Deformation characteristics of the ‘7.20’heavy rainfall event in North China

RAN Lingkun,LI N,b,JIAO Yyin,JIAO Bofeng,nd ZHANG Linn,d

aKey Laboratory of Cloud-Precipitation Physics and Severe Storms,Institute of Atmospheric Physics,Chinese Academy of Sciences,Beijing,China;bPlateau Atmosphere and Environment Key Laboratory of Sichuan Province,Sichuan,China;cHandan Meteorological Bureau,Handan,China;dBeijing Meteorological Bureau,Beijing,China

ABSTRACT A heavy-rainfall event that occurred in North China during 19-20 July 2016,resulting in severeflooding,was investigated in this study.In this event,high-value total deformation overlapped the precipitation region,implying a close relationship between them.By deriving the nongeostrophic ω equation in a non-uniformly saturated moist atmosphere,the relation between vertical velocity and deformation was diagnosed.The Q-vector divergence on the right-hand side of the new ω equation was divided into three compositions,associated with horizontal divergence,vertical vorticity,and horizontal-wind deformation,respectively.It was found that the deformation component of Q-vector divergence contributed most to the negative Q-vector divergence in the precipitation region,implying an important role of deformation forcing in facilitating the vertical motion.In order to track the precipitation on the basis of deformation,potential deformation was proposed by virtue of the generalized potential temperature.The high-value potential deformation and precipitation were always overlapping,and shared an analogous temporal trend.This means that potential deformation can reflect the variation of heavy precipitation to a certain extent,and can serve as a tracker of the precipitation region.

KEYWORDS Deformation;Q-vector;precipitation;ascending motion

1.Introduction

Horizontal velocity can be decomposed into deformation,rotation,and divergence fields(Liu et al.2006).Tao(1953)showed that the upper-level deformation fields are very useful and have a wider range of forecasting possibilities compared to the primary synoptic systems(e.g.cyclones,anticyclones,and others).As an important characteristic of the horizontal wind field,deformation is usually associated with heavy rainfall near fronts due to its important role in enhancing frontogenesis(Han et al.2005;Jiang et al.2011).Gao,Yang,and Xue(2008)derived the tendency equation for deformation and studied the role of deformation on redistributing the moisture.Li et al.(2013)showed the deformation vector had a small angle with the isothermal line for the precipitation that occurred in Beijing on 21 July 2012,and the local frontogenesis process was strongly forced by the deformation field.The calculation of the frontogenesis function also showed that the deformation term had an important contribution to the low-level frontogenesis resulting in the rainstorm.Li et al.(2011)studied a blizzard due to a cold front in Wuhan,and revealed that the elongated axis of deformation and the great-value divergence field were coincident with a cold front,keeping in step with the appearance and ending of the snowfall.Yang(2007)proposed a generalized scalar frontogenesis function(Yang,Gao,and Lu 2014)and an inhomogeneous saturated moist atmospheric frontogenesis function by the local change in the deformation gradient(Yang,Gao,and Lu 2015).The frontogenesis process and dynamic process of torrential rainfall in North China have been investigated-in-detail.-Specifically,-two-heavyprecipitation events in North China were characterized by the dry intrusion and frontogenesis.Jiang,Wang,and Lv(2013)showed that the total deformation near the saddle-shaped expansion shaft was the maximum;its position and stretching axis were basically identical with the rainfall belt,being advantageous to the frontogenesis and the formation of the mesoscale cyclone.Sun and Du(1996)studied the roles of deformation vectors and diverging winds in maintaining fronts and perturbations by computing frontal functions.Wang et al.(2009)observed that the northeastern cold vortex has a mesoscale deformation field structure by using a new generation of weather radar;that is,there is a two-negative and two-positive symmetrical structure of radar velocity.

Theoretical and numerical research of deformation is another interesting subject.Wang and Wu(2000)discussed the development of symmetric baroclinic wave packetswith-the-Wentzel-Kramers-Brillouim-Jeffreys(WKBJ)method.It was found that the development of symmetric disturbance is affected by the large-scale deformation field,frontogenesis circulation,and stability parameters under the conditions of symmetrical stability.Xiao,Wu,and Zhang(1997)established a frontal model,considering the synoptic-scale horizontal deformation field,to study the frontogenesis mechanism of acoldfrontovermountains.Iftherewasnoterraineffect,the front reached a quasi-steady state due to the combination of deformation frontogenesis and friction.Lu and Nong(1995)used a semi-geostrophic model to reveal a phenomenon that two upper-level cold fronts can merge during the migration process under the action ofthedeformation field.ShenandChen(1993)discussed the physical mechanism of frontogenesis with dust radiative forcing,and showed that the diurnal frontogenesis was mainly caused by the diabatic heating and the deformation of horizontal velocity.

In short,the development of high-impact weather,such as heavy rain and severe convection,may be promoted by deformation.On the one hand,deformation of horizontal wind can be converted into vertical vorticity and horizontal divergence to promote an increase in vorticity and divergence that can lead to heavy rain and severe convection indirectly.On the other hand,horizontal wind deformation is the main dynamic cause of frontogenesis.Cold air and warm air stand facing each other near the frontal area.The deformation will strengthen the divergence of cold and warm air flow,which will likely lead to a frontal rainstorm.In addition,the deformation can also result in a change of perturbation pressure,as well as an enhancement of horizontal pressure gradient force and promotion of the development of severe convection and surface wind.

Much effort in previous research has focused on deformation frontogenesis.However,the in fluence of deformation on heavy rainfall,especially on the vertical motion,is still unclear.What role does deformation play in the precipitation process?Can deformation serve as a tool to trace heavy precipitation?Obviously,the deformation that takes place during heavy rainfall should be further investigated.Therefore,this paper focuses on the property of deformation and its extension in a heavy rainfall event in North China during 19-20 July 2016.Q-vector divergence in the moist nongeostrophic Omega equation is used to analyze the forcing of deformation contributing to the vertical motion.Based on the stretch and shear deformation,potential deformation is defined to track and indicate the precipitation region.The heavy rainfall event is introduced in section 2.A modified Q-vector divergence and its diagnosis are presented in section 3.Potential deformation is defined and applied to heavy precipitation in section 4.Conclusions are given in section 5.

2.Overview of the ‘7.20’heavy rainfall event

A continuous torrential rain event occurred in North China during 19-20 July 2016,and led to heavy flooding.The extreme and heavy precipitation lay in the central-southern parts of Hebei Province and Tianjin,with a maximum of 400 mm.The event was characterized by a long duration,wide range,and high intensity.The precipitation spread widely throughout the region of Beijing,Tianjin,Hebei Province,and Shandong Province.The capital,Beijing,was significantly in fluenced by the precipitation,which lasted for about 37 hours.The average accumulated precipitation in downtown Beijing from 0100 UTC 19 July to 14 UTC 20 July 2016 was 169 mm.

The heavy precipitation took place in a favorable large-scale circulation( figure omitted).In the upper level,the heavy precipitation region was located on the right-hand side of the upper-level jet stream entrance at 1800 UTC 19 July 2016,and was matched with the upper-level divergent region.In the middle level,North China was under the control of a low vortex next to the subtropical high.The low vortex moved northeastwards along the edge of the subtropical high.A narrow northeast-southwest-oriented channel appeared between the two systems,transporting warm and moist air flow to the precipitation region.The southwesterly air flow was divided into two branches at the end of the channel near 40°N.One rotated cyclonically and led to significant convergence in the northeastern periphery of the low vortex.The other rotated anticyclonically in the northwestern periphery of the subtropical high.This structure showed obvious characteristics of deformation.In the lower level,the warm and moist southerly air flow transported the water vapor to the precipitation region in North China,which supported the continuity of precipitation.

3.Analysis of vertical motion

In this section,the non-geostrophic ω-equation for a moist atmosphere is derived for analysis of how vertical motion was forced under the weather pattern described above.A non-geostrophic ω-equation with the consideration of diabatic heating in isobaric coordinates is given by

where ω is vertical velocity in the p coordinate,σ =is the static stability parameter,f is the Coriolis parameter,θ =T （ps/p）R/cpis potential temperature,,psis the reference pressure,p is pressure,R is the dry air gas constant,cpis the specific heat at constant pressure,and Q is the so-called Q-vector,which is given by

where qxand qyare the x-component and y-component of the Q vector,u and v are the horizontal wind speed,H=is the diabatic heating,and S=is the diabatic heating rate.The non-geostrophic ωequation and Q-vector are widely used to diagnose the vertical motion in heavy rainfall events and extratropical cyclones.In this equation,the treatment of diabatic heating is an important physical factor that affects vertical motion(Yao,Yu,and Shou 2004).In this paper,we consider it in a nonuniformly saturated atmosphere.Gao,Wang,and Zhou(2004)proposed the generalized potential temperature considering that latent heat is released in a nonuniformly saturated atmosphere,and Cao and Gao(2008)proved its conservation character,

Here,θ*= θexp（ β）is the generalized potential temperature,,T is temperature,qis specificvhumidity,qsis the saturated specific humidity,and k is an empirical constant.According to Equation(5),the diabatic heating can be written as

Substituting the above equation into Equations(3)and(4),one obtains S

ubstituting Equations(7)and(8)into Equation(1),one can obtain the ω-equation with generalized potential temperature,

where σ*=is the static stability parameter composed of the generalized potential temperature(Gao,Wang,and Zhou 2004).The two components of the Q-vector with generalized potential temperature is given by

It is also noted that the right-hand side of the new ωequation includes the divergence of the new version of the Q-vector（（q*x,q*y））,which is obviously different to the previous version （（qx,qy））.It is derived by the generalized potential temperature rather than the potential temperature.

Further,-using-the-horizontal-divergencerelative vertical vorticitystretching deformationand shearing deformationEquations(10)and(11)can be rewritten as

where

Here,Hxand Hyare diabatic heating forcing terms associated with the phase transfer of moisture.Since it is difficult to calculate accurately the local changes in water vapor and its gradients in practice,the last two terms on the right-hand side of Equations(12)and(13)are ignored in the actual diagnostic analysis.This does not imply that the diabatic heating term is unimportant.Then,the ω-equation becomes

It can be seen that the Q-vector divergence in the above equation is composed of the horizontal divergence forcing(the first term on the right-hand side of Equation(18)),the vorticity forcing(the second term on the righthand side of Equation(18)),and the deformation forcing(the third term on the right-hand side of Equation(18)).They represent the in fluences of horizontal divergence,verticalrelativevorticity,andhorizontalwinddeformation on vertical velocity,respectively.

The Q-vector divergence and its three components on the right-hand side of Equation(18)were calculated and analyzed using NCEP GFS analysis data(Figure 1).The dataset includes temperature,specific humidity,geopotential height,wind velocities,and other variables,with a horizontal resolution of 0.5°× 0.5°and 32 vertical pressure levels.

As shown in Figure 1(a),at 1800 UTC 19 July 2016,the precipitation presented a meridional belt covering Hebei,Shandong,and Henan provinces,with a center in the southwest of Hebei Province(approximately(114.5°E,37°N)).The rainfall intensity in the center reached 100 mm/6 h.Corresponding to the center,the vertical ascending motion in the lower level(700 hPa)was obvious,and the maximum ascending speed reached-3 Pa s-1.Since the primary weather system inducing the precipitation was the low vortex,the cyclonic vorticity was strong,with a positive high value on the southeast side of the precipitation center,corresponding to the vertically ascending motion.The convergence region was located on the east side of the precipitation area,which meant that the 700 hPa lowlevel air flow converged there.It is worth noting that high values of deformation covering the precipitation region also overlapped with the precipitation center.The relative spatial configuration of vorticity,divergence,and deformation indicated a close relationship between deformation and precipitation.

The distribution of Q-vector divergence is also shown in Figure 1,with vertical velocity overlapped.As shown in Figure 1(e),it was clear the negative values of Q-vector divergence in the lower troposphere mainly covered the ascending regions （ω ＜ 0）,which verified the role of the new Q-vector on the forcing of vertical motion.The high values of the three components of Q-vector divergence were also confined to the heavy rainfall area,with the deformation component(Figure 1(h)sharing the most similar pattern with the total Q-vector divergence(Figure 1(e)).This means that in the lower-level troposphere,the deformation forcing has an important in fluence on the vertical circulation in the precipitation region.

The above analysis shows the close relationship between the horizontal wind deformation and precipitation.Therefore,can the deformation serve as tracker to indicate the strong precipitation region?To solve this problem,the deformation and generalized potential temperature were used to quantify the physical variable-potential deformation,as reported in the next section.

4.Potential deformation

To extend the application of deformation in precipitation diagnosis and forecasting,the potential stretching deformation(qst)and shearing deformation(qsh)are introduced.They are defined based on the generalized potential vorticity(Gao,Wang,and Zhou 2004),i.e.

Figure 1.The(a)700 hPa vertical velocity(units:Pa s-1;interval:1),(b)horizontal divergence(units:s-1),(c)vertical vorticity(units:s-1),(d)total deformation(units:s-1),(e)Q-vector divergence(units:pa-1s-3;interval:2),(f)vorticity component of Q-vector divergence(units:pa-1s-3;interval:2),(g)divergence component of Q-vector divergence(units:pa-1s-3;interval:2),and(h)deformation component of Q-vector divergence(units:pa-1s-3;interval:2),at 1800 UTC 19 July 2016.The shaded areas in(a-d)denote the observation of 6 h accumulated rainfall(units:mm),and those in(e-h)denote the vertical velocity.

where vr= （-u,v）and vs= （v,u）are transformers of the original wind vector v= （u,v）.These two physical quantities contain the stretching and shear deformations as well as the vertical shear of horizontal wind and the spatial gradient of generalized potential temperature.They are capable of presenting the dynamic and thermal characteristics of the atmosphere synthetically.The potential deformation is further defined as

Its tendency equation is given by

where

are the potential shear deformation and stretching deformation associated with geostrophic wind,respectively.ug=and vg=are the zonal and meridional geostrophicwind,respectively,where ?isthe geopotential height.If the ageostrophic wind is very weak,or the actual wind,the forcing term on the right-hand side of Equation(22)tends to be zero,which indicates the potential deformation is conserved.Therefore,the forcing term presents the in fluence of ageostrophic wind on the change in potential deformation.It can be seen the potential deformation describes the synthetic characteristics of vertical shear,deformation,and the spatial gradient of generalized potential temperature.

The potential deformation and the forcing terms in Equation(22)were calculated using the GFS analysis data.As shown in Figure 2,high values of potential deformation were consistent with the heavy precipitation region,although the centers of potential deformation and precipitation were different in location.This implied a close relationship between potential deformation and precipitation.It is primarily because the potentialstretching-deformation-and-potentialshear deformation include the dynamic and thermodynamic factors,such as vertical wind shear,deformation,and generalized potential temperature,and so on.These factors are critical to promote precipitation.

Figure 2.The 700 hPa potential deformation(contours;units:10-14K m-1s-1;interval:1)at(a)1200 UTC 19 July,(b)1800 UTC 19 July,(c)0000 UTC 20 July,and(d)0600 UTC 20 July 2016,where the shading denotes the observation of 6 h accumulated rainfall(units:mm).

Figure 3.The temporal variations of 700 hPa potential deformation(black lines;units:10-14K m-1s-1)near(a)downtown Beijing,(b)Miyun,and(c)Fangshan,where the red line denotes the observation of 6 h accumulated rainfall(units:mm).

Further analysis(Figure 3)shows that the precipitation of three observation stations(Beijing center,Miyun,and Fangshan)reached their peaks at 0600 UTC 20 July 2016.At the same time,the potential deformation reached its maximum.The precipitation shared an analogous temporal trend with the potential deformation.This means that the potential deformation can reflect the variation of heavy precipitation to a certain extent,and can serve as a tracker to trace the precipitation region.

To examine the generality of the usefulness of potential deformation in indicating precipitation,diagnosis for a different rainfall event was conducted.As shown in Figure 4,this rainfall happened in South China and was induced by the southward movement of a strong shear line( figure omitted).In fluenced by the shear line,the rainfall area presented a northeast-southwest-oriented belt shape.Corresponding to the precipitation belt,potential deformation anomalies mainly appeared over the rainfall area and also displayed a belt shape.This partly hints at the generality of the applicability of potential deformation.Two factorsare consideredtocontribute to this.The first is that potential deformation includes the deformationofthe wind,moistbaroclinicity,vertical wind shear,and moist static stability,which are common characteristics ofheavyprecipitation.The second isdue to the ageostrophic forcing term on the right-hand side of the potential deformation equation.The ageostrophic wind,whichisanecessaryfactorfor theoccurrenceofprecipitation,is usually strong in the precipitation region.Its couplingwiththegeneralizedpotentialtemperatureprompts the development ofpotential vorticity when precipitation occurs( figure omitted).

5.Conclusion

A heavy precipitation event took place in North China during 19-20 July 2016,resulting in severeflooding.Diagnosis showed that the vertical motion was closely related to the lower-level convergence of air flow in the northeast of the lower vortex,cyclonic vorticity,and horizontal-wind deformation.The high values of stretching and shear deformations covered the precipitation region,and overlapped with the ascending and descending motion.This indicated that there was a close relationship between the horizontal wind deformation and precipitation.The Q-vector divergence in the non-geostrophic ωequation for a moist atmosphere was used for analyzing vertical motion.It was composed of the horizontal divergence forcing,vorticity forcing,and deformation forcing.It was shown that the positive Q-vector divergence in the precipitation area primarily resulted from the deformation forcing.Relatively,the deformation forcing was stronger thanthedivergenceforcingandvorticityforcing,andfacilitated the vertical circulation in the precipitation region.

In order to indicate the strong precipitation region,the generalized potential temperature and deformation were used to develop the potential deformation.It was found to becapable of synthetically describing the dynamic and thermodynamic characteristics of vertical shear,deformation,and the spatial gradient of generalized potential temperature.These factors are critical to promote precipitation.So,thehighvaluesofpotential deformation and precipitation are always overlapping,and share an analogous temporal trend.This means that the potential deformation can reflect the variation of heavy precipitation to a certain extent,and can serve as a tracker to trace the precipitation region.

Figure 4.The 700 hPa potential deformation(contours;units:10-14K m-1s-1;interval:1)at(a)1200 UTC 15 June and(b)1800 UTC 15 June 2016,where the shading denotes the observation of 6 h accumulated rainfall(units:mm).

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This study was supported by the Strategic Pilot Science and Technology Special Program of the Chinese Academy of Sciences(XDA17010105),the-SpecialScientificResearch Fund of the Meteorological Public Welfare of the Ministry of Sciences and Technology(GYHY201406002),the Science and TechnologyProjectofGuangzhou-(201604020069),the National Natural Science Foundation of China(41505040,41575065,and 4177510),and the Open Projects of the Plateau Atmosphere and Environment Key Laboratory of Sichuan Province(PAEKL-2015-K2).