Intensity Evolution of Zonal Shear Line over the Tibetan Plateau in Summer:A Perspective of Divergent and Rotational Kinetic Energies※

Xiaohong BAO and Xiuping YAO

1State Key Laboratory on Severe Weather, Chinese Academy of Meteorological Sciences,Beijing 100081,China

2China Meteorological Administration Training Centre,Beijing 100081,China

ABSTRACT Based on the ERA5 reanalysis datasets during 1980-2019,a total of eleven zonal shear lines (ZSLs) that caused heavy precipitation and lasted more than 60 hours over the Tibetan Plateau in summer are selected for composite analysis.By decomposing the kinetic energy (K) near the ZSL into divergent and rotational kinetic energies (KD and KR) and the kinetic energy of interaction between the divergent wind and the rotational wind (KRD),the influence of the rotational and divergent winds on the evolution of the ZSL intensity is investigated from the perspective of KD and KR.The main results are as follows.The ZSL is a comprehensive reflection of rotation and convergence.The intensity evolution of ZSL is essentially synchronized with those of K,KR,and KRD but lags behind KD by about three hours.The enhancement of K is mainly contributed by KR,which is governed by the conversion from KD to KR.Furthermore,the increase in the conversion from KD to KR is controlled by the geostrophic effect term Af,which is determined by the joint enhancement of the zonal rotational and meridional divergent wind components (uR and vD).Therefore,the joint enhancement of uR and vD controls the increase of the ZSL intensity,leading to increased precipitation.

Key words:zonal shear line over the Tibetan Plateau,intensity evolution,divergent and rotational kinetic energies,joint action of the zonal rotational and meridional divergent wind components

1.Introduction

As a plateau with the highest elevation in the world and the largest area in the Northern Hemisphere,the Tibetan Plateau (TP) has an average elevation of more than 4000 m and accounts for one-quarter of China's land area.It has unique weather and climate characteristics that significantly affect the atmospheric circulation,weather,and climate in China,Asia,and globally.Therefore,TP meteorology,which focuses on its dynamic and thermal forcing,was recognized early by researchers and has since become an important research field in weather and climate (Bolin,1950;Flohn,1957;Wu et al.,2004).

Under the unique dynamic and thermal effects of the TP,two types of typical cyclonic circulation systems with low-geopotential-height structures are isolated and named the plateau shear line and the plateau vortex.Both are formed in the near-surface layer over the TP.Research has shown that the occurrence frequency of plateau shear lines and the frequency of shear line-induced precipitation are greater than those of plateau vortexes (The Tibetan Plateau Science Research Group,1981;He et al.,2009).Furthermore,the plateau shear lines can be categorized into the zonal shear lines with a quasi-east-west orientation and the meridional shear lines with a quasi-south-north orientation.Comparatively,zonal shear lines occur more often and have a longer duration;moreover,they experience greater difficulty to propagating out of the TP and thereby more likely to cause potential disastrous heavy precipitation over the TP(Ye and Gao,1979;Tao et al.,1984;Zhang et al.,2016;Zhang et al.,2019;Yao et al.,2020).Statistics have shown that during the boreal summer half-year over the TP,more than 50% of zonal shear lines caused heavy precipitation,and about 40% of heavy precipitation days are related to zonal shear lines (Zhang et al.,2016).Therefore,the zonal shear line (ZSL) over the TP in summer is one of the essential factors accounting for the occurrence of disastrous weather over the TP (Note:ZSL mentioned in this research all refers to ZSL over the TP in summer),and the study on the ZSL evolution is of great significance to the forecasting and early-warning of disastrous weather.

Key to this complex research,it is generally accepted that the evolution of ZSLs is mainly driven by the dynamic and thermal effects of the TP (The Tibetan Plateau Science Research Group,1981;Ye,1981;Tao,1980) and is subject to large-scale circulation systems such as the western Pacific subtropical high (The Tibetan Plateau Science Research Group,1981),the Iran high (Tang,2002) and the South Asia high (Shi and He,2011).Many diagnostic analyses on ZSL evolution have been carried out.The results show that the formation,development,and maintenance of the ZSL are closely associated with the development of various factors,including the large-scale ascending motion at 500 hPa (Yu,1994),the local vorticity center or vorticity zone (Tu and He,2010),the generalized moist potential vorticity center (Chen and Li,2018),the apparent heat source and apparent moisture sink (Zhao and Yao,2018),etc.In addition,some scholars have obtained significant results from the perspective of kinetic energy for individual cases.For example,the main energy source during the processes of ZSL evolution is the transformation from available potential energy into kinetic energy (Yu and Luo,1993).The conversion from eddy available potential energy to eddy kinetic energy (Luo and Li,2019a) and the downscaled energy cascade of kinetic energy caused by the interaction between the background circulation and eddy field are conducive to the formation and development of ZSLs (Luo and Li,2019b).

The ZSL is a discontinuous line in the cyclonic rotational wind field in the near-surface layer over the TP (Tao,1980),featured by mid-tropospheric cyclonic rotation and horizontal wind field convergence.In addition,both the convergence (Fu et al.,2011;Zhou et al.,2014) and the rotation (Zhao et al.,2009;Fu et al.,2013;Li et al.,2019;Jin et al.,2020) of the wind field play essential roles in the development of weather systems.So,what are the respective effects of the divergent and rotational winds on the evolution of ZSLs? Research into this problem will help further promote the understanding of why ZSLs evolve.However,it is difficult to study the ZSL evolution using only the rotational and divergent winds by themselves.It is well known that kinetic energy plays a vital role in the evolution of weather systems and is directly related to the wind field.Therefore,it is helpful to study the problem mentioned above from the perspective of kinetic energy.

According to the Helmholtz theorem,the horizontal velocity can be uniquely decomposed into the rotational and divergent winds (Hawkins and Rosenthal,1965),and correspondingly,the kinetic energy can be decomposed,in a similar manner,into its divergent and rotational kinetic energies and the kinetic energy of interaction between the divergent wind and the rotational wind.On this basis,numerous investigations have been conducted on weather systems from the perspective of divergent and rotational kinetic energies,such as tropical cyclones (Ding and Liu,1986;Yu et al.,1999a,b;Zhao et al.,2009),extratropical cyclones (Pearce,1974;Chen et al.,1978;Li et al.,2019;Jin et al.,2020),mesoscale convective complexes in North America (Fuelberg and Browning,1983;Buechler and Fuelberg,1986),circulation systems during the mei-yu periods (Fu et al.,2013) and the northeast cold vortex (Deng et al.,2012).The results revealed that the enhancement of weather systems is mainly caused by the increase in the rotational kinetic energy in the lower troposphere (Zhao et al.,2009;Fu et al.,2013;Li et al.,2019;Jin et al.,2020).Although the divergent kinetic energy is usually less than 10% of the kinetic energy(Pearce,1974;Ding and Liu,1986),it is critical to the generation and conversion of kinetic energy (Fuelberg and Browning,1983;Buechler and Fuelberg,1986).However,there is no precedent to investigate the ZSL evolution through the perspective of divergent and rotational kinetic energies,although great achievements have been made in studying the evolution of many other weather systems through this theorem.

Therefore,it is of great significance to study the influence of the rotational and divergent winds on the evolution of the ZSL intensity from the perspective of the rotational and divergent kinetic energies,which provides a new point of view and insight for the in-depth understanding of the ZSL evolution.

The remainder of this paper is organized as follows.Section 2 introduces the data and methods.Section 3 provides the relationship of the ZSL intensity evolution with the rotational and divergent kinetic energies.Section 4 illustrates the mechanisms for the ZSL intensity evolution.Finally,section 5 presents the main conclusions and final discussion.

2.Data and Methods

2.1.Data

The data adopted in this study includes two datasets (1)the hourly wind dataset with a horizontal resolution of 1°×1° from June to August during 1980-2019 derived from the ERA5 reanalysis dataset and (2) the daily precipitation data (1200 UTC-1200 UTC) over the same period from the daily dataset of basic meteorological elements of China’s National Surface Weather Station (version 3.0) released by the National Meteorological Information Centre of China Meteorological Administration.

2.2.Methods

2.2.1.Case selecting for composite analysis of ZSLs

Based on the wind data from the ERA5 reanalysis dataset at 500 hPa from June to August during 1980-2019,the ZSLs are identified by an objective method with three parameters:the zonal shear of the meridional wind,the relative vorticity,and the zero line of meridional wind (Ma and Yao,2015;Zhang et al.,2016).The specific criteria are as follows.

whereuis the zonal wind component,yindicates the meridional coordinate,ζis the vertical component of the relative vorticity.When the three criteria in Eq.(1) are met at each grid point,the line connecting these grids,with a zonal span of more than 5 degrees of longitude,is identified as a ZSL.

Subsequently,in the high-frequency area of ZSLs(32°-35°N),which is located in a region with an altitude of more than 3000 m over the TP,the ZSLs with a lifetime longer than 24 hours are selected to form a dataset of ZSL cases.Furthermore,based on the daily precipitation data mentioned above,the ZSL case that causes heavy precipitation is defined by following these steps:

(1) The precipitation averaged at all stations on a certain day near each ZSL case (30°-36°N) in the dataset is defined as the average precipitation of that day (xi,i=1,n.nindicates the total ZSL days in the dataset).

(2) The average daily precipitation for all cases and their standard deviation are expressed as:

(3) If thexiin a certain ZSL at any time over the course of its lifetime is oneσgreater than,then this case is defined as a ZSL case that caused heavy precipitation.

Consequently,11 typical cases that caused heavy precipitation and have a similar lifetime of more than 60 hours are selected from the above cases (Table 1).The distribution of the lifetime-averaged ZSLs from the 11 cases is shown in Fig.1a.

Table 1.Elevent typical cases of zonal shear lines (ZSLs) over the Tibetan Plateau (TP) in summer (Note:ZSL mentioned in this research all refers to ZSL over the TP in summer.The avereage precipitation at all stations of each ZSL process near each ZSL case(30°-36°N) is defined as the accumulated precipitation.The LST represents the local solar time,which is six hours ahead of the coordinated universal time (UTC),that is,LST=UTC+6 h,the same below.).

Finally,the arithmetic average method is performed on each physical quantity of all typical cases at individual moments,with the intent of obtaining a composite ZSL for subsequent diagnostic analysis.The composite ZSL has a life-time of 72 hours (1300 LST 1st-1200 LST 4th,short for 1300 LST on the 1st day to 1200 LST on the 4th day,the same below).Here,the LST represents the local solar time,six hours ahead of the coordinated universal time (UTC),LST=UTC+6 h.It is important to note that the ZSL mentioned in the section below all refer to the composite ZSL from the 11 typical cases.

Fig.1.(a) The distribution of 11 typical cases of lifetime-averaged ZSLs at 500 hPa (color contours),(b) The synthetic precipitation near the ZSL during its whole lifetime,the three stages,namely 1800 LST 1st-1800 LST 2nd,1800 LST 2nd -1800 LST 3rd,and 1800 LST 3rd -1800 LST 4th (units:mm d-1).The solid gray line outlines the region with an altitude of 3000 m,which indicates the major body of the TP (the same below).

Given that the starting time of the ZSL is close to the starting time of the 24-hour accumulated precipitation,the precipitation near the ZSL during its whole lifetime is represented by the precipitation of the three stages,namely 1800 LST 1st-1800 LST 2nd,1800 LST 2nd -1800 LST 3rd,and 1800 LST 3rd -1800 LST 4th (Fig.1b).

2.2.2.Stages of intensity evolution processes of ZSL

The arithmetic average method is performed on the ZSL over the course of its lifetime.Considering the high-frequency region for the ZSL’s occurrence (Zhang et al.,2016)and the large-value region of theζ(greater than 2×10-5s-1),the region of 32°-35°N,81°-99°E is selected as the study area,as shown in the red dashed box in Fig.2a.The ZSL represents a unique weather system in the boundary layer over the TP,generally referring to a 500-hPa convergence line with opposite wind directions at more than three stations(The Tibetan Plateau Science Research Group,1981).Therefore,the ZSL intensity is expressed by the regional-averagedζin the study area at 500 hPa.According to the ZSL intensity evolution (Fig.4),the evolutionary processes are divided into the development stage (1300 LST 1st-1200 LST 2nd),the vigorous stage (1300 LST 2nd -1200 LST 3rd),and the decay stage (1300 LST 3rd -1200 LST 4th).The mean values of the physical quantities at each stage represent the environment of the ZSL evolution at each stage.There is an enhancement of the ZSL from the development stage to the vigorous stage and a weakening from the vigorous stage to the decay stage.The evolution of ZSL intensity is essentially synchronized with that of precipitation related to the ZSL (Fig.1b).Note that the thermal effects of the TP exhibit significant diurnal variations,but this is not the focus of this study.To remove the influence of the diurnal variation on the ZSL evolution,the same start and end times are set for each stage to maintain consistency regarding the effect of diurnal variations.

2.2.3.Divergent and rotational kinetic energies

Based on the hourly wind dataset mentioned above,an iterative method (Endlich,1967) with high computational efficiency and high accuracy is used to decompose the original horizontal wind (V) into the rotational wind (VR) and the divergent wind (VR):

The bias for the divergence at each grid is less than or equal to 1×10-8s-1during the iterative process,which is less than or equal to 0.1% of the maximum divergence of the original horizontal wind field.The formulas for divergent and rotational kinetic energies are as follows.

Fig.2.(a) 500-hPa wind field (V) (black wind vectors;units:m s-1) and the vertical component of the relative vorticity (ζ)(＞0,shading;units:10-5 s-1),(b) 500-hPa rotational wind (VR)and its specific value (black wind vectors and shading;units:m s-1) and (c) 500-hPa convergent wind (VR) and its specific value (black wind vectors and shading;units:m s-1) averaged in the whole lifetime of the ZSL.The black dashed box represents the study area (32°-35°N,81°-99°E),and the black thick solid line denotes the lifetime-averaged ZSL (the same below).

The kinetic energy per unit mass is expressed as:

where

The kinetic energy of an atmospheric volume in isobaric coordinates (Ais the horizontal computational area)is given by:

where

Kis the kinetic energy in a limited area (hereafter referred to as kinetic energy),KRis the rotational kinetic energy,KDthe divergent kinetic energy,andKRDis the kinetic energy of the interaction between the divergent wind and the rotational wind.Note that the sign ofKRDdepends on the divergent and rotational wind directions.

The equation for rotational kinetic energy (Buechler and Fuelberg,1986) is expressed as follows.

Here,uRanduDare the zonal rotational and divergent wind components,vRandvDare the meridional rotational and divergent wind components,ωis the vertical velocity(Pa s-1),fis the Coriolis parameter,φis the geopotential,andFis the frictional force.

For Eq.(8),the sum of Af,Az,B,andCis hereafter denoted asC(KD,KR).Therefore,Eq.(8) can be simplified as DKR=IR+C(KD,KR)+GR+HFR+FR.The term on the left-hand side,DKR,is the change term ofKRand denotes the local change ofKR.The termIRis the change ofKRcaused by the nonlinear interaction between the rotational wind and divergent wind.The termC(KD,KR) is a conversion term betweenKDandKR,including four terms of Af,Az,B,andC,aC(KD,KR) greater than zero indicates a conversion fromKDtoKR.The term Af is the geostrophic effect term.Both terms Af and Az are affected by relative orientations and magnitudes ofVRandVD.Term B describes the vertical exchange ofKR,while termCis related to the configuration ofVDwithVDand the vertical distribution ofVD.TermGRis the generation term forKR,indicating the conversion betweenKRand the available potential energy due to the cross-contour flow ofVR.The term HFRdenotes the horizontal flux divergence ofKbyVR.The term FRrepresents friction and is related to the rotational wind,denoting frictional processes and the energy transfer between resolvable and unresolvable scales of motion.As it is calculated as the residual,possible errors from other terms are also included in Eq.(8).

3.Relationship of the ZSL intensity evolution with the divergent and rotational kinetic energies

Previous studies have revealed that the ZSL is mainly located below 400 hPa (Tao,1984),indicating a relatively shallow system.Therefore,this study mainly targets levels below 400 hPa.

3.1.Distribution Characteristics of the divergent and rotational winds

Figures 2b-c illustrate thatVat 500 hPa is well-decomposed intoVRandVD.The magnitude and distribution ofVRare similar to those ofV,while the magnitude ofVDis obviously smaller than that ofV(Fig.2a).Moreover,the wind speeds ofVRandVDtend to be small near the ZSL but are larger on the north and south sides,in the vicinity of ZSL,especially on the south side.A cyclonic circulation ofVRand the convergence ofVDappears near the ZSL.In addition,the circulation center ofVRis located on the ZSL,but the strongest convergence appears on the south side of the ZSL.

In summary,there are cyclonicVRand convergentVDnear the ZSL,and the magnitude ofVRis larger than that ofVD.

3.2.Spatial evolution characteristics of the kinetic energy and its components

Figure 3 shows that during the entire lifetime of the ZSL at 500 hPa,K,KR,KD,the absolute value ofKRDare smaller near the ZSL but larger on its north and south sides,especially in the southeast quadrant of the ZSL.The distribution characteristics of these physical quantities depend on the distribution of the horizontal wind field,as shown in Fig.2.Specifically,there is a dense zone ofKcontours in the southeast quadrant of the study area at the development stage,and the maximumKreaches 25 J m-2at this stage(Fig.3a).In the vigorous stage (Fig.3b),Kincreases throughout the entire study area,and the maximum value increases to 35 J m-2.In addition,the increase in the gradient ofKin the southeast quadrant of the study area is especially significant.Figure 3c shows thatKdecreases throughout the entire study area in the decay stage,noting that the gradient ofKin the southeast quadrant decreases significantly,with the maximumKdropping down to 30 J m-2.The change of gradient ofKnear the ZSL is basically consistent with the ZSL intensity evolution,which agrees with the results in Luo and Li (2019a).The evolution ofKR(Figs.3a1-c1) andKD(Figs.3a2-c2) near the ZSL are similar to that ofKbut numerically smaller.TheKRDshows uneven distributions (Figs.3a3-c3),with positive (negative) values in the western (eastern) part of the study area,but its absolute values also increase (decrease) with the development(decay) of the ZSL.The evolution trend of the kinetic energy and its components in the vertical direction is similar to that in the horizontal direction (figure omitted).

Fig.3.(a-c) The kinetic energy (K),(d-f) the rotational kinetic energy (KR),(g-i) the divergent kinetic energy(KD),and (j-l) the kinetic energy for the interaction between the divergent wind and the rotational wind (KRD)at 500 hPa (contours,units:J m-2) averaged at different stages of the ZSL.(a,d,g,j) denote the development stage,(b,e,h,k) the vigorous stage,and (c,f,i,l) the decay stage.

3.3.Response of the kinetic energy and its components to the evolution of the ZSL intensity

The above analysis is based on the mean ZSL averaged at each stage,through which how much time the response ofKand its components (KR,KD,KRD) to the evolution of the ZSL intensity takes cannot be determined.As mentioned above,the 500 hPa relative vorticityζrepresents the ZSL intensity.Therefore,the following section compares the regional-averaged hourlyK,KR,KD,andKRDwithζat 500 hPa to investigate the response relationship ofK,KR,KD,andKRDwith the evolution of the ZSL intensity.

As revealed by Deng et al.(2012),Fig.4 also shows that the variations ofK,KR,andζare generally synchronous,all with three obvious peaks.The peak values ofK,KR,andζin the three stages generally appear at 0000 LST of each day,with the maximums occurring at the vigorous stage,followed by the development stage.The minimums occur in the decay stage.The divergent kinetic energyKDalso exhibits three peaks simultaneous to whenζhas the most significant positive change at each stage of the ZSL evolution,i.e.,when the ZSL develops most rapidly at each stage.The peak value ofKDis largest in the development stage,slightly smaller in the vigorous stage,and rapidly decreases in the decay stage.Note that the variation ofKDoccurs roughly three hours earlier than that ofζ.One possible reason why the kinetic energy of divergent wind increases earlier than that of rotational wind is that the upper-level divergence and the low-level convergence produce ascending motion,precipitation,and consequent latent heat release,which leads to strengthened rotation.The reason for the three-hour delay may be attributed to the accuracy of the ERA5 reanalysis dataset.In addition,the evolution ofKRDis essentially consistent with that ofζ.However,due to the opposite signs ofKRDin the eastern and western parts of the ZSL (figure omitted),the hourly evolutionary characteristics of the regional-averagedKRDare weaker than those ofK,KR,andKD,as shown in Fig.4.

In summary,the evolution of the ZSL intensity is related toK,KR,KD,andKRD.The ZSL intensity enhances(weakens) whenK,KR,KD,and the absolute value ofKRDincrease (decrease),which leads to increased (decreased) precipitation.Particularly,the evolution ofKandKRare basically synchronous with the ZSL intensity,and the variation ofKDis about three hours earlier than that of the ZSL intensity.

4.Evolutionary mechanisms of the ZSL intensity

It can be seen from the above analysis that the evolution ofKandKRare basically synchronous with the ZSL intensity,and the variations inKDoccur about three hours earlier than that of the ZSL intensity.Therefore,it is reasonable to explore the evolution mechanism of the ZSL intensity by discussing the evolution ofKand its components.

4.1.Preliminary analysis of the effect of divergent and rotational winds on the kinetic energy

The preliminary analysis of the effects ofVDandVRonKwill be discussed through the relative contributions ofKR,KD,andKRDtoK,

Table 2 reveals thatK,KR,KD,andKRDincrease(decrease) with the development (decay) of the ZSL,which agrees with previous conclusions.For the entire lifetime-averaged ZSL,Kreaches 13.6 ×103J m-2,whereKRmakes the largest contribution,accounting for 79.1%,followed byKD(14.9%) and the smallest byKRD(only 5.9%).Noting that although the relative contributions ofKR,KD,andKRDtoKvary during different stages of the ZSL evolution,KRalways contributes the most (above 76%) at each stage,followed byKD(more than 11%) and the smallest byKRD(about 6%).

Fig.4.Evolution of ζ (solid red lines;units:10-5 s-1),K (black hollow lines;units:J m-2),KR (hollow blue lines;units:J m-2),KD (hollow purple lines;units:J m-2) and KRD (hollow green line;units:J m-2) averaged in the study area near the ZSL at 500 hPa.The black coordinate axis is for K,the purple coordinate axis for KD,the blue coordinate axis for KR,the green coordinate axis for KRD,and the red coordinate axis for ζ.

Table 2.Area-time averaged vertical integrals of K,KR,KD, and KRD from the surface up to 450 hPa (units:103 J m-2).

During the evolutionary processes ofK,KRis much larger thanKDandKRD,and it contributes the most toK,accounting for about 79%,followed byKD(about 15%) and the smallest byKRD(only about 6%).Therefore,KRplays a leading role in the evolutionary process ofK,while the effects ofKDandKRDare rather small.

4.2.Influence factors of the rotational kinetic energy

The rotational kinetic energyKR,which contributes the most toK,is far greater thanKDandKRD.Besides,the intensity evolution trend ofKandKRat 500 hPa is consistent with its evolution in the layer near the ZSL.Hence,the source ofKRat 500 hPa is investigated to reveal factors that trigger the evolution ofK,with the intent of exploring the evolutionary mechanism of the ZSL intensity.

4.2.1.Generation and transportation of the rotational kinetic energy

At 500 hPa,the term DKRin the development stage is only positive in the eastern part of the study area (Figs.5a-c),and this positive-value area generally extends to the entire study area in the vigorous stage.In contrast,the entire study area is basically dominated by negative values in the decay stage.This indicates that the termKRincreases(decreases) with the strengthening (weakening) of the ZSL intensity,consistent with the results discussed above.In Figs.5a1-c1,the termGRis negative as the work done by the pressure gradient force consumesKRat 500 hPa around 85°-90°E near the ZSL (figure omitted).While in the eastern and western parts near the ZSL,the pressure gradient force does positive work to produceKR(figure omitted),which induces positiveGR(Figs.5a1-c1).For the term HFR,the southwardVRon the south side of the ZSL transportsKto the vicinity of the ZSL (Figs.2a-c and Figs.4a-c),mainly causing positive HFRnear the ZSL (Figs.5a3-a3).However,on the north side of the ZSL,the term HFRpresents an alternative distribution of positive and negative values along the latitudinal direction.Furthermore,the values ofGRand HFRbasically increase (decrease) with the enhancement (decay) of the ZSL intensity.Therefore,from the development stage to the vigorous stage of the ZSL,the termGRin the eastern and western parts of the ZSL and the term HFRin most areas near the ZSL are conducive to the increase ofKR,especially theKRto the south of the ZSL.However,the termsGRand HFRin the abovementioned regions remain positive from the vigorous stage to the decay stage,which is not favorable for the decrease ofKR.

4.2.2.Conversion between the divergent and rotational kinetic energies

Figure 6 shows that the termC(KD,KR) is positive throughout the whole lifetime of the ZSL,with a similar horizontal distribution to those ofK,KR,andKDat 500 hPa.In addition,the values ofC(KD,KR) are significantly larger than those ofGRand HFR(Fig.5),basically above 4×10-4W m-2Pa-1.This indicates a conversion fromKDtoKRthroughout the whole lifetime of the ZSL,and the influence ofC(KD,KR) is more significant than those ofGRand HFRonKR.At the development and vigorous stages,the termC(KD,KR) near the ZSL is positive and increases with the development of the ZSL (same as Table 3),indicating that the term C(KD,KR) is favorable for the increase ofKR.However,the termC(KD,KR) is still positive at the decay stage but smaller than that at the vigorous stage.In addition,the values ofIRare relatively small (figure omitted).Combined with the distributions ofGRand HFR(Fig.5),it can be concluded that the decrease ofKRis mainly caused byFR(figure omitted).

As shown in Table 3,during the evolution process of the ZSL,the four terms inC(KD,KR) are all positive,and the geostrophic effect term Af always contributes the most toC(KD,KR).For the lifetime-averaged ZSL,the contribution rate of Af toC(KD,KR) reaches 59.6%,followed byB(26.4%),while the contributions of Az andCare relatively smaller,being 11.3% and 2.7%,respectively.In addition,the four terms Af,Az,B,andCalso increase (decrease)with the strengthening (weakening) of the ZSL intensity.Therefore,the geostrophic effect term Af among the four terms inC(KD,KR) affectsKRthe most.

Table 3.Same as Table 2,but for C(KD,KR) (units:103 J m-2).

4.2.3.Geostrophic effect

The following discussion will shed light on how Af works.The Coriolis parameterfdoes not change with time,so the evolution of Af is determined by the members in the term -(vRuD-uRvD).It follows:

wheretis time,note thatuRvDand -vRuDhave different effects on Af,as shown below.

It can be seen from Fig.7 that the values ofuRvD(Figs.7a1-c1) and -vRuD(Figs.7a2-c2) are basically positive near the ZSL,and the values ofuRvDare greater than those of -vRuDduring the entire lifetime of the ZSL.In the development stage (Fig.7a1),there is a dense zone of theuRvDvalues to the south of the study area,and the maximumuRvDreaches 10 m2s-2.In the vigorous stage,the values ofuRvD(Fig.7b1) increase rapidly,with the maximumuRvDreaching 20 m2s-2.There is also a significant reduction ofuRvDfrom the vigorous stage to the decay stage,whose magnitude is less than the observed increase from the development stage to the vigorous stage (Figs.7b1-c1).For the values of -vRuD,there is no obvious change from the development stage to the decay stage (Figs.7a2-c2).Thus,the evolution of Af is essentially governed by the values ofuRvD.

Furthermore,the values of bothuRandvDchange with the ZSL intensity evolution.Specifically,both of them increase (decrease) with the developing (decay) of the ZSL intensity (figure omitted).Therefore,the evolution of Af is caused by the joint actions ofuRandvD.

Fig.5.Same as Fig.3,but for (a-c) the local change of KR (DKR),(d-f) the generation term of KR(GR),and (g-i) the horizontal flux divergence of K by VR (HFR)(contours;units:10-4 W m-2 Pa-1).

The mechanism of shear line evolution is summarized as follows.In the vicinity of the ZSL,the terms ofC(KD,KR) near the ZSL,GRin the eastern and western parts,and HFRin most areas are all favorable factors for increasingKR.Specifically,the term C(KD,KR) is far larger thanGRand HFRand thus represents the dominant factor for increasingKR,while the decrease ofKRis mainly caused byFR.The plausible reason for this is that energy transfer between resolvable and unresolvable scales of motion is possible because of the multi-scale ZSL in this study and that the friction near the ground is considerable because of the complex topography of the TP.Furthermore,the most important part of the conversion term is the geostrophic effect term Af,and the joint action ofuRandvDdetermines the evolution of Af.

Fig.6.Same as Fig.3,but for conversion term between KD and KR (C(KD,KR)) (contours;units:10 -4 W m-2 Pa-1).

5.Conclusions and discussion

By using the ERA5 reanalysis dataset and the daily precipitation data from the daily meteorological dataset of basic meteorological elements of China National Surface Weather Station (version 3.0) from June to August during 1980-2019,11 cases of ZSLs that cause heavy precipitation and have a lifetime of more than 60 hours in a high-frequency region for ZSL occurrence (32°-35°N) are selected for composite analysis.By decomposingKinto the terms ofKD,KR,andKRD,the relationship ofKD,KR,andKRDwith the evolution of the ZSL intensity is investigated.In addition,the evolution mechanisms of the ZSL intensity are also preliminarily explored from the perspective ofKDandKR.The main conclusions are as follows.

(1) There are cyclonicVRand convergentVDnear the ZSL,and the magnitude ofVRis generally larger than that ofVD.

(2) The ZSL intensity evolution is basically synchronous with that ofK,KR.,andKRDbut lags behind that ofKDby about three hours.Therefore,the precipitation caused by ZSLs could be predicted by monitoring the evolution ofKD.

(3) During the processes of the ZSL intensity evolution,KRcontributes the most toK,accounting for about 79%,while the effects ofKDandKRDtoKare rather small.

(4) The rotational kinetic energy budget shows that the increase inKRis governed by the conversion fromKDtoKR.Furthermore,the most important part of the conversion term is the geostrophic effect term Af,and the evolution of Af is determined by the joint action of the zonal rotational and meridional divergent wind components.Therefore,the enhancement of the ZSL intensity is mainly controlled by the joint increase of the zonal rotational and meridional divergent wind components.In contrast,the attenuation of the ZSL intensity is primarily attributed to friction and transfers of energy between resolvable and unresolvable scales of motion.

Fig.7.(a1-c1) Same as Fig.3,but for (a1-c1).The values of times zonal rotational wind component times meridional divergent wind component (uRvD) and (a2-b2) the opposite values of zonal divergent wind component times meridional rotational wind component (-vRuD) are shown (contours;units:m2 s-2).

In this research,from a large sample of ZSLs over the TP during a long summertime period,11 typical cases of ZSLs that cause heavy precipitation and maintain for a long time are systematically selected for composite analysis,aiming to overcome the limitations in analysis with individual case and thus get more representative results.From the perspective of the divergent and rotational kinetic energies (KDandKR),the relationship ofKDandKRwith the evolution of the ZSL intensity is obtained,which further improves the understanding of the ZSL evolution.In addition,during the evolutionary process of ZSLs,the source ofKDand the kinetic energy balance betweenKRandKDrequire further study.It should be noted that the results in this study are based on the composite analysis of 11 cases of ZSLs of a specific type,and the evolutionary mechanisms of other types of zonal shear lines over the TP need to be further explored.

Acknowledgements.The authors thank Jiali MA and Qiaohua LIU for their help with this study.This work was supported by the Key Program of the National Science Foundation of China(Grant No.42030611),the Second Tibetan Plateau Scientific Expedition and Research (STEP) program (Grant No.2019QZKK0105),the Integration Project of Major Research Program of the National Natural Science Foundation of China (Grant No.91937301),the General Program of the National Science Foundation of China(Grant No.42175008).

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