phenomenon for the El Nino-Southern Oscillation (ENSO) was provided based on a theoretical model. To improve the forecast skill of an intermediate coupled ENSO model, a new initialization scheme was developed, and its applicability was illustrated by hindcast experiments. Using the reconstruction phase space theory and the spatio-temporal series predictive method, Chinese scientists also proposed a new approach to improve dynamical extended range (monthly) prediction and successfully applied it to the monthly-scale predictability of short-term climate variations. In statistical forecasts, it was found that the effects of sea surface temperature on precipitation in China have obvious spatial and temporal distribution features, and that summer precipitation patterns over east China are closely related to the northern atmospheric circulation. For ensemble forecasts, a new initial perturbation method was used to forecast heavy rain in Guangdong and Fujian Provinces on 8 June 1998. Additionally, the ensemble forecast approach was also used for the prediction of a tropical typhoons. A new downscaling model consisting of dynamical and statistical methods was provided to improve the prediction of the monthly mean precipitation. This new downscaling model showed a relatively higher score than the issued operational forecast.

Changes in the leading ENSO modes associated with the late 1970s climate shift: Role of surface zonal current

In this study, using the nonlinear principal analysis (NLPCA) technique, we demonstrated that the leading El Nino‐Southern Oscillation (ENSO) mode in a physical basis changed since the late 1970s. The ENSO mode during the pre‐1980s resembles the destabilized ‘ocean basin mode’, while during the post‐1980s does ‘the recharge‐mode’. In particular, for the pre‐1980s, the surface zonal current mainly acts as an intensifier of the ENSO, while that during post‐1980s it plays a role in the transition of the ENSO cycle. The NLPCA results are reconfirmed by the eigen analysis of the linearized intermediated ENSO model. Over a reasonable parameter range, the leading eigen modes associated with the pre‐1980s are completely separable from those associated with the post‐1980s. The eigen structures for each decadal‐period resemble the corresponding NLPCA patterns.

Variational iteration method for solving the mechanism of the Equatorial Eastern Pacific El Niño–Southern Oscillation

A class of coupled system for the El Nino–Southern Oscillation (ENSO) mechanism is studied. Using the method of variational iteration for perturbation theory, the asymptotic expansions of the solution for ENSO model are obtained and the asymptotic behaviour of solution for corresponding problem is considered.

Periodic Forcing and ENSO Suppression in the Cane-Zebiak Model

The effect of a periodic forcing on the intensity of El Nino-Southern Oscillation (ENSO) is studied using the Cane-Zebiak model. With a basic seasonal climate close to the present, ENSO can be suppressed by a substantially enhanced seasonal external equatorial wind, which could be induced by monsoon forcing. ENSO suppression is usually more effective for an unstable self-exciting ENSO than for a stable stochastic-exciting ENSO. In addition, ENSO also tends to be suppressed by sufficiently strong periodic forcings of longer periods. The suppression of ENSO seems to be related to the nonlinear mechanism of frequency entrainment. These conclusions are in qualitative agreement with previous studies of conceptual ENSO models, although the Cane-Zebiak model shows a much more complicated dependence of the amplitude of ENSO on periodic forcing.

Designing Efficient Observing Networks for ENSO Prediction

The Tropical Atmosphere Ocean (TAO) array of moored buoys in the tropical Pacific Ocean is a major source of data for understanding and predicting El Nino-Southern Oscillation (ENSO). Despite the importance of the TAO array, limited work has been performed where observations are most important for predicting ENSO effectively. To address this issue, this study performs a series of observing system simulation experiments (OSSEs) with a linearized intermediate coupled ENSO model, stochastically forced. ENSO forecasts are simulated for a variety of observing network configurations, and forecast skill averaged over many simulated ENSO events is compared. The first part of this study examined the relative importance of sea surface temperature (SST) and subsurface ocean observations, requirements for spacing and meridional extent of observations, and important regions for observations in this system. Using these results as a starting point, this paper develops efficient observing networks for forecasting ENSO in this system, where efficient is defined as providing reasonably skillful forecasts for relatively few observations. First, efficient networks that provide SST and thermocline depth data at the same locations are developed and discussed. Second, efficient networks of only thermocline depth observations are addressed, assuming that many SST observations are available from another source (e.g., satellites). The dependence of the OSSE results on the duration of the simulated data record is also explored. The results suggest that several decades of data may be sufficient for evaluating the effects of observing networks on ENSO forecast skill, despite being insufficient for evaluating the long-term potential predictability of ENSO.

How Predictability Depends on the Nature of Uncertainty in Initial Conditions in a Coupled Model of ENSO

Abstract The predictability of any complex, inhomogeneous system depends critically on the definition of analysis and forecast errors. A simple and efficient singular vector analysis is used to study the predictability of a coupled model of El Nino–Southern Oscillation (ENSO). Error growth is found to depend critically on the desired properties of the forecast errors (“where and what one wants to predict”), as well as on the properties of the analysis error (“what information is available for that prediction”) and choice of optimization time. The time evolution of singular values and singular vectors shows that the predictability of the coupled model is clearly related to the seasonal cycle and to the phase of ENSO. It is found that the use of an approximation to the analysis error covariance to define the relative importance of errors in different variables gives very different results to the more frequently used “energy norm,” and indicates a much larger role for sea surface temperature information in s...

A Linear Stochastic Dynamical Model of ENSO. Part I: Model Development

Singular vector analysis and Floquet analysis are carried out on a linearized variant of the Zebiak-Cane atmosphere-ocean model of El Nino-Southern Oscillation (ENSO), hereinafter called the nominal model. The Floquet analysis shows that the system has a single unstable mode. This mode has a shape and frequency similar to ENSO and is well described by delayed oscillator physics. Singular vector analysis shows two interesting features. (i) For any starting month and time period of optimization the singular vector is shaped like one of two nearly orthogonal patterns. These two patterns correspond approximately to the real and imaginary parts of the adjoint of the ENSO mode for the time-invariant basic-state version of the system that was calculated in previous work. (ii) Contour plots of the singular values as a function of starting month and period of optimization show a ridge along end times around December. This result along with a study of the time evolution of the associated singular vectors shows that the growth of the singular vectors has a strong tendency to peak in the boreal winter. For the case of a stochastically perturbed ENSO model, this result indicates that the annual cycle in the basic state of the ocean is sufficient to produce strong phase locking of ENSO to the annual cycle; it is not necessary to invoke either nonlinearity or an annual cycle in the structure of the noise. The structures of the ENSO mode, of the optimal vectors, and of the phase locking to the annual cycle are robust to a wide range of values for the following parameters: the coupling strength, the ocean mechanical damping, and the reflection efficiency of Rossby waves that are incident on the western boundary. Four variant models were formed from the nominal coupled model by changing the aforementioned parameters in such a way as to (i) make the model linearly stable and (ii) affect the ratio of optimal transient growth to the amplitude of the first Floquet multiplier (i.e., the decay rate of the ENSO mode). Each of these four models is linearly stable to perturbations but is shown to support realistic ENSO variability via transient growth for plausible values of stochastic forcing. For values of these parameters that are supported by observations and theory, these results show the coupled system to be linearly stable and that ENSO is the result of transient growth. Supporting evidence is found in a companion paper.

Predictability of a Coupled Model of ENSO Using Singular Vector Analysis. Part II: Optimal Growth and Forecast Skill

Abstract The fastest perturbation growth (optimal growth) in forecasts of El Nino–Southern Oscillation (ENSO) with the Zebiak and Cane model is analyzed by singular value decomposition of forward tangent models along forecast trajectories in a reduced EOF space. The authors study optimal growth in forecast runs using two different initialization procedures and discuss the relationship between optimal growth and forecast skill. Consistent with Part I of this work, one dominant growing singular vector is found. Most of the variation of optimal growth, measured by the largest singular value, for warm events and mean condition is seasonal, attributable to the seasonal variations in the background states. For cold events the seasonal optimal growth is substantially suppressed. The first singular vector is approximately white in EOF space, while its final pattern after a 6-month evolution is dominated by the first EOF. The energy norm amplifies between 5- and 24-fold in 6 months. This indicates that small-scale...

Predictability of a Coupled Model of ENSO Using Singular Vector Analysis. Part I: Optimal Growth in Seasonal Background and ENSO Cycles

The fastest initial error growth (optimal growth) in the Zebiak and Cane (ZC) forecast model for the El Nino- Southern Oscillation (ENSO) is analyzed by singular value decomposition of a forward tangent model along a trajectory in a reduced EOF space. In this paper (Part I of II), optimal growth about the seasonally varying background and ENSO cycles from a long model run are discussed. Among the many forms of nonlinearity in ZC, the discontinuity of the slope in subsurface temperature at zero thermocline depth and the nonlinear advection of SST are the most significant. That positive perturbations grow much faster than negative perturbations around the seasonally varying background is first attributable to the discontinuity and, second, attributable to nonlinear advection. About the seasonally varying background, 6-month optimal growth is largest for early (boreal) spring starts, which is related to the enhanced atmospheric heating due to equatorward movement of the ITCZ. One dominant growing structure is found, characterized by north-south and east-west SST dipoles, convergent winds on the equator in the eastern Pacific, and a deepened thermocline in the whole equatorial belt. This structure is insensitive to start month and optimization time. Optimal growth about ENSO cycles in a long model run is generally much smaller than that about the seasonally varying background. As before, one dominant growing structure, insensitive to start time and optimization time, is found. During the warm phase of ENSO, optimal growth is modulated by season as is that about the seasonal varying background. During the onset and mature phases of ENSO, the final pattern of the optimal structure in 6 months is confined to the eastern Pacific; during the decay phase of ENSO, it spreads to the western Pacific as well. During the cold phase of ENSO, optimal growth has two maxima in a year—early spring and fall; the optimal perturbation propagates westward associated with surface layer-wind interaction. The authors also compare the singular vector analysis in EOF space and the standard one in physical space. The importance of norm definition to optimal growth and optimal structure is discussed.