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Youmin Tang
,
Richard Kleeman
, and
Andrew M. Moore

Abstract

In this study, ensemble predictions of the El Niño–Southern Oscillation (ENSO) were conducted for the period 1981–98 using two hybrid coupled models. Several recently proposed information-based measures of predictability, including relative entropy (R), predictive information (PI), predictive power (PP), and mutual information (MI), were explored in terms of their ability of estimating a priori the predictive skill of the ENSO ensemble predictions. The emphasis was put on examining the relationship between the measures of predictability that do not use observations, and the model prediction skills of correlation and root-mean-square error (RMSE) that make use of observations. The relationship identified here offers a practical means of estimating the potential predictability and the confidence level of an individual prediction.

It was found that the MI is a good indicator of overall skill. When it is large, the prediction system has high prediction skill, whereas small MI often corresponds to a low prediction skill. This suggests that MI is a good indicator of the actual skill of the models. The R and PI have a nearly identical average (over all predictions) as should be the case in theory.

Comparing the different information-based measures reveals that R is a better predictor of prediction skill than PI and PP, especially when correlation-based metrics are used to evaluate model skill. A “triangular relationship” emerges between R and the model skill, namely, that when R is large, the prediction is likely to be reliable, whereas when R is small the prediction skill is quite variable. A small R is often accompanied by relatively weak ENSO variability. The possible reasons why R is superior to PI and PP as a measure of ENSO predictability will also be discussed.

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Youmin Tang
,
Richard Kleeman
, and
Andrew M. Moore

Abstract

With a simple 3DVar assimilation algorithm, a new scheme of assimilating sea surface temperature (SST) observations is proposed in this paper. In this new scheme, the linear relation between any two neighboring depths was derived using singular value decomposition technique and then was applied to estimate the temperatures at deeper levels using the temperature analyses at shallower levels. The estimated temperatures were assimilated into an ocean model, and the procedure was run iteratively at each time step from the surface to a depth of 250 m. The oceanic analyses show that the new scheme can more effectively adjust oceanic thermal and dynamical fields and lead to a more realistic subsurface thermal structure when compared with the control run and another scheme that is usually used for SST assimilation. An ensemble of predictions for the Niño-3 region SST anomalies was performed to test the new scheme. It was found that the new scheme can improve fairly well ENSO prediction skills at all lead times, in particular for anomalous warm events, and for lead times of 4–7 months.

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Richard Kleeman
,
Andrew M. Moore
, and
Neville R. Smith

Abstract

An adjoint variational assimilation technique is used to assimilate observations of both the oceanic state and wind stress data into an intermediate coupled ENSO prediction model. This method of initialization is contrasted with the more usual method, which uses only wind stress data to establish the initial state of the ocean. It is shown that ocean temperature data has a positive impact on the prediction skill in such models. On the basis of hindcasts for the period 1982–91, it is shown that NIN03 SST anomaly correlations greater than 0.7 can be obtained for hindcasts of duration up to 13 months and greater than 0.6 up to 16 months. There are also clear indications of skill at two years.

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Rong-Hua Zhang
,
Stephen E. Zebiak
,
Richard Kleeman
, and
Noel Keenlyside

Abstract

A new intermediate coupled model (ICM) is presented and employed to make retrospective predictions of tropical Pacific sea surface temperature (SST) anomalies. The ocean dynamics is an extension of the McCreary baroclinic modal model to include varying stratification and certain nonlinear effects. A standard configuration is chosen with 10 baroclinic modes plus two surface layers, which are governed by Ekman dynamics and simulate the combined effects of the higher baroclinic modes from 11 to 30. A nonlinear correction associated with vertical advection of zonal momentum is incorporated and applied (diagnostically) only within the two surface layers, forced by the linear part through nonlinear advection terms. As a result of these improvements, the model realistically simulates the mean equatorial circulation and its variability. The ocean thermodynamics include an SST anomaly model with an empirical parameterization for the temperature of subsurface water entrained into the mixed layer (Te ), which is optimally calculated in terms of sea surface height (SSH) anomalies using an empirical orthogonal function (EOF) analysis technique from historical data. The ocean model is then coupled to a statistical atmospheric model that estimates wind stress (τ) anomalies based on a singular value decomposition (SVD) analysis between SST anomalies observed and τ anomalies simulated from ECHAM4.5 (24-member ensemble mean). The coupled system exhibits realistic interannual variability associated with El Niño, including a predominant standing pattern of SST anomalies along the equator and coherent phase relationships among different atmosphere–ocean anomaly fields with a dominant 3-yr oscillation period.

Twelve-month hindcasts/forecasts are made during the period 1963–2002, starting each month. Only observed SST anomalies are used to initialize the coupled predictions. As compared to other prediction systems, this coupled model has relatively small systematic errors in the predicted SST anomalies, and its SST prediction skill is apparently competitive with that of most advanced coupled systems incorporating sophisticated ocean data assimilation. One striking feature is that the model skill surpasses that of persistence at all lead times over the central equatorial Pacific. Prediction skill is strongly dependent on the season, with the correlations attaining a minimum in spring and a maximum in fall. Cross-validation experiments are performed to examine the sensitivity of the prediction skill to the data periods selected for training the empirical Te model. It is demonstrated that the artificial skill introduced by using a dependently constructed Te model is not significant. Independent forecasts are made for the period 1997–2002 when no dependent data are included in constructing the two empirical models (Te and τ). The coupled model has reasonable success in predicting transition to warm phase and to cold phase in the spring of 1997 and 1998, respectively. Potential problems and further improvements are discussed with the new intermediate prediction system.

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Cristina L. Perez
,
Andrew M. Moore
,
Javier Zavala-Garay
, and
Richard Kleeman

Abstract

A currently popular idea is that El Niño–Southern Oscillation (ENSO) can be viewed as a linear deterministic system forced by noise representing processes with periods shorter than ENSO. Also, there is observational evidence to suggest that the Madden–Julian oscillation (MJO) acts to trigger and/or amplify the warm phase of ENSO in this way. The feedback of the slower process, ENSO, to higher-frequency atmospheric phenomena, of which a large part of the variability in the intraseasonal band is due to the MJO, has received little attention. This paper considers the hypothesis that the probability of an El Niño event is modified by high MJO activity and that, in turn, the MJO is regulated by ENSO activity. If this is indeed the case, then viewing ENSO as a low-frequency oscillation forced by additive stochastic noise would not present a complete picture.

This paper tests the above hypothesis using a stochastically forced intermediate coupled model by allowing ENSO to directly influence the stochastic forcing. The model response to a variety of stochastic forcing types is found to be sensitive to the type of forcing applied. When the model is operated beyond its intrinsic Hopf bifurcation, its probability distribution function (PDF) is fundamentally altered when the stochastic forcing is changed from additive to multiplicative. The model integration period also influences the shape of the PDF, which is also compared to the PDF derived from observations. It is found that multiplicative stochastic forcing reproduces some measures of the observations better than the additive stochastic forcing.

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Amy Solomon
,
Julian P. McCreary Jr.
,
Richard Kleeman
, and
Barry A. Klinger

Abstract

Processes that cause decadal variability in an intermediate coupled ocean–atmosphere model of the Pacific basin, both at northern midlatitudes and in the Tropics, are studied. The model's ocean component is a variable-temperature 3½-layer system. Its atmospheric component consists of two basic parts: an empirical model, constructed from patterns obtained by the singular value decomposition (SVD) statistical technique that determines wind stress anomalies from model sea surface temperature (SST), and a simple representation of the planetary boundary layer to calculate the surface heat flux anomalies. A third part specifies stochastic wind stress forcing from observed variability. In addition, the model is specifically designed to separate tropical and extratropical interactions, such that the Tropics can force the extratropics through the atmosphere but the extratropics can only feed back to the Tropics through the ocean.

Solutions develop two types of oscillations: an ENSO-like interannual mode and a decadal mode. As in many models of ENSO, the interannual mode is driven by positive, ocean–atmosphere feedbacks near the equator, and time-delayed negative feedback is provided by off-equatorial Rossby waves. For parameter choices that amplify midlatitude coupling by 30% (ϕ o = 1.3), a self-sustained decadal oscillation develops in the North Pacific without any tropical interactions. Diagnostic analyses show that it is maintained by ocean-to-atmosphere feedbacks in the northwest and subtropical northeast Pacific, and by atmospheric teleconnections from those regions to the northeast ocean. For weaker coupling (ϕ o = 1.2), the decadal mode is damped. In this case, the mode can be sustained by atmospheric teleconnections from the Tropics associated with the interannual mode, but not by extratropical stochastic forcing. Although including stochastic forcing does generate variability at decadal timescales, a distinct decadal spectral peak only exists when the decadal mode is active.

Decadal variability is carried to the equator by variations in the transport, rather than temperature, of the North Pacific subtropical cell. These variations modulate near-equatorial SST by altering the amount of cool, thermocline water that upwells in the eastern equatorial Pacific, which in turn feeds back to the interannual mode.

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Barry A. Klinger
,
Julian P. McCreary Jr.
, and
Richard Kleeman

Abstract

An earlier study showed that an atmosphere–ocean model of the Pacific develops a midlatitude oscillation that produces decadal sea surface temperature (SST) variability on the equator. The authors use the ocean component of this model to understand better how subtropical wind stress oscillations can cause such SST variability. The model ocean consists of three active layers that correspond to the mixed layer, the thermocline, and intermediate water, all lying above a motionless abyss.

For a steady wind, the model develops a subtropical cell (STC) in which northward surface Ekman transport subducts, flows equatorward within the thermocline, and returns to the surface at the equator. Analytic results predict the model's equatorial temperature, given some knowledge of the circulation and external forcing. A prescribed subtropical wind stress anomaly perturbs the strength of the STC, which in turn modifies equatorial upwelling and equatorial SST.

The transient response to a switched-on wind perturbation is used to predict the ocean response to an oscillating wind. This method correctly predicts the results of several numerical experiments, and extends these results to a wide range of forcing periods. For an oscillating wind, there is a more complicated relationship between perturbations to equatorial SST and the various branches of the STC. The thermocline-branch anomalies are generally weaker than those in the surface and equatorial-upwelling branches. Equatorial SST anomalies lead, follow, and are roughly coincident with, variations in the thermocline, surface, and upwelling branches, respectively. Thus, while recent studies have suggested using the subsurface branch variations as a predictor of tropical–subtropical interactions, the surface branch may be a better predictor.

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Richard Kleeman
,
Naomi H. Naik
, and
Mark A. Cane

Abstract

The observed subtropical gyre in the North Pacific shows a shift in meridional location with depth. At shallow levels the density deviation peaks at around 15°N while at deep levels the peak is more like 30°N. It is argued here using analytical solutions to the beta-plane shallow-water equations that such a shift can be explained by the effects of oceanic dissipation processes. These solutions show that the highly damped solution is approximately proportional to Ekman pumping whereas the lightly damped case tends toward the classical Sverdrup solution. In the North Pacific, Ekman pumping peaks near 15°N while the Sverdrup solution peaks at 30°N. It is further demonstrated that 1) density deviations in the upper ocean are more highly influenced by higher order baroclinic modes than those in the deep, which are influenced by the lower modes, and 2) constant dissipation effectively acts much more strongly on the higher order baroclinic modes because of their slower speeds and smaller Rossby radii. These two factors thus explain the observed shift in the gyre with depth.

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Rong-Hua Zhang
,
Richard Kleeman
,
Stephen E. Zebiak
,
Noel Keenlyside
, and
Stephane Raynaud

Abstract

An empirical model for the temperature of subsurface water entrained into the ocean mixed layer (Te ) is presented and evaluated to improve sea surface temperature anomaly (SSTA) simulations in an intermediate ocean model (IOM) of the tropical Pacific. An inverse modeling approach is adopted to estimate Te from an SSTA equation using observed SST and simulated upper-ocean currents. A relationship between Te and sea surface height (SSH) anomalies is then obtained by utilizing a singular value decomposition (SVD) of their covariance. This empirical scheme is able to better parameterize Te anomalies than other local schemes and quite realistically depicts interannual variability of Te , including a nonlocal phase lag relation of Te variations relative to SSH anomalies over the central equatorial Pacific. An improved Te parameterization naturally leads to better depiction of the subsurface effect on SST variability by the mean upwelling of subsurface temperature anomalies. As a result, SSTA simulations are significantly improved in the equatorial Pacific; a comparison with other schemes indicates that systematic errors of the simulated SSTAs are significantly small—apparently due to the optimized empirical Te parameterization. Cross validation and comparisons with other model simulations are made to illustrate the robustness and effectiveness of the scheme. In particular it is demonstrated that the empirical Te model constructed from one historical period can be successfully used to improve SSTA simulations in another.

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Andrew M. Moore
,
Jérôme Vialard
,
Anthony T. Weaver
,
David L. T. Anderson
,
Richard Kleeman
, and
Jolie R. Johnson

Abstract

In this paper the structure and dynamics of the optimal perturbations of tropical low-frequency coupled ocean–atmosphere oscillations relevant to El Niño–Southern Oscillation (ENSO) are explored. These optimal perturbations yield information about potential precursors for ENSO events, and about the fundamental dynamical processes that may control perturbation growth and limit the predictability of interannual variability. The present study uses a hierarchy of hybrid coupled models. Each model is configured for the tropical Pacific Ocean and shares a common ocean general circulation model. Three different atmospheric models are used: a statistical model, a dynamical model, and a combination of a dynamical model and boundary layer model. Each coupled model possesses a coupled ocean–atmosphere eigenmode oscillation with a period of the order of several years. The properties of these various eigenmodes and their corresponding adjoint eigenmodes are explored.

The optimal perturbations of each coupled model for two different perturbation growth norms are also examined, and their behavior can be understood in terms of the properties of the aforementioned eigenmode oscillations. It is found that the optimal perturbation spectrum of each coupled model is primarily dominated by one member. The dominant optimal perturbation evolves into the most unstable eigenmode of the system. The structure of the optimal perturbations of each model is found to be controlled by the dynamics of the atmospheric model and air–sea interaction processes. For the coupled model with a statistical atmosphere, the optimal perturbation center of action is spread across the entire tropical Pacific in the form of a dipole. For the coupled models that include deep atmospheric convection, the optimal perturbation center of action is primarily confined to the western Pacific warm pool. In addition, the degree of nonnormality of the eigenmodes is controlled by the atmospheric model dynamics. These findings are in general agreement with the results obtained from intermediate coupled models. In particular, the atmospheric models used here have also been used in intermediate coupled models that have been employed extensively in previous studies of the optimal perturbations of El Niño–Southern Oscillation. Thus, a direct comparison of the optimal perturbation behavior of those intermediate models and the optimal perturbations of the hybrid models used here can be made.

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