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Andrew M. Moore

Abstract

A global coupled ocean-atmosphere-sea ice general circulation model is used to study interannual variability in the Tropics. Flux correction is used to control the mean climate of the coupled system, and in one configuration of the coupled model, interannual variability in the tropical Pacific is dominated by westward moving anomalies. Through a series of experiments in which the equatorial ocean wave speeds and ocean-atmosphere coupling strength are varied, it is demonstrated that these westward moving disturbances are probably some manifestation of what Neelin describes as an “SST mode.” By modifying the flux correction procedure, the mean climate of the coupled model can be changed. A fairly modest change in the mean climate is all that is required to excite eastward moving anomalies in place of the westward moving SST modes found previously.

The apparent sensitivity of the nature of tropical interannual variability to the mean climate state in a coupled general circulation model such as that used here suggests that caution is advisable if we try to use such models to answer questions relating to changes in ENSO-like variability associated with global climate change.

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Andrew M. Moore

Abstract

Subsurface temperature data from the ship-of-opportunity network in the tropical Pacific Ocean was assimilated into a simple reduced-gravity model. A large initialization shock was found to occur in the model which takes the form of equatorially trapped waves. Observations in the western tropical Pacific are found to generate a more severe case of initialization shock than observations in the eastern half of the basin. In addition, the magnitude of the initialization shock was found to be dependent upon the strength of the sea surface forcing. Attempts to suppress the large amplitude equatorial Kelvin waves and Yanai waves excited as part of the initialization shock are partially successful, but the damage inflicted on the model first-guess fields by this procedure is greater than that which ensues if the Kelvin waves and Yanai waves are left unchecked. Despite the initialization shock, the model is able to predict the large-wale structure and variability of the major near surface currents in the currents in the central tropical Pacific. The spinup time of these currents was ∼1 year.

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Andrew M. Moore

Abstract

The method of adjoint data assimilation is applied in a quasi-geostrophic (QG) open-ocean model of the Gulf Stream region. The results of data assimilation experiments are presented in which simulated AXBT and satellite altimeter observations are assimilated into the QG model. The adjoint data assimilation scheme has the ability to correct for large errors in the speed and position of the Gulf Stream jet. These experiments provide valuable insight into the dynamics of the assimilation procedure, and highlight the limitations of the adjoint method in the Gulf Stream region. The adjoint variables of the linearized QG model are approximations of the Green's functions of the adjoint equations. By examining maps of the adjoint variables, one can determine the domain of influence of individual observations. The results of assimilation experiments in which GEOSAT sea surface height observations are assimilated into the QG model are also presented. The results of the GEOSAT assimilation experiments can be interpreted using the insight gained from the simulated data assimilation experiments. It is found that not only can the adjoint method correct the position of the Gulf Stream axis, but it can also reconstruct observed features present in the real ocean (such as Gulf Stream rings) which were originally absent in the model.

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Andrew M. Moore

Abstract

Data assimilation in models of the tropical oceans can generate spurious equatorial wave modes which are potentially harmful to the model background fields. The amplitudes of these spurious wave modes can often be large and, in general, depend upon the nature and size of the imbalances introduced into the model by the data assimilation process. Spurious equatorial Kelvin waves are likely to give rise to the most detrimental effects since they are dynamically very important in the real ocean, and am responsible for a variety of phenomena in the equatorial and coastal regions of the ocean. In this paper, an initialization scheme based on the technique of normal mode initialization (used for many years by meteorologists) is developed, which can be used to suppress spurious equatorial wave modes during data assimilation experiments. The initialization scheme maps information from observational data onto the linear planetary wave solutions of the discretized model equations of motion. In addition, equatorial Kelvin waves and Yanai waves driven by sea surface forcing in the model are retained. Using this method, the rate of growth of the assimilation errors between one assimilation time and the next can be reduced considerably. It is shown that the model need only he initialized in a narrow channel spanning the equator, and that the initialization method also works well in a fully nonlinear model.

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Andrew M. Moore

Abstract

For any forecasting system, the ability to reliably estimate the skill of a forecast in advance (i.e., at the time the forecast is issued) is clearly desirable. In this paper the potential of ensemble prediction for estimating both the skill of forecasts of the Gulf Stream and the predictability of the ocean is examined. Using ensemble prediction methods the author has investigated how effective different types of perturbations are for perturbing the initial conditions of the ensemble members. The perturbations considered include the singular vectors, finite-time normal modes, and adjoint finite-time normal modes of a linearized version of the forecast model. The relationship between the skill of a forecast and the spread of an ensemble of forecasts about a reference forecast (the“control”) is examined as a function of (a) the type of perturbations used to perturb the ensemble members and (b) various different measures of forecast skill and ensemble spread.

Assuming that the forecast model is perfect the author finds that a statistically significant relationship exists between skill and spread for forecast periods beyond one week. Specifically, a low (high) spread in the ensemble members relative to a control forecast is accompanied by a high (low) control forecast skill. In a nonperfect model, a statistically significant relation still exists between skill and spread, but it tends to deteriorate after forecast times of about a week.

In general, singular vectors and linear transformations of the adjoint finite-time normal modes are most effective for perturbing ensemble members and yield statistically significant relationships between skill and spread over a wide range of skill and spread values. The skill–spread relationships identified appear to be insensitive to the details of the ensemble experiment.

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Richard Kleeman
and
Andrew M. Moore

Abstract

Determination of the reliability of particular ENSO forecasts is of particular importance to end users. Theoretical arguments are developed that indicate that the amplitudes of slowly decaying (or growing) normal modes of the coupled system provide a useful measure of forecast reliability. Historical forecasts from a skillful prediction model together with a series of ensemble predictions from a “perfect model” experiment are used to demonstrate that these arguments carry over to the practical prediction situation. In such a setting it is found that the amplitude of the dominant normal mode, which strongly resembles the observed ENSO cycle, is a potentially useful index of reliability. The fact that this index was generally lower in the 1970s than the 1980s provides an explanation for why many coupled models performed better in the latter decade. It does not, however, explain the low skill of some coupled models in the early 1990s as the index defined here was then moderate.

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Richard Kleeman
and
Andrew M. Moore

Abstract

It is argued that a major fundamental limitation on the predictability of the El Niño–Southern Oscillation phenomenon is provided by the stochastic forcing of the tropical coupled ocean–atmosphere system by atmospheric transients. A new theoretical framework is used to analyze in detail the sensitivity of a skillful coupled forecast model to this stochastic forcing. The central concept in this analysis is the so-called stochastic optimal, which represents the spatial pattern of noise most efficient at causing variance growth within a dynamical system. A number of interesting conclusions are reached. (a) Sensitivity to forcing is greatest during the northern spring season and prior to warm events. (b) There is little sensitivity to meridional windstress noise. (c) A western Pacific dipole pattern in heat flux noise is most efficient in forcing eastern Pacific SST variance. An estimate of the actual wind stress stochastic forcing is obtained from recent ECMWF analyses and it is found that “unavoidable” error growth within the model due to this stochastic forcing saturates at approximately 0.5°C in the NINO3 region with very rapid error growth during the first 6 months. The noise projects predominantly onto the first stochastic optimal and, in addition, around 95% of the error growth can be attributed to stochastic forcing with a strong synoptic character.

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Andrew M. Moore
and
Richard Kleeman

Abstract

Using the ideas of generalized linear stability theory, the authors examine the potential role that tropical variability on synoptic–intraseasonal timescales can play in controlling variability on seasonal–interannual timescales. These ideas are investigated using an intermediate coupled ocean–atmosphere model of the El Niño–Southern Oscillation (ENSO). The variability on synoptic–intraseasonal timescales is treated as stochastic noise that acts as a forcing function for variability at ENSO timescales. The spatial structure is computed that the stochastic noise forcing must have in order to enhance the variability of the system on seasonal–interannual timescales. These structures are the so-called stochastic optimals of the coupled system, and they bear a good resemblence to variability that is observed in the real atmosphere on synoptic and intraseasonal timescales. When the coupled model is subjected to a stochastic noise forcing composed of the stochastic optimals, variability on seasonal–interannual timescales develops that has spectral characteristics qualitatively similar to those seen in nature. The stochastic noise forcing produces perturbations in the system that can grow rapidly. The response of the system to the stochastic optimals is to induce perturbations that bear a strong resemblence to westerly and easterly wind bursts frequently observed in the western tropical Pacific. In the model, these “wind bursts” can act as efficient precursors for ENSO episodes if conditions are favorable. The response of the system to noise-induced perturbations depends on a number of factors that include 1) the phase of the seasonal cycle, 2) the presence of nonlinearities in the system, 3) the past history of the stochastic noise forcing and its integrated effect, and 4) the stability of the coupled ocean–atmosphere system. Based on their findings, they concur with the view adopted by other investigators that ENSO may be explained, at least partially, as a stochastically forced phenomena, the source of the noise in the Tropics being synoptic–intraseasonal variability, which includes the Madden–Julian oscillation, and westerly/easterly wind bursts. These ideas fit well with the observed onset and development of various ENSO episodes, including the 1997–98 El Niño event.

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Andrew M. Moore
and
Richard Kleeman

Abstract

The idea that intraseasonal variability in the tropical west Pacific can act as an effective means of stochastically forcing ENSO episodes is explored. Using the ideas of generalized linear stability theory as they apply to nonnormal dynamical systems, the physical attributes of the coupled ocean–atmosphere system in the Tropics that allow perturbations with structures that are dissimilar to ENSO to act as precursors for ENSO episodes are examined. Using a coupled ocean–atmosphere model, two particularly important factors are identified that contribute to the nonnormality of the coupled system: nonsolar atmospheric heating directly related to SST changes, and the dissimilarity between the equatorial ocean wave reflection process at eastern and western boundaries. The latter is intrinsic to the dynamics of the ocean, while the former is related to the presence of the west Pacific warm pool and its relationship with the Walker circulation.

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Andrew M. Moore
and
Richard Kleeman

Abstract

The optimal perturbations (singular vectors) of a dynamical coupled model, a hybrid coupled model, and a linear inverse model of ENSO are compared. The hybrid coupled model consists of a dynamical ocean model and a statistical atmospheric model. The dynamical ocean model is identical to that used in the dynamical coupled model, and the atmospheric model is a statistical model derived from long time series of the dynamical coupled model. The linear inverse model was also derived from long time series from the dynamical coupled model. Thus all three coupled models are very closely related and all produce similar ENSO oscillations. The dynamical model and hybrid model also possess similar levels of hindcast skill. However, the optimal perturbations of the tangent linear versions of each model are not the same. The hybrid and linear inverse models are unable to recover the SST structure of the optimal perturbations of the dynamical model. The SST structure of the dynamical coupled model is a result of nonnormality introduced by latent heating of the atmosphere by deep convection over the west Pacific warm pool. It is demonstrated that standard statistical techniques remove the effects of the latent heating on the nonnormality of the hybrid and linear inverse models essentially rendering them more normal than their dynamical model counterpart. When the statistical components of the hybrid coupled model and the linear inverse models were recomputed using SST anomalies that are appropriately scaled by the standard deviation of SST variability, nonnormality was reintroduced into these models and they recovered the optimal perturbation structure of the dynamical model. Even though the hybrid and linear inverse model with scaled SSTs can recover the large-scale features of the correct optimal structure, state space truncation means that the dynamics of the resulting optimal perturbations is not the same as that governing optimal perturbation growth in the dynamical model. The consequences of these results for observed estimates of optimal perturbations for ENSO are discussed.

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