Potential Vorticity Perspective of Vortex Structure ... - AMS Journals

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Potential Vorticity Perspective of Vortex Structure Changes of Tropical Cyclone Bilis (2006) during a Heavy Rain Event following Landfall DIFEI DENG,a,b,c NOEL E. DAVIDSON,a LIANG HU,d,e KEVIN J. TORY,a MAI C. N. HANKINSON,f b,d AND SHOUTING GAO a

Research and Development Branch, Bureau of Meteorology, Melbourne, Victoria, Australia b Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China c School of Physical, Environmental and Mathematical Sciences, University of New South Wales, Canberra, Australian Capital Territory, Australia d State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing, China e National Satellite Meteorological Center, Chinese Meteorological Administration, Beijing, China f Centre for Climate Research, Singapore (Manuscript received 19 July 2016, in final form 23 February 2017) ABSTRACT Tropical Cyclone (TC) Bilis made landfall on the China coast at 0500 UTC 14 July 2006. Following the landfall, sudden and unforecast torrential rain commenced some 400 km southwest of the weakening circulation center at around 1200 UTC 14 July 2006. At least 843 people were killed and the direct economic loss was estimated at up to $5 billion (U.S. dollars) in this event. Prior to the rain event, as the environmental fields evolved, the vertical vorticity weakened and deformation increased around Bilis’s circulation. It is illustrated that a strong gradient wind imbalance (GWI) through midlevels became established over the northwestern quadrant of Bilis, from which a large quantity of air with high potential vorticity (PV) was redistributed from the inner circulation to the outer radii. Both backward and forward Lagrangian trajectories show this redistribution as an outward bulge of midlevel PV toward the rainfall areas. The transport of midlevel PV from inner to outer radii provides a dynamical reason for the rapid decline in rainfall around Bilis’s center. It is also associated with large differential horizontal PV advection below 400 hPa over the rainfall area. Diagnostic analysis further demonstrates that the redistribution of high PV to over the rainfall areas is associated with a raising of the local isentropic surfaces and the formation of a cold dome in the mid- to lower troposphere. This is not only a direct lifting mechanism but also establishes favorable conditions for warm advection and ascent on the raised isentropic surfaces. These adiabatic ascent mechanisms are considered to have released conditional instability, resulting in broadscale convection and heavy rainfall.

1. Introduction Through significant scientific developments, forecasts of tropical cyclone (TC) motion have steadily improved over the last several decades, but there has been generally little progress in the prediction of TC intensity and rainfall (Wang and Wu 2004; Houze et al. 2007). Forecasting the precipitation of landfalling TCs is a complicated problem, as rainfall is influenced by many factors such as speed of motion, intensity, size, and structure; the coastal and inland topography; land surface and boundary layer conditions; as well as the TC’s interaction with multiscale environmental systems (Rogers et al. 2003). Consequently,

Corresponding author e-mail: Difei Deng, [email protected]

precipitation can vary greatly from storm to storm and even at different times for the same storm. In China, an average of nine TCs make landfall every year, 1.9 of which exhibit rainfall enhancement. Sudden rainfall amplification during landfall occurs mostly from July to August. It is one of the most difficult and important forecast challenges for meteorologists (Chen and Ding 1979, 440–473; Dong et al. 2010). It is also worth noting that a cyclone does not have to be intense in order to have a significant impact, as flooding can accompany relatively weak, remnant cyclones (Atallah et al. 2007). But what are the processes associated with such events? TC Bilis (2006) was one of these weakening TCs that caused sudden inland heavy rainfall. Bilis formed over the northwest Pacific Ocean and attained its peak

DOI: 10.1175/MWR-D-16-0276.1 Ó 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

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intensity with maximum winds of approximately 30 m s21 at 0600 UTC 13 July when moving northwestward. It made its first landfall on Taiwan at 1500 UTC 13 July and its second landfall in Fujian Province at 0500 UTC 14 July. After that, Bilis continued to move slowly westward and rapidly weakened. However, sudden, unforecasted, localized torrential rain, up to 200 mm in 12 h, occurred over its southwest quadrant near the juncture of the three provinces of Hunan, Jiangxi, and Guangdong (near 258N, 1148E) during the period from 1200 UTC 14 July to 1200 UTC 15 July. The rainfall caused widespread catastrophic flooding, subsequent considerable loss of life, and significant damage to property. More than 843 people were killed and the direct economic loss was estimated at up to $5 billion [U.S. dollars; Gao et al. (2009)]. Figure 1 shows analyses of 6-hourly accumulated rainfall during the event. Note the heavy rainfall near the coast at landfall and the rapid decrease in rainfall near the TC center thereafter. However, precipitation increased abruptly approximately 300–500 km to the southwest of Bilis’s center. Prior to 0600 UTC 14 July, little rainfall occurred inland and rainfall was mostly confined to the coastal fringe (Fig. 1a). At 1200 UTC 14 July (Fig. 1b), an observing station recorded 37 mm in 6 h near the border of Hunan and Jiangxi Provinces. The localized maximum rainfall rate centered at (258N, 1148E) increased abruptly from 51 mm (6 h)21 at 1800 UTC 14 July (Fig. 1c), up to 96 mm (6 h)21 by 0600 UTC 15 July (Figs. 1d,e), and 77 mm (6 h)21 at 1200 UTC 15 July (Fig. 1f). Because of the suddenness of the flooding and the severity of the event, Bilis has attracted widespread attention in China and elsewhere. Early studies of Bilis focused on large-scale moisture transport in association with cross-equatorial flows at 808–1008E, the southwesterly monsoon over the South China Sea (SCS), the extensive northeasterly flow from the continental high in the lower troposphere (Liu et al. 2008; Ye and Li 2011; Cheng et al. 2013; Dai et al. 2014), instability of the atmospheric stratification, and wind shear during the extreme rainfall period (Shi et al. 2009). In addition, Gao et al. (2009) also suggested that topography, vortex–shear interaction, warm-air advection, and frontogenesis may all have contributed to the development of the heavy rain. These studies documented the large-scale background to the rainfall and the presence of the necessary ingredients for deep, moist convection (Doswell et al. 1996). However, we still do not fully understand (i) how these important ingredients were established and (ii) the operative mechanisms of this type of rainfall event. Few studies have focused on the relationship between vortex structure changes in landfalling TCs and the occasional associated extreme

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rainfall, especially the triggering mechanism prior to the occurrence of rainfall. This will be the focus of the current study. Potential vorticity (PV) is a useful variable for diagnosing dynamical processes in the atmosphere because of the physical insight that can be gleaned from changes in the PV distribution. Any redistribution of PV in a balanced fluid requires an adjustment toward a new state of balance, which from the invertibility principle, is to a large extent predictable (e.g., Hoskins et al. 1985). Hence, it has been widely used in diagnosing the motion and structure features of cyclones in the tropics and mid- to high latitudes (Davis 1992; Wu et al. 2004; Nguyen et al. 2011). In this paper, PV was used to study the vortex structural changes during the extreme rainfall event. As the extreme rainfall following the landfall of Bilis has been described and discussed in previous studies, we will pay special attention to the triggering mechanism of the rainfall and the period primarily before the occurrence of heavy rainfall. The remainder of the manuscript is divided into the following sections. Section 2 describes the data and methods used in the study, followed by the related synoptic background of the extreme rainfall event associated with TC Bilis in section 3. In section 4, the PV structure is first analyzed over the rainfall area and TC Bilis. The phenomenon of PV redistribution from Bilis’s circulation to outer radii over the rainfall areas is demonstrated in section 5. The possible explanation of the redistribution of PV is proposed in section 6. The dynamical effect of the PV transport on the rainfall event is discussed in section 7. Our conclusions are presented in the last section.

2. Data and method The data used for this study include (i) the Final Operational Global Analysis (FNL) fields of the Global Forecast System of the National Centers for Environmental Prediction (NCEP), (ii) conventional 6-h accumulated station rainfall observations provided by the China National Meteorological Center (CNMC) of the China Meteorological Administration (CMA), and (iii) TC best tack datasets from the Japan Meteorological Agency (JMA). The single-particle trajectories are from the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT_4) model developed at NOAA (Draxler and Hess 1998) and implemented at the Australian Bureau of Meteorology (http://www.wmo.int/pages/ prog/www/DPS/WMOTDNO778/rsmc-melbourne-a. htm). The input data for the HYSPLIT_4 model are taken from the FNL dataset.

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FIG. 1. Observed 6-h accumulated rainfall from CMA ending at (a) 0600 UTC 14 Jul, (b) 1200 UTC 14 Jul, (c) 1800 UTC 14 Jul, (d) 0000 UTC 15 Jul, (e) 0600 UTC 15 Jul, and (f) 1200 UTC 15 Jul 2006. The first number in the top-left corner of each panel is the station recorded maximum 6-h rainfall [mm (6 h)21]. The second number is the minimum central surface level pressure (hPa) of Bilis, indicated by the red typhoon symbol. The red triangle indicates the main center of rainfall.

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3. The synoptic pattern As indicated above, many articles have studied the large-scale weather background of this event; so in this section, we will give just a brief description of the environmental flow changes prior to the rainfall from 1200 UTC 12 July (2 days prior to rainfall) to 1200 UTC 14 July (the commencement of rainfall). From Figs. 2a and 2b, at 200 hPa, a strong anticyclone developed across South Asia over the low to midlatitudes, with Bilis located on the equatorward, eastern flank of the anticyclone. As an equatorward-extending midlatitude trough and ridge intensified, a strengthening northeasterly upper-tropospheric flow can be seen over southern China. At 500 hPa (Figs. 2c,d), the continental ridge over mainland China intensified and further connected with the subtropical high over the western Pacific Ocean. The monsoon trough (MT) region near 208N developed and is seen as a major asymmetry in Bilis’s circulation to its west. These changes steered Bilis on its westward track after landfall and also, importantly, resulted in an increase in easterly flow over the northern part of the MT. At 850 hPa (Figs. 2e,f), two branches of the MT can be observed: one portion was located to the south and west of the Tibetan Plateau, the other was located over the SCS and merged with Bilis’s circulation. The southwesterly monsoon flow gradually broadened and strengthened over the Bay of Bengal (BOB) and SCS by 1200 UTC 14 July. At mean sea level (Figs. 2g,h), the asymmetry to the west of Bilis is even more evident as the MT intensified. These variations in synoptic systems resulted in changes of pressure and wind near Bilis’s circulation. Note that (i) the rapid and large-scale decrease in pressure near the MT is closely related to the asymmetry of Bilis and (ii) the development of the continental high results in the acceleration of easterly flow, north of the MT, and further contributes to the increase of flow over Bilis’s northwest quadrant.

4. PV structure over the rainfall area and TC Bilis a. PV over the rainfall area Figure 3 shows time–height sections of wind, PV, and omega over the rain area (238–278N, 1128–1168E) during the event. Prior to the commencement of rainfall (1200 UTC 14 July), the strongest signal evident in the cross section is the increase in mid- to upper-level PV from 700 to 300 hPa, commencing at approximately 0000 UTC 14 July. At this time Bilis had not yet made landfall and its center was located at approximately 25.78N, 120.58E, some 700 km to the east of the rain area. During the rainfall period from 1200 UTC 14 July, large increases in midlevel PV and vertical velocity are

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diagnosed. Note that the increases in PV at low levels (beneath 700 hPa) are quite small so that there are vertical, differential PV changes over the rain area.

b. PV following Bilis’s circulation Time–height azimuthally averaged PV is plotted over regions centered on Bilis’s path. Three regions are considered: 1) within a radius of 320 km of its center, which covers the inner circulation (Fig. 4a); 2) inside an annulus between 320 and 540 km, where the extreme rainfall eventually occurred in the southwest sector (Fig. 4b); and 3) within a radius of 540 km from the center (Fig. 4c). From Fig. 4a, the variation of Bilis’s intensity is clearly reflected by the evolution of PV summed within a 320-km radius. PV increased as Bilis intensified before 0600 UTC 13 July, but decreased after that. These changes are consistent with the TC best track record from JMA. It is noticeable that prior to rainfall, from 0000 to 1200 UTC 14 July, the average PV was significantly reduced through the midtroposphere within a 320-km radius of the center, while the PV summed within the 320–540-km annulus increases to 3 PVU (1 PVU 5 1026 K kg21 m2 s21) between 600 and 300 hPa. The main contribution to this increase in azimuthally averaged PV over the annulus is largely from the region located to the southwest of Bilis’s center over the sudden rainfall areas that later occurred (Fig. 3). In Fig. 4c, the PV within a radius of 540 km varies very little in the mid- to upper levels, even after 0000 UTC 14 July. That is, the net PV changes very little over the total circulation, but there has been a significant redistribution of the PV within the circulation, with high PV moving from inner to outer radii through the midlevels.

5. PV transport from the inner to the outer circulation of Bilis into the rainfall areas The variation of PV around Bilis suggests that high PV may be transferred from the inner circulation to the outer regions (including the rainfall areas) prior to the commencement of rainfall. In this section, the redistribution of PV is examined in detail within both Eulerian and Lagrangian frameworks.

a. Eulerian framework Cross sections of PV and vertical motion along a line joining the rainfall center to Bilis’s center at 12-h intervals are shown in Fig. 5. At 1200 UTC 13 July, a monolithic vertical PV core and coincident ascent region (indicative of Bilis’s circulation) are evident to the east of the rainfall area, which at this time is characterized by weak descent and low values of PV (denoted by a

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FIG. 2. Analyses of the wind vector (m s21) and geopotential height (contour; dam) at (a),(b) 200; (c),(d) 500; and (e),(f) 850 hPa; and (g),(h) MSLP (hPa) at (left) 1200 UTC 12 Jul and (right) 1200 UTC 14 Jul 2006. Contour interval for MSLP is 2 hPa. The thick brown line denotes the axis of the MT. The centers of continental high pressure and subtropical high pressure are labeled H. The South China Sea and Bay of Bengal are abbreviated by SCS and BOB, respectively.

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FIG. 3. Time–height mean PV (shaded; PVU), horizontal wind (barbs, a full barb indicates 4 m s21), and vertical motion (Pa s21, red dashed contours) over the rainfall area (238–278N, 1128–1168E). Contour interval for PV is 0.1 PVU. The black dot denotes the commencement time of rainfall.

black dot). At 0000 UTC 14 July (Fig. 5b), the PV column begins to broaden with a bulge evident over the western sector, particularly through the mid- to high levels. At this time the ascent maximum to the west of Bilis begins to separate from the main PV tower. At 1200 UTC 14 July (Fig. 5c), the extension of PV toward the west continues and by this time two separate and distinct PV columns emerge. The width of the PV region over the mid- to upper troposphere has doubled in size from that at 1200 UTC 13 July. Note that the PV tower does not seem to tilt but rather extends westward as the event develops. In accordance with the PV changes, two ascent maxima are also evident: a weakening maximum, which is likely the remnants of Bilis’s inner core, and a strengthening ascent maximum, located more than 400 km from the center of Bilis. At 0000 UTC 15 July, (Fig. 5d), the PV and upward motion over the rain area continue to develop rapidly in an atmosphere with abundant moisture and convective instability (Gao et al. 2009).

b. Lagrangian framework The westward expansion of the PV column prior to the rainfall is further examined within a Lagrangian framework. Here, we use backward trajectories from the rainfall area to track the origin of those air parcels that

entered the rain area between 0000 and 1200 UTC 14 July, as well as forward trajectories from the center of Bilis to demonstrate the structural changes that were affecting Bilis’s circulation and influencing the rain event.

1) BACKWARD TRAJECTORIES Backward trajectories from the rainfall area are calculated using the HYSPLIT model and are shown in Fig. 6. A total of 13 grid points, separated by 18, are chosen surrounding the rainfall center (258N, 1148E) within a radius of 28 at a height of 7 km (close to 400 hPa). Back trajectories are calculated from each of these grid points. The starting times of these trajectories are 1200 UTC 13 July (Fig. 6a; well prior to the rain), 1200 UTC 14 July (Fig. 6b; the start of the rain), and 0000 UTC 15 July (Fig. 6c; during the heavy rain). The trajectories in Figs. 6a and 6d show that well prior to the rainfall the areas over the rainfall region are influenced only by parcels in the easterlies, which descended from the north in the mid- to upper levels of the anticyclone. The PV values are not large, only around 0.2–0.5 PVU. Just before the rainfall (Figs. 6b,e), a large amount of high-PV air began entering the rainfall area. These parcels can be traced back to the air from the southwesterly monsoon flows at lower levels over the

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FIG. 4. Time–height azimuthal-mean PV (PVU) moving with Bilis’s circulation summed within (a) a radius of 320 km, (b) an annulus between 320 and 540 km, and (c) a radius of 540 km. The black dot denotes the commencement time of rainfall.

South China Sea, where the air was warm and moist (not shown) but with small PV values. They converge and ascend within Bilis’s circulation, acquire high values of PV (up to 1 PVU), and finally exit the inner circulation

of Bilis toward the rain area. As may be seen in Figs. 6b and 6e, these parcels first rise and spiral through the circulation from 240 to 212 h (2000 UTC 12 July– 0000 UTC 14 July), and then move more horizontally

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FIG. 5. Longitude–height cross sections of PV (contour interval is 0.2 PVU), overlain with omega (shaded; Pa s21), along a line between the rainfall center and Bilis’s center during the heavy rain. The black dot represents the rainfall center, and the red typhoon symbol indicates Bilis’s center.

from 212 to 0 h (0000–1200 UTC 14 July) at mid- to upper levels, indicating the parcels move out of the ascent flow within Bilis and toward the rain area. During the rainfall (Figs. 6c,f), as weakening and dissipation of the inner Bilis circulation occurs, the parcels with high PV rotate and continue to be ejected toward the rainfall area, but instead of horizontal motion, a broad ascent of the air parcels can be seen.

2) FORWARD TRAJECTORIES To indicate the structural changes in Bilis associated with the high-PV redistribution, we have used 48-h forward trajectories from Bilis’s center. The starting points are chosen near the center of Bilis within a radius of 28, at the low level of 1.5 km so that we can see the complete trajectory of the air parcels from low to high levels.

In Fig. 7a, well prior to the rainfall (1200 UTC 11 July– 1200 UTC 13 July), the parcels from Bilis are well constrained within its rotating circulation and very few parcels escape from the circulation below 5 km. In Fig. 7b (1200 UTC 12 July–1200 UTC 14 July), the parcels are at first constrained within the core of Bilis, and then a large number of parcels begin to flow horizontally out of the inner circulation of Bilis between 5 and 9 km, move outward from the northwestern quadrant, and arrive over the rainfall area at around 1200 UTC 14 July. The backward and forward trajectories both demonstrate that in association with the westward expansion of the PV column, a large number of air parcels with high PV move from the northwestern sector of Bilis’s core in the mid- to upper levels (5–9 km) and travel toward the rainfall area prior to the commencement of rainfall

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FIG. 6. (a)–(c) Horizontal plots and (d)–(f) time–height plots of 72-h backward trajectories from the rainfall center: the starting times are (a),(d) 1200 UTC 13 Jul; (b),(e) 1200 UTC 14 Jul; and (c),(f) 0000 UTC 15 Jul 2006. The initial parcel elevation is 7 km. The color denotes different PV values (PVU) as shown in the color bar.

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FIG. 7. The 48-h forward trajectories from Bilis’s center, with starting times at (a) 1200 UTC 11 Jul and (b) 1200 UTC 12 Jul. The initial parcel elevation is 1.5 km. The different heights of the air parcels are indicated in the color bar (km).

(from 0000 to 1200 UTC 14 July). In addition, the outflow of high PV from Bilis’s inner circulation results in a decrease in PV values over the inner core through the mid- to upper levels and may contribute to the demise of its inner circulation and a rapid weakening of the inner-core rainfall as observed (see Fig. 1). But why do the parcels suddenly begin to move from the inner to the outer circulation of Bilis during this time and why do they exit the circulation above 5 km and from the northwestern sector? In the following sections we address these interesting questions.

6. Possible explanation for the midlevel redistribution of PV The process of high-PV redistribution within a Lagrangian framework is accompanied by the expansion of the PV column westward within an Eulerian framework, which is crucial for the local increase in PV over the rainfall areas in the mid- to upper troposphere. In this section, we explore some factors that may have contributed to the PV redistribution from about 12 h before the commencement of the rainfall.

a. Evolution of Bilis’s tangential and radial winds Analysis of Bilis’s wind field shows that the azimuth of the maximum radial wind outflow occurs over the western sector between angles from 08 to 1208. (Here, north and south are defined as 08 and 1808 and the angle increases when it rotates anticlockwise.) So we have plotted time–height sections of the average radial wind (shaded)

and tangential wind (solid lines) over the western sector. In Fig. 8a, before 0000 UTC 14 July, the tangential wind structure is a deep, nearly barotropic vortex, as indicated by the isoline of 14 m s21 below 400 hPa, which is present for about 30 h. The tangential wind then decreases rapidly after that. The radial outflow (positive shaded areas represent outward radial wind) is mainly located within the rapidly rotating tangential wind column beneath 400 hPa before 0000 UTC 14 July, with two maxima at 0000 and 1200 UTC 13 July near 700 and 650 hPa. This radial wind maximum develops upward of the mid- to upper troposphere between 0000 and 1200 UTC 14 July, with the maximum relocating to near 400–500 hPa. Hence, it seems that, because of the strong rotation of the circulation over the mid- to lower troposphere before 1800 UTC 13 July, it is difficult for air parcels to escape from the inner circulation. After this time, the tangential wind begins to weaken and the flow becomes less inertially stable. At this time, we expect parcels to be less constrained by the weakening rotational flow and to more easily move radially and flow out of the inner circulation. The ventilation resulting from strengthening easterly winds in the mid- to high troposphere, illustrated in Fig. 8b, further helps these parcels to escape from the western sector and move toward the rain areas.

b. Gradient wind imbalance (GWI) of Bilis’s circulation The outward radial-wind acceleration through the midto upper levels prior to the rainfall implies that the

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FIG. 8. (a) Time–height section of mean tangential wind (solid line) and outward radial wind (shaded) relative to TC over the western sector. (b) Time–height section of the mean environmental wind (a full barb indicates 4 m s21) within a 540-km radius. The black dot represents the commencement of rainfall.

gradient wind balance (GWB) relationship or, in fact, the gradient wind imbalance (GWI) should be examined. As GWB is a good approximation of the azimuthally averaged wind above the boundary layer of TCs (e.g., Wang and Zhang 2003), an acceleration of the radial wind can

be associated with an imbalance between the three forces in Eq. (1) (Liu and Liu 1991, 533–535): dyr ›f y 2 5 2 1 u 1 f0 y u , ›r dt r

(1)

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FIG. 9. Time–height sections of (a) the mean GWI (shaded; 1023 m s22) within a 540-km radius of Bilis over the western sector and (b) the mean environmental VWS between 200 and 850 hPa within a 320–800-km annulus. The black dot represents the commencement of rainfall.

where y r and y u are the radial and tangential wind, respectively; f is the geopotential; the term on the lefthand side is the acceleration of the radial wind, which we term GWI; and the terms on the right-hand side are the pressure gradient force (PG), the centrifugal force, and the Coriolis force, respectively. Figure 9a shows time–height series of the agradient force or GWI during the event. Even though the resolution of the FNL datasets is only 18, a strong and time-coherent, positive anomaly of GWI can be seen near the mid- to upper troposphere at most times during the evolving event, corresponding to the acceleration of the radial outflow prior to rainfall (Fig. 8a). To try to understand the origin of the GWI, the specific horizontal distribution of the PG, Coriolis, and centrifugal forces, and GWI at 400 hPa, are illustrated in Fig. 10 at 1800 UTC 13 July (left; when Bilis reached its peak intensity), 0000 UTC 14 July (middle), and 1200 UTC 14 July (right). To emphasize the differences of these forces, each force at 0000 and 1200 UTC 14 July is subtracted from the one at 1800 UTC 13 July (when Bilis attained its maximum at this time) and the significant positive differences are denoted by white dots in Fig. 10. Recall from section 3, prior to the rainfall, that the variation of asymmetric features of wind and pressure can be seen around Bilis’s circulation, which is also reflected in Fig. 10. Note that although the central pressure of Bilis weakened during this time period, the most significant decrease of the inward PG force occurs in the southwestern semicircle (the white dotted areas in Figs. 10b and 10c) as Bilis was finally embedded in the eastern end of the MT. Basically, the intensities of the Coriolis force (Figs. 10d–f) and the centrifugal force (Figs. 10g–i) tend to decrease

around Bilis, while asymmetric increases in the outward forces can be observed as they gradually move to the northwestern quadrant (the dotted areas in Figs. 10e,f and 10h,i) as the easterly component near the northwest quadrant of Bilis increased. The anomalies in the Coriolis and centrifugal forces correspond in many respects to maxima in the wind. With the weakening of the PG, and the asymmetric increase (or at least maintenance) of the Coriolis and centrifugal forces in the western sector, GWI (Figs. 10j–l) indicates a net outward force acting at mid- to upper levels, which opens up the circular flow to the west and creates the outflow evident in Fig. 9a. We have dramatically described the regions with large GWI as being a ‘‘wound’’ in the northwestern sector of Bilis, from which PV bled to outer radii. We suggest that an interaction with the environment was a possible key to the GWI. We plan to study this aspect in more detail in the future. We also consider the Okubo–Weiss parameter OW 5 z2 2 (Sn2 1 Ss2 ) (Okubo 1970; Weiss 1991; Dunkerton et al. 2009; Tory et al. 2013) as a means of demonstrating the relative importance of vorticity and deformation. And it is found that during this time a nonuniform expansion of the vortex core (with positive values of the OW parameter) occurred, as the positive value region of OW almost doubled in size from 1800 UTC 13 July to 1200 UTC 14 July in the west–east direction (Fig. 11). Inside the vortex core, the values of OW began to weaken over the west quadrant beginning at 0000 UTC 14 July (Figs. 11b–d) and, finally, were distorted into two parts after that (not shown), suggesting the increased deformation and weakening of vertical vorticity as Bilis evolved from a closed, tight circulation with trapped air parcels, into a loosely

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FIG. 10. Horizontal distribution of (a)–(c) pressure gradient force, (d)–(f) Coriolis force, (g)–(i) centrifugal force, and (j)–(l) GWI within an 800-km radius of Bilis’s center at (left) 1800 UTC 13 Jul, (middle) 0000 UTC 14 Jul, and (right) 1200 UTC 14 Jul. Red (blue) shaded area denotes outward (inward) forces (intervals are 0.25 3 1023 m s22) and contours denote geopotential height (intervals are 3 dam) at 400 hPa. The white dots denote the regions with the most significant decreases in pressure gradient force (the first row) and increases in Coriolis force (the second row), centrifugal force (the third row), and GWI (the fourth row) at 0000 UTC 14 Jul (middle column) and 1200 UTC 14 Jul (right column) compared to 1800 UTC 13 Jul.

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FIG. 11. The 500-hPa streamlines in the reference frame moving with the storm, geopotential height (contour; dam), and OW parameter (1029 s22; positive values are shaded) at (a) 1800 UTC 13 Jul, (b) 0000 UTC 14 Jul, (c) 0600 UTC 14 Jul, and (d) 1200 UTC 14 Jul. The red dot denotes the center of rainfall.

distributed circulation, which may allow air parcels to move from its inner western flank. As vertical wind shear (VWS) has been demonstrated to have an influence on the rainfall asymmetry of TCs (Corbosiero and Molinari 2002, 2003; Chen et al. 2006), we ask the following question: Is the westward expansion

of Bilis’s PV column prior to the rainfall also related to VWS? Figure 8b shows the vertical structure of the environmental wind, from 1200 UTC 12 July to 1200 UTC 14 July, is nearly constant with height up to 300 hPa. Figure 9b shows that the magnitude of the deep-tropospheric VWS attains a minimum (6–10 m s21)

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from 0000 to 1200 UTC 14 July. So it is suggested that the VWS and its associated resolvable tilt are likely too weak to be the dominant factor influencing the expansion of the PV core and initiating the asymmetry of rainfall before 1200 UTC 14 July. But after the rainfall is triggered, as indicated by Gao et al. (2009) and Shi et al. (2009), the wind direction became opposed at upper and lower levels. Thus, the increasing VWS at this later time and during the frontogenesis process may become important.

7. Discussion of the effects of PV redistribution on rainfall We have shown that a large PV redistribution from inner to outer radii within Bilis was crucial to the increase in PV at mid- to upper levels over rainfall areas prior to the commencement of extreme precipitation. Here, we use a PV budget and isentropic analysis to further demonstrate the link between PV vortex structural changes and the triggering of heavy rainfall. We consider the traditional PV tendency (e.g., Tory et al. 2012): ›PV ›PV 1 1 5 2Vh =PV 2 v 1 (ja =u)1 (=u =3 Fr ) . ›t ›p r r term a term b term c term d term e (2) All of the variables have their conventional meanings; ja is the three-dimensional absolute vorticity and u is the diabatic heating tendency. As a result of the fact that the diabatic heating (term d) and friction (term e) in Eq. (2) are not available in the 18 FNL reanalysis dataset, these two contributions can only be obtained as the residual calculated from the difference between the PV tendency (term a) and advection terms (terms b and c). From Fig. 12a, the PV tendency over the rainfall areas increases significantly at mid- to upper levels from 0000 to 1200 UTC 14 July but varies little during the rainfall. The PV tendency distribution and magnitude are very similar to the horizontal advection of PV, which increases with height prior to the increase of heavy rainfall, and attains its maximum of 1.5 PVU day21 at 1200 UTC 14 July (Fig. 12b). The vertical advection of PV (Fig. 12c) and the residual term (Fig. 12d), clearly show the very strong cancellation between the two terms mentioned above, but they only become dominant after the convection has been initiated over the rain area from 1200 UTC 14 July. We also note that due to (i) the coarse temporal resolution, (ii) uncertainties with the diabatic heating term d in Eq. 2, and (iii) the cancellation between terms c and d in convective systems (Tory et al. 2012),

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there are uncertainties about the usefulness of term c and the residual (term d plus term e). Fortunately, an analysis of the alternative PV tendency equations (Tory et al. 2012), which do not suffer from the cancellation between terms c and d and do not require calculation of the diabatic heating, still indicate that the dominant contributor to the PV tendency over the rainfall area, but before the rain commences, is horizontal PV advection. In addition, the strong vertical advection (term c) and diabatic tendencies (term d) are known to be associated with active, deep convection after the rainfall increases. But here we have paid special attention to the prerain signal (before 1200 UTC 14 July), and we are not so concerned with the tendencies after the commencement of heavy rainfall. The budget calculations suggest that the results from Eq. (2) are reliable before 1200 UTC 14 July and the redistribution of PV is mainly composed of the horizontal transfer of PV from the inner region of Bilis to the future rainfall areas. Furthermore, from the horizontal distribution of PV advection at mid- to upper levels (Fig. 13), as the positive PV advection moved from Bilis’s center to outer rainfall areas, the negative PV advection near Bilis’s center appears from 0000 to1200 UTC 14 July (Figs. 13a–c). As the advection at the lower levels is weak, the negative differential PV advection (or vorticity advection) between the lower and mid- to upper levels is associated with a decrease in vertical motion over the inner circulation of Bilis. So the horizontal PV advection not only played a key role in establishing favorable rainfall conditions over the outer circulation but also contributes to the decrease in PV and vorticity at mid- to lower levels over the inner region of Bilis prior to the sudden rainfall event. We suggest that these are the reasons, essentially the PV redistribution, for the weakening of Bilis and the large rainfall amount at outer radii. Figure 14 shows, at various times, the horizontal distribution of PV at 400 hPa (black contours) and 850 hPa (red contours), together with the distribution of vertical motion (shading). The westward extension of the midlevel PV and the separation of low-level and midlevel PV can be seen in the diagrams. To be specific, at 1200 UTC 13 July (Fig. 14a), the 850-hPa PV center coincided with the one at 400 hPa, indicating Bilis had a vertically aligned PV core. Upward motion (shaded areas) is distributed relatively uniformly around Bilis’s circulation. In time, the western side of the isentropic PV through the midlevels extends westward relative to the PV anomaly at 400 hPa, suggesting the mid- to upper-level PV of Bilis expanded westward over the western quadrant and an asymmetric structure formed (Fig. 14b). At 1200 UTC 14 July (Fig. 14c), a more pronounced

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FIG. 12. Time–height PV budget based on Eq. (2) (PVU day21), horizontal wind (a full barb indicates 4 m s21), and vertical motion (red dashed contours; interval is 0.1 Pa s21) over the rainfall area (238–278N, 1128–1168E). Shown are (a) PV tendency, (b) horizontal advection of PV, (c) vertical advection of PV, and (d) the residual term. The black dot denotes the commencement time of rainfall.

southwestward expansion can be seen in the mid- to upper levels and the upward motion moved in accordance to the southwestern quadrant. Following the onset of rainfall, a strong region of ascent can be seen over the southwestern quadrant at 1800 UTC 14 July (Fig. 14d). The high, inner-core PV in the mid- to upper troposphere was redistributed outward toward the rain area during the overall storm expansion. Since the redistribution of midlevel PV from Bilis provides a possible dynamical cause for the collapse of

rainfall around Bilis’s center and the increase over the southwestern quadrant, the linkage between PV advection and upward motion needs to be clarified. It is useful to consider the physical changes in the fluid in response to differential PV advection prior to the commencement of rainfall. As the anomaly of PV is advected over the rain area, it casts a low pressure shadow below, which requires some adjustment to bring the fluid below to a new state of balance [isentropic PV thinking; Bluestein (1993, 180–203)].

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FIG. 13. The 500–350-hPa layer-mean horizontal PV advection (shaded; PVU day21), layer-mean wind vector (m s21), and layer-mean geopotential height (contour; dam) at (a) 0000, (b) 0600, (c) 1200, and (d) 1800 UTC 14 Jul 2006.

From Fig. 15a, the adjustment response to mid- to upper-level PV advection includes the lowering of upper-level isentropes (e.g., 345 K, approximately 9 km) and increases in the mid- to lower-level isentropes (e.g., 320 K) from 1800 UTC 13 July to 1200 UTC 14 July. This reflected a warming at upper levels and cooling over the

mid- to lower troposphere. With the rising isentropic surfaces over the mid- to lower troposphere, a direct adiabatic ascent, although relatively small, occurred accordingly (red dotted line in Fig. 15b). In addition, the total vertical velocity (black solid line in Fig. 14b) also starts to increase from 0000 UTC 14 July as the

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FIG. 14. The 400-hPa PV (black contours; PVU), 850-hPa PV (red contours), and horizontal wind vectors (m s21) at (a) 1200 UTC 13 Jul, (b) 0600 UTC 14 Jul, (c) 1200 UTC 14 Jul, and (d) 1800 UTC 14 Jul. Total vertical ascent (Pa s21) at 500 hPa is indicated by the shaded areas. The PV centers at 400 and 850 hPa are denoted by the red dot and blue cross, respectively.

isentropic surfaces are raised over these levels at this time. Note that this process is active prior to the rainfall, and can be considered to provide a direct lifting mechanism over the future rainfall center and also establishes favorable conditions (a cold dome of raised isentropes)

for the future warm advection. With the mid- to lowlevel wind directed toward the raised isentropes (or cold dome), isentropic ascent (warm advection) was then present. We thus see that positive horizontal advection of PV (increasing with height above 700 hPa) mainly

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We propose that the redistribution of PV from Bilis to the rainfall areas prior to the heavy rainfall provided local conditions very favorable for triggering deep convection before 1200 UTC 14 July. The midlevel PV advection was associated with (i) adiabatic ascent in the fluid below, (ii) the establishment of a cold dome, and (iii) the building of this thermal structure favorable for isentropic ascent in the lower-level flow directed toward the cold dome. In the very moist and conditionally unstable environment, these adiabatic lifting mechanisms further destabilized the column and contributed to the increase in deep moist convection throughout much of the heavy rain period from 1200 UTC 14 July to 1200 UTC 15 July.

8. Discussion and conclusions Bilis rapidly weakened after it made landfall along the south China coast at 0500 UTC 14 July 2006. However, sudden extreme rain developed over a region approximately 300–500 km to the southwest of its center. The rain event, following the landfall of Bilis, caused widespread catastrophic flooding and subsequent large loss of life and property. Different from, but complementary to, previous studies, we use PV as an important parameter in exploring the influence of TC Bilis on the extreme rainfall event, especially prior to the occurrence of rainfall. We have demonstrated the following points.

FIG. 15. Time series over the rain area of (a) geopotential height on the 345-K (red solid line; m) and 320-K (black dashed line) isentropic surfaces, and (b) total vertical velocity (black solid line) and isentropic vertical velocity (red dotted line; Pa s21) on the 320-K surface. The black dot represents the starting time of rainfall. The isentropic vertical motion, which can be viewed as the adiabatic vertical motion, is computed using the thermodynamic Eq. (1) in Tory (2014).

occurred prior to the rainfall (from 1800 UTC 13 July to 1200 UTC 14 July in Fig. 12b), and then conditions for warm advection were established that gradually increased from the lower levels to the midlevels during the rainfall and became the dominant forcing of vertical motion from 1800 UTC 14 July to 0600 UTC 15 July (Gao et al. 2009). After 1200 UTC 14 July, a sharp increase can be seen in the total vertical ascent, but not from the isentropic motion since diabatic heating is accompanied by adiabatic cooling, so together they do not cause much movement of isentropes after the rainfall has developed.

1) As the decaying TC Bilis moved westward, its circulation expanded westward and a large amount of high-PV air was redistributed from its northwestern quadrant through the midlevels, and flowed to the future rainfall area from 0000 to 1200 UTC 14 July (12 h prior to the commencement of extreme rainfall). 2) The occurrence of this redistribution phenomenon, which is different from the direct vortex tilting in environmental vertical wind shear, can be related to a developing GWI within Bilis, which was associated with the strong radial outflow of high-PV air through the midlevels. 3) As the nonuniform westward expansion of Bilis’s vortex occurred, the redistribution of high-PV air from Bilis’s inner circulation resulted in a local PV increase over rainfall areas through the midlevels. A PV budget further indicated the redistribution was dominated by horizontal PV advection with maximum amplitude in the mid- to upper troposphere, prior to the commencement of heavy rain. The direct effect of differential PV advection was to raise midto lower-level isentropes to try to maintain a gradient

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wind balance, which created a cold dome. The PV advection was thus critical in raising isentropes that triggered convection before 1200 UTC 14 July. The indirect effect of lower-level adiabatic flow relative to the raised isentropes was warm advection as the fluid flowed up and over the cold dome. This was a major contributor to the development of deep moist convection throughout much of the heavy rain period [from 1200 UTC 14 July to 1200 UTC 15 July; Gao et al. (2009)]. With an abundant moisture supply and conditional instability of the atmospheric stratification, the ascent significantly increased and resulted in extreme rainfall. 4) We suggest that an interaction with the environment was a possible key to the development of GWI and deformation of Bilis. As Bilis approached and was finally embedded in the intensifying MT, a major asymmetry was created to the west-southwest of Bilis’s circulation, including a bulge in geopotential height to its southwest and an increase in the easterly wind component over the northwestern quadrant due to the development of the continental high and the asymmetry of Bilis’s circulation. The changes resulted in a net increase in GWI near the westnorthwest quadrant of Bilis and also produced an increase in deformation over the western quadrant, which is reflected in the OW parameter. The increase in the easterly wind component near the northwestern quadrant acts as a ‘‘bridge’’ and makes the air parcels within the inner circulation with high PV values move outward more easily than in a tight closed circulation. Consequently, a positive PV advection and outward transfer of those air parcels can be observed. PV redistribution occurred. From this point, the deformation and GWI are closely related and both appear to contribute to the PV redistribution. They are also closely related to the interaction with the MT. More detailed study on this environmental interaction will be addressed in a follow-up article.

Acknowledgments. The authors are grateful for the help and thoughtful advice from Alan Wain, Greg Roff, Xingbao Wang, Simon Ching, William Thurston, and Beth Ebert. This study is cofunded by grants from the National Natural Science Foundation of China (Grants 41405057, 41375052, and 41575045) and a scholarship from the China Scholarship Council under Grant CSC 201404910072. This research was undertaken with the assistance of resources from the National Computational Infrastructure (NCI), which is supported by the Australian Government via the Bureau of Meteorology.

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