Fine-tuning Atmospheric Parameters for Improving ENSO Simulation in the Zebiak–Cane Model

With the Zebiak-Cane (ZC) model, the initial error that has the largest effect on ENSO prediction is explored by conditional nonlinear optimal perturbation (CNOP). The results demonstrate that CNOP-type errors cause the largest prediction error of ENSO in the ZC model. By analyzing the behavior of CNOPtype errors, we find that for the normal states and the relatively weak El Nino events in the ZC model, the predictions tend to yield false alarms due to the uncertainties caused by CNOP. For the relatively strong El Nino events, the ZC model largely underestimates their intensities. Also, our results suggest that the error growth of El Nino in the ZC model depends on the phases of both the annual cycle and ENSO. The condition during northern spring and summer is most favorable for the error growth. The ENSO prediction bestriding these two seasons may be the most difficult. A linear singular vector (LSV) approach is also used to estimate the error growth of ENSO, but it underestimates the prediction uncertainties of ENSO in the ZC model. This result indicates that the different initial errors cause different amplitudes of prediction errors though they have same magnitudes. CNOP yields the severest prediction uncertainty. That is to say, the prediction skill of ENSO is closely related to the types of initial error. This finding illustrates a theoretical basis of data assimilation. It is expected that a data assimilation method can filter the initial errors related to CNOP and improve the ENSO forecast skill.

An intermediate tropical Pacific Ocean model is developed to bridge the gap between anomaly models of El Nino and ocean general circulation models. The model contains essential physics for reproducing both the annual and interannual variations of sea surface temperature (SST). A new parameterization scheme for entrained water temperature is shown to work satisfactorily in both the cold tongues and warm pools. This scheme combines the Cane-Zebiak (CZ) model's dynamic framework and mixed layer physics, giving a more realistic description of the active tropical ocean. Incorporation of the Niiler-Kraus scheme for turbulent entrainment enables the model to better simulate El Nino-Southern Oscillation in the central equatorial Pacific where the CZ model considerably underestimates observed SST variations. It also improves the model's performance on the seasonal cycle, especially in the central-eastern equatorial Pacific and the intertropical convergence zone (ITCZ). The potential energy generation indu...

In this paper, an optimal forcing vector (OFV) approach is proposed. The OFV offsets tendency errors and optimizes the agreement of the model simulation with observation. We apply the OFV approach to the well-known Zebiak–Cane model and simulate several observed eastern Pacific (EP) El Nino and central Pacific (CP) El Nino events during 1980–2004. It is found that the Zebiak–Cane model with a proper initial condition often reproduces the EP-El Nino events; however, the Zebiak–Cane model fails to reproduce the CP-El Nino events. The model may be much more influenced by model errors when simulating the CP-El Nino events. As expected, when we use the OFV to correct the Zebiak–Cane model, the model reproduces the three CP-El Nino events well. Furthermore, the simulations of the corresponding winds and thermocline depths are also acceptable. In particular, the thermocline depth simulations for the three CP-El Nino events lead us to believe that the discharge process of the equatorial heat content associated with the CP-El Nino is not efficient and emphasizes the role of the zonal advection in the development of the CP-El Nino events. The OFVs associated with the three CP-El Nino events often exhibit a sea surface temperature anomaly (SSTA) tendency with positive anomalies in the equatorial eastern Pacific; therefore, the SST tendency errors occurring in the equatorial eastern Pacific may dominate the uncertainties of the Zebiak–Cane model while simulating CP-El Nino events. A further investigation demonstrates that one of the model errors offset by the OFVs is of a pattern similar to the SST cold-tongue cooling mode, which may then provide one of the climatological conditions for the frequent occurrence of CP-El Nino events. The OFV may therefore be a useful tool for correcting forecast models and then for helping improve the forecast skill of the models.

The influence of the uncertainties of intra-seasonal wind stress forcing on Spring Predictability Barrier (SPB) in El Nino–Southern Oscillation (ENSO) prediction is studied with the Zebiak–Cane model and observational wind data which are analyzed with Continuous Wavelet Transform (CWT) and utilized to extract intra-seasonal wind stress signals as external forcing. The observational intra-seasonal wind stress forcing are joined into Zebiak–Cane model to get the Zebiak–Cane-add model and subsequently with the Conditional Nonlinear Optimal Perturbation (CNOP) method, the evolutions of the optimal initial errors (i.e., CNOPs), model errors caused by intra-seasonal wind stress uncertainties, and their joint errors based on ENSO events are calculated. By investigating their error growth rates and prediction errors of Nino-3 indices, the effect of observational intra-seasonal wind stress forcing on seasonal error growth of ENSO is explored and the impact of initial error and model error on ENSO predictability is compared quantitatively. The results show that the model errors led by observational intra-seasonal wind stress forcing could scarcely cause a significant SPB whereas the initial errors and their joint errors can do; hence, the initial errors are most likely the main error source of SPB. In fact, this result emphasizes the primary influence of initial errors on ENSO predictability and lays the basis of adaptive data assimilation for ENSO forecast.

Model errors offset by constant and time-variant optimal forcing vector approaches (termed COF and OFV, respectively) are analyzed within the framework of El Ni˜no simulations. Applying the COF and OFV approaches to the well-known Zebiak–Cane model, we re-simulate the 1997 and 2004 El Ni˜no events, both of which were poorly degraded by a certain amount of model error when the initial anomalies were generated by coupling the observed wind forcing to an ocean component. It is found that the Zebiak–Cane model with the COF approach roughly reproduced the 1997 El Ni˜no, but the 2004 El Ni˜no simulated by this approach defied an ENSO classification, i.e., it was hardly distinguishable as CP-El Ni˜no or EP-El Ni˜no. In both El Ni˜no simulations, substituting the COF with the OFV improved the fit between the simulations and observations because the OFV better manages the time-variant errors in the model. Furthermore, the OFV approach effectively corrected the modeled El Ni˜no events even when the observational data (and hence the computational time) were reduced. Such a cost-effective offset of model errors suggests a role for the OFV approach in complicated CGCMs.

The peaks of El Niño in the Cane–Zebiak (CZ) model tend to appear most frequently around November when the ocean Rossby waves, which were amplified during the previous unstable season (February–May), turn back to the eastern Pacific and when the local instability in the eastern Pacific is very weak. The peaks of La Niña in the CZ model occur most frequently in boreal summer, in contrast to the observed counterpart that usually occurs in boreal winter. Sensitivity experiments indicate that the phase locking of the La Niña to boreal summer is primarily caused by seasonal variations of the tropical convergence zone, which regulate convective heating through atmospheric convergence feedback. The observed thermocline and the wind anomalies in the western Pacific exhibit considerable seasonal variations. These were missed in the original CZ model. In a modified CZ model that includes the seasonal variations of the western Pacific wind anomalies and the basic-state thermocline depth, the peaks of La Niña preferably occur in boreal winter, suggesting that the seasonal variation of the western Pacific surface wind anomalies and the mean thermocline depth are critical factors for the phase locking of the mature La Niña to boreal winter. The mechanisms by which these factors affect ENSO phase locking are also discussed.

Abstract. Accurate prediction of the extreme phases of the El Niño–Southern Oscillation (ENSO) is important to mitigate the socioeconomic impacts of this phenomenon. It has long been thought that prediction skill was limited to a 6-month lead time. However, machine learning methods have shown to have skill at lead times of up to 21 months. In this paper, we aim to explain for one class of such methods, i.e. reservoir computers (RCs), the origin of this high skill. Using a conditional nonlinear optimal perturbation (CNOP) approach, we compare the initial error propagation in a deterministic Zebiak–Cane (ZC) ENSO model and that in an RC trained on synthetic observations derived from a stochastic ZC model. Optimal initial perturbations at long lead times in the RC involve both sea surface temperature and thermocline anomalies, which leads to decreased error propagation compared to the ZC model, where mainly thermocline anomalies dominate the optimal initial perturbations. This reduced error propagation allows the RC to provide a higher skill at long lead times than the deterministic ZC model.

In an effort to apply the interactive Kalman filter to higher-dimensional systems, the concept of a quasi-fixed point is introduced. This is defined to be a system state where the tendency, in a suitable reduced space, is at a minimum. It allows one to use conventional search algorithms for the detection of quasi-fixed points. In Part I quasi-fixed points of the ENSO model of Zebiak and Cane are found when run in a permanent monthly mode, the reduced space being defined via a multiple EOP projection. The stability characteristics of the quasi-fixed points are analyzed, and it is shown that they are significantly different from the (in)stabilities of the average monthly models. With these quasi-fixed points, assimilation experiments are carried out with the interactive Kalman filter for the Zebiak–Cane model in the reduced space. It is demonstrated that the results are superior to both a seasonal Kalman filter and the extended Kalman filter.

Modern instrumental records reveal that El Niño events differ in their spatial patterns and temporal evolutions. Attempts have been made to categorize them roughly into two main types: eastern Pacific (EP; or cold tongue) and central Pacific (CP; or warm pool) El Niño events. In this study, a modified version of the Zebiak–Cane (MZC) coupled model is used to examine the dynamics of these two types of El Niño events. Linear eigenanalysis of the model is conducted to show that there are two leading El Niño–Southern Oscillation (ENSO) modes with their SST patterns resembling those of two types of El Niño. Thus, they are referred to as the EP and CP ENSO modes. These two modes are sensitive to changes in the mean states. The heat budget analyses demonstrate that the EP (CP) mode is dominated by thermocline (zonal advective) feedback. Therefore, the weak (strong) mean wind stress and deep (shallow) mean thermocline prefer the EP (CP) ENSO mode because of the relative dominance of thermocline (zonal advective) feedback under such a mean state. Consistent with the linear stability analysis, the occurrence ratio of CP/EP El Niño events in the nonlinear simulations generally increases toward the regime where the linear CP ENSO mode has relatively higher growth rate. These analyses suggest that the coexistence of two leading ENSO modes is responsible for two types of El Niño simulated in the MZC model. This model result may provide a plausible scenario for the observed ENSO diversity.

Abstract. Lovejoy and Varotsos (2016) (L&V) analyse the temperature response to solar, volcanic, and solar plus volcanic forcing in the Zebiak–Cane (ZC) model, and to solar and solar plus volcanic forcing in the Goddard Institute for Space Studies (GISS) E2-R model. By using a simple wavelet filtering technique they conclude that the responses in the ZC model combine subadditively on timescales from 50 to 1000 years. Nonlinear response on shorter timescales is claimed by analysis of intermittencies in the forcing and the temperature signal for both models. The analysis of additivity in the ZC model suffers from a confusing presentation of results based on an invalid approximation, and from ignoring the effect of internal variability. We present tests without this approximation which are not able to detect nonlinearity in the response, even without accounting for internal variability. We also demonstrate that internal variability will appear as subadditivity if it is not accounted for. L&V's analysis of intermittencies is based on a mathematical result stating that the intermittencies of forcing and response are the same if the response is linear. We argue that there are at least three different factors that may invalidate the application of this result for these data. It is valid only for a power-law response function; it assumes power-law scaling of structure functions of forcing as well as temperature signal; and the internal variability, which is strong at least on the short timescales, will exert an influence on temperature intermittence which is independent of the forcing. We demonstrate by a synthetic example that the differences in intermittencies observed by L&V easily can be accounted for by these effects under the assumption of a linear response. Our conclusion is that the analysis performed by L&V does not present valid evidence for a detectable nonlinear response in the global temperature in these climate models.

Abstract. The El Niño–Southern Oscillation (ENSO) is a significant climate phenomenon that appears periodically in the tropical Pacific. The intermediate coupled ocean–atmosphere Zebiak–Cane (ZC) model is the first and classical one designed to numerically forecast the ENSO events. Traditionally, the conditional nonlinear optimal perturbation (CNOP) approach has been used to capture optimal precursors in practice. In this paper, based on state-of-the-art statistical machine learning techniques1, we investigate the sampling algorithm proposed in Shi and Sun (2023) to obtain optimal precursors via the CNOP approach in the ZC model. For the ZC model, or more generally, the numerical models with a large number O(104−105) of degrees of freedom, the numerical performance, regardless of the statically spatial patterns and the dynamical nonlinear time evolution behaviors as well as the corresponding quantities and indices, shows the high efficiency of the sampling method compared to the traditional adjoint method. The sampling algorithm does not only reduce the gradient (first-order information) to the objective function value (zeroth-order information) but also avoids the use of the adjoint model, which is hard to develop in the coupled ocean–atmosphere models and the parameterization models. In addition, based on the key characteristic that the samples are independently and identically distributed, we can implement the sampling algorithm by parallel computation to shorten the computation time. Meanwhile, we also show in the numerical experiments that the important features of optimal precursors can still be captured even when the number of samples is reduced sharply.

In atmospheric and oceanic studies, it is important to investigate the uncertainty of model solutions. The conditional non-linear optimal perturbation (CNOP) method is useful for addressing the uncertainty. This paper reviews the development of the CNOP method and its computational aspects in recent years. Specifically, the CNOP method was first proposed to investigate the effects of the optimal initial perturbation on atmosphere and ocean model results. Then, it was extended to explore the influences of the optimal parameter perturbation, model tendency perturbation and boundary condition perturbation. To obtain solutions to these optimal perturbations, four kinds of optimization approaches were developed: the adjoint-based method, the adjoint-free method, the intelligent optimization method and the unconstrained optimization method. We illustrate the calculation process of each method and its advantages and disadvantages. Then, taking the Zebiak–Cane model as an example, we compare the CNOPs related to initial conditions (CNOP-Is) calculated by the above four methods. It was found that the dominant structures of the CNOP-Is for different methods are similar, although some differences in details exist. Finally, we discuss the necessity and possible direction for designing a more effective optimization approach related to the CNOP in the future.

The equatorial tropical Pacific climate system is a delicate coupled system in which winds driven by gradients of sea surface temperature (SST) within the basin interact with the ocean circulation to maintain SST gradients. This results in a time mean state having a strong zonal temperature contrast along the equator with an eastern cold tongue and a western warm pool. By the same coupled processes, interannual variability, known as the El Nino–Southern Oscillation (ENSO), is present in the Pacific. This variability can be attributed to an oscillatory coupled mode, the ENSO mode, in the equatorial ocean–atmosphere system. Using a Zebiak–Cane-type intermediate coupled model, the coexistence of an eastern cold tongue in the annual mean state and ENSO in the Pacific climate system is investigated. The ENSO mode arises as a robust oscillatory mode on a coupled mean state and becomes unstable if the cold tongue of the mean state is sufficiently strong. The origin of this mode, its propagation mechanis...

Heavy rainfall occurs twice a year in the country and lately, thousands of people are always left homeless and hundreds lose life due to floods and landslides where rivers, dams, lakes and sewages overflow enhancing the spread of corona virus in slums. Agricultural products in the farms are also destroyed by floods, affecting agricultural performance to decline as it the key driver of the economy growth. Therefore we used inter-crossed model which was the combination of autoregressive moving average and artificial neural network. Zebiak cane model was also used for selection of variables that were associated to physical processes and testing the network variables. Climate networks were found to be effective tool for more qualitative El Nino Southern Oscillation prediction, by looking at a warning of the oncoming of El Nino when a predestined network attribute surpasses some critical value and also feed forward artificial neural network structures were found to be the first performing structure in terms of normalized root mean squared error at a three month head time prediction. By adding the network variable, we came up with a twelve month lead time prediction with same skill to the predictions at lower set times.

The mature phases of El Niño events show a strong tendency of locking to the end of the calendar year. The roles of seasonal variations of the basic state and the relative contributions of individual components of the basic state in this phase locking are investigated using the Zebiak–Cane model. It is shown that seasonal variations of the mean state from July to November have a positive contribution and those from December to June have a negative contribution to preexisting warm SST anomalies. Among the basic-state parameters, the sea surface temperature (SST) is a major factor for the locking of the El Niño mature phase through the anomalous advection of the mean SST gradient. This result differs from previous studies that attribute the El Niño phase locking mainly to seasonal changes in the mean wind divergence. The present result indicates the importance of a proper simulation of mean SST and its seasonal evolution for the simulation of El Niño phase locking in coupled models. Further experiments show that the phase locking of the El Niño mature phase cannot be explained by a balance between the warming trend due to downwelling Kelvin waves and the cooling trend due to upwelling Rossby waves.