Youmin Tang

Interdecadal Variation of ENSO Predictability in Multiple Models

In this study, El Nino–Southern Oscillation (ENSO) retrospective forecasts were performed for the 120 yr from 1881 to 2000 using three realistic models that assimilate the historic dataset of sea surface temperature (SST). By examining these retrospective forecasts and corresponding observations, as well as the oceanic analyses from which forecasts were initialized, several important issues related to ENSO predictability have been explored, including its interdecadal variability and the dominant factors that control the interdecadal variability. The prediction skill of the three models showed a very consistent interdecadal variation, with high skill in the late nineteenth century and in the middle–late twentieth century, and low skill during the period from 1900 to 1960. The interdecadal variation in ENSO predictability is in good agreement with that in the signal of interannual variability and in the degree of asymmetry of ENSO system. A good relationship was also identified between the degree of asymmetry and the signal of interannual variability, and the former is highly related to the latter. Generally, the high predictability is attained when ENSO signal strength and the degree of asymmetry are enhanced, and vice versa. The atmospheric noise generally degrades overall prediction skill, especially for the skill of mean square error, but is able to favor some individual prediction cases. The possible reasons why these factors control ENSO predictability were also discussed.

Reliability of ENSO Dynamical Predictions

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...

The Calculation of Climatically Relevant Singular Vectors in the Presence of Weather Noise as Applied to the ENSO Problem

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.

ENSO Predictability of a Fully Coupled GCM Model Using Singular Vector Analysis

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 subs...

Effects of westerly wind bursts on El Niño: A new perspective

Daily observations from 1971 to 2010 reveal that every El Nino during this period was accompanied by congregated westerly wind bursts, suggesting a close relationship of these bursts with both “cold tongue” and “warm pool” El Nino events. With the addition of burst-like multiplicative noise to an intermediate ocean-atmosphere coupled model, it is shown that westerly wind bursts, by generating eastward equatorial surface currents and downwelling Kelvin waves, could be responsible for the existence of the warm pool El Nino and for the irregularity and extremes of the cold tongue El Nino. Whether these bursts give rise to one type of El Nino or the other depends on the timing of their occurrence relative to the phase of the recharge-discharge cycle of the equatorial upper ocean heat content.

Optimal Forcing Patterns for Coupled Models of ENSO

The optimal forcing patterns for El Nino–Southern Oscillation (ENSO) are examined for a hierarchy of hybrid coupled models using generalized stability theory. Specifically two cases are considered: one where the forcing is stochastic in time, and one where the forcing is time independent. The optimal forcing patterns in these two cases are described by the stochastic optimals and forcing singular vectors, respectively. The spectrum of stochastic optimals for each model was found to be dominated by a single pattern. In addition, the dominant stochastic optimal structure is remarkably similar to the forcing singular vector, and to the dominant singular vectors computed in a previous related study using a subset of the same models. This suggests that irrespective of whether the forcing is in the form of an impulse, is time invariant, or is stochastic in nature, the optimal excitation for the eigenmode that describes ENSO in each model is the same. The optimal forcing pattern, however, does vary from model to model, and depends on air–sea interaction processes. Estimates of the stochastic component of forcing were obtained from atmospheric analyses and the projection of the dominant optimal forcing pattern from each model onto this component of the forcing was computed. It was found that each of the optimal forcing patterns identified may be present in nature and all are equally likely. The existence of a dominant optimal forcing pattern is explored in terms of the effective dimension of the coupled system using the method of balanced truncation, and was found to be O(1) for the models used here. The implications of this important result for ENSO prediction and predictability are discussed.

SST Assimilation Experiments in a Tropical Pacific Ocean Model

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 — — — — — — — — —

A Predictability Measure Applied to Seasonal Predictions of the Arctic Oscillation

Abstract In this study, ensemble seasonal predictions of the Arctic Oscillation (AO) were conducted for 51 winters (1948–98) using a simple global atmospheric general circulation model. A means of estimating a priori the predictive skill of the AO ensemble predictions was developed based on the relative entropy (R) of information theory, which is a measure of the difference between the forecast and climatology probability density functions (PDFs). Several important issues related to the AO predictability, such as the dominant precursors of forecast skill and the degree of confidence that can be placed in an individual forecast, were addressed. It was found that R is a useful measure of the confidence that can be placed on dynamical predictions of the AO. When R is large, the prediction is likely to have a high confidence level whereas when R is small, the prediction skill is more variable. A small R is often accompanied by a relatively weak AO index. The value of R is dominated by the predicted ensemble m...

Comparison of Information-Based Measures of Forecast Uncertainty in Ensemble ENSO Prediction

Abstract In this study, ensemble predictions of the El Nino–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 l...

Coupling Neural Networks to Incomplete Dynamical Systems via Variational Data Assimilation

Abstract The advent of the feed-forward neural network (N) model opens the possibility of hybrid neural–dynamical models via variational data assimilation. Such a hybrid model may be used in situations where some variables, difficult to model dynamically, have sufficient data for modeling them empirically with an N. This idea of using an N to replace missing dynamical equations is tested with the Lorenz three-component nonlinear system, where one of the three Lorenz equations is replaced by an N equation. In several experiments, the 4DVAR assimilation approach is used to estimate 1) the N model parameters (26 parameters), 2) two dynamical parameters and three initial conditions for the hybrid model, and 3) the dynamical parameters, initial conditions, and the N parameters (28 parameters plus three initial conditions). Two cases of the Lorenz model—(i) the weakly nonlinear case of quasiperiodic oscillations, and (ii) the highly nonlinear, chaotic case—were chosen to test the forecast skills of the hybrid m...