Figure 5 shows the differences in the 700-hPa wind speed and geopotential height between EXP2 and EXP1. After 1 h of integration (i.e., t=18 h) as the MWP is introduced into the model, the wind speed near the perturbation in EXP2 is slightly greater than that in EXP1. The maximum difference is about 0.6 m s-1. However, the geopotential height near the perturbation in EXP2 is greater than that in EXP1, with a maximum difference greater than 4 gpm. With the intensification of rainfall in EXP2, the latent heat increases. An MβV forms to the northwest of the perturbation at t=19 h. The wind speeds decrease near the vortex center and increase to the northeast and southwest of the vortex. The geopotential heights in EXP2 also decrease quickly near the vortex center, with a difference of less than -8 gpm at t=20 h and less than -14 gpm at t=24 h. The wind speeds to the south and north of the vortex in EXP2 increase with the integration, respectively. The maximum wind speed differences are greater than 2.5 m s-1 at t=24 h and greater than 4 m s-1 at t=30 h. As the scale of the strong wind region is about 100 to 200 km, we follow (Chen et al., 1998) and define it as an mLLJ. This mLLJ can be regarded as the mesoscale disturbance associated with the rainstorms in their study. Our simulation results suggest that the low-level pressure drops are caused by the LHR, and then the mLLJ intensifies and the MβV develops. The southwesterly and northeasterly mLLJs to the south and north of the MβV play important roles in the development of the MβV.
Figure 6 shows the differences in the 500-hPa wind speed and geopotential height between EXP2 and EXP1. The wind speeds above the perturbation in EXP2 increase clearly from t=18 h to t=20 h, while the wind speeds to the southwest of the perturbation decrease. A weak wind speed difference center forms above Wuhan at t=24 h, along with a weak cyclonic circulation. At the same time, the wind speeds to the north and south of the weak vortex in EXP2 increase and decrease, respectively. The evolution of the 500-hPa geopotential height is markedly different from that at 700 hPa. Under the influence of the latent heat in EXP2, the 500-hPa geopotential height rises near the perturbation, leading to a difference greater than 10 gpm by t=20 h.
According to hydrostatic balance theory, the thickness of the air column is proportional to average temperature, \begin{equation} \Delta z=\frac{R\overline{T}}{g_0}\ln\frac{p_{\rm b}}{p_{\rm t}} , \ \ (2)\end{equation} where p b and p t are the pressure of isobaric surfaces; ∆ z and $\overline T$ are the thickness and average temperature of the air column between p b and p t, respectively; R is the gas constant; and g0 is the average of the gravitational acceleration. We define the thickness of the air column and average temperature between 400 and 700 hPa as DH and TA, respectively: \begin{eqnarray} {\rm DH}&=&{\rm {H}}_{400}-{\rm {H}}_{700} ;\ \ (3)\\ {\rm TA}&=&\frac{1}{{\rm log}p_{\rm 6}-{\rm log}p_1}\sum_{n=2}^{5}T_n({\rm log}p_{n+1}-{\rm log}p_{n-1}) . \ \ (4)\end{eqnarray} Here, H is the geopotential height; Tn (n=2...5) is the temperature at the 400, 500, 600 and 700 hPa levels; and pn (n=1...6) is the pressure at 300, 400, 500, 600, 700 and 800 hPa. Next, we define the differences in DH and TA between EXP2 and EXP1 as DDH and DTA: \begin{eqnarray} {\rm DDH}&=&{\rm DH}_{{\rm EXP2}}-{\rm DH}_{{\rm EXP1}} ;\ \ (5)\\ {\rm DTA}&=&{\rm TA}_{{\rm EXP2}}-{\rm TA}_{{\rm EXP1}} . \ \ (6)\end{eqnarray} Figure 7 shows the evolution of average DH and average TA within (30°-31°N, 113.5°-114.5°E). The evolution of average DH is similar to that of average TA, because DH is directly proportional to TA under the hydrostatic balance constraint. In EXP1, average DH decreases from 4504.3 gpm at t=17 h to 4484.2 gpm at t=24 h, and varies little after that; whereas, in EXP2, average DH increases rapidly from about 4495.8 gpm at t=19 h to about 4514.0 gpm at t=21 h. During this period, the upper-level pressure rises and the low-level pressure drops, resulting in the increase in DH. The value of average TA in EXP2 rises by 2.7°C at t=21 h compared with that in EXP1.
The horizontal cross sections of DDH and DTA are shown in Fig. 8. DDH is negative near the perturbation at t=18 h, which corresponds to a weakly negative DTA center. The DDH intensifies quickly with the integration. The maximum DDH is greater than 21 gpm in association with a positive DTA center with a maximum DTA greater than 2.7°C at t=20 h. The regions of positive DDH and DTA extend, whereas the intensities weaken with the integration before t=24 h. By t=30 h, the maximum values of DDH and DTA decrease to about 18 gpm and 1.6°C, respectively.
Figure 9 shows the horizontal cross section of the 700-hPa difference vorticity and wind between EXP2 and EXP1. Both the difference in vorticity and wind is very small at t=18 h. The difference in vorticity increases in association with the intensification of the difference in wind. The maximum value of the difference in vorticity is greater than 3× 10-5 s-1 near the perturbation at t=20, and it increases rapidly after t=21 h, with the maximum value being greater than 16× 10-5 s-1 at t=24 h. A mesoscale cyclonic circulation forms in the difference in the wind field at t=21 h (not shown). By t=30 h, the difference in vorticity is rather large, with the positive-value region and the cyclonic circulation extending to the meso-α scale. We also see that the regions of positive difference in vorticity all correspond to the cyclonic circulations, suggesting that the latent heating is responsible for the intensification of the MβV.
To analyze the energy difference between the two simulations, we defined the difference in the total energy (DTE) per unit mass (Zhang et al., 2003a; Tan et al., 2004) and total kinetic energy per unit mass. The DTE is expressed as \begin{equation} {\rm DTE}=\frac{1}{2}\sum(U'^2_{i,j,k} +V'^2_{i,j,k}+\kappa T'^2_{i,j,k}) , \ \ (7)\end{equation} where U\prime, V\prime and T\prime are the differences in the wind components and the difference in temperature between EXP2 and EXP1; \(\kappa=C_p/R\); i and j run over x and y grid points over the region (20°-50°N, 80°-120°E); and k runs over the 11 levels of 1000, 925, 850, 775, 700, 600, 500, 400, 300, 200 and 100 hPa. The total kinetic energy (TKE) per unit mass is defined as \begin{equation} \label{eq7} {\rm TKE}=\frac{1}{2}\sum(U_{i,j,k}^2+V_{i,j,k}^2+W_{i,j,k}^2) , \ \ (8)\end{equation} where U and V are the x- and y-components of wind speed, respectively, and W is the vertical velocity in the z coordinate.
The evolution of the DTE is shown in Fig. 10a. After the MWP is introduced into the model, DTE increases linearly with the integration. However, both TKEs over the same region in EXP1 and EXP2 decrease with the integration (shown in Fig. 10b). This indicates that the decrease of the total energy is compensated by the latent heat energy in EXP2. As some of the latent heat energy is converted into the kinetic energy, the TKE in EXP2 decreases more slowly than that in EXP1.
To reveal the development of the MβV, we calculated the 700-hPa TKE over the MβV circulation field (Fig. 10c). The TKE varies little in EXP1, whereas in EXP2 the TKE increases linearly after t=18 h. Consequently, the LHF plays an important role in the evolution of the dynamic fields and the development of the MβV.