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Ziwang Deng and Youmin Tang

Abstract

An important step in understanding the climate system is simulating and studying the past climate variability, using oceanic models, atmospheric models, or both. Toward this goal, long-term wind stress data, as the forcing of oceanic or climate models, are often required. In this study, the possibility of reconstructing the past winds of the tropical Pacific Ocean using historical sea surface temperature (SST) and sea level pressure (SLP) datasets was explored. Four statistical models, based on principal component (PC) regression and singular vector decomposition (SVD), were developed for reconstructing monthly pseudo wind stress over the tropical Pacific for the period 1875–1947. The high-frequency noise was removed from the raw data prior to the reconstruction. These models are SST-based PC regression (model 1), SLP-based PC regression (model 2), SST-based SVD (model 3), and SLP-based SVD (model 4). The results show that reconstructed wind stresses from all models can account for more than one-half of the total variances. In general, the SLP is better than SST as a predictor and the SVD method is superior to the PC regression. Forced by these reconstructed wind stresses, an oceanic general circulation model can simulate realistic interannual variability of the tropical Pacific SST. However, the wind stress reconstructed by SST-based models leads to better simulation skill in comparison with that from SLP-based models. Last, a long-term wind stress dataset was constructed for the period from 1875 to 1947 by the SST-based SVD model, which provides a useful tool for studying the past climate variability over the tropical Pacific, especially for El Niño–Southern Oscillation.

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Youmin Tang and Ziwang Deng

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In this study, a breeding analysis was conducted for a hybrid coupled El Niño–Southern Oscillation (ENSO) model that assimilated a historic dataset of sea surface temperature (SST) for the 120 yr between 1881 and 2000. Meanwhile, retrospective ENSO forecasts were performed for the same period. For a given initial state, 15 bred vectors (BVs) of both SST and upper-ocean heat content (HC) were derived. It was found that the average structure of the 15 BVs was insensitive to the initial states and independent of season and ENSO phase. The average structure of the BVs shared many features already seen in both the final patterns of leading singular vectors and the ENSO BVs of other models. However, individual BV patterns were quite different from case to case. The BV rate (the average cumulative growth rate of BVs) varied seasonally, and the maximum value appeared at the time when the model ran through the boreal spring and summer. It was also sensitive to the strength of the ENSO signal (i.e., the stronger ENSO signal, the smaller the BV rate).

Furthermore, ENSO predictability was explored using BV analysis. Emphasis was placed on the relationship between BVs, which are able to characterize potential predictability without requiring observations, and actual prediction skills, which make use of real observations. The results showed that the relative entropy, defined using breeding vectors, was a good measure of potential predictability. Large relative entropy often leads to a good prediction skill; however, when the relative entropy was small, the prediction skill seemed much more variable. At decadal/interdecadal scales, the variations in prediction skills correlated with relative entropy.

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Youmin Tang and Jaison Ambadan
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Waqar Younas and Youmin Tang

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In this study, the predictability of the Pacific–North American (PNA) pattern is evaluated on time scales from days to months using state-of-the-art dynamical multiple-model ensembles including the Canadian Historical Forecast Project (HFP2) ensemble, the Development of a European Multimodel Ensemble System for Seasonal-to-Interannual Prediction (DEMETER) ensemble, and the Ensemble-Based Predictions of Climate Changes and their Impacts (ENSEMBLES). Some interesting findings in this study include (i) multiple-model ensemble (MME) skill was better than most of the individual models; (ii) both actual prediction skill and potential predictability increased as the averaging time scale increased from days to months; (iii) there is no significant difference in actual skill between coupled and uncoupled models, in contrast with the potential predictability where coupled models performed better than uncoupled models; (iv) relative entropy (REA) is an effective measure in characterizing the potential predictability of individual prediction, whereas the mutual information (MI) is a reliable indicator of overall prediction skill; and (v) compared with conventional potential predictability measures of the signal-to-noise ratio, the MI-based measures characterized more potential predictability when the ensemble spread varied over initial conditions.

Further analysis found that the signal component dominated the dispersion component in REA for PNA potential predictability from days to seasons. Also, the PNA predictability is highly related to the signal of the tropical sea surface temperature (SST), and SST–PNA correlation patterns resemble the typical ENSO structure, suggesting that ENSO is the main source of PNA seasonal predictability. The predictable component analysis (PrCA) of atmospheric variability further confirmed the above conclusion; that is, PNA is one of the most predictable patterns in the climate variability over the Northern Hemisphere, which originates mainly from the ENSO forcing.

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Xiaojing Li and Youmin Tang

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This work uses a 19-yr ensemble hindcast of the European Centre for Medium-Range Weather Forecasts (ECMWF) and the average predictable time (APT) method to detect the most predictable tropical intraseasonal variability (ISV) mode. The first and most predictable mode (APT1) of tropical ISV is similar to a joint merger of the two Madden–Julian oscillation (MJO) modes with more weight on the second mode and is characterized by a tripole pattern with two positive centers in the equatorial western Indian Ocean and central Pacific Ocean and a negative center over the Maritime Continent. The APT1 doubles the skillful prediction period made by the MJO defined by a correlation skill of 0.5 (approximately 25 days in the ECMWF model), demonstrating its potential to become a skillful prediction target and to offer powerful subseasonal prediction sources. The underlying physical process and predictability source of the APT1 are further analyzed. The APT1 is very similar to the pattern triggered by the most predictable tropical intraseasonal sea surface temperature (SST) anomalies mode, suggesting its oceanic origin. Tropical ocean–atmosphere interaction plays a critical role in the APT1 by enhancing the evolution of tropical convection cells under WES (wind–evaporation–SST) and Bjerknes feedbacks. The internal atmospheric processes also have an important impact on the formation and maintenance of the APT1.

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Youmin Tang and William W. Hsieh

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 model. Numerical experiments showed that for the weakly nonlinear case, the hybrid model can be very successful, with forecast skills similar to the original Lorenz model. For the highly nonlinear case, the hybrid model could produce reasonable predictions for at least one cycle of oscillation for most experiments, although poor results were obtained for some experiments. In these failed experiments, the data used for assimilation were often located on one wing of the Lorenz butterfly-shaped attractor, while the system moved to the second wing during the forecast period. The forecasts failed as the model had never been trained with data from the second wing.

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Jaison Thomas Ambadan and Youmin Tang

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Performance of an advanced, derivativeless, sigma-point Kalman filter (SPKF) data assimilation scheme in a strongly nonlinear dynamical model is investigated. The SPKF data assimilation scheme is compared against standard Kalman filters such as the extended Kalman filter (EKF) and ensemble Kalman filter (EnKF) schemes. Three particular cases—namely, the state, parameter, and joint estimation of states and parameters from a set of discontinuous noisy observations—are studied. The problems associated with the use of tangent linear model (TLM) or Jacobian when using standard Kalman filters are eliminated when using SPKF data assimilation algorithms. Further, the constraints and issues of SPKF data assimilation in real ocean or atmospheric models are emphasized. A reduced sigma-point subspace model is proposed and investigated for higher-dimensional systems.

A low-dimensional model and a higher-dimensional Lorenz 1995 model are used as the test beds for data assimilation experiments. The results of SPKF data assimilation schemes are compared with those of standard EKF and EnKF, in which a highly nonlinear chaotic case is studied. It is shown that the SPKF is capable of estimating the model state and parameters with better accuracy than EKF and EnKF. Numerical experiments showed that in all cases the SPKF can give consistent results with better assimilation skills than EnKF and EKF and can overcome the drawbacks associated with the use of EKF and EnKF.

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Richard Kleeman, Youmin Tang, and Andrew M. Moore

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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.

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Youmin Tang, Richard Kleeman, and Andrew M. Moore

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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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Youmin Tang, Richard Kleeman, and Andrew M. Moore

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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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