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Potential Deformation and Its Application to the Diagnosis of Heavy Precipitation in Mesoscale Convective Systems


doi: 10.1007/s00376-017-6282-4

  • Many observational studies have shown that deformation, like vertical vorticity and divergence, is closely related to the occurrence and distribution of strong precipitation. In this paper, to involve deformation in precipitation diagnosis, a new parameter called potential deformation (PD) is derived and then applied to precipitation detection within a simulated mesoscale convective system (MCS). It is shown that PD includes both stretching deformation and shearing deformation and shares similar characteristics with deformation insofar as it does not change with the rotating coordinate. Diagnosis of the simulated MCS reveals that PD performs well in tracing the MCS' precipitation. In terms of their distributional pattern, the large-value areas of PD are similar to the precipitation in the different development stages of the MCS. A detailed analysis of the physical processes contained within the PD shows that it can reflect the three-dimensional moisture variation, vertical wind shear and wind deformation within the MCS. These structures are usually a comprehensive reflection of the characteristics of the surface cold pool, rear inflow jet, downward cold air flow and upward warm moist flow within the precipitating convective cells. For this reason, the PD shows much stronger anomalies in the precipitating atmosphere than the non-precipitating atmosphere, which implies considerable potential for its application in detecting heavy precipitation within MCSs.
    摘要: 许多研究表明,变形和涡度、散度一样与强降水的发生发展及分布密切相关。为了将变形引入到降水的诊断中,本文提出了一个新的参数—位势形变。位势形变包含位势伸缩形变和位势切变形变,且可证明其和形变一样不随坐标的旋转而改变。将位势形变应用到一次MCS降水过程的诊断分析发现,位势形变对MCS降水有良好指示意义,在MCS降水发展的不同阶段,位势形变的大值区均随着降水的移动而移动。对包含在位势形变中的物理过程的分析发现位势形变包含三维水汽梯度、垂直风切变和变形,这些物理信息能够综合反映MCS中降水单体内的冷池、尾部入流、下沉冷气流与上升暖气流的对峙等结构。因此,位势形变能够显著区分降水大气与非降水大气,这体现了位势形变在MCS降水追踪方面的潜力。
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Manuscript History

Manuscript received: 16 June 2016
Manuscript revised: 22 November 2016
Manuscript accepted: 28 February 2017
通讯作者: 陈斌, bchen63@163.com
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Potential Deformation and Its Application to the Diagnosis of Heavy Precipitation in Mesoscale Convective Systems

  • 1. Key Laboratory of Cloud-Precipitation Physics and Severe Storms, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
  • 2. State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing 100081, China
  • 3. Beijing Meteorological Bureau, Beijing 100089, China

Abstract: Many observational studies have shown that deformation, like vertical vorticity and divergence, is closely related to the occurrence and distribution of strong precipitation. In this paper, to involve deformation in precipitation diagnosis, a new parameter called potential deformation (PD) is derived and then applied to precipitation detection within a simulated mesoscale convective system (MCS). It is shown that PD includes both stretching deformation and shearing deformation and shares similar characteristics with deformation insofar as it does not change with the rotating coordinate. Diagnosis of the simulated MCS reveals that PD performs well in tracing the MCS' precipitation. In terms of their distributional pattern, the large-value areas of PD are similar to the precipitation in the different development stages of the MCS. A detailed analysis of the physical processes contained within the PD shows that it can reflect the three-dimensional moisture variation, vertical wind shear and wind deformation within the MCS. These structures are usually a comprehensive reflection of the characteristics of the surface cold pool, rear inflow jet, downward cold air flow and upward warm moist flow within the precipitating convective cells. For this reason, the PD shows much stronger anomalies in the precipitating atmosphere than the non-precipitating atmosphere, which implies considerable potential for its application in detecting heavy precipitation within MCSs.

摘要: 许多研究表明,变形和涡度、散度一样与强降水的发生发展及分布密切相关。为了将变形引入到降水的诊断中,本文提出了一个新的参数—位势形变。位势形变包含位势伸缩形变和位势切变形变,且可证明其和形变一样不随坐标的旋转而改变。将位势形变应用到一次MCS降水过程的诊断分析发现,位势形变对MCS降水有良好指示意义,在MCS降水发展的不同阶段,位势形变的大值区均随着降水的移动而移动。对包含在位势形变中的物理过程的分析发现位势形变包含三维水汽梯度、垂直风切变和变形,这些物理信息能够综合反映MCS中降水单体内的冷池、尾部入流、下沉冷气流与上升暖气流的对峙等结构。因此,位势形变能够显著区分降水大气与非降水大气,这体现了位势形变在MCS降水追踪方面的潜力。

1. Introduction
  • During the past few decades, a considerable amount of research has been carried out on mesoscale convective systems (MCSs) due to their important role in producing severe weather (flash flooding, damaging winds, large hail, and tornadoes), and thus their substantial impact on human society (Fritsch et al., 1986; Doswell et al., 1996; Schumacher and Johnson, 2005). In China, flood-producing rainfall is often closely related to the activities of MCSs, especially over the Yangtze-Huaihe river basins, where the warm and moist summer monsoons from the oceans often encounter cold, dry continental flows from the high latitudes. Research on MCS precipitation diagnosis or forecasting is therefore relevant for the improvement of precipitation forecasting skill and the reduction of fatalities caused by heavy rainfall.

    Vorticity, divergence and deformation are the three basic characteristics of wind fields. While much previous research has revealed and confirmed the close relationship between both vorticity and divergence and the occurrence of precipitation, few studies have sought to address the possible impact of deformation on heavy precipitation. A possible reason for this is that deformation cannot induce vertical motions directly through the pumping effect, but forecasting of ascending motion is probably the most important aspect of precipitation forecasts. However, deformation does influence precipitation. For example, (Bluestein, 1977) found a close correlation between synoptic-scale deformation and tropical cloud band orientation, and emphasized the effects of deformation on vertical motion in the tropical boundary layer. (Weldon, 1979) showed that, in satellite images, along the dilatation axis of the deformation field, elongated cloud bands called "deformation zones" often exist. These zones can affect very deep layers of the atmosphere and show connections with precipitation (including snowfall) (Steigerwaldt, 1986; Market and Cissell, 2002). (Deng, 1986) found that, in most of the 18 heavy precipitation cases during the Mei-yu season in China that they chose, the precipitation centers corresponded well to strong deformation zones, which was seen as a good indicator of the occurrence of precipitation 12-24 hours in advance. Apart from these observational facts, deformation and precipitation are also dynamically correlated. For example, deformation has been shown in many studies to be highly capable of redistributing atmospheric properties, and to be a highly effective mechanism for the formation of gradients in these properties. Deformation can increase the gradient of temperature or potential temperature, drive frontogenesis, and then trigger the frontal transverse vertical circulation under the control of geostrophic balance and thermal wind balance (Sawyer, 1956; Eliassen, 1962). The ascending flow of the frontal transverse circulation has a substantial impact on the formation of frontal cloud or precipitation bands (e.g., Koch and McCarthy, 1982; Koch, 1984; Keyser et al., 1988; Karyampudi and Carlson, 1988; Schultz and Knox, 2007). Through a simple numerical study, (Gao et al., 2008) also found that deformation can result in a confluence of moisture and increase the moisture gradient, which is crucial to the organization of MCSs (such as squall lines) (Ziegler et al., 1995; Cho and Cao, 1998; Market and Cissell, 2002; Gao et al., 2008). In addition, Li et al. (2016) found that deformation can induce the development of precipitating vortices by changing the distribution of equivalent potential temperature. The above facts imply that, analogous to tracing strong vorticity and convergence zones, deformation may also be involved in the diagnosis of strong precipitation in MCSs, in such a way that our understanding of their dynamics and even our ability to forecast them may be improved. This is the purpose of the present paper.

    When using the dynamic fields (vorticity, divergence and deformation) in precipitation detection, a major problem is that large values of these fields are not always collocated with strong precipitation, which is often caused by a coupling effect of both dynamic and thermodynamic factors, such as instability and moisture. To avoid this, (Doswell et al., 1996) proposed an ingredients-based methodology for precipitation forecasting, which uses high rainfall rates, vertical motions, humidity, and so on, to simultaneously detect the severe weather. (Fritsch and Carbone, 2004) proposed determining these critical factors by considering the evolution, structure and propagation of convection. These factors can include high equivalent potential temperature and its gradients (strong baroclinicity), strong convergence, high humidity, and vertical wind shear, according to (Schumacher and Johnson, 2005). In order to apply these ingredients in a combined way, numerous statistical studies need to be carried out according to the different types of heavy precipitation-producing storms. Therefore, (Gao et al., 2007) suggested using diagnostic parameters to couple the precipitation ingredients physically instead of statistically. A typical example of these diagnostic parameters is generalized potential vorticity (GPV), which is derived by considering the non-uniform saturation state of the precipitating atmosphere within the potential vorticity (Ertel, 1942; Hoskins et al., 1985). GPV, which is defined as the dot product of the three-dimensional vorticity vector and the generalized potential temperature (GPT) gradient, couples the rotation state of the atmosphere with other thermodynamic factors, such as moist baroclinicity and convective stability, and has been shown to perform well in many heavy precipitation diagnoses (Gao et al., 2004a, 2004b; Mofor and Lu, 2009). In this paper, to involve the deformation field in precipitation diagnosis, a similar diagnostic parameter, based on GPV and called potential deformation (PD), is derived and used in the detection of heavy precipitation within a simulated MCS. The derivations are given in section 2; section 3 introduces the MCS used to examine the ability of PD in diagnosing precipitation; the results are examined in section 4, together with the physical basis of the relationship between PD and precipitation; and section 5 concludes the paper.

2. Potential deformation
  • In a non-uniformly saturated atmosphere in Cartesian coordinates, taking the dot product of the three-dimensional vorticity vector and the GPT gradient obtains GPV: \begin{equation} \label{eq1} P={\omega}\cdot\nabla\theta^\ast=-\frac{\partial v}{\partial z}\frac{\partial\theta^\ast}{\partial x}+ \frac{\partial u}{\partial z}\frac{\partial\theta^\ast}{\partial y}+\left(\frac{\partial v}{\partial x}- \frac{\partial u}{\partial y}\right)\frac{\partial\theta^\ast}{\partial z} , \ \ (1)\end{equation} where P is GPV, ω=∇×v h=(-∂ v/∂ z,∂ u/∂ z, ∂ v/∂ x-∂ u/∂ y) is the vorticity vector, v h=(u,v,0) is the horizontal wind vector, \(\theta^\ast=\theta\exp[(Lq_\rm vs/c_pT)(q_\rm v/q_\rm vs)^k]\) is GPT, θ=T(p s/p)R/cp is potential temperature, p s is the reference pressure, p is pressure, T is temperature, R is the dry air gas constant, cp is the specific heat at constant pressure, L is latent heat, q v is specific humidity, q vs is the saturated specific humidity, and k is an empirical constant. When the vertical coordinate is transformed from z to θ* (supposing that θ* changes monotonously with height), the horizontal part of GPV disappears and GPV can be written as \begin{equation} \label{eq2} P=\left(\frac{\partial v}{\partial x}-\frac{\partial u}{\partial y}\right)_{\theta^\ast}\left/\frac{\partial z}{\partial\theta^\ast}\right. , \ \ (2)\end{equation} which means that GPV is only determined by the moist isentropic vertical vorticity and the thickness of the moist isentropic surface.

    In a similar way, to combine deformation with the thermodynamic factors, one can substitute vertical vorticity in Eq. (3) with stretching deformation (E st=∂ u/∂ x-∂ v/∂ y) or shearing deformation (E sh=∂ v/∂ x+∂ u/∂ y) (Bluestein, 1992) to obtain the PD; that is, \begin{eqnarray} \label{eq3} R&=&\left(\frac{\partial v}{\partial x}+\frac{\partial u}{\partial y}\right)_{\theta^\ast}\left/\frac{\partial z}{\partial\theta^\ast}\right. ;\ \ (3)\\ \label{eq4} S&=&\left(\frac{\partial u}{\partial x}-\frac{\partial v}{\partial y}\right)_{\theta^\ast}\left/\frac{\partial z}{\partial\theta^\ast}\right. .\ \ (4) \end{eqnarray} Analogous to the potential vorticity, R can be defined as potential shearing deformation (PRD), while S can be defined as potential stretching deformation (PSD). Transformed back into the z-coordinate, these two parameters are \begin{equation} \label{eq5} R=-\frac{\partial v}{\partial z}\frac{\partial\theta^\ast}{\partial x}-\frac{\partial u}{\partial z}\frac{\partial\theta^\ast}{\partial y}+ \left(\frac{\partial v}{\partial x}+\frac{\partial u}{\partial y}\right)\frac{\partial\theta^\ast}{\partial z} \ \ (5)\end{equation} and \begin{equation} \label{eq6} S=-\frac{\partial u}{\partial z}\frac{\partial \theta^\ast}{\partial x}+\frac{\partial v}{\partial z}\frac{\partial \theta^\ast}{\partial y}+ \left(\frac{\partial u}{\partial x}-\frac{\partial v}{\partial y}\right)\frac{\partial \theta^\ast}{\partial z} ,\ \ (6) \end{equation} which can be further rewritten into vector forms as follows: \begin{eqnarray} \label{eq7} R&=&(\nabla\times {v}_{\rm r})\cdot\nabla\theta^\ast ;\ \ (7)\\ \label{eq8} S&=&(\nabla\times {v}_{\rm s})\cdot\nabla\theta^\ast . \end{eqnarray} Here, v r=(-u,v,0) and v s=(v,u,0) are transformations of the original wind vector v h=(u,v,0).

    However, it is noted that R and S respectively contain part of the deformation; R includes shearing deformation, while S includes stretching deformation. Since stretching deformation and shearing deformation are not independent variables of the coordinates (Bluestein, 1992), R and S may also change with the coordinates' rotation. Suppose that the coordinates (x,y,z) are anticlockwise-rotated to (x1,y1,z1) through an angle μ, the horizontal wind vector then changes from (u,v) to (u1,v1). ∂ u1/∂ x1, ∂ u1/∂ y1, ∂ u1/∂ z, ∂ v1/∂ x1, ∂ v1/∂ y1, ∂ v1/∂ z, ∂θ*/∂ x1 and ∂θ*/∂ y1 can be respectively written as \begin{eqnarray} \label{eq9} \frac{\partial u_1}{\partial x_1}&=&\frac{\partial u}{\partial x}\cos^2\mu+\frac{\partial v}{\partial x}\cos \mu \sin \mu +\frac{\partial u}{\partial y}\cos \mu \sin \mu +\frac{\partial v}{\partial y}\sin ^2\mu , \ \ (9)\nonumber\\\\ \label{eq10} \frac{\partial u_1}{\partial y_1}&=&-\frac{\partial u}{\partial x}\cos\mu\sin\mu-\frac{\partial v}{\partial x}\sin^2\mu +\frac{\partial u}{\partial y}\cos^2\mu +\frac{\partial v}{\partial y}\cos \mu \sin \mu ,\ \ (10)\nonumber\\\\ \label{eq11} \frac{\partial u_1}{\partial z}&=&\frac{\partial u}{\partial z}\cos \mu+\frac{\partial v}{\partial z}\sin \mu ,\ \ (11)\\ \label{eq12} \frac{\partial v_1}{\partial x_1}&=&-\frac{\partial u}{\partial x}\cos \mu\sin \mu +\frac{\partial v}{\partial x}\cos ^2\mu -\frac{\partial u}{\partial y}\sin^2\mu +\frac{\partial v}{\partial y}\cos \mu \sin \mu ,\ \ (12)\nonumber\\\\ \label{eq13} \frac{\partial v_1}{\partial y_1}&=&-\frac{\partial v}{\partial x}\cos \mu\sin \mu +\frac{\partial u}{\partial x}\sin^2\mu -\frac{\partial u}{\partial y}\cos \mu \sin \mu+\frac{\partial v}{\partial y}\cos ^2\mu ,\ \ (13)\nonumber\\\\ \label{eq14} \frac{\partial v_1}{\partial z}&=&-\frac{\partial u}{\partial z}\sin \mu+\frac{\partial v}{\partial z}\cos \mu ,\ \ (14)\\ \label{eq15} \frac{\partial \theta^\ast}{\partial x_1}&=&\frac{\partial \theta ^\ast}{\partial x}\cos \mu +\frac{\partial \theta ^\ast }{\partial y}\sin\mu \ \ (15)\end{eqnarray} and \begin{equation} \label{eq16} \frac{\partial\theta^\ast}{\partial y_1}=\frac{\partial \theta ^\ast}{\partial x}\sin \mu +\frac{\partial \theta ^\ast }{\partial y}\cos \mu , \ \ (16)\end{equation} according to the coordinate-transformation matrix (Bluestein, 1992, p. 83) that \begin{equation} \label{eq17} \left( \begin{array}{c} x_1\\ y_1 \end{array} \right)=\left( \begin{array}{c@{\quad}c} {\cos\mu} & {\sin\mu}\\ {-\sin\mu} & {\cos\mu} \end{array} \right)\left( \begin{array}{c} x\\ y \end{array} \right) . \ \ (17)\end{equation} From Eqs. (6)-(7) and (10)-(17), we can derive that \begin{equation} \label{eq18} R_1 =-S\sin 2\mu +R\cos 2\mu \ \ (18)\end{equation} and \begin{equation} \label{eq19} S_1=-S\cos 2\mu +R\sin 2\mu , \ \ (19)\end{equation} where R1 and S1 are the PRD and PSD, respectively, in the rotated coordinates. Equations (19)-(20) present the dependence of R and S on the orientation of the coordinate system. However, we find that R and S share similar properties to shearing deformation and stretching deformation insofar as the sum of their squares is rotationally invariant: \begin{equation} \label{eq20} R_1^2 +S_1^2 =R^2 +S^2 =D^2 ,\ \ (20) \end{equation} where the quantity D is defined as PD and, here, we only consider D≥ 0. According to Eqs. (4)-(5), D in isentropic coordinates is \begin{equation} \label{eq21} D=\frac{|E|}{|\partial z/\partial\theta|} ,\ \ (21) \end{equation} where E2=(∂ v/∂ x+∂ u/∂ y)θ2+(∂ u/∂ x-∂ v/∂ y)θ2 =E sh2+E st2 is total deformation.

    Figure 1.  The (a) 200 hPa high-level wind speed (color shaded; units: m s-1) and positive horizontal divergence (blue solid lines; units: 10-5 s-1), (b) 500 hPa geopotential height (blue solid lines; units: 10 gpm), (c) 800 hPa geopotential height (blue solid lines; units: 10 gpm) and wind speed (color shaded; units: m s-1), and (d) 800 hPa negative values of moisture flux divergence (color shaded; units: 10-2 g kg-1 s-1 hPa-1 m-1) and wind vectors (black arrows; units: m s-1), at 1200 UTC 17 August 2009. The black solid lines in (a-c) and the red solid lines in (d) denote the 10-mm, 6-h observational precipitation, which indicates the location of the current rainfall area. The black short line in (b) is the low trough. The open arrows in (b-d) indicate the directions of the air flows. The letters "J", "D" and "G" represent the jet stream, low-pressure vortex, and high-pressure ridge, respectively.

3. Simulation of an MCS causing heavy precipitation in East China
  • In this section, an MCS that occurred on 17 August 2009 and caused heavy precipitation in East China is simulated and analyzed, to examine the performance of the newly derived PD parameter on the diagnosis of heavy precipitation. The simulation is performed with the aim of obtaining a whole dataset that permits detailed study of the precipitation and corresponding thermodynamic and dynamic structures within the MCS. Figure 1 shows the basic large-scale patterns of the MCS in the troposphere. The black solid lines in Figs. 1a-c and the red solid lines in Fig. 1d are the 10-mm, 6-h (0600-1200 UTC) accumulated observational precipitation contours, which indicate the precipitation or the MCS region. As is shown in Fig. 1a, in the upper troposphere at 200 hPa, two head-to-tail jet streams exist at approximately 40°N in the midlatitudes. A northeast-southwest oriented divergence region is located at the entrance of the eastern jet. This high-level divergence is quite favorable for the development of low-level convection, due to the pumping effect, which can be seen by the collocation of the precipitation region and the high-level divergence region in Fig. 1a. In the mid-troposphere at 500 hPa (Fig. 1b), the subtropical high has a significant westward extension, reaching the southwest border of China (approximately 90°E). The north of the high is a shallow low trough and the heavy precipitation region is just located in the front part of the low trough. The low trough tends to bring cold and dry air into the rainfall area in the middle levels of the MCS, which favors the accumulation of unstable energy. In the low levels, as shown in Fig. 1c, the MCS is mainly influenced by a meso-α scale (Orlanski, 1975) low vortex. Southeast of the low vortex is a southwest-northeast oriented strong wind band, which brings moisture and energy for the development of the MCS and precipitation. The moisture comes from two sources according to Fig. 1d: the westerly flow from the Bay of Bengal and the easterly flow from the South China Sea. These two moisture transport belts encounter each other at about (20°N, 105°E), and together veer to a southwest flow which then penetrates into inland China. When arriving to the east of the low-level vortex, the southwest flow appears cyclonically shear and forms strong moisture convergence, which in turn provides favorable moisture and energy conditions for the maintenance and development of the MCS.

  • The Advanced Regional Prediction System (ARPS; Xue et al., 1995, 2000, 2001, 2003) from the Center for Analysis and Prediction of Storms at Oklahoma University is used to simulate the MCS. In the simulation, the initial field of ARPS comes from the NCEP-NCAR GFS 0.5°× 0.5° analysis data. To improve the quality of the initial field, both the conventional surface sounding data and the high-resolution radar data from nine Doppler radars around East China are assimilated into the initial field with the three-dimensional variational data assimilation programs in ARPS. The physical configuration includes fourth-order advection in both the horizontal and vertical direction, a 1.5-order turbulent kinetic energy-based subgrid-scale turbulent mixing scheme, fourth-order computational mixing, anisotropic acoustic wave divergence damping, the 6-category water/ice microphysics of (Lin et al., 1983) with the convective cumulus parameterization switched off, NASA's atmospheric radiation transfer parameterization, and a two-layer force-restore model (Noilhan/Planton scheme) for the surface layer.

    The simulation is designed to run at 0000 UTC 17 August, with the first two hours assimilating the radar reflectivity and radial velocity every 15 minutes. Then, from 0200 UTC, the model integrates forwards for 22 hours, which outputs simulation results every 15 minutes. The domain in which the simulation is performed is a one-layer area, with a horizontal grid spacing of 2.5 km and a vertical resolution of 500 m. Grids in the horizontal direction are 363× 363 in arrangement, with 53 levels in the vertical direction. An overview of the domain can be seen in Fig. 1 [approximately (31°-39°N, 110°-120°E)].

    Figure 2.  The 6-h accumulated precipitation during 0600-1200 UTC and 1200-1800 UTC of (a, c) Obs and (b, d) Sim (units: mm) on 17 August 2009, and the 18-h accumulated precipitation from 0600 UTC 17 August to 0000 UTC 18 August 2009 of (e) Obs and (f) Sim (units: mm). The black dots denote the simulated 18-h accumulated extreme precipitation center (EPC). The dashed boxes indicate the difference between the observed and the simulated precipitation.

  • Here, we use observational 6-h accumulated rainfall data from the National Meteorological Center of the China Meteorological Administration to verify the simulation. In Fig. 2, "Obs" refers to the observed precipitation and "Sim" denotes the simulated precipitation. From Fig. 2, we can see that the model simulates the evolutionary features of the MCS well. As shown in Fig. 2, which presents the 6-h accumulated precipitation amount from 0600 UTC to 1200 UTC, and from 1200 to 1800 UTC, 17 August, the simulation reflects the two evolutionary stages of the MCS well (i.e., a banding convection stage and a cluster convection stage). During 0600-1200 UTC, the precipitation mainly shows a northeast-southwest oriented belt (red rectangle), with the maximum precipitation center (indicated by "A", above 60 mm) located southwest of Shandong Province. Compared to Fig. 2a, the simulated 6-h accumulated precipitation also presents a northeast-southwest oriented belt, albeit the length of the belt is longer than observed (area enclosed by the red dashed box in Fig. 2b). This is quite possibly due to the convective cell that produces rainfall in the dashed box developing earlier in the simulation than in reality, because the precipitation occurs during 1200-1800 UTC in Fig. 2c (also enclosed by the red dashed box). A similar phenomenon also appears in the main precipitation area around Shandong Province. As shown in Figs. 2c and d, in the 1200-1800 UTC time interval, both the observational and simulated accumulated precipitation areas present a cluster-shaped pattern, albeit with the precipitation center in the simulation being east of the observed precipitation center. Apart from the evolution, another success of the simulation is the extreme rain within the MCS. As shown in Fig. 2e, a heavy precipitation center is located in (35.3°N, 118.4°E), with the maximum precipitation amount reaching 300 mm in 18 hours. The modeled precipitation seems to be higher than observed, with a 400-mm extreme precipitation center (black dots, denoted as "EPC") located around (35.28°N, 118.43°E). However, since this "EPC" in Sim only exists in a very small area, the modeled precipitation amount is thus considered reasonable; plus, the resolution of Sim is much higher than that of Obs. Calculating the area average of precipitation around the Sim "EPC", we find that the average precipitation amount (331.7 mm) is quite close to the observation (above 300 mm). According to Figs. 2b and d, the Sim "EPC" is mainly caused by the clustered MCS, which will be our focus in the following diagnosis.

4. Application of PD in tracing heavy precipitation
  • When using diagnostic quantities to detect meso- or small-scale precipitation, the most anticipated result is that the diagnostic quantities can grasp all the direct precipitation-producing information within the whole atmosphere. However, due to the strong "noisiness" of the atmosphere, and also some influence from large-scale systems (such as upper-level jets, high-latitude and mid-level troughs etc.), these quantities also show strong anomalies outside of the precipitation region (Ran and Li, 2014). To avoid this problem, an objective analysis technique from (Barnes, 1964) is firstly applied to the model output to filter the large-scale information that may not have direct links with the MCS precipitation. This method, used for this scale separation, can be expressed by the following formulae (Barnes, 1973; Maddox, 1980): \begin{eqnarray} \label{eq22} F_{\rm b}(i,j)&=&\frac{\sum\limits_{n=j-N}^{j+N}{\sum\limits_{m=i-N}^{i+N}{F(m,n)W(m,n)}}}{\sum\limits_{k=1}^K{W(m,n)}} ;\ \ (22)\\ \label{eq23} W(i,j)&=&\exp(-r_{m,n}^2/4a) ;\ \ (23)\\ \label{eq24} F_{\rm o}(i,j)&=&F(i,j)-F_{\rm b}(i,j) ;\ \ (24) \end{eqnarray} where (i,j) is the grid point analyzed by the method, F b is the field after the objective analysis that will be filtered from the original field, F is the original field, and F o is the filtered field that will be used to carry out the diagnosis. N is the radius of influence denoted by the grid number, (m,n) is the latitude and longitude grid points within the radius of influence, rm,n is the distance from (m,n) to the analyzed point (i,j), and a is a constant. The wavelength response function of this method is \begin{equation} \label{eq25} R(\lambda,a)=\exp(-4\pi^2a/\lambda^2) ,\ \ (25) \end{equation} where Λ is the wavelength. Equation (26) shows that the horizontal scale of the field (F b) that we can reduce from the total field is mostly determined by the value of a. In this paper, we adopt a=200, and the corresponding relationship between the response function and the wavelength can be seen in Fig. 3a. According to Fig. 3a, after objective analysis, most large-scale information with wavelength approximately greater than 200 km is contained in F b. This means the field F o F o includes all the meso-γ-scale information and a large part of the meso-β-scale information, which is suitable for our research on the diagnosis of high-resolution small-scale precipitation in an MCS. The technique is firstly applied to the basic variables, including horizontal wind (u,v), potential temperature (θ), GPT (θ*) and specific humidity (q v), and then the analyzed fields u o, v o and θ* o are used to calculated the PD to detect the precipitation area, while other variables (such as q vo) may also be analyzed to help understand the MCS' inner dynamics and thermodynamics.

    Figure 3.  (a) The wavelength response function of the Barnes objective analysis method. (b) Temporal evolution of the correlation between the 15-min accumulated precipitation and the vertically integrated absolute GPV and PD calculated from the model output, and the PD o calculated from the objectively analyzed field, respectively, during 0200-2400 UTC 17 August 2009.

    Figure 4.  The horizontal distributions of simulated 15-min accumulated precipitation and PD (units: 10-2 K s-1) at (a, b) 1000 UTC, (c, d) 1200 UTC, (e, f) 1400 UTC, and (g, h) 1600 UTC, on 17 August 2009. The black dot denotes the "EPC" location.

    The relations of the GPV (calculated from the original field), PD (calculated from the original field), and PD o (calculated from the filtered field) with heavy precipitation are compared by calculating the spatial correlation coefficients between these three quantities and the simulated 15-min accumulated precipitation. The term "spatial" refers to the whole area of the model domain [approximately (31°-39°N, 110°-120°E). In addition, the three quantities are integrated in the vertical direction, which can be represented by \(\langle|\ |\rangle=\int_z=0.5\;\rm^z=9.75\;\rm|\ |dz\). This operator is used to obtain a one-level field of the diagnostic variable to correspond to the precipitation data, and also to include all the important information at different levels that may be relevant to the precipitation. Regardless of the spin-up time interval (approximately 0200-0500 UTC), one can see in Fig. 3b that \(\langle|\rm PD|\rangle\) (red line) shows an evidently higher correlation with precipitation than \(\langle|\rm GPV|\rangle\) (blue line), which gives further validation to the application of deformation in precipitation diagnosis, as well as vorticity. On the other hand, after filtering the large-scale information, the correlation between \(\langle|\rm PD_\rm o|\rangle\) and precipitation increases significantly compared with that between \(\langle|\rm PD|\rangle\) and precipitation, with the highest correlation coefficient reaching 0.7. This gives a sound reason for carrying out the objective analysis before using the new quantity describing the small-scale precipitation in the MCS.

    Figure 5.  Vertical cross sections of PD (units: 10-6 K m-1 s-1) along 35.3°N when the precipitating cell goes through the "EPC" location. The red solid lines denote the 0.5 g kg-1 specific mixing ratio of the total hydrometers, which basically represent the convective cell. The gray bars are the 15-min accumulated precipitation.

  • Figure 4 shows the horizontal distribution of the 15-min accumulated precipitation and PD (also, a vertical integration of PD absolute values; PD here, and in the following parts, indicates the variable calculated from F o fields) during the banding convective stage and the cluster convective stage of the MCS. As shown in Fig. 4a, at 1000 UTC, two main precipitation regions exist in East China: one located in approximately (35°-36.5°N,116°-119°E), which shows a cluster-shaped pattern; and the other stretching from approximately (34°N, 117°E) westwards to (32°N,112°E), which shows a band-shaped pattern. Correspondingly, strong anomalies of PD in Fig. 4b also present a cluster-band-united distributional pattern. At 1200 UTC (Figs. 4c and d), the band-shaped precipitation has a weakening trend, especially in Anhui, where the precipitation almost disappears. Meanwhile, the cluster-shaped precipitation evolves into two parallel bands (indicated by the red straight line), with high values of PD also organized into two corresponding bands. At 1400 UTC (Figs. 4e and f), the band-shaped precipitation pattern disappears. A cluster-shaped pattern of precipitation remains , and it shows an intensifying trend. Corresponding to this, PD also shows a similar evolution. At 1600 UTC (Figs. 4g and h), with the eastward movement of the MCS system, the latitudinal scale of the precipitation region decreases evidently, and PD also presents a trend to mainly develop longitudinally.

    From the above analysis, it can be concluded that the newly derived parameter PD describes the strong rainfall within the MCS well, thus showing great potential to be used in detecting the evolution of small-scale precipitation operationally.

    To explain the close correlation between PD and heavy precipitation in the MCS physically, Fig. 5 shows the distribution of PD in the whole atmosphere along the "EPC" location (35.3°N) during the passage of a precipitating cell. From Figs. 5a-d, the most evident distinction between the precipitating and non-precipitating atmosphere is that the PD shows strong anomalies in the whole precipitating troposphere. This means that this quantity can grasp the typical structures of the precipitating atmosphere, as distinguished from the non-precipitating atmosphere. To see these typical structures, PD is written as follows by incorporating Eqs. (8) and (9) into Eq. (21): \begin{eqnarray} \label{eq26} D^2&=&\left(\frac{\partial {v}_{\rm h}}{\partial z}\right)^2\nabla_{\rm h}^2\theta^\ast+E^2\left(\frac{\partial\theta^\ast}{\partial z}\right)^2+ \Bigg[2\left(-\frac{\partial v}{\partial z}\frac{\partial \theta^\ast}{\partial x}-\frac{\partial u}{\partial z} \frac{\partial \theta^\ast}{\partial y}\right)E_{\rm sh}\frac{\partial \theta^\ast}{\partial z}+2\left(-\frac{\partial u}{\partial z}\frac{\partial \theta^\ast}{\partial x}+ \frac{\partial v}{\partial z}\frac{\partial \theta^\ast}{\partial y}\right)E_{\rm st}\frac{\partial \theta^\ast}{\partial z}\Bigg], \ \ (26)\end{eqnarray} where E2=E st2+E sh2 is the total deformation. Equation (27) shows that PD is a complete reflection of vertical wind shear, moist baroclinicity, flow deformation and convective stability of the atmosphere. By analyzing these elements, including the thermodynamic element denoted by GPT and the dynamic element such as deformation and vertical wind shear, physical processes associated with heavy precipitation that are able to be reflected by PD can thus be discussed.

    4.2.1. Thermodynamic processes

    According to its definition, GPT is the potential temperature multiplied by the condensation latent heat release function, which can be written as \begin{equation} \label{eq27} \theta^\ast=\theta\eta , \ \ (27)\end{equation} where \(\eta=\exp[(Lq_\rm vs/c_p T)(q_\rm v/q_\rm vs)]^k\) is the condensation latent heat release function. The most significant characteristic of GPT is the involvement of the weight coefficient (q v/q vs)k into η. This means that the amount of water vapor that can condense will depend on the current humidity of the atmosphere. In an absolutely dry atmosphere with a weight coefficient of (q v/q vs)k=0, GPT reduces to potential temperature and no moisture condenses. In a saturated atmosphere with a weight coefficient of (q v/q vs)k=1, all the moisture can be condensed and GPT thus becomes equivalent potential temperature. Accordingly, in a neither entirely dry nor entirely saturated atmosphere, GPT assumes only part of the moisture in an air parcel can be condensed by (q v/q vs)k« 1, which theoretically conforms more to the real atmosphere (Mason, 1971). In this paper, as shown above, all the fields are given an objective scale-separation analysis before they are applied, which means the GPT we use for the PD calculation is actually \begin{eqnarray} \label{eq28} \theta_{\rm o}^\ast&=&\theta^\ast-\theta_{\rm b}^\ast=\theta\eta-\theta_{\rm b}\eta_{\rm b}=(\theta_{\rm o}+\theta_{\rm b})(\eta_{\rm o}+\eta_{\rm b})-\theta_{\rm b}\eta_{\rm b}\theta_{\rm b}\eta_{\rm o}+\theta_{\rm o}\eta_{\rm b}+\theta_{\rm o}\eta_{\rm o} , (28)\end{eqnarray} where θ* and η are the GPT and condensation latent heat function evaluated by the model ouput, θ* b and η b are the analyzed large-scale GPT and condensation latent heat function obtained by Eq. (23), and θ o and η o (θ o=θ-θ b, η o=η-η b) represent the small-scale information obtained by filtering θ* b and η b from the original field. From Eq. (29), it can be seen that, after scale separation, θ* o is composed of three parts: the coupling of large-scale potential temperature and the small-scale condensation latent heat function (denoted by θ o1*=θ bη o); the coupling of small-scale potential temperature and the large-scale condensation latent heat function (denoted by θ o2*=θ oη b); and the coupling of small-scale potential temperature and the small-scale condensation latent heat function (denoted by θ o3*=θ oη o).

    Figure 6 shows the vertical cross sections of θ* o and its three components at 1400 UTC when a precipitation cell is passing "EPC". The cell is profiled by the 0.5 g kg-1 contour of total hydrometers' specific mixing ratios, and the precipitation caused by it is denoted by the gray bars. As shown in Fig. 6a, within the convective cell, evident horizontal variations of GPT are found. In the mid-lower troposphere below 6 km, "EPC" (118.43°E) is located between a positive GPT anomaly area and a negative GTP anomaly area, which makes a strong horizontal gradient of GPT over "EPC". By comparing Figs. 6b-d to Fig. 6a, it can be seen that θ o1*, which is the coupling of large-scale potential temperature and the small-scale condensation latent heat function, is the leading factor determining θ o*. Since the large-scale potential temperature (θ b, figure omitted) mainly shows a vertical variation, it actually acts as a weight function that makes the low-level information more dominant. The small-scale condensation latent heat function (η o) thus becomes the main factor that influences θ o*. As shown in Fig. 6e, the configuration of positive and negative values of η o is highly in accordance with those of θ* o in Fig. 6a. According to the definition of η o, its distribution is actually related to the moisture content of the atmosphere that can be reflected by the weight function (q v/q vs)k (k is 45 here). As shown in Fig. 6f, evident small-scale relative humidity anomalies appear around the "EPC" location at 118.43°E. The positive anomaly is in the front (east) part of the cell, where warm moist inflow ascends and brings the moisture upwards, indicated by the streamlines in Fig. 6f. The negative humidity anomaly is at the back (west) part of the cell, where the rear-inflow downward motions prevail. Correspondingly, negative anomalies of the condensation latent heat function in Fig. 7e show downward motions, while positive anomalies have upward motions. This means that PD includes the small-scale moisture variation caused by the convective cell inner motions through the condensation latent heat function.

    Figure 6.  Vertical cross sections of (a) GPT (θ o*, units: K), (b) θ o1* (units: K), (c) θ o2* (units: K), (d) θ o3* (units: K), (e) condensation latent heat function (magnitude: 10-1), and (f) water vapor (units: g kg-1), along 35.3°N at 1400 UTC, when the precipitation cell is passing EPC at 1400 UTC on 17 August 2009. The stream lines are composed of the zonal wind (units: m s-1) and vertical velocity (units: 10-1 m s-1). The black solid lines without arrows are the 0.5 g kg-1 specific mixing ratio of the total hydrometers, which basically represent the convective cell. The gray bars are the 15-min accumulated precipitation.

    4.2.2. Dynamic processes

    With θ o*≈θ bη o, the PSD and PRD can be respectively written as \begin{eqnarray} \label{eq29} S&=&(\nabla\times {v}_{\rm so})\cdot\nabla(\theta_{\rm b}\eta_{\rm o})=\eta_{\rm o}(\nabla\times {v}_{\rm so})\cdot\nabla\theta_{\rm b} +\theta_{\rm b}(\nabla\times {v}_{\rm so})\cdot\nabla\eta_{\rm o}\approx&\theta_{\rm b}(\nabla\times {v}_{\rm so})\cdot\nabla\eta_{\rm o} \ \ (29)\end{eqnarray} and \begin{eqnarray} \label{eq30} R&=&(\nabla\times {v}_{\rm ro})\cdot\nabla(\theta_{\rm b}\eta_{\rm o})=\eta_{\rm o}(\nabla\times {v}_{\rm ro})\cdot\nabla\theta_{\rm b}+ \theta_{\rm b}(\nabla\times {v}_{\rm ro})\cdot\nabla\eta_{\rm o}\approx&\theta_{\rm b}(\nabla\times {v}_{\rm ro})\cdot\nabla\eta_{\rm o} ,\ \ (30) \end{eqnarray} where v ro=(-u o,v o,0) and v so=(v o,u o,0) are transformers of the wind vector v ho=(u o,v o,0). In Eqs. (30)-(31), the term that relates the three-dimensional gradient of the large-scale potential temperature θ b is neglected because of its much smaller magnitude than the other part (figure omitted). With Eqs. (30)-(31), PD can be written as \begin{eqnarray} \label{eq31} D^2&=&[\theta_{\rm b}(\nabla\times {v}_{\rm so})\cdot\nabla\eta_{\rm o}]^2+[\theta_{\rm b}(\nabla\times {v}_{\rm ro})\cdot\nabla\eta_{\rm o}]^2\nonumber\\[1mm] &=&\theta_{\rm b}^2\left[\left(\frac{\partial u_{\rm o}}{\partial z}\right)^2+\left(\frac{\partial v_{\rm o}}{\partial z}\right)^2\right] \left[\left(\frac{\partial\eta_{\rm o}}{\partial x}\right)^2\!+\!\left(\frac{\partial\eta_{\rm o}}{\partial y}\right)^2\right]\!+\! \theta_{\rm b}^2E_{\rm o}^2\left(\frac{\partial\eta_{\rm o}}{\partial z}\right)^2\!-\nonumber\\[1mm] &&2\left(\frac{\partial v_{\rm o}}{\partial x}+\frac{\partial u_{\rm o}}{\partial y}\right)\left(\frac{\partial v_{\rm o}}{\partial z} \frac{\partial\eta_{\rm o}}{\partial x}+\frac{\partial u_{\rm o}}{\partial z}\frac{\partial\eta_{\rm o}}{\partial y}\right) \frac{\partial\eta_{\rm o}}{\partial z}\theta_{\rm b}^2-\nonumber\\[1mm] &&2\left(\frac{\partial u}{\partial x}-\frac{\partial v}{\partial y}\right)\left(\frac{\partial u}{\partial z} \frac{\partial \eta }{\partial x}-\frac{\partial v}{\partial z}\frac{\partial \eta }{\partial y}\right)\frac{\partial \eta }{\partial z}\theta _{\rm b}^2\nonumber\\[1mm] &=&D_1^2+D_2^2 +D_3^2, (31)\end{eqnarray} where \begin{eqnarray} \label{eq32} D_1^2&=&\theta_{\rm b}^2\left[\left(\frac{\partial u_{\rm o}}{\partial z}\right)^2+\left(\frac{\partial v_{\rm o}}{\partial z}\right)^2\right]\left[ \left(\frac{\partial\eta_{\rm o}}{\partial x}\right)^2+\left(\frac{\partial\eta_{\rm o}}{\partial y}\right)^2\right] ,\ \ (32)\\[1mm] \label{eq33} D_2^2&=&\theta_{\rm b}^2 E_{\rm o}^2\left(\frac{\partial \eta_{\rm o}}{\partial z}\right)^2 ,\ \ (33)\\[-2mm]\nonumber \end{eqnarray} and \begin{eqnarray} \label{eq34} D_3^2&=&-2\left(\frac{\partial v_{\rm o}}{\partial x}+\frac{\partial u_{\rm o}}{\partial y}\right)\left(\frac{\partial v_{\rm o}}{\partial z} \frac{\partial\eta_{\rm o}}{\partial x}+\frac{\partial u_{\rm o}}{\partial z}\frac{\partial \eta_{\rm o}}{\partial y}\right) \frac{\partial\eta_{\rm o}}{\partial z}\theta _{\rm b}^2-\nonumber\\ &&2\left(\frac{\partial u_{\rm o}}{\partial x}-\frac{\partial v_{\rm o}}{\partial y}\right) \left(\frac{\partial u_{\rm o}}{\partial z}\frac{\partial \eta_{\rm o}}{\partial x}-\frac{\partial v_{\rm o}}{\partial z} \frac{\partial \eta_{\rm o}}{\partial y}\right)\frac{\partial \eta_{\rm o}}{\partial z}\theta_{\rm b}^2. \ \ (34)\end{eqnarray}

    Figure 7.  Vertical cross sections of (a) PD (units: 10-6 K m-1 s-1), (b) PD2, (c) D12, (d) D22, and (e) D32 (units: 10-10 K2 m-2 s-2), along 35.3°N at 1400 UTC, on 17 August 2009. The red solid lines are the 0.5 g kg-1 specific mixing ratio of the total hydrometers, which basically represent the convective cell. The gray bars are the 15-min accumulated precipitation.

    In Eq. (32), PD squared (i.e., PD2) contains several terms that respectively couple vertical wind shear, the horizontal and vertical gradient of the condensation latent heat function, and deformation, comprehensively. Figure 7 shows the vertical distributions of the magnitude of PD, PD2 and the three components of PD at 1400 UTC 17 August 2009, along the same section as in Fig. 5. As in Fig. 7a, within the convective cell enclosed by the red line, strong precipitation occurs, with the 15-min maximum accumulated rainfall amount reaching 60 mm (118.43°E, also the "EPC" location). Over the precipitation region, PD exhibits large positive anomalies below the height of 6 km, which further verifies its ability in diagnosing strong precipitation. Strong centers of PD are mainly oriented in the boundary layer below the height of 2 km (within approximately 118.05°E, 118.5°E and 118.81°E, respectively), with the largest center (approximately 118.5°E) almost collocated with the precipitation center (118.43°E, also the "EPC" location). On the other hand, it seems that PD in the strong precipitation area develops much higher than that in the weak precipitation area, which is likely due to the deep convection in the strong precipitation area. As in Fig. 7a, the convective cell over the "EPC" area reaches up to a height of 14 km and positive anomalies of PD extend up to 6 km. This is also a factor that contributes to the large vertically integrated absolute PD values in the strong precipitation area (Fig. 4f). Comparing Figs. 7a and b, we can see that PD and PD2 show very similar distributions, which then gives us a reasonable basis upon which we can use PD2 to analyze the physical processes contained within PD. According to Figs. 7c-f, the three components of PD2 basically have comparable magnitude over the precipitation area, which implies an equal importance of containing vertical wind shear, a horizontal and vertical gradient of the condensation latent heat function, and deformation, in precipitation diagnosis. The process associated with the condensation latent heat function has been explained in the previous section. In this section, we focus on the dynamic processes associated with vertical wind shear and deformation.

    Since vertical wind shear describes the vertical structure of the flow in a cell, as an example, Figs. 8a and b show the distributions of the original zonal wind and perturbation potential temperature (obtained from the model output), with the streamlines superposed along the same section as in Fig. 7. As indicated by the solid arrows in Figs. 8a and b, the same as in Fig. 7, two significant flows prevail in the convective cell: a westward ascending inflow that moves into the cell in the boundary layer and out of the cell in the upper level at the front (east side) of the cell; and an eastward descending inflow that penetrates into the cell from the 6-km mid-levels at the back (west side) of the cell and pours down to surface. Corresponding to this flow structure, vertical wind shear presents three main large-value regions in the cell, denoted by "I", "II" and "III". Region "I" is associated with wind streaks caused by the descending flow and the front ascending flow. As in Fig. 8a, a positive zonal wind center (indicated by "H") can be found at the boundary layer at approximately 118.5°E, which is likely related to be related to the strong pressure gradient induced by the cold pool. On the other hand, in the front of the cell is a strong negative zonal wind center (indicated by "L"), with a clockwise vertical circulation superposed. With strong wind centers mostly confined in the levels below 2 km, strong wind shear thus develops. Region "II" is associated with a positive wind streak at a height of about 6 km, when the mid-level eastward flow penetrates into the cell. The flow is also denoted as the rear inflow jet, which is quite important to surface high winds (Markowski and Richardson, 2010). Region "III" is related to the upper outflow. Among these three regions, as can be seen by comparing Fig. 7c and Fig. 8c, Region "I" in the boundary layer is the most dominant shear contained in PD, because of its coupling with the condensation latent heat function (Fig. 6e) and large-scale potential temperature. This means, due to vertical wind shear, PD includes the process of the interaction between cold-pool outflow and warm inflow in the boundary, which is one of the most important processes in triggering and maintaining convection systems within MCSs.

    Figure 8.  Vertical cross sections of the (a) zonal wind (color shaded; units: m s-1), (b) perturbation potential temperature (color shaded; units: K), and (c) vertical wind shear square (color shaded; units: 10-5 s-2), along 35.3°N at 1400 UTC, on 17 August 2009. The stream lines are composed of the zonal wind (units: m s-1) and vertical velocity (units: 10-1 m s-1). The black (red) solid lines are the 0.5 g kg-1 specific mixing ratio of the total hydrometers, which basically represent the convective cell. The black solid arrow curves indicate the vertical circulations within the cell. The gray bars are the 15-min accumulated precipitation. The letters "H" and "L" denote the high-value and low-value centers respectively. The numerals "I", "II" and "III" denote the large shear centers.

    Since deformation describes the horizontal structure of the flow, Fig. 9 shows the horizontal distributions of the wind stream, the deformation tick marks, the total deformation, and its two components at z=1.25 km and at 1400 UTC in the precipitation area of focus. The "deformation tick marks" are a series of short straight lines, which are like wind vectors but without arrows. The orientation of the tick marks is parallel to the dilatation axis, and their length is the magnitude of the total deformation. As shown in Fig. 9a, the wind over the precipitation region presents a significant deformational pattern. The deformation magnitude represented by the length of the deformation tick marks (Fig. 9b) is obviously larger in the precipitation area than the surrounding non-precipitation area. It is also noted that, in Fig. 9b, in the strong precipitation area of focus (black box), the deformation tick marks are consistently south-north oriented, largely parallel to the y-axis, which further verifies the confluence pattern of the flow. West of these south-north oriented tick marks is the westerly divergent outflow formed by the downward cold air at the back of the convective cell (Figs. 8a and 9a). East of them is the easterly caused by the inflow in the front of the convective cell (Figs. 8a and 9a). As noted above, the confluence of these two flows is the basic factor that produces the heavy precipitation. The overlap of the band structure of the precipitation area and the deformation pattern of the flow shows that this rain-producing process is contained in PD by the deformation.

    Figure 9.  Horizontal distributions of (a) stream lines and (b) deformation tick marks at the z=1.25 km level at 1400 UTC 17 August 2009. The black boxes are the strong precipitation area of focus. The color shaded areas are the 15-min accumulated simulated precipitation (mm). The orientation of the tick marks is parallel to the dilatation axis and the length of the tick marks is the magnitude of the total deformation. The black dot denotes the "EPC" location.

    Figure 10.  Schematic illustration of the structure of the precipitation cell.

5. Conclusions
  • On the basis of the close relationship between deformation and precipitation, this paper introduces a new diagnostic parameter, PD (potential deformation), for a more flexible application of deformation in the diagnosis of heavy precipitation. To define PD, two other parameters, PRD (potential shearing deformation) and PSD (potential stretching deformation), are firstly derived. PRD and PSD, which are respectively defined as the dot product of a transformed vorticity vector and the GPT gradient, contain shearing deformation and stretching deformation, respectively. Although PRD and PSD change with coordinate rotation, the sum of their squares, i.e., PD, does not.

    After a simple objective analysis, PD is used in a simulated MCS to include the deformation in precipitation diagnosis. It is shown that PD performs well in indicating the heavy precipitation area within the MCS. During the two band-shaped and cluster-shaped stages of the MCS, large-value areas of PD also present corresponding bands and clusters. An analysis of the physical basis for the close correlation between the PD and precipitation shows that PD can reflect the precipitation area because it contains the typical processes for the production of MCS precipitation, which is depicted in Fig. 10. As Fig. 10 shows, in the front of the precipitating cell, warm and moist inflow ascends and brings the moisture upwards. At the back of the cell, cold and dry flow penetrates into the cell and goes down to the surface, forming the surface cold pool. These two flows cause strong moisture anomalies that are contained in the PD. In addition, the convective cell features an opposing structure of positive and negative zonal wind. The overturning of the warm inflow and the acceleration of the downward rear inflow by the cold pool cause strong vertical wind shear in the precipitation atmosphere. At the surface, the divergent outflow of the cold pool encounters the warm inflow in the front of the cell and forms a strong confluence deformation pattern, which is the basis for the triggering and maintenance of convection in the MCS. All these processes are contained in the PD by the three-dimensional gradient of the GPT (or moisture), the vertical wind shear and deformation, and thus PD correlates closely with precipitation. The correlation coefficient can reach up to 0.7. This implies great potential for using PD in precipitation detection and forecasting.

    At present, numerical models represent one of the main ways for predicting precipitation. Precipitation in numerical models is mainly obtained by parameterization schemes (microphysical parameterization and cumulus parameterization), which contain strong uncertainties. In order to improve the prediction skill of precipitation by numerical modeling, a number of extended methods have been developed, based on the numerical results, as a complement to the numerical predictions. For example, (Yue et al., 2007) developed the wet Q vector interpretation technique. In a similar way, PD can also be calculated from numerical prediction results and used as an interpretation technique to indicate precipitation. The application of the parameter in forecasting precipitation and its comparison to numerical precipitation is a possible avenue of research for our group in the future.

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