Abstract

A predictability framework, based on relative entropy, is applied here to low-frequency variability in a standard T21 barotropic model on the sphere with realistic orography. Two types of realistic climatology, corresponding to different heights in the troposphere, are used. The two dynamical regimes with different mixing properties, induced by the two types of climate, allow the testing of the predictability framework in a wide range of situations. The leading patterns of empirical orthogonal functions, projected onto physical space, mimic the large-scale teleconnections of observed flow, in particular the Arctic Oscillation, Pacific–North American pattern, and North Atlantic Oscillation. In the ensemble forecast experiments, relative entropy is utilized to measure the lack of information in three different situations: the lack of information in the climate relative to the forecast ensemble, the lack of information by using only the mean state and variance of the forecast ensemble, and information flow—the time propagation of the lack of information in the direct product of marginal probability densities relative to joint probability density in a forecast ensemble. A recently developed signal–dispersion–cross-term decomposition is utilized for climate-relative entropy to determine different physical sources of forecast information. It is established that though dispersion controls both the mean state and variability of relative entropy, the sum of signal and cross-term governs physical correlations between a forecast ensemble and EOF patterns. Information flow is found to be responsible for correlated switches in the EOF patterns within a forecast ensemble.

Abstract

An ocean general circulation model, forced with idealized, purely oscillating wind stresses over the western equatorial Pacific similar to those observed during the Madden–Julian oscillation (MJO), developed rectified low-frequency anomalies in SST and zonal currents, compared to a run in which the forcing was climatological. The rectification in SST resulted from increased evaporation under stronger than normal winds of either sign, from correlated intraseasonal oscillations in both vertical temperature gradient and upwelling speed forced by the winds, and from zonal advection due to nonlinearly generated equatorial currents. The net rectified signature produced by the MJO-like wind stresses was SST cooling (about 0.4°C) in the west Pacific, and warming (about 0.1°C) in the central Pacific, tending to flatten the background zonal SST gradient. It is hypothesized that, in a coupled system, such a pattern of SST anomalies would spawn additional westerly wind anomalies as a result of SST-induced changes in the low-level zonal pressure gradient. This was tested in an intermediate coupled model initialized to 1 January 1997, preceding the 1997–98 El Niño. On its own, the model hindcast a relatively weak warm event, but when the effect of the rectified SST pattern was imposed, a coupled response produced the hypothesized additional westerlies and the hindcast El Niño became about 50% stronger (measured by east Pacific SST anomalies), suggesting that the MJO can interact constructively with the ENSO cycle. This implies that developing the capacity to predict, if not individual MJO events, then the conditions that affect their amplitude, may enhance predictability of the strength of oncoming El Niños.

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.

Abstract

Using a recently developed method of computing climatically relevant singular vectors (SVs), the error growth properties of ENSO in a fully coupled global climate model are investigated. In particular, the authors examine in detail how singular vectors are influenced by the phase of ENSO cycle—the physical variable under consideration as well as the error norm deployed. Previous work using SVs for studying ENSO predictability has been limited to intermediate or hybrid coupled models.

The results show that the singular vectors share many of the properties already seen in simpler models. Thus, for example, the singular vector spectrum is dominated by one fastest growing member, regardless of the phase of ENSO cycle and the variable of perturbation or the error norm; in addition the growth rates of the singular vectors are very sensitive to the phase of the ENSO cycle, the variable of perturbation, and the error norm. This particular CGCM also displays some differences from simpler models; thus subsurface temperature optimal patterns are strongly sensitive to the phase of ENSO cycle, and at times an east–west dipole in the eastern tropical Pacific basin is seen. This optimal pattern also appears for SST when the error norm is defined using Niño-4. Simpler models consistently display a single-sign equatorial signature in the subsurface corresponding perhaps to the Wyrtki buildup of heat content before a warm event. Some deficiencies in the CGCM and their possible influences on SV growth are also discussed.

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.

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.

Abstract

A simple model of the lower atmospheric layers and land/sea ice surface is described and analyzed. The model is able to depict with reasonable accuracy the global ocean heat fluxes. Due to the model's simplicity, insight into the mechanisms underlying particular heat flux responses is possible. Such an analysis is carried out for the regional Gulf Stream heat flux response (which is gualitatively correct in the model), and it is shown that atmospheric transient eddy heat transport is crucial to the modeled response. The perturbation response of the model to tropical SST anomalies is also analyzed, and it is demonstrated that the atmospheric transport processes incorporated in the model are responsible for a scale-dependent response. The magnitude of this response is shown to be significantly different to that obtained with formulations previously used by ocean modelers.

Abstract

In this study, ensemble predictions were constructed using two realistic ENSO prediction models and stochastic optimals. By applying a recently developed theoretical framework, the authors have explored several important issues relating to ENSO predictability including reliability measures of ENSO dynamical predictions and the dominant precursors that control reliability. It was found that prediction utility (R), defined by relative entropy, is a useful measure for the reliability of ENSO dynamical predictions, such that the larger the value of R, the more reliable the prediction. The prediction utility R consists of two components, a dispersion component (DC) associated with the ensemble spread and a signal component (SC) determined by the predictive mean signals. Results show that the prediction utility R is dominated by SC.

Using a linear stochastic dynamical system, SC was examined further and found to be intrinsically related to the leading eigenmode amplitude of the initial conditions. This finding was validated by actual model prediction results and is also consistent with other recent work. The relationship between R and SC has particular practical significance for ENSO predictability studies, since it provides an inexpensive and robust method for exploring forecast uncertainties without the need for costly ensemble runs.

Abstract

An efficient technique for the extraction of climatically relevant singular vectors in the presence of weather noise is presented. This technique is particularly relevant to the analysis of coupled general circulation models where the fastest growing modes are connected with weather and not climate. Climatic analysis, however, requires that the slow modes relevant to oceanic adjustment be extracted, and so effective techniques are required to essentially filter the stochastic part of the system. The method developed here relies on the basic properties of the evolution of first moments in stochastic systems. The methodology for the climatically important ENSO problem is tested using two different coupled models. First, the method using a stochastically forced intermediate coupled model for which exact singular vectors are known is tested. Here, highly accurate estimates for the first few singular vectors are produced for the associated dynamical system without stochastic forcing. Then the methodology is applied to a relatively complete coupled general circulation model, which has been shown to have skill in the prediction of ENSO. The method is shown to converge rapidly with respect to the expansion basis chosen and also with respect to ensemble size. The first climatic singular vector calculated shows some resemblance to that previously extracted by other authors using observational datasets. The promising results reported here should hopefully encourage further investigation of the methodology in a range of coupled models and for a range of physical problems where there exists a clear separation of timescales.

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.