A Diagnostic Study of the Asymmetric Distribution of Rainfall during the Landfall of Typhoon Haitang (2005)

The heavy rainfall that occurs during the landfall of tropical cyclones (TCs) often has disastrous consequences, such as flooding and debris flow. On the other hand, they can also ease drought during hot summers. Predicting the occurrence and development of TCs is therefore important, but the asymmetric distribution of the rainfall during landfall makes this task difficult. Furthermore, such a rainfall distribution varies among different TCs.

(Cline, 1926) analyzed the hourly precipitation data within 500 km of hurricane centers from eight moving hurricanes and three stationary hurricanes and found that the rainfall was distributed on the front-right side for moving hurricanes and at the rear for stationary hurricanes. (Miller, 1958) analyzed 16 hurricanes over Florida and showed that the rain rates ahead of the center were greater than those to the rear, which was later proved by (Marks, 1985). (Frank, 1977) conducted a composite analysis of 21 years of rawinsonde data from 13 islands over the Northwest Pacific and found that rainfall was distributed more in the right-rear quadrant. Similarly, (Chen and Ding, 1979), (Chen and Meng, 2001) and Chen et al. (2002, 2004) showed that the rainfall and rainfall area of landfalling typhoons was larger on the right side than on the left side along their tracks, which was also found by (Powell, 1987) on the basis of hurricane Alicia (1983). In contrast, (Parrish et al., 1982) found that the strongest rainfall was located on the left side of hurricane Frederic (1979) during landfall, and a similar conclusion was also reached by (Wu et al., 2011) and (Wang et al., 2012) based upon typhoon Morakot (2009) across Taiwan. These previous studies suggest that the asymmetric distribution characteristics of rainfall during the landfall of TCs is not always consistent among different cases. Thus, it is important to investigate the physical processes involved.

In terms of the reasons for the asymmetric distribution of rainfall, (Dunn and Miller, 1964) speculated that, due to the contrast in surface friction between land and sea in the Northern Hemisphere, convergence will occur on the right side of landfalling TCs, causing the strong rainfall rate in that area. (Tuleya and Kurihara, 1978) supported Dunn's speculation with idealized experiments that showed that the coastward moisture advection and convergence at the boundary layer gave rise to precipitation on the right side. (Tao, 1980) and (Si, 1990) also found that, because of coastal terrain forcing, rainfall was stronger on the right side than on the left side. Similarly, (Powell, 1982), (Jones, 1987) and (Chan and Liang, 2003) proposed that, in addition to frictional convergence, the effects of local orography should also be considered. (Niu et al., 2005) simulated typhoon Sinlaku (2002) and showed that, due to topography, rainfall was enhanced over the windward side, whereas it was weakened over the leeward side. (Ji et al., 2007) also suggested the important role of topography in the production of the asymmetric distribution of rainfall generated by typhoons. (Yang et al., 2011) simulated typhoon Nari (2001) and showed that the symmetric structures of the typhoon changed into asymmetric structures during and after its landfall in Taiwan because of the local topography. Thus, topography is an important factor affecting the distribution of rainfall during the landfall of TCs.

On the other hand, the influence of atmospheric factors cannot be ignored. (Tao et al., 1994) linked the asymmetric distribution of rainfall to asymmetrical patterns in dynamic and thermodynamic atmospheric structures. (Wang et al., 2007) studied the formation of the asymmetric rainfall of Matsa (2005) in terms of vertical velocity, vorticity, potential pseudo-equivalent temperature, water vapor flux, and dry cold airflow intrusion. (Li et al., 2007) performed a diagnostic study of typhoon Imbudo (2003) and showed that the asymmetric low-level flow field led to the asymmetry in vorticity, divergence and vertical velocity in the lower troposphere, which caused the asymmetric distribution of moisture convergence and upward motion, and thus the asymmetric distribution of rainfall. The aforementioned studies have enhanced our understanding of the mechanisms involved in the formation of the asymmetric distribution of rainfall during the landfall of TCs, which in turn has contributed to improvements in precipitation forecasts.

Haitang (2005) is a typical example of a typhoon showing an asymmetric structure in its rainfall during landfall, which took place in Fujian Province, China. (Yue et al., 2008) analyzed the IR1 infrared cloud imagery and found that dynamic factors were more important than thermodynamic factors. (Yue, 2009a) simulated Haitang (2005) and found that the asymmetric rainfall distribution was mainly associated with asymmetry in the upward motion, itself caused by asymmetry in the distribution of atmospheric forcing. Indeed, recently, (Yue and Cao, 2014) also concluded that atmospheric forcing plays an important role in the formation and development of asymmetric structures. (Ding et al., 2009) and (Wang et al., 2010) described the breakdown of rainband-enhanced asymmetric precipitation, and concluded that such a breakdown is related to both topography and the interactions between the typhoon and midlatitude systems in the upper troposphere.

The aforementioned studies discussed the cause of the asymmetric distribution of rainfall during the landfall of typhoon Haitang (2005), but none of them provided comparisons between the two sides of the storm track in terms of any physical variables/parameters. Thus, in the present reported work, we analyzed the effects of stability and different scales, through diagnosis of the moist potential vorticity (MPV) and Q vector, as well as terrain forcing, on the asymmetric rainfall distribution of typhoon Haitang (2005). In the next section, the asymmetric distribution characteristics of the rainfall and numerical simulation are described. The diagnostic methods, such as MPV, Q vector partitioning and terrain forcing are described in section 3. The results from the diagnosis of water vapor, stability and upward motion are presented in section 4 and, finally, a summary of the key findings is provided in section 5.

Typhoon Haitang (2005) moved across the Taiwan Strait and made landfall in Fujian Province, China, in 2005 (Fig. 1a). There was an asymmetric distribution of the associated rainfall over the land (Fig. 1b) for 24 h before and after landfall (0000 UTC 19 to 0000 UTC 20 July 2005). Figure 1b shows that the rainfall of greater than 10 mm was mainly located over the northern coastlines of Fujian Province, Zhejiang Province and southeastern Anhui Province. Meanwhile, the rainfall of greater than 50 mm occurred over the northeast coast of Fujian Province and the coast and northern region of Zhejiang Province, and the rainfall of greater than 200 mm occurred over Zhejiang Province, where the two largest rainfall amounts were 411 mm at (28.1^°N, 121^°E) and 336 mm at (27.9^°N, 120.5^°E). However, on the left side of the typhoon track, in southern Fujian Province and Guangdong Province, less than 10 mm of rainfall was recorded. Thus, there was an asymmetric structure to typhoon Haitang's rainfall during landfall.

Also of note is that the height of the topography reaches 600 m in Fujiang and Zhejiang provinces (Fig. 1a). The height was almost the same on both sides of the typhoon. The orientation of the terrain in this region is northeast-southwest, along the coast. Previous studies (Tuleya and Kurihara, 1978; Bender et al., 1985; Lin et al., 2002) have indicated that the terrain and surface friction play important roles in determining the distribution and variation of precipitation. Thus, we studied the impacts of the terrain on the asymmetric distribution of the rainfall associated with typhoon Haitang (2005).

The Weather Research and Forecasting (WRF) model is a new mesoscale model developed by U.S. meteorological communities. In this study, version 2.0 of the WRF model was used to simulate typhoon Haitang (2005). The initial and lateral boundary conditions were from the Global Forecast System reanalysis dataset (horizontal resolution: 1^°× 1^°). The simulation did not have a "bogus" scheme. Two-way nested grids were used; the fine grid mesh was 15 km and the grid number was 121× 121, while the coarse grid mesh was 45 km and the grid number 81× 81. The number of vertical levels was 31. The dynamical core option of the simulation was based on the advanced research WRF core (Eulerian mass-coordinate), and the main physics options consisted of the Yonsei University planetary boundary layer scheme (Hong and Pan, 1996), the Kain-Fritsch (new Eta) cumulus parameterization scheme (Kain and Frisch, 1993), the (Lin et al., 1983) microphysics process scheme, the Rapid Radiative Transfer Model longwave radiation scheme (Malwer et al., 1997), the Dudhia shortwave radiation scheme (Dudhia, 1989), and a surface layer thermal diffusion scheme (Ek et al., 2003). The same physics processes were adopted for both the coarse and fine grid meshes.

Figure 1.  Typhoon track (thick line) and terrain distribution (color scale; units: m) (a) and the 24 h accumulated (b) observed and (c) simulated rainfall (units: mm).

The model was integrated from 0000 UTC 19 July to 0000 UTC 20 July (a total of 24 h). The simulated 24-h rainfall is shown in Fig. 1c. Compared with observation (Fig. 1b), the greater than 10 mm rainfall in the simulation was similar, and the greater than 50 mm rainfall mainly occurred in Zhejiang Province——apart from that in northwestern Zhejiang Province and southeastern Anhui Province, where the simulated rainfall was stronger than observed. The rainfall of greater than 200 mm occurred over Zhejiang Province and, specifically, rainfall peaks of 463 mm at (28.1^°N, 121^°E) and 343 mm at (27.9^°N, 120.5^°E) were simulated, which was consistent with observation.

Overall, the simulated and observed rainfall showed good agreement. Thus, we analyzed the model data to facilitate the following discussion. In the analysis that follows, the right side (26.5^°-30^°N, 119^°-122^°E) is referred to as the "R region" and the left side (24^°-26.5^°N, 116^°-120^°E) as the "L region" (Figs. 1b and c). Figure 2 shows the simulated hourly averaged rain rate in the R and L regions. The hourly rain rate in the R region ranged from 2.4 to 8.8 mm h^-1, and the average rain rate was 6.2 mm h^-1. Meanwhile, the hourly rain rate in the L region ranged from 0.2 to 0.6 mm h^-1, and the average rain rate was 0.4 mm h^-1. This clearly shows the difference in rainfall between the right and left sides of the typhoon.

Figure 2.  Temporal evolution of the rainfall in the R (bars) and L (line) regions (units: mm).

The evolution of rainfall is associated with atmospheric stability, which can be measured by MPV (Bennetts and Hoskins, 1979). Under the assumption that the horizontal variation of vertical velocity is much larger than the vertical shear of horizontal velocity, and the horizontal change of vertical velocity ω is ignored, the MPV equation (Wu et al., 1995) can be expressed as \begin{eqnarray} \label{eq1} {\rm MPV}=-g(\xi_p+f)\dfrac{\partial\theta_{\rm e}}{\partial p}+g\dfrac{\partial v}{\partial p}\dfrac{\partial\theta_{\rm e}}{\partial x} -g\dfrac{\partial u}{\partial x}\dfrac{\partial \theta_{\rm e}}{\partial y} ,(1)\\\nonumber \end{eqnarray} where \(\xi_p\) is the vertical projection of the absolute vorticity, f is geostrophic vorticity, u and v are zonal and meridional wind components, respectively, p is atmospheric pressure, g is acceleration of gravity, and θ _e is potential temperature. Furthermore, \beginsubequations \begin{align} \label{eq2} {\rm MPV}_1&=-g(\xi_p+f)\dfrac{\partial\theta_{\rm e}}{\partial p} ,(1a)\\ \label{eq3} {\rm MPV}_2&=g\dfrac{\partial v}{\partial p}\dfrac{\partial \theta_{\rm e}}{\partial x}-g\dfrac{\partial u}{\partial p}\dfrac{\partial\theta_{\rm e}}{\partial y}, (1b)\end{align} \endsubequations where MPV₁ is the moist barotropic item, dependent on the vertical component of the absolute vorticity and vertical gradient of equivalent potential temperature, which represents the effects of inertial stability \((\xi_p+f)\) and convective stability (∂θ _e/∂ p). Since absolute vorticity is always positive, when the atmosphere is convectively unstable, ∂θ _e/∂ p>0 and MPV₁<0; and when the atmosphere is stable, ∂θ _e/∂ p<0 and MPV₁>0. MPV₂ is the moist baroclinic item, dependent on the moist baroclinicity (▽_pθ _e) and vertical shear of horizontal wind. (Wu et al., 1995) proposed that when the atmosphere is convectively stable (∂θ _e/∂ p>0) and MPV₂>0, vertical vorticity increases quickly. MPV₁ (MPV₂) is less than (greater than) zero, which is deduced by slantwise-vorticity development, linked to the convective instability and baroclinic instability.

The development of precipitation systems results from the interaction between multi-scale weather systems. The rainfall is related to upward motion, and its variation is associated with multi-scale upward motion. The Q vector is a powerful tool for estimating the vertical motion (Dunn, 1991). Recently, (Yue, 2009b) proposed an ageostrophic Q vector (Q _D) that can be calculated using one-layer data. In the pressure coordinate system,

\begin{eqnarray} \label{eq4} {Q}_{\rm D}&=&(Q_{{\rm D}x},Q_{{\rm D}y})=-\left(\dfrac{\partial u}{\partial x}\dfrac{\partial\alpha}{\partial x}+ \dfrac{\partial v}{\partial x}\dfrac{\partial\alpha}{\partial y}\right){i}-\left(\dfrac{\partial u}{\partial y}\dfrac{\partial\alpha}{\partial x}+ \dfrac{\partial v}{\partial y}\dfrac{\partial\alpha}{\partial y}\right){j} , (2)\end{eqnarray}

where α=1/ρ=RT/p; α is special volume, ρ is air density, R is gas constant, T is temperature, and Q _Dx and Q _Dy are the x and y components of Q _D, respectively. When geostrophic winds are used, Q _D becomes the quasi-geostrophic Q vector (Hoskins et al., 1978).

The ω equation, with the forcing of Q _D vector divergence, can be expressed by \begin{equation} \label{eq5} \nabla^2(\sigma\omega)+f^2\dfrac{\partial^2\omega}{\partial p^2}=-2\nabla\cdot{Q}_{\rm D} ,(3) \end{equation} in which ω has a wave solution, and the left side of Eq. (6) is proportional to -ω. Thus, ▽•Q _D∝ω. Furthermore, when ▽•Q _D<0,ω<0; and when ▽•Q _D>0,ω>0. The divergence of Q _D can describe the vertical motion well.

Previous studies (Keyser et al., 1988, 1992; Martin, 1999, 2007; Yue et al., 2003, 2011) have shown that partitioning of the Q vector can provide useful information about the forcing from multi-scale weather systems. The Q vector is often decomposed into two components: one along the direction of potential temperature (Q_s) and the other along the direction of the potential temperature gradient (Q_n). Q_s represents the thermal wind direction with quasi-geostrophic characteristics, denoting large-scale information; Q_n is the geostrophic departure, denoting mesoscale weather. According to the traditional Q vector partitioning method, the Q _D vector is decomposed into two parts: Q _Ds and Q _Dn, and they can be expressed as follows in the p-coordinate system: \endmulticols

\begin{eqnarray} \label{eq6} {Q}_{{\rm D}n}&=&[\dfrac{\left(\frac{\partial\theta}{\partial x}Q_{\rm D{x}}+\frac{\partial\theta}{\partial y}Q_{\rm D{y}}\right) \frac{\partial\theta}{\partial x}}{\left(\frac{\partial\theta}{\partial x}\right)^2+\left(\frac{\partial\theta}{\partial y}\right)^2}]{i}+ [\dfrac{\left(\frac{\partial\theta}{\partial x}Q_{\rm D{x}}+\frac{\partial\theta}{\partial y}Q_{\rm D{y}}\right) \frac{\partial\theta}{\partial y}}{\left(\frac{\partial\theta}{\partial x}\right)^2+\left(\frac{\partial\theta}{\partial y}\right)^2}]{j} ,(4)\\[-1mm] \label{eq7} {Q}_{{\rm D}s}&=&[\dfrac{\left(\frac{\partial\theta}{\partial y}Q_{\rm D{x}}-\frac{\partial\theta}{\partial x}Q_{\rm D{y}}\right) \frac{\partial\theta}{\partial y}}{\left(\frac{\partial\theta}{\partial x}\right)^2+\left(\frac{\partial\theta}{\partial y}\right)^2}]{i}+ [\frac{\left(-\frac{\partial\theta}{\partial y}Q_{\rm D{x}}+\frac{\partial\theta}{\partial x}Q_{\rm D{y}}\right) \frac{\partial\theta}{\partial x}}{\left(\frac{\partial\theta}{\partial x}\right)^2+\left(\frac{\partial\theta}{\partial y}\right)^2}]{j} .(5) \end{eqnarray}

\beginmulticols2 Both Q _Ds and Q _Dn have the same diagnostic characteristics as Q _D, and 2▽•Q _Dn and 2▽•Q _Ds can reveal the forcing effects of different scale weather systems, the results of which are discussed later in the paper.

Figure 3.  Temporal evolution of RH (units: %) in the (a) R and (b) L regions.

The effects of topography on rainfall come from orographic lift and surface friction. In the pressure coordinate, vertical velocity caused by orographic lift (Zhu et al., 1992) can be written as \begin{equation} \label{eq8} \omega_{{\rm T}xy}=-\rho_0g\left(u_0\dfrac{\partial H_{\rm h}}{\partial x}+v_0\dfrac{\partial H_{\rm h}}{\partial y}\right) , (6)\end{equation} where H _h is the height of the terrain.

The vertical velocity caused by surface friction (Miller et al., 1972) is written as \begin{equation} \label{eq9} \omega_{{\rm F}xy}=\dfrac{\rho_0g}{f}\left[\frac{\partial}{\partial y}(C_{\rm d}u_0\sqrt{u_0^2+v_0^2})-\dfrac{\partial}{\partial x}(C_{\rm d}v_0\sqrt{u_0^2+v_0^2})\right] , (7)\end{equation} where C _d is the drag coefficient (=2.5× 10^-3). In both Eqs. (9) and (10), ρ₀ is surface air density, and u₀ and v₀ are the zonal and meridional components of surface wind, respectively.

To calculate the 3D topography-induced vertical velocity, we set ω=0 at the top boundary (p=100 hPa) and (ω) _p900=ω _Txy (or ω _Fxy) at the low boundary. Here, the low boundary was set to 900 hPa: \begin{equation} \label{eq10} \left. \begin{array}{rcl} \nabla^2(\sigma\omega)+f^2\dfrac{\partial^2\omega}{\partial p^2}&=&0\\[3.5mm] (\omega)_{{\rm p}_{100}}=0,(\omega)_{{\rm p}_{900}}&=&\omega_{T_{xy}} \end{array} \right\} , (8)\end{equation} where vertical velocity is zero at the lateral boundaries. Stability, σ=-h(∂θ/∂ p)[h=(R/p)(p/1000)^R/c_p] was averaged in each layer. The relaxation method was used to solve Eq. (11) and to construct the vertical velocity.

The results of our diagnosis showed that the development of the rainfall was primarily associated with water vapor, stability and upward motion.

Figure 4.  Temporal evolution of water vapor flux(units: g cm^-1 hPa^-1 s^-1) and its divergence (units:10-6 g cm-2 hPa-1 s-1) in the (a) R and (b) L regions.

4.1.1. Relative humidity

Usually, a relative humidity (RH) of greater than 80% is a necessary condition for rainfall (Ding, 1989; Sinclair, 1994). As shown in Fig. 3a, RH was greater than 80% from 1000 hPa to 350 hPa during landfall. RH was greater than 95% from 900 hPa to 800 hPa. Over the L region (Fig. 3b), RH was greater than 80% from 900 hPa to 400 hPa. After landfall (0900 UTC 19 to 0000 UTC 20 July 2005), RH was greater than 95%. It is worth noting that RH was less than 80% below 950 hPa. RH was greater than 80% from the surface to 900 hPa over the R region, whereas it was less than 80% over the L region during the 24 h integration. The depth of RH in the R region was from 900 hPa to 400 hPa, but in the L region it was 900 hPa to 650 hPa. RH of greater than 95% appeared at 800 hPa to 900 hPa during 0300 UTC 19 July to 0000 UTC 20 July 2005 and extended to 700 hPa to 500 hPa during 1500 to 2100 UTC 19 July 2005, while the L region only featured an RH of 95% at 950 hPa to 700 hPa during 0900 UTC 19 July to 0000 UTC 20 July. The comparison reveals that the depth of RH at greater than 80% in the R region was similar to that in the L region. The main differences in the RH of 95% between the R and L regions included the following: (2) the R region led the L region by 6 h and the R region lasted longer than the L region; and (5) the depth was greater in the R region than in the L region; and (6) during 1500 to 2100 UTC 19 July 2005, the R region extended to 700 hPa to 500 hPa. Thus, the RH in both the R and L regions was greater than 80% and the R region held more water vapor than the L region.

4.1.2. Water flux and its divergence

The transport of water vapor is an important source for rainfall development. The water vapor flux (qV/g) and its divergence [(1/g)▽(Vq)] can depict the water vapor transport. Before 1200 UTC 19 July 2005, easterly and southeasterly winds transported water vapor to the R region, while northerly and northwesterly winds transported water vapor to the L region (Fig. 4). The convergence of water vapor flux (>0.1× 10^-6 g cm^-2 hPa^-1 s^-1) in the R region appeared in the range 1000-800 hPa, and the other convergence zone occurred in the range 600-300 hPa at 0900-1500 UTC 19 July 2005. In the L region, the convergence of water vapor flux (0.1× 10^-6 g cm^-2 hPa^-1 s^-1) appeared in the range 1000-800 hPa, and the convergence of water vapor flux occurred in the range 800-300 hPa at 0100-1500 UTC 19 July 2005. The convergence of water vapor flux was 10 times larger in the R region than in the L region.

Typhoon Haitang (2005) made landfall in Fujian Province, China. The mountains in this region are oriented in the northeast-southwest direction (Fig. 1a). The easterly and southeasterly winds (Fig. 4a) on the right side of the typhoon track transported water vapor from the ocean to the rainfall region. On the left side of the track (Fig. 4b), westerly winds on the leeward slope transported dry air to the typhoon center. This caused asymmetric rainfall and is further analyzed in section 4.3.2.

(Bennetts and Hoskins, 1979) proposed conditional symmetric instability (CSI), which is moist hydrostatic inertial instability. CSI represents one of the mechanisms that explain the development of slantwise convection, which has a close relationship with severe storms. The atmosphere usually possesses convective stability and inertial stability, but CSI is very likely to occur when upward slantwise motion takes place. MPV represents dynamic, thermodynamic and water vapor effects. (Bennetts and Hoskins, 1979) showed that when MPV is negative ( MPV<0), CSI may occur. MPV theory has been applied widely in analyses of the precipitation of landfalling typhoons for several decades (Wang and Chen, 1997; Zhao and Wu, 2004; Lai et al., 2007; Huang et al., 2009).

4.2.1. Spatiotemporal comparison of MPV

Figures 5a and b show the appearance in the R region of negative MPV in the range 900-1000 hPa, with a maximum of -2.0 PVU (1 PVU=10^-6 K m² kg^-1 s^-1). During 1800 UTC 19 July to 0000 UTC 20 July 2005, negative MPV also occurred in the range 900-700 hPa. In the L region, negative MPV mainly occurred in the range 900-1000 hPa, with a maximum of -3.5 PVU; and during 0100-0900 UTC 19 July 2005, negative MPV appeared in the range 900-800 hPa. The comparison suggests that negative MPV mainly appeared in the range 900-1000 hPa and the MPV in the L region was stronger than that in the R region.

Figure 5.  Temporal evolution of MPV in the (a) R and (b) L regions, MPV₁ in the (c) R and (d) L regions, and MPV₂ in the (e) R and (f) L regions (solid line = positive; dashed line = negative; units: PVU, 1 PVU = 10^-6 K m² s^-1 kg^-1).

Figure 6.  Temporal evolution of vertical motion in the (a) R and (b) L regions (solid line = downward motion; dashed line = upward motion; units: Pa s^-1).

4.2.2. Comparison of MPV1

Figures 5c and d show that, in the R region, negative MPV₁ occurred in the range 800-1000 hPa, with a maximum of -2.0 PVU. Negative MPV₁ also appeared in the range 800-700 hPa during 1800 UTC 19 July to 0000 UTC 20 July 2005. In the L region, negative MPV₁ mainly appeared in the range 900-1000 hPa, with a maximum of -3.5 PVU, meanwhile, negative MPV₁ occurred in the range 900-800 hPa during 0100-0900 UTC 19 July 2005. The comparison reveals that negative MPV₁ mainly appeared in the range 900-1000 hPa and that the MPV₁ in the L region was stronger than that in the R region. Further analysis showed that the distribution of negative MPV₁ was similar to positive ∂θ _e/∂ p. Thus, there was convective instability in the lower troposphere in both the R and L regions, but it was stronger in the L region.

4.2.3. Comparison of MPV2

Figures 5e and f show that, in the range 900-1000 hPa, MPV₂ was generally positive in the R region, with a maximum of 1 PVU, and negative above 800 hPa. In the L region, positive MPV₂ occurred in the range 900-1000 hPa, and negative MPV₂ appeared above 900 hPa. The former MPV₂ was stronger than the latter in the range 1000-800 hPa.

Comparison between MPV₂ and MPV₁ indicates that, in the R region, the MPV₁ and MPV₂ were out of phase, and that the MPV₁>0 (MPV₁<0) responded to MPV₂<0 (MPV₂>0). The criteria of MPV₁<0 and MPV₂>0 was outstanding in the R region. Thus, the R region was more conducive to the development of rainfall than the L region.

Rainfall associated with upward motion is the secondary circulation. Figure 6a shows that, before landfall, upward motion in the lower troposphere was stronger than in the upper troposphere. The maximum upward motion of -1.3 Pa s-1 appeared at 850 hPa. During landfall, the upward motion weakened in the range 900-600 hPa and its maximum was -0.8 Pa s^-1 at 850 hPa. Upward motion enhanced in the range 400-200 hPa and its maximum reached -0.5 Pa s-1. This may have been related to the coastal terrain. After landfall, upward motion increased to -0.5 Pa s^-1. Upward motion of -1.0 Pa s^-1 occurred in the ranges 450-200 hPa and 900-700 hPa. From 1500-1800 UTC 19 July 2005, upward motion increased continuously in the range 900-500 hPa, but decreased above 500 hPa. During 1800 UTC 19 July to 0000 UTC 20 July 2005, upward motion weakened below 500 hPa. This suggests that there was always upward motion in the R region. During landfall, upward motion became weak. Twelve hours after landfall, upward motion increased again. Figure 6b shows that upward motion mainly appeared below 700 hPa and its maximum was -0.3 Pa s^-1. During landfall, upward motion decreased gradually and, after landfall, it barely changed. It is worth noting that the maxima of upward motion in the R region were about five times stronger than those in the L region, which was conducive to the asymmetric distribution of rainfall. Next, we analyzed the contributions of different scale weather systems and terrain to upward motion.

4.3.1 Forcing of different-scale weather systems

Before landfall, the convergence of the Q _Ds vector occurred in the ranges 1000-900 hPa and 400-200 hPa, with a maximum of -0.03× 10^-13 hPa^-1 s^-3 (Fig. 7a). After landfall, it weakened in the lower troposphere. During 0900-1600 UTC 19 July 2005, the convergence of Q _Ds was enhanced in the range 700-200 hPa and its maximum was -0.03× 10^-13 hPa^-1 s^-3 at 550 hPa. During 1500-2000 UTC 19 July 2005, the convergence of Q _Ds appeared in the range 850-500 hPa and the maximum was -0.03× 10^-13 hPa^-1 s^-3 at 700 hPa. The convergence of Q _Ds moved downward. The low-level convergence of the Q _Ds vector weakened after landfall but it was enhanced in the upper troposphere. The convergence of the Q _Ds vector mainly appeared in the ranges 800-900 hPa and 600-450 hPa (Fig. 7b). The convergence depth in the air column and the intensity of the Q _Ds vector almost barely changed. Comparing Figs. 7a and b shows that the convergence intensity of the former was much stronger than the latter, indicating that the large-scale forcing in the R region was stronger, and there was a greater contribution to the difference in rainfall intensity, compared to in the L region.

The convergence of Q _Dn mainly occurred in the range 1000-800 hPa during landfall and, after landfall, it weakened (Fig. 7c). Before landfall, the convergence of Q _Dn mainly appeared in the range 500-200 hPa, with a maximum of -0.08× 10^-13 hPa^-1 s^-3 at 350 hPa. After landfall, the convergence of the Q _Dn vector of -0.06× 10-13 hPa-1 s-3 moved downward to 500-350 hPa, but was enhanced to -0.12× 10^-13 hPa-1 s-3 at 400 hPa. During 1700-2100 UTC 19 July 2005, the maximum of -0.06× 10-13 hPa-1 s-3 appeared in the range 700-500 hPa, and it was maintained but moved downward persistently. From the above analysis, the convergence of Q _Dn in the lower troposphere decreased and the convergence in the lower troposphere increased after landfall. The convergence of Q _Dn moved downward. During landfall, the convergence of Q _Dn barely changed (Fig. 7d). The comparison between the R and L regions reveals that the convergence of Q _Dn was more intensive and thicker in the R region than in the L region. Thus, the R region possessed stronger mesoscale forcing than the L region, which contributed to the asymmetric rainfall distribution.

Figure 7.  Temporal evolution of (a, b) Q _Ds and (c, d) Q _Dn in the (a, c) R and (b, d) L regions (solid line = divergence; dashed line = convergence; units: 10^-13 hPa^-1 s^-3).

Figure 8.  Temporal evolution of vertical motion forced by (a, b) orographic lift and (c, d) surface friction in the (a, c) R and (b, d) L regions (solid line = downward motion; dashed line = upward motion; units: Pa s^-1).

4.3.2. Forcing of terrain

Figure 8a shows that, during landfall, orographic lift forced upward motion, and that upward motion decreased rapidly with height. Upward motion at 800 hPa was only about one ninth of that near the surface. Downward motion occurred (Fig. 8b). The difference in vertical velocity between the R and L regions caused the asymmetric rainfall distribution.

Surface friction produced downward motion before landfall and generated upward motion after landfall (Fig. 8c). Upward motion decreased rapidly. Upward motion at 700 hPa was about one order of magnitude smaller than that near the surface. Surface friction forced upward motion during landfall, and it decreased rapidly with height (Fig. 8d). Upward motion at 700 hPa was about one seventh of that near the surface. The comparison shows that, before landfall, downward motion appeared in the R region but upward motion occurred in the L region. After landfall, friction-induced upward motion was present in both the R and L regions. The magnitude of upward motion was twice as large in the R region than in the L region, which was conducive to the development of the asymmetric rainfall distribution.

The 24-hour accumulated precipitation data for typhoon Haitang (2005) reveal an asymmetric rainfall distribution between each side of its track. The WRF model successfully simulated this asymmetric distribution. Analysis of the simulated hourly high-resolution data showed that the rain rate was about 15 times larger on the right side of the track than on the left side. The major results from the diagnostic study were as follows:

(2) The calculations of RH, water vapor flux and its divergence indicated that there was sufficient water vapor with RH greater than 80% on both sides, but the right side was more humid than the left side. Easterly and southeasterly winds transported water vapor to the right side, while northerly wind transported water vapor to the left side. The convergence of water vapor flux on the right side was stronger than on the left side.

(5) The MPV results revealed that both sides featured CSI (MPV<0). Slantwise vorticity development (MVP₁<0 and MPV₂>0) was more favorable on the right side than on the left side.

(6) Upward motion was significantly different between the right and left sides. The right side had stronger upward motion than the left side. Analysis of the Q vector demonstrated that both large-scale and mesoscale forcing were attributable to the rainfall difference between the two sides. The forcing of orographic lift produced upward and downward motion over the right and left sides, respectively. Surface friction contributed to the asymmetric rainfall structures after landfall.

On the right side, there was stronger water vapor flux and unstable energy, followed by stronger upward motion that released a substantial amount of unstable energy and that transported the water vapor from the lower troposphere to the upper troposphere, which in turn promoted the development of rainfall. On the left side, weak baroclinic instability was associated with weak water vapor flux, and weak upward motion in the lower troposphere only triggered the weak release of unstable energy and upward transport of water vapor, which in turn weakened the development of rainfall. This led to the asymmetric distribution of rainfall between the two sides of the track.

The asymmetric rainfall distribution in this study was primarily associated with humidity, stability and vertical upward motion forced by multi-scale systems. Terrain also played an important role in the production of the distribution. In more general terms, many other factors, and the differences among them, can affect and result in an asymmetric distribution of rainfall. In this study, only macroscopical factors, such as water vapor, stability and vertical motion, have been discussed. However, microphysical processes are also important, which we intend to examine in future work.