Influence of the Preceding Austral Summer Southern Hemisphere Annular Mode on the Amplitude of ENSO Decay

There is increasing evidence of the possible role of extratropical forcing in the evolution of ENSO. The Southern Hemi- sphere Annular Mode （SAM） is the dominant mode of atmospheric circulation in the Southern Hemisphere extratropics. This study shows that the austral summer （December-January-February; DJF） SAM may also influence the amplitude of ENSO decay during austral autumn （March-April-May; MAM）. The mechanisms associated with this SAM-ENSO relationship can be briefly summarized as follows： The SAM is positively （negatively） correlated with SST in the Southern Hemisphere middle （high） latitudes. This dipole-like SST anomaly pattern is referred to as the Southern Ocean Dipole （SOD）. The DJF SOD, caused by the DJF SAM, could persist until MAM and then influence atmospheric circulation, including trade winds, over the Nifio3.4 area. Anomalous trade winds and SST anomalies over the Nifio3.4 area related to the DJF SAM are further developed through the Bjerkness feedback, which eventually results in a cooling （warming） over the Nifio3.4 area followed by the positive （negative） DJF SAM.

Relationships between the Extratropical ENSO Precursor and Leading Modes of Atmospheric Variability in the Southern Hemisphere

Previous studies suggest that the atmospheric precursor of E1 Nifio-Southern Oscillation （ENSO） in the extratropical Southern Hemisphere （SH） might trigger a quadrapole sea surface temperature anomaly （SSTA） in the South Pacific and subsequently influence the following ENSO. Such a quadrapole SSTA is referred to as the South Pacific quadrapole （SPQ）. The present study investigated the relationships between the atmospheric precursor signal of ENSO and leading modes of atmospheric variability in the extratropical SH [including the SH annular mode （SAM）, the first Pacific-South America （PSA1） mode, and the second Pacific-South America （PSA2） mode]. The results showed that the atmospheric precursor signal in the extratropical SH basically exhibits a barotropic wavenumber-3 structure over the South Pacific and is significantly correlated with the SAM and the PSA2 mode during austral summer. Nevertheless, only the PSA2 mode was found to be a precursor for the following ENSO. It leads the SPQ-like SSTA by around one month, while the SAM and the PSA1 mode do not show any obvious linkage with either ENSO or the SPQ. This suggests that the PSA2 mode may provide a bridge between the preceding circulation anomalies over the extratropical SH and the following ENSO through the SPQ-like SSTA.

Recent Advances in China on the Predictability of Weather and Climate

This article summarizes the progress made in predictability studies of weather and climate in recent years in China,with a main focus on advances in methods to study error growth dynamics and reduce uncertainties in the forecasting of weather and climate.Specifically,it covers(a)advances in methods to study weather and climate predictability dynamics,especially those in nonlinear optimal perturbation methods associated with initial errors and model errors and their applications to ensemble forecasting and target observations,(b)new data assimilation algorithms for initialization of predictions and novel assimilation approaches to neutralize the combined effects of initial and model errors for weather and climate,(c)applications of new statistical approaches to climate predictions,and(d)studies on meso-to small-scale weather system predictability dynamics.Some of the major frontiers and challenges remaining in predictability studies are addressed in this context.

Impact of Perturbation Schemes on the Ensemble Prediction in a Coupled Lorenz Model

Based on a simple coupled Lorenz model,we investigate how to assess a suitable initial perturbation scheme for ensemble forecasting in a multiscale system involving slow dynamics and fast dynamics.Four initial perturbation approaches are used in the ensemble forecasting experiments:the random perturbation(RP),the bred vector(BV),the ensemble transform Kalman filter(ETKF),and the nonlinear local Lyapunov vector(NLLV)methods.Results show that,regardless of the method used,the ensemble averages behave indistinguishably from the control forecasts during the first few time steps.Due to different error growth in different time-scale systems,the ensemble averages perform better than the control forecast after very short lead times in a fast subsystem but after a relatively long period of time in a slow subsystem.Due to the coupled dynamic processes,the addition of perturbations to fast variables or to slow variables can contribute to an improvement in the forecasting skill for fast variables and slow variables.Regarding the initial perturbation approaches,the NLLVs show higher forecasting skill than the BVs or RPs overall.The NLLVs and ETKFs had nearly equivalent prediction skill,but NLLVs performed best by a narrow margin.In particular,when adding perturbations to slow variables,the independent perturbations(NLLVs and ETKFs)perform much better in ensemble prediction.These results are simply implied in a real coupled air–sea model.For the prediction of oceanic variables,using independent perturbations(NLLVs)and adding perturbations to oceanic variables are expected to result in better performance in the ensemble prediction.

Influence of the NAO on Wintertime Surface Air Temperature over East Asia:Multidecadal Variability and Decadal Prediction

In this paper,we investigate the influence of the winter NAO on the multidecadal variability of winter East Asian surface air temperature(EASAT)and EASAT decadal prediction.The observational analysis shows that the winter EASAT and East Asian minimum SAT(EAmSAT)display strong in-phase fluctuations and a significant 60-80-year multidecadal variability,apart from a long-term warming trend.The winter EASAT experienced a decreasing trend in the last two decades,which is consistent with the occurrence of extremely cold events in East Asia winters in recent years.The winter NAO leads the detrended winter EASAT by 12-18 years with the greatest significant positive correlation at the lead time of 15 years.Further analysis shows that ENSO may affect winter EASAT interannual variability,but does not affect the robust lead relationship between the winter NAO and EASAT.We present the coupled oceanic-atmospheric bridge(COAB)mechanism of the NAO influences on winter EASAT multidecadal variability through its accumulated delayed effect of~15 years on the Atlantic Multidecadal Oscillation(AMO)and Africa-Asia multidecadal teleconnection(AAMT)pattern.An NAO-based linear model for predicting winter decadal EASAT is constructed on the principle of the COAB mechanism,with good hindcast performance.The winter EASAT for 2020-34 is predicted to keep on fluctuating downward until~2025,implying a high probability of occurrence of extremely cold events in coming winters in East Asia,followed by a sudden turn towards sharp warming.The predicted 2020/21 winter EASAT is almost the same as the 2019/20 winter.

Determining the Spectrum of the Nonlinear Local Lyapunov Exponents in a Multidimensional Chaotic System

For an n-dimensional chaotic system, we extend the definition of the nonlinear local Lyapunov exponent （NLLE） from one- to n-dimensional spectra, and present a method for computing the NLLE spectrum. The method is tested on three chaotic systems with different complexity. The results indicate that the NLLE spectrum realistically characterizes the growth rates of initial error vectors along different directions from the linear to nonlinear phases of error growth. This represents an improvement over the traditional Lyapunov exponent spectrum, which only characterizes the error growth rates during the linear phase of error growth. In addition, because the NLLE spectrum can effectively separate the slowly and rapidly growing perturbations, it is shown to be more suitable for estimating the predictability of chaotic systems, as compared to the traditional Lyapunov exponent spectrum.

Comparison of Nonlinear Local Lyapunov Vectors with Bred Vectors, Random Perturbations and Ensemble Transform Kalman Filter Strategies in a Barotropic Model

The breeding method has been widely used to generate ensemble perturbations in ensemble forecasting due to its simple concept and low computational cost. This method produces the fastest growing perturbation modes to catch the growing components in analysis errors. However, the bred vectors （BVs） are evolved on the same dynamical flow, which may increase the dependence of perturbations. In contrast, the nonlinear local Lyapunov vector （NLLV） scheme generates flow-dependent perturbations as in the breeding method, but regularly conducts the Gram-Schmidt reorthonormalization processes on the perturbations. The resulting NLLVs span the fast-growing perturbation subspace efficiently, and thus may grasp more com- ponents in analysis errors than the BVs. In this paper, the NLLVs are employed to generate initial ensemble perturbations in a barotropic quasi-geostrophic model. The performances of the ensemble forecasts of the NLLV method are systematically compared to those of the random pertur- bation （RP） technique, and the BV method, as well as its improved version--the ensemble transform Kalman filter （ETKF） method. The results demonstrate that the RP technique has the worst performance in ensemble forecasts, which indicates the importance of a flow-dependent initialization scheme. The ensemble perturbation subspaces of the NLLV and ETKF methods are preliminarily shown to catch similar components of analysis errors, which exceed that of the BVs. However, the NLLV scheme demonstrates slightly higher ensemble forecast skill than the ETKF scheme. In addition, the NLLV scheme involves a significantly simpler algorithm and less computation time than the ETKF method, and both demonstrate better ensemble forecast skill than the BV scheme.

Determination of the Backward Predictability Limit and Its Relationship with the Forward Predictability Limit

In this work, two types of predictability are proposed—forward and backward predictability—and then applied in the nonlinear local Lyapunov exponent approach to the Lorenz63 and Lorenz96 models to quantitatively estimate the local forward and backward predictability limits of states in phase space. The forward predictability mainly focuses on the forward evolution of initial errors superposed on the initial state over time, while the backward predictability is mainly concerned with when the given state can be predicted before this state happens. From the results, there is a negative correlation between the local forward and backward predictability limits. That is, the forward predictability limits are higher when the backward predictability limits are lower, and vice versa. We also find that the sum of forward and backward predictability limits of each state tends to fluctuate around the average value of sums of the forward and backward predictability limits of sufficient states.Furthermore, the average value is constant when the states are sufficient. For different chaotic systems, the average value is dependent on the chaotic systems and more complex chaotic systems get a lower average value. For a single chaotic system,the average value depends on the magnitude of initial perturbations. The average values decrease as the magnitudes of initial perturbations increase.

Quantitative Comparison of Predictabilities of Warm and Cold Events Using the Backward Nonlinear Local Lyapunov Exponent Method

The backward nonlinear local Lyapunov exponent method(BNLLE)is applied to quantify the predictability of warm and cold events in the Lorenz model.Results show that the maximum prediction lead times of warm and cold events present obvious layered structures in phase space.The maximum prediction lead times of each warm(cold)event on individual circles concentric with the distribution of warm(cold)regime events are roughly the same,whereas the maximum prediction lead time of events on other circles are different.Statistical results show that warm events are more predictable than cold events.

Dominant SST Mode in the Southern Hemisphere Extratropics and Its Influence on Atmospheric Circulation

The variability in the Southern Ocean（SO） sea surface temperature（SST） has drawn increased attention due to its unique physical features; therefore, the temporal characteristics of the SO SST anomalies（SSTA） and their influence on extratropical atmospheric circulation are addressed in this study. Results from empirical orthogonal function analysis show that the principal mode of the SO SSTA exhibits a dipole-like structure, suggesting a negative correlation between the SSTA in the middle and high latitudes, which is referred to as the SO Dipole（SOD） in this study. The SOD features strong zonal symmetry, and could reflect more than 50% of total zonal-mean SSTA variability. We find that stronger（weaker） Subantarctic and Antarctic polar fronts are related to the positive（negative） phases of the SOD index, as well as the primary variability of the large-scale SO SSTA meridional gradient. During December–January–February, the Ferrel cell and the polar jet shift toward the Antarctic due to changes in the SSTA that could be associated with a positive phase of the SOD, and are also accompanied by a poleward shift of the subtropical jet. During June–July–August, in association with a positive SOD, the Ferrel cell and the polar jet are strengthened, accompanied by a strengthened subtropical jet. These seasonal differences are linked to the differences in the configuration of the polar jet and the subtropical jet in the Southern Hemisphere.

Estimating the Predictability Limit of Tropical Cyclone Tracks over the Western North Pacific Using Observational Data

In this study,the nonlinear local Lyapunov exponent(NLLE)approach was used to quantitatively determine the predictability limit of tropical cyclone(TC)tracks based on observed TC track data obtained from the Joint Typhoon Warning Center.The results show that the predictability limit of all TC tracks over the whole western North Pacific(WNP)basin is about 102 h,and the average lifetime of all TC tracks is about 174 h.The predictability limits of the TC tracks for short-,medium-,and long-lived TCs are approximately 72 h,120 h,and 132 h,respectively.The predictability limit of the TC tracks depends on the TC genesis location,lifetime,and intensity,and further analysis indicated that these three metrics are closely related.The more intense and longer-lived TCs tend to be generated on the eastern side of the WNP(EWNP),whereas the weaker and shorter-lived TCs tend to form in the west of the WNP(WWNP)and the South China Sea(SCS).The relatively stronger and longer-lived TCs,which are generated mainly in the EWNP,have a longer travel time before they curve northeastwards and hence tend to be more predictable than the relatively weaker and shorter-lived TCs that form in the WWNP region and SCS.Furthermore,the results show that the predictability limit of the TC tracks obtained from the best-track data may be underestimated due to the relatively short observational records currently available.Further work is needed,employing a numerical model to assess the predictability of TC tracks.

Application of Backward Nonlinear Local Lyapunov Exponent Method to Assessing the Relative Impacts of Initial Condition and Model Errors on Local Backward Predictability

Initial condition and model errors both contribute to the loss of atmospheric predictability.However,it remains debatable which type of error has the larger impact on the prediction lead time of specific states.In this study,we perform a theoretical study to investigate the relative effects of initial condition and model errors on local prediction lead time of given states in the Lorenz model.Using the backward nonlinear local Lyapunov exponent method,the prediction lead time,also called local backward predictability limit(LBPL),of given states induced by the two types of errors can be quantitatively estimated.Results show that the structure of the Lorenz attractor leads to a layered distribution of LBPLs of states.On an individual circular orbit,the LBPLs are roughly the same,whereas they are different on different orbits.The spatial distributions of LBPLs show that the relative effects of initial condition and model errors on local backward predictability depend on the locations of given states on the dynamical trajectory and the error magnitudes.When the error magnitude is fixed,the differences between the LBPLs vary with the locations of given states.The larger differences are mainly located on the inner trajectories of regimes.When the error magnitudes are different,the dissimilarities in LBPLs are diverse for the same given state.

Predictability of Ensemble Forecasting Estimated Using the Kullback–Leibler Divergence in the Lorenz Model

A new method to quantify the predictability limit of ensemble forecasting is presented using the Kullback–Leibler(KL)divergence(also called the relative entropy), which provides a measure of the difference between the probability distributions of ensemble forecasts and local reference(true) states. The KL divergence is applicable to a non-normal distribution of ensemble forecasts, which is a substantial improvement over the previous method using the ensemble spread. An example from the three-variable Lorenz model illustrates the effectiveness of the KL divergence, which can effectively quantify the predictability limit of ensemble forecasting. On this basis, the KL divergence is used to investigate the dependence of the predictability limit of ensemble forecasting on the initial states and the magnitude of initial errors. The local predictability limit of ensemble forecasting varies considerably with the initial states, as well as with the magnitude of initial errors. Further research is needed to examine the real-world applications of the KL divergence in measuring the predictability of ensemble weather forecasts.

The Relationship between Deterministic and Ensemble Mean Forecast Errors Revealed by Global and Local Attractor Radii

It has been demonstrated that ensemble mean forecasts, in the context of the sample mean, have higher forecasting skill than deterministic(or single) forecasts. However, few studies have focused on quantifying the relationship between their forecast errors, especially in individual prediction cases. Clarification of the characteristics of deterministic and ensemble mean forecasts from the perspective of attractors of dynamical systems has also rarely been involved. In this paper, two attractor statistics—namely, the global and local attractor radii(GAR and LAR, respectively)—are applied to reveal the relationship between deterministic and ensemble mean forecast errors. The practical forecast experiments are implemented in a perfect model scenario with the Lorenz96 model as the numerical results for verification. The sample mean errors of deterministic and ensemble mean forecasts can be expressed by GAR and LAR, respectively, and their ratio is found to approach2^(1/2) with lead time. Meanwhile, the LAR can provide the expected ratio of the ensemble mean and deterministic forecast errors in individual cases.

Evaluation of the performance of CMIP5 and CMIP6 models in simulating the South Pacific Quadrupole-ENSO relationship

先前的观测研究表明,南太平洋四极子海温模态(SPQ)可以有效地作为ENSO的前兆信号.本文利用20个CMIP6模式及其对应的20个先前的CMIP5模式的工业化前气候模拟试验数据,评估和比较了CMIP6以及CMIP5模式对SPQ与ENSO的关系的模拟能力.结果表明,大多数CMIP5和CMIP6模式可以合理地模拟SPQ的基本特征.与早期的CMIP5模式相比,CMIP6模式能够更加真实地模拟SPQ与ENSO之间的关系.进一步分析表明,CMIP6模式模拟SPQ与ENSO关系的能力提高,是因为CMIP6模式能够更好地模拟出在副热带/热带太平洋上与SPQ相关的表面海气热力耦合过程,以及在赤道太平洋上与SPQ相关的次表层海温的异常相应.

Influence of the North American Dipole on ENSO onset as simulated by a coupled ocean-Atmosphere model

北美偶极子(NAD)是热带北大西洋西部和北美东北部的南北向海平面气压异常偶极型模态.以往的观测研究表明,NAD可以有效地影响ENSO事件的爆发.本文利用全球耦合模式FGOALS-g2,评估了NAD与ENSO的关系.结果表明,该模式能较好地重现NAD模态.进一步的分析验证了冬季NAD可以通过强迫冬末春初副热带东北太平洋上空的反气旋和暖海温的出现,在随后的冬季触发El Nino事件.此外,在同化NAD实验中,发生El Niño事件的概率增加了将近一倍.相比之下,NAO未能在副热带东北太平洋上空引起表面风和海温的异常,因而不能有效地激发次年冬季ENSO事件.

The Predictability Limit of Oceanic Mesoscale Eddy Tracks in the South China Sea

Employing the nonlinear local Lyapunov exponent (NLLE) technique, this study assesses the quantitative predictability limit of oceanic mesoscale eddy (OME) tracks utilizing three eddy datasets for both annual and seasonal means. Our findings reveal a discernible predictability limit of approximately 39 days for cyclonic eddies (CEs) and 44 days for anticyclonic eddies (AEs) within the South China Sea (SCS). The predictability limit is related to the OME properties and seasons. The long-lived, large-amplitude, and large-radius OMEs tend to have a higher predictability limit. The predictability limit of AE (CE) tracks is highest in autumn (winter) with 52 (53) days and lowest in spring (summer) with 40 (30) days. The spatial distribution of the predictability limit of OME tracks also has seasonal variations, further finding that the area of higher predictability limits often overlaps with periodic OMEs. Additionally, the predictability limit of periodic OME tracks is about 49 days for both CEs and AEs, which is 5-10 days higher than the mean values. Usually, in the SCS, OMEs characterized by high predictability limit values exhibit more extended and smoother trajectories and often move along the northern slope of the SCS.

Application of the Conditional Nonlinear Local Lyapunov Exponent to Second-Kind Predictability

In order to quantify the influence of external forcings on the predictability limit using observational data,the author introduced an algorithm of the conditional nonlinear local Lyapunov exponent(CNLLE)method.The effectiveness of this algorithm is validated and compared with the nonlinear local Lyapunov exponent(NLLE)and signal-to-noise ratio methods using a coupled Lorenz model.The results show that the CNLLE method is able to capture the slow error growth constrained by external forcings,therefore,it can quantify the predictability limit induced by the external forcings.On this basis,a preliminary attempt was made to apply this method to measure the influence of ENSO on the predictability limit for both atmospheric and oceanic variable fields.The spatial distribution of the predictability limit induced by ENSO is similar to that arising from the initial conditions calculated by the NLLE method.This similarity supports ENSO as the major predictable signal for weather and climate prediction.In addition,a ratio of predictability limit(RPL)calculated by the CNLLE method to that calculated by the NLLE method was proposed.The RPL larger than 1 indicates that the external forcings can significantly benefit the long-term predictability limit.For instance,ENSO can effectively extend the predictability limit arising from the initial conditions of sea surface temperature over the tropical Indian Ocean by approximately four months,as well as the predictability limit of sea level pressure over the eastern and western Pacific Ocean.Moreover,the impact of ENSO on the geopotential height predictability limit is primarily confined to the troposphere.