Impacts of Two Types of Northward Jumps of the East Asian Upper-tropospheric Jet Stream in Midsummer on Rainfall in Eastern China

The East Asian upper-tropospheric jet stream （EAJS） typically jumps north of 45~N in midsummer. These annual northward jumps are mostly classified into two dominant types： the first type corresponds to the enhanced westerly to the north of the EAJS＇s axis （type A）, while the second type is related to the weakened westerly within the EAJS＇s axis （type B）. In this study, the impacts of these two types of northward jumps on rainfall in eastern China are investigated. Our results show that rainfall significantly increases in northern Northeast China and decreases in the Yellow River-Huaihe River valleys, as well as in North China, during the type A jump. As a result of the type B jump, rainfall is enhanced in North China and suppressed in the Yangtze River valley. The changes in rainfall in eastern China during these two types of northward jumps are mainly caused by the northward shifts of the ascending air flow that is directly related to the EAJS. Concurrent with the type A （B） jump, the EAJS-related ascending branch moves from the Yangtze-Huai River valley to northern Northeast （North） China when the EAJS＇s axis jumps from 40~N to 55~N （50~N）. Meanwhile, the type A jump also strengthens the Northeast Asian low in the lower troposphere, leading to more moisture transport to northern Northeast China. The type B jump, however, induces a northwestward extension of the lower-tropospheric western North Pacific subtropical high and more moisture transport to North China.

Interannual Meridional Displacement of the East Asian Upper-tropospheric Jet Stream in Summer

On the interannual timescale, the meridional displacement of the East Asian upper-tropospheric jet stream (EAJS) is significantly associated with the rainfall anomalies in East Asia in summer. In this study, using the data from the National Centers for Environmental Prediction-Department of Energy (NCEP/DOE) reanalysis-2 from 1979 to 2002, the authors investigate the interannual variations of the EAJS's meridional displacement in summer and their associations with the variations of the South Asian high (SAH) and the western North Pacific subtropical high (WNPSH), which are dominant circulation features in the upper and lower troposhere, respectively. The result from an EOF analysis shows that the meridional displacement is the most remarkable feature of the interannual variations of the EAJS in each month of summer and in summer as a whole. A composite analysis indicates that the summer (June-July-August, JJA) EAJS index, which is intended to depict the interannual meridional displacement of the EAJS, is not appropriate because the anomalies of the zonal wind at 200 hPa (U200) in July and August only, rather than in June, significantly contribute to the summer EAJS index. Thus, the index for each month in summer is defined according to the location of the EAJS core in each month. Composite analyses based on the monthly indexes show that corresponding to the monthly equatorward displacement of the EAJS, the South Asian high (SAH) extends southeastward clearly in July and August, and the western North Pacific subtropical high (WNPSH) withdraws southward in June and August.

Interdecadal variability of summer precipitation in the Three River Source Region: Influences of SST and zonal shifts of the East Asian subtropical westerly jet

Summer precipitation in the Three Rivers Source Region(TRSR)of China is vital for the headwaters of the Yellow,Yangtze,and Lancang rivers and exhibits significant interdecadal variability.This study investigates the influence of the East Asian westerly jet(EAWJ)on TRSR rainfall.A strong correlation is found between TRSR summer precipitation and the Jet Zonal Position Index(JZPI)of the EAWJ from 1961 to 2019(R=0.619,p<0.01).During periods when a positive JZPI indicates a westward shift in the EAWJ,enhanced water vapor anomalies,warmer air,and low-level convergence anomalies contribute to increased TRSR summer precipitation.Using empirical orthogonal function and regression analyses,this research identifies the influence of large-scale circulation anomalies associated with the Atlantic–Eurasian teleconnection(AEA)from the North Atlantic(NA).The interdecadal variability between the NA and central tropical Pacific(CTP)significantly affects TRSR precipitation.This influence is mediated through the AEA via a Rossby wave train extending eastward along the EAWJ,and another south of 45°N.Moreover,the NA–CTP Opposite Phase Index(OPI),which quantifies the difference between the summer mean sea surface temperatures of the NA and the CTP,is identified as a critical factor in modulating the strength of this teleconnection and influencing the zonal position of the EAWJ.

Weakening of Interannual Variability in the Summer East Asian Upper-tropospheric Westerly Jet since the Mid-1990s

In this study,we found that the intensity of interannual variability in the summer upper-tropospheric zonal wind has significantly weakened over Northeast Asia and the subtropical western North Pacific（WNP） since the mid-1990s,concurrent with the previously documented decrease of the westerly jet over North China and Northwest China.Corresponding to this weakening of zonal wind variability,the meridional displacement of the East Asian westerly jet（EAJ） manifested as the leading mode of zonal wind variability over the WNP and East Asia（WNP-EA） before the mid-1990s but not afterward.The energetics of the anomalous pattern associated with the meridional displacement of the EAJ suggests that barotropic energy conversion,from basic flow to anomalous patterns,has led to the weakening of the variability in the EAJ meridional displacement and to a change in the leading dominant mode since the mid-1990s.The barotropic energy conversion efficiently maintained the anomalies associated with the variability in the EAJ meridional displacement during 1979-1993 but acted to dampen the anomalies during 1994-2008.A further investigation of the energetics suggests that the difference in the patterns of the circulation anomaly associated with either the first leading mode or the meridional displacement of the EAJ,i.e.,a southwest-northeast tilted pattern during 1979-1993 and a zonally oriented pattern during 1994-2008,has contributed greatly to the change in barotropic energy conversion.

Predictability of the Summer East Asian Upper-Tropospheric Westerly Jet in ENSEMBLES Multi-Model Forecasts

The interannual variation of the East Asian upper-tropospheric westerly jet （EAJ） significantly affects East Asian climate in summer. Identifying its performance in model prediction may provide us another viewpoint, from the perspective of uppertropospheric circulation, to understand the predictability of summer climate anomalies in East Asia. This study presents a comprehensive assessment of year-to-year variability of the EAJ based on retrospective seasonal forecasts, initiated from 1 May, in the five state-of-the-art coupled models from ENSEMBLES during 1960-2005. It is found that the coupled models show certain capability in describing the interannual meridional displacement of the EAJ, which reflects the models＇ performance in the first leading empirical orthogonal function （EOF） mode. This capability is mainly shown over the region south of the EAJ axis. Additionally, the models generally capture well the main features of atmospheric circulation and SST anomalies related to the interannual meridional displacement of the EAJ. Further analysis suggests that the predicted warm SST anomalies in the concurrent summer over the tropical eastern Pacific and northern Indian Ocean are the two main sources of the potential prediction skill of the southward shift of the EAJ. In contrast, the models are powerless in describing the variation over the region north of the EAJ axis, associated with the meridional displacement, and interannual intensity change of the EAJ, the second leading EOF mode, meaning it still remains a challenge to better predict the EAJ and, subsequently, summer climate in East Asia, using current coupled models.

Meridional Displacement of the East Asian Upper-tropospheric Westerly Jet and Its Relationship with the East Asian Summer Rainfall in CMIP5 Simulations

As the first leading mode of upper-tropospheric circulation in observations, the meridional displacement of the East Asian westerly jet (EAJ) varies closely with the East Asian rainfall in summer. In this study, the interannual variation of the EAJ meridional displacement and its relationship with the East Asian summer rainfall are evaluated, using the historical simulations of CMIP5 (phase 5 of the Coupled Model Intercomparison Project). The models can generally reproduce the meridional displacement of the EAJ, which is mainly manifested as the first principal mode in most of the simulations. For the relationship between the meridional displacement of the EAJ and East Asian rainfall, almost all the models depict a weaker correlation than observations and exhibit considerably large spread across the models. It is found that the discrepancy in the interannual relationship is closely related to the simulation of the climate mean state, including the climatological location of the westerly jet in Eurasia and rainfall bias in South Asia and the western North Pacific. In addition, a close relationship between the simulation discrepancy and intensity of EAJ variability is also found: the models with a stronger intensity of the EAJ meridional displacement tend to reproduce a closer interannual relationship, and vice versa.

Seasonal Variation of the East Asian Subtropical Westerly Jet and Its Association with the Heating Field over East Asia

The structure and seasonal variation of the East Asian Subtropical Westerly Jet （EAWJ） and associations with heating fields over East Asia are examined by using NCEP/NCAR reanalysis data. Obvious differences exist in the westerly jet intensity and location in different regions and seasons due to the ocean-land distribution and seasonal thermal contrast, as well as the dynamic and thermodynamic impacts of the Tibetan Plateau. In winter, the EAWJ center is situated over the western Pacific Ocean and the intensity is reduced gradually from east to west over the East Asian region. In summer, the EAWJ center is located over the north of the Tibetan Plateau and the jet intensity is reduced evidently compared with that in winter. The EAWJ seasonal evolution is characterized by the obvious longitudinal inconsistency of the northward migration and in-phase southward retreat of the EAWJ axis. A good correspondence between the seasonal variations of EAWJ and the meridional differences of air temperature （MDT） in the mid-upper troposphere demonstrates that the MDT is the basic reason for the seasonal variation of EAWJ. Correlation analyses indicate that the Kuroshio Current region to the south of Japan and the Tibetan Plateau are the key areas for the variations of the EAWJ intensities in winter and in summer, respectively. The strong sensible and latent heating in the Kuroshio Current region is closely related to the intensification of EAWJ in winter. In summer, strong sensible heating in the Tibetan Plateau corresponds to the EAWJ strengthening and southward shift, while the weak sensible heating in the Tibetan Plateau is consistent with the EAWJ weakening and northward migration.

The Effect of Transient Eddy on Interannual Meridional Displacement of Summer East Asian Subtropical Jet

Using ERA-40 reanalysis daily data for the period 1958-2002, this study investigated the effect of tran- sient eddy （TE） on the interannual meridional displacement of summer East Asian subtropical jet （EASJ） by conducting a detailed dynamical diagnosis. The summer EASJ axis features a significant interannual coherent meridional displacement. Associated with such a meridional displacement, the TE vorticity forcing anomalies are characterized by a meridional dipole pattern asymmetric about the climatological EASJ axis. The TE vorticity forcing anomalies yield barotropic zonal wind tendencies with a phase meridionally lead- ing the zonal wind anomalies, suggesting that they act to reinforce further meridional displacement of the EASJ and favor a positive feedback in the TE and time-mean flow interaction. However, The TE thermal forcing anomalies induce baroclinic zonal wind tendencies that reduce the vertical shear of zonal wind and atmospheric baroclinicity and eventually suppress the TE activity, favoring a negative feedback in the TE and time-mean flow interaction. Although the two types of TE forcing tend to have opposite feedback roles, the TE vorticity forcing appears to be dominant in the TE effect on the time-mean flow.

Has the East Asian Westerly Jet Experienced a Poleward Displacement in Recent Decades?

Previous studies have suggested a poleward shift of the zonally averaged jet stream due to rapid warming over continents.However,the regional characteristics of the change in the jet stream are not yet understood.Here,we present evidence suggesting that the East Asian westerly jet did not shift poleward in past decades（1980-2004 relative to 1958-1979）,both in winter and summer.Rather,the jet axis has moved southward in summer,but its meridional position is steady in winter.The main change of the jet stream in winter is the enhancement of its intensity.These changes in both summer and winter are consistent with the corresponding changes in the large meridional tropospheric temperature-gradient zone.Based on these results,we suggest that the changes of the jet stream over East Asia are unique and are different from the zonal mean jet stream over the Northern Hemisphere and over the North Atlantic region.

Intermodel Diversity in the Zonal Location of the Climatological East Asian Westerly Jet Core in Summer and Association with Rainfall over East Asia in CMIP5 Models

The East Asian westerly jet(EAJ), an important midlatitude circulation of the East Asian summer monsoon system,plays a crucial role in affecting summer rainfall over East Asia. The multimodel ensemble of current coupled models can generally capture the intensity and location of the climatological summer EAJ. However, individual models still exhibit large discrepancies. This study investigates the intermodel diversity in the longitudinal location of the simulated summer EAJ climatology in the present-day climate and its implications for rainfall over East Asia based on 20 CMIP5 models. The results show that the zonal location of the simulated EAJ core is located over either the midlatitude Asian continent or the western North Pacific(WNP) in different models. The zonal shift of the EAJ core depicts a major intermodel diversity of the simulated EAJ climatology. The westward retreat of the EAJ core is related to a warmer mid–upper tropospheric temperature in the midlatitudes, with a southwest–northeast tilt extending from Southwest Asia to Northeast Asia and the northern North Pacific, induced partially by the simulated stronger rainfall climatology over South Asia. The zonal shift of the EAJ core has some implications for the summer rainfall climatology, with stronger rainfall over the East Asian continent and weaker rainfall over the subtropical WNP in relation to the westward-located EAJ core.

Simulations of the East Asian Subtropical Westerly Jet by LASG/IAP AGCMs

Performances of two LASG/IAP （State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics/Institute of Atmospheric Physics） Atmospheric General Circulation Models （AGCMs）, namely GAMIL and SAMIL, in simulating the major characteristics of the East Asian subtropical westerly jet （EASWJ） in the upper troposphere are examined in this paper. The mean vertical and horizontal structures and the correspondence of the EASWJ location to the meridional temperature gradient in the upper troposphere are well simulated by two models. However, both models underestimate the EASWJ intensity in winter and summer, and are unable to simulate the bimodal distribution of the major EASWJ centers in mid-summer, relative to the observation, especially for the SAMIL model. The biases in the simulated EASWJ intensity are found to be associated with the biases of the meridional temperature gradients in the troposphere, and furthermore with the surface sensible heat flux and condensation latent heating. The models capture the major characteristics of the seasonal evolution of the diabatic heating rate averaged between 30°-45°N, and its association with the westerly jet. However, the simulated maximum diabatic heating rate in summer is located westward in comparison with the observed position, with a relatively strong diabatic heating intensity, especially in GAMIL. The biases in simulating the diabatic heating fields lead to the biases in simulating the temperature distribution in the upper troposphere, which may further affect the EASWJ simulations. Therefore, it is necessary to improve the simulation of the meridional temperature gradient as well as the diabatic heating field in the troposphere for the improvement of the EASWJ simulation by GAMIL and SAMIL models.

Relationship between Meridional Displacement of the Monthly East Asian Jet Stream in the Summer and Sea Surface Temperature in the Tropical Central and Eastern Pacific

Previous studies have shown that meridional displacement of the East Asian upper-tropospheric jet stream (EAJS) dominates interannual variability of the EAJS in the summer months.This study investigates the tropical Pacific sea surface temperature (SST) anomalies associated with meridional displacement of the monthly EAJS during the summer.The meridional displacement of the EAJS in June is significantly associated with the tropical central Pacific SST anomaly in the winter of previous years,while displacements in July and August are related to tropical eastern Pacific SST anomalies in the late spring and concurrent summer.The EAJS tends to shift southward in the following June (July and August) corresponding to a warm SST anomaly in the central (eastern) Pacific in the winter (late spring-summer).The westerly anomaly south of the Asian jet stream is a result of tropical central Pacific warm SST anomaly-related warming in the tropical troposphere,which is proposed as a possible reason for southward displacement of the EAJS in June.The late spring-summer warm SST anomaly in the tropical eastern Pacific,however,may be linked to southward displacement of the EAJS in July and August through a meridional teleconnection over the western North Pacific (WNP) and East Asia.

An Assessment of the Predictability of the East Asian Subtropical Westerly Jet Based on TIGGE Data

The predictability of the position,spatial coverage and intensity of the East Asian subtropical westerly jet （EASWJ） in the summers of 2010 to 2012 was examined for ensemble prediction systems （EPSs） from four representative TIGGE centers,including the ECMWF,the NCEP,the CMA,and the JMA.Results showed that each EPS predicted all EASWJ properties well,while the levels of skill of all EPSs declined as the lead time extended.Overall,improvements from the control to the ensemble mean forecasts for predicting the EASWJ were apparent.For the deterministic forecasts of all EPSs,the prediction of the average axis was better than the prediction of the spatial coverage and intensity of the EASWJ.ECMWF performed best,with a lead of approximately 0.5-1 day in predictability over the second-best EPS for all EASWJ properties throughout the forecast range.For probabilistic forecasts,differences in skills among the different EPSs were more evident in the earlier part of the forecast for the EASWJ axis and spatial coverage,while they departed obviously throughout the forecast range for the intensity.ECMWF led JMA by about 0.5-1 day for the EASWJ axis,and by about 1-2 days for the spatial coverage and intensity at almost all lead times.The largest lead of ECMWF over the relatively worse EPSs,such as NCEP and CMA,was approximately 3-4 days for all EASWJ properties.In summary,ECMWF showed the highest level of skill for predicting the EASWJ,followed by JMA.

The Relationship between the East Asian Subtropical Westerly Jet and Summer Precipitation over East Asia as Simulated by the IAP AGCM4.0

Based on a 30-year Atmospheric Model Intercomparison Project(AMIP) simulation using IAP AGCM4.0, the relationship between the East Asian subtropical westerly jet(EASWJ) and summer precipitation over East Asia has been investigated, and compared with observation. It was found the meridional displacement of the EASWJ has a closer relationship with the precipitation over East Asia both from model simulation and observation, with an anomalous southward shift of EASWJ being conducive to rainfall over the Yangtze-Huaihe River Valley(YHRV), and an anomalous northward shift resulting in less rainfall over the YHRV. However, the simulated precipitation anomalies were found to be weaker than observed from the composite analysis, and this would be related to the weakly reproduced mid-upper-level convergence in the mid-high latitudes and ascending motion in the lower latitudes.

Improvement of the simulation of the summer East Asian westerly jet from CMIP5 to CMIP6

The East Asian westerly jet(EAJ)plays a crucial role in affecting the East Asian summer rainfall(EASR).Therefore,evaluations of EAJ simulations are vital for improving the understanding and projections of climate change in East Asia.This study evaluates the simulations of the climatology and interannual variability in the present-day summer EAJ in the CMIP6 models and compares the results with those in the CMIP5 models by analyzing the historical climate simulations of 29 CMIP5 models and 21 CMIP6 models during the period from 1986–2005.In general,the CMIP6 models capture the EAJ more realistically than the CMIP5 models.The results show that the CMIP6 models reasonably capture the spatial features of the climatological zonal wind at 200 hPa and simulate a smaller zonal wind bias along the EAJ.The locations of the EAJ’s core are at the observed location in nearly all CMIP6 models but in only approximately two-thirds of the CMIP5 models.The EAJ’s intensity is closer to the observed value and exhibits a smaller intermodel dispersion in the CMIP6 models.The CMIP6 models also show an improved ability to reproduce the interannual variability in the EAJ’s meridional displacement and have a stronger relationship with the EASR.

Simulation of the East Asian Subtropical Westerly Jet Stream with GFDL AGCM (AM2.1)

The present study validated the capability of the AM2.1,a model developed at NOAA's Geophysical Fluid Dynamics Laboratory (GFDL),in reproducing the fundamental features of the East Asian Subtropical Westerly Jet Stream (EASWJ).The main behaviors of the EASWJ are also investigated through the reanalysis of observational NCEP/NCAR data.The mean state of the EASWJ,including its intensity,location,structure,and seasonal evolution is generally well-portrayed in the model.Compared with the observation,the model tends to reproduce a weaker jet center.And,during summer,the simulated jet center is northward-situated.Results also demonstrate the model captures the variability of EASWJ during summer well.The results of the empirical orthogonal function (EOF) applied on the zonal wind at 200 hPa (U200) over East Asia for both the observation and simulation indicate an inter-decadal shift around the late 1970s.The correlation coefficient between the corresponding principle components is as great as 0.42 with significance at the 99% confidence level.

Responses of the East Asian Jet Stream to the North Pacific Subtropical Front in Spring

This study concerns atmospheric responses to the North Pacific subtropical front （NPSTF） in boreal spring over the period 1982-2014. Statistical results show that a strong NPSTF in spring can significantly enhance the East Asian jet stream （EAJS）. Both transient eddy activity and the atmospheric heat source play important roles in this process. The enhanced atmospheric temperature gradient due to a strong NPSTF increases atmospheric baroclinicity, resulting in an intensification of transient eddy and convection activities. On the one hand, the enhanced transient eddy activities can excite an anomalous cyclonic circulation with a quasi-baraotropical structure in the troposphere to the north of the NPSTF. Accordingly, the related westerly wind anomalies around 30°N can intensify the component of the EAJS over the Northeast Pacific. On the other hand, an enhanced atmospheric heat source over the NPSTF, which is related to increased rainfall, acts to excite an anomalous cyclonic circulation system in the troposphere to the northwest of the NPSTF, which can explain the enhanced component of the EAJS over the Northwest Pacific. The two mechanisms may combine to enhance the EAJS.

Different Configurations of Interannual Variability of the Western North Pacific Subtropical High and East Asian Westerly Jet in Summer

This study investigates the circulation and precipitation anomalies associated with different configurations of the western North Pacific subtropical high(WNPSH)and the East Asian westerly jet(EAJ)in summer on interannual timescales.The in-phase configuration of the WNPSH and EAJ is characterized by the westward(eastward)extension of the WNPSH and the southward(northward)shift of the EAJ,which is consistent with the general correspondence between their variations.The out-of-phase configuration includes the residual cases.We find that the in-phase configuration manifests itself as a typical meridional teleconnection.For instance,there is an anticyclonic(cyclonic)anomaly over the tropical western North Pacific and a cyclonic(anticyclonic)anomaly over the mid-latitudes of East Asia in the lower troposphere.These circulation anomalies are more conducive to rainfall anomalies over the Yangtze River basin and south Japan than are the individual WNPSH or EAJ.By contrast,for the out-of-phase configuration,the mid-latitude cyclonic(anticyclonic)anomaly is absent,and the lower-tropospheric circulation anomalies feature an anticyclonic(cyclonic)anomaly with a large meridional extension.Correspondingly,significant rainfall anomalies move northward to North China and the northern Korean Peninsula.Further results indicate that the out-of-phase configuration is associated with the developing phase of ENSO,with strong and significant sea surface temperature(SST)anomalies in the tropical central and eastern Pacific which occur simultaneously during summer and persist into the following winter.This is sharply different from the in-phase configuration,for which the tropical SSTs are not a necessity.

THE FEATURES OF EAST ASIAN JET STREAM IN PERSISTENT SNOWSTORM AND FREEZING RAIN PROCESSES OVER SOUTHERN CHINA IN EARLY 2008

Based on the National Centers for Environmental Prediction and National Center for Atmospheric Research(NCEP/NCAR) daily reanalysis data and the upper-level objective analysis data provided by the Meteorological Information Comprehensive Analysis and Process System(MICAPS),the feature of the spatio-temporal variation of the East Asian jet stream(EAJS) in persistent snowstorm and freezing rain processes over southern China in January 2008 have been investigated.Each of the storm events was closely linked with the extraordinarily abnormal variations of East Asian subtropical jet(EASJ) and East Asian polar front jet(EAPJ) at that time.The stronger EASJ with abnormally northward position of the jet axis corresponded to the more intense storm event with broader ranges and longer duration time.The heavy freezing-rain-and-snow event occurred over the region where a strong southerly wind of EASJ prevailed.Meanwhile,the westerly and northerly winds of the EAPJ were significantly intensified,which were also closely related to the beginning,enhancement,and ending of the heavy snowfall.The meridional component of the EAPJ was dominated by the northerly wind during the snowstorm.Thus,the intensification of the snowstorm was attributed to both the strengthening of the meridional wind of EAPJ and the southerly wind of EASJ.Further analysis indicated that wind speed and the zonal wind of the two jets exhibited precursory signals about half a month prior to this extreme event,and the precursory signals were found in the meridional components of the two jets about 20 days preceding the event.The sudden weakening of the meridional component of EASJ and the zonal component of EAPJ signified the ending of this persistent snowstorm.

VARIATION OF THE EAST ASIAN SUBTROPICAL WESTERLY JET AND ASSOCIATED QUANTIFIED OBJECTIVE INDEXES

In order to understand the role of East Asian subtropical westerly jet (EASWJ) in forecasting summer precipitation in East China,interseasonal pentad characteristics of the EASWJ and their relation to summer precipitation in East China are analyzed with the daily reanalysis data provided by National Centers for Environmental Prediction (NCEP,USA) and daily precipitation data from 714 Chinese meteorological stations during the period 1960-2009.In addition,the daily evolution of the EASWJ and objective quantification of the EASWJ are investigated for the Meiyu season over the middle and lower reaches of the Yangtze River valley.It is found that the EASWJ and summer precipitation bands in East China move simultaneously.Especially,the stationary state and northward shift of the EASWJ are closely associated with the beginning,ending and stabilization of the annually first raining season in South China and Meiyu over these reaches.Analysis on the characteristics of the EASWJ in typical (atypical) Meiyu years over these reaches shows that the EASWJ swings steadily around its climatological position in meridional orientation (with large amplitude).Numerical experiments on an example in 2005 shows that indexes proposed in this study can depict the EASWJ well and should be valuable for application in the operation.