Features of Rainbands and Asymmetric Structure

84 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 67

Impacts of Evaporation from Raindrops on Tropical Cyclones. Part II: Features of Rainbands and Asymmetric Structure

MASAHIRO SAWADA AND TOSHIKI IWASAKI Atmospheric Science Laboratory, Department of Geophysics, Graduate School of Science, Tohoku University, Sendai, Miyagi, Japan

(Manuscript received 4 May 2009, in ﬁnal form 6 August 2009)

ABSTRACT

In this study, the impacts of evaporative cooling from raindrops on a tropical cyclone (TC) are examined using cloud-resolving simulations under an idealized condition. Part I of this study showed that evaporative cooling greatly increases the kinetic energy of a TC and its size because rainbands provide a large amount of condensation heating outside the eyewall. Part II investigates characteristics of simulated rainbands in detail. Rainbands are actively formed, even outside the eyewall, in the experiment including evaporative cooling, whereas they are absent in the experiment without evaporative cooling. Rainbands propagate in the counterclockwise and radially outward direction, and such behaviors are closely related to cold pools. New convective cells are successively generated at the upstream end of a cold pool, which is referred to here as the upstream development. The upstream development organizes spiral-shaped rainbands along a low-level streamline that is azimuthally averaged and propagates them radially outward. Asymmetric ﬂows from azimuthally averaged low-level wind advance cold pool fronts in the normal direction to rainbands, which are referred to here as cross-band propagation. The cross-band propagation deﬂects the movement of each cell away from the low-level streamlines and rotates it in the counterclockwise direction. Cross-band propagation plays an essential role in the maintenance of rainbands. Advancement of cold pool fronts lifts up the warm and moist air mass slantwise and induces heavy precipitation. Evaporative cooling from raindrops induces downdrafts and gives feedback to the enhancement of cold pools.

1. Introduction the NOEVP experiment rainbands hardly appear outside the eyewall and it retains its size very well. Roles Evaporative cooling has signiﬁcant impacts on the of rainbands are considered to be important for TC development and structure of a tropical cyclone (TC) characteristics because TC size is closely related with through changes of convective activity. In Sawada and rainband activity. Thus, herein we aim to study the for- Iwasaki (2010, hereafter Part I), it is shown that when mation, propagation, and maintenance mechanism of evaporative cooling is included (control experiment) rainbands through the cloud-resolving simulations of rainbands are actively formed, which produce large the Japan Meteorological Agency (JMA) Nonhydrostatic amounts of condensation heating at not only the eyewall Model (NHM). but also the outside. The diabatic heating associated Many observational studies by radar or aircraft have with rainbands greatly drives the secondary circulation been done on the shape, structure, and propagation of of the TC and transports the absolute angular momen- rainbands in a TC. Wexler (1947) showed the spiral tum inward. The enhanced angular momentum con- shape of rainbands from radar observation and sug- tinuously increases the kinetic energy of a TC and gested inﬂuences from the low-level streamlines on its expands the TC size (radius of gale-force wind), when formation. Observed radar echo patterns elongate at the compared with the experiment excluding evaporative upstream end of rainbands and propagate radially out- cooling (NOEVP experiment). On the other hand, in ward (Senn and Hiser 1959; Tatehira 1961). Senn and Hiser (1959) indicated that the internal gravity waves and cross-band shear of the upper-level winds provide Corresponding author address: Masahiro Sawada, Graduate School of Science, 6-3, Aramaki, Aoba, Aoba-ku, Sendai, Miyagi the mechanism for the outward propagation of the in- 980-8578, Japan. dividual echoes. Tatehira (1962) remarked that the old E-mail: [email protected] eyewall propagates outward from the TC center and the

DOI: 10.1175/2009JAS3195.1

Ó 2010 American Meteorological Society Unauthenticated | Downloaded 09/29/21 08:41 PM UTC JANUARY 2010 S A W A D A A N D I W A S A K I 85 new one is formed inside the old one. MacDonald (1968) the linearized equations for small perturbations that described the shape of rainbands from radar scope rainbands might be interpreted as outward-propagating and satellite images and its analogy of the propagation internal gravity waves. Some numerical simulations to tropospheric troughs of general circulation (Rossby showed that the rainbands seem to act as internal gravity waves). Willoughby et al. (1984) and Shimazu (1997) waves (Anthes 1972; Kurihara and Tuleya 1974; Jones classified types of rainbands from their movement speed, 1977). However, Yamasaki (1983) indicated a possibility where one type featured almost motionless rainbands that cumulus parameterization misleads characteristics with respect to the TC center (a stationary band complex, of gravity waves in their models. or slow-moving band) and the other featured cyclonically Guinn and Schubert (1993) remarked that inner rain- rotating rainbands (a moving band, or fast-moving band). bands are interpreted as potential vorticity wave break- Stationary and long-lived rainbands, which were found by ing, and the merger uses f -plane shallow-water equations. photographic mapping (Malkus et al. 1961), are formed Montgomery and Kallenbach (1997) examined outward- by the interaction between the TC vortex and its envi- propagating spiral rainbands such as VRWs. In spite of ronmental flows (Willoughby et al. 1984; Shapiro 1983), many attempts to understand the rainbands’ formation and moving rainbands have a close relationship with in- and propagation, the impacts of evaporative cooling on ternal gravity waves (Willoughby et al. 1984). In contrast, rainbands behaviors using 3D cloud-resolving simula- Shimazu (1997) showed that features of moving rain- tions are not fully understood yet. bands contradict internal gravity waves. These observa- Thus, the purpose of this study is to clarify what roles tional studies can capture parts of rainband features; evaporative cooling has in rainband formation, propa- however, it is not sufficient to bring out the dynamical and gation, and maintenance using 3D cloud-resolving sim- thermodynamic structure of rainbands yet. ulations of the TC under an idealized environment. Barnes et al. (1991) suggested that cold pools play an Section 2 presents shape, propagation, maintenance important role in the rainband maintenance, from air- mechanisms, and downdraft formation of simulated borne observation. Some observational studies reported rainbands from numerical experiments. In section 3, the decrease of temperature with the passage of rainbands whether features of simulated rainbands are consistent (Ushijima 1958; Tatehira 1962; Barnes et al. 1983; Powell with those of observed ones, and the relationship be- 1990b). However, such cold pools are not always observed tween present results and proposed mechanisms for (Tatehira 1961; Ishihara et al. 1986; Shimazu 1997). It is rainband propagation in the previous numerical studies very difficult to capture a three-dimensional (3D) struc- are discussed. Finally, section 4 concludes the signifi- ture of cold pools and to reveal its roles in rainbands from cant results in this study. only observational data. Hence, 3D cloud-resolving sim- Detailed model descriptions and the experimental ulations are desired to clarify the cold pool behaviors. design are given in the companion paper (Part I). Here, Theoretical and numerical studies on rainband forma- the same simulations will be analyzed focusing on the tion and propagation are roughly classified into the fol- behavior of rainbands. lowing three categories: cold pools (Yamasaki 1983, 1986), internal gravity waves (Abdullah 1966; Kurihara 1976; 2. Results Willoughby 1978; Chow et al. 2002), and vortex Rossby a. Impact of evaporation on rainband formations waves (VRWs; Guinn and Schubert 1993; Montgomery and Kallenbach 1997). Yamasaki (1983) showed from In Part I, the evaporation from raindrops was shown cloud-resolving simulations of two-dimensional axisym- to cause considerable amounts of precipitation on the metric models that cold pools are essential for rainband outside of the eyewall. Figure 1 shows time–radius cross formation and radially outward propagation. Though sections of azimuthally averaged precipitation and tan- axisymmetric models cannot explain the spiral-shaped gential wind speed averaged from the surface to 5.14-km structure and azimuthal propagation of rainbands, 3D height (same as Fig. 3 in Part I). In the control experi- simulations are desired. Yamasaki (1986, 2005) remarked ment, precipitation areas begin to form around the TC that rainbands are reproduced using a 3D model with center at T 5 24 h and intense precipitation areas parameterized cold pool effects. However, it is not [.5 mm (10 min)21] are seen around a radius of 20 km enough to resolve the detailed structure of rainbands from the TC center at T 5 48 h. On the outside of an resulting from coarse horizontal grid spacing (about 15 eyewall, heavy precipitation areas propagate radially or 20 km). outward from a radius of 40 km to greater than 200 km Abdullah (1966) attempted to model observed fea- from the TC center whose speeds are 1–4 m s21. Here, tures of rainbands as propagating internal gravity waves the radially outward propagation of azimuthally aver- and to explain its features. Kurihara (1976) showed from aged precipitation is referred to as ‘‘radially outward

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FIG. 1. Time–radius cross sections of azimuthally averaged precipitation (shaded) and tangential wind averaged azimuthally and vertically from surface to z 5 5.14 km (contour), with contour values of 15, 25, and 50 m s21 in (a) the control and (b) the NOEVP experiments. As in Fig. 3 of Part I. propagation.’’ As mentioned in Part I, the strong wind rative cooling has signiﬁcant impacts on propagation of area gradually enlarges outward in the control experi- convective activity and TC size. ment. On the other hand, in the NOEVP experiment Radially outward propagation of precipitation shown the precipitation areas are observed around a radius of by Fig. 1 is mainly attributed to rainbands. Figure 2 40–100 km from the TC center at T 5 12–36 h, which displays the temporal change of horizontal structures of almost do not extend radially outward. At an inten- precipitation (left columns) and potential temperature siﬁcation stage (T 5 36–48 h), intense precipitation at a height of 20 m (right columns) from 48 to 96 h with areas concentrate around the TC center. After T 5 48 h, 12-h intervals over a domain of 300 3 300 km2 in the precipitation areas hardly form outside the eyewall control and NOEVP experiments. In the control exper- (greater than a radius of 60 km from the TC center) and iment, precipitation areas are organized into the ring the outward propagation is not observed at all. In ac- shape around the eyewall and the spiral shape (rain- cordance with these features, the strong wind area does bands) on the outside. Spiral-shaped rainbands frequently not expand after T 5 30 h. It is evidenced from the emerge outside the eyewall. Rainbands are 10–30 km comparison between the two experiments that evapo- wide and 50–500 km long and their lifetimes are about

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FIG. 2. (left) Temporal change of horizontal structure of precipitation and (right) potential temperature at a height of 20 m from 48 to 96 h, with 12-h intervals over a domain of 300 3 300 km2 in the control and the NOEVP experiments, respectively. The interval of radii for circles is 30 km. Contour values of the precipitation are 2, 10, and 30 mm h21.

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12 h or less. Rainbands rotate in a counterclockwise inflows within the planetary boundary layer (PBL). To direction around the TC center. In the NOEVP experi- investigate the process of the upstream development, ment, precipitation areas are almost absent on the outside detailed horizontal structures of a rainband are shown in of a radius of 60 km from the TC center. Band-shaped Fig. 4. Shaded regions show vertically accumulated rain- precipitation areas are formed around the eyewall; how- water (rainbands) and contours show precipitation (left ever, these do not propagate radially outward and their column), azimuthally averaged potential temperature lifetimes are 2 h at most. By comparison with the control anomaly (middle column), and horizontal convergence experiment, the evaporative cooling is considered to play (right column). Solid, thick lines with arrows are stream- an essential role in the formation of radially outward- lines drawn from azimuthally averaged wind at a height of propagating rainbands. 260 m temporally averaged from 64 h to 64 h 40 min. There appear to be significant cold anomalies, so- Labels A–D indicate individual convective cells. Cold called cold pools, below the rainbands in the control pools appear markedly below the convective cells in the experiment in the right column in Fig. 1. They are gen- middle column. They are formed by evaporative cooling erated by evaporative cooling from raindrops and form from raindrops as will be discussed in section 2d. Cold axially asymmetric structures. In the control experiment, pools produce horizontal convergences at the near sur- the radial distribution of potential temperature fluctuates face between the upstream side of cold pools and low- significantly with time. In contrast, the NOEVP experi- level inflows along streamlines, and its lifting forms new ment cannot form cold pools resulting from a lack of convective cells B–D. New convective cells are succes- evaporative cooling, and it has an almost symmetric sively generated at the upstream end of a convective cell structure of potential temperature. In the NOEVP ex- A, which are organized into the spiral-shaped rainband periment, the radial distribution of potential temperature along the low-level, azimuthally averaged streamlines hardly changes with time and decreases with radius— propagate radially outward. Thus, cold pools play an these features are significantly different from those in the essential role in the upstream development. control experiment. The basic-state potential tempera- c. Cross-band propagation of rainbands ture is 1–3 K greater in the NOEVP experiment than in the control experiment. Although the NOEVP experi- As shown in Figs. 3 and 4, moving rainbands signifi- ment has a larger static instability, rainbands are absent. cantly deflect from the low-level streamlines and almost The results indicate that cold pools may have an impor- follow along concentric circles, although the spiral shape tant role in the formation of rainbands. of rainbands is roughly arranged along the streamlines. This deflection means that the moving direction is dif- b. Upstream development of rainbands ferent from the azimuthally averaged wind. As will be Rainbands tend to lie along low-level streamlines. shown later (Fig. 6), anomalous winds near cold pools, Figure 3 displays horizontal distributions of simulated which steer convective cells, are almost normal to the rainbands and streamlines at a height of 260 m hourly band. Thus, the movement of rainbands is referred to as from 65 to 70 h over a domain of 300 3 300 km2 in the ‘‘cross-band propagation.’’ control experiment. The same streamlines are drawn in To examine movement of individual convective cells, all the panels, following averaged wind azimuthally and Fig. 5 illustrates the positions and shapes of the rainband temporally for T 5 65–70 h, so streamlines at each of the from 63 h 50 min to 64 h 40 min with 10-min intervals. panels are the same. Low-level streamlines blow toward Here, only focusing convective cells are plotted. Dashed the TC center from the outer side, where the angle to lines are concentric circles where the distance from the a concentric circle (crossing angle) is 108–208. Individual TC center is indicated. Solid lines with arrows are azi- convective cells are roughly arranged in a spiral shape muthally averaged streamlines at 260-m height, which along streamlines and the crossing angle of some rain- are roughly arranged along a spiral rainband. A con- bands is smaller than that of streamlines. It is notewor- vective cell seen at T 5 63 h 50 min moves along the thy that rainbands deflect on the right-hand side (outer concentric circle and hardly propagates radially. At the side) from low-level streamlines, although those do not upstream side of the cell, a new convective cell is gen- propagate along the streamlines. The propagation mech- erated by upstream development and also moves in the anism for rainbands will be discussed next in section 2c. counterclockwise direction not in the radial direction. The spiral shape of rainbands is caused by the suc- The counterclockwise motion of cells consists of a vec- cessive development of convective cells at the upstream torial sum of azimuthally averaged flows and cross-band end of the rainband, which is referred to here as ‘‘up- motion, which deflects movement of cells away from the stream development.’’ For the upstream development, it streamlines. Hence, each cell tends to move along the is found that cold pools are a key factor to interact with concentric circle by propagating cross-band direction,

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FIG. 3. Horizontal distributions of simulated rainbands and low-level streamlines hourly from 65 to 70 h over a domain of 300 3 300 km2 in the control experiment. Shaded areas display vertically accumulated rainwater. Thick solid lines with arrows are the azimuthally and temporally averaged streamline for T 5 65–70 h at a height of 260 m.

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2 FIG. 4. The rainband formation from 64 h to 64 h 40 min over a domain of 120 3 120 km in the control experiment. Contours depict horizontal distribution of vertically accumulated rainwater with contour values of 2, 10, and 30 kg m2. Shaded areas display (left) precipitation, (middle) potential temperature anomaly from an azimuthally averaged temperature at 20-m height, and (right) horizontal convergence. Thick solid lines with arrows are streamlines azimuthally and temporally averaged at a height of 260 m.

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plays a significant role in the maintenance mechanism for rainbands and prevents rainbands from being en- trained into the eyewall. Figure 7 shows vertical structures of the rainband along line A1–A2 shown in Fig. 6b. Progression of the cold pool forces high equivalent potential temperature air to lift up, and it easily reaches the condensation level of lower than 1-km height (Figs. 7a,b). The condensation heating accelerates the updraft, whose axis slants inward with height, to its vertical velocity of more than 8 m s21 around 4.5-km height. On the inner side of the updraft, cloud water is converted into rainwater and its peak is seen at around 3-km height. Its evaporative cooling produces the cold downdraft, and the downdraft and the diabatic cooling enhance cold pool within the PBL. The downdraft pro- vides dry air from the midtroposphere to the PBL (Fig. 7c), which has an effect of keeping the evaporation of rainwater within the PBL. Momentum transport and horizontal divergence resulting from the downdraft advance the cold pool front in the normal direction to the FIG. 5. Cross-band propagation of rainbands from 63 h 50 min rainband (cross-band propagation). Cross-band propa- to 64 h 40 min with 10-min intervals over a domain of 100 3 100 km2 in the control experiment. Thin and thick solid lines plot gation of cold pools produces lifting for the next con- vertically accumulated rainwater and solid lines with arrows are vective cells at their fronts, giving a positive feedback to streamlines, as in Fig. 4. Dashed circles depict a distance from the the maintenance of rainbands. TC center with an interval of 20 km. Numbers represent the in- tegration times. e. Effects of water loading on downdraft It is important to clarify contributing factors of downdrafts, because downdrafts have a large impact on rain- and the rainband seems to propagate radially outward, band behavior through divergent flows and downward combined mainly with upstream development. momentum transport. As shown in Fig. 7a, downdrafts Cross-band propagation of rainbands has a close re- are generated below the melting layer so that ice-phase lationship with cold pools accompanied with cold down- processes do not affect the formation of downdrafts, drafts. Figure 6 displays horizontal structures of the cold which is consistent with Sawada and Iwasaki (2007). It pool at 64 h 30 min. It must be noted that a wind remains possible that not only evaporative cooling, but anomaly is normal to the rainband near the cold pool also water loading, contribute to the downdraft forma- front. Within the cold pool, evaporative cooling associ- tion. Thus, a sensitivity experiment to water loading ated with a strong precipitation forms the cold down- (NOWL), which excludes an effect of water loading of draft (Figs. 6a,b), and the evaporative cooling mainly rainwater, is performed. forms and maintains cold pools within the PBL. The The occurrence of downdrafts is not significantly downdraft might transport horizontal momentum down- different among the control, NOEVP, and NOWL ex- ward from midtroposphere into the PBL. Within the periments at 4.22-km height in Fig. 8a. At 1.14-km PBL, a positive pressure anomaly induced by the down- height, the occurrence of downdrafts has little differ- draft and the cold pool drives the wind anomaly near the ence between the control and NOWL experiments in surface (Fig. 6c), which causes asymmetric flows radially Fig. 8b; however, the occurrence of strong downdrafts outward. Actual movements of convective cells, which (,23ms21) is about one digit less in the NOEVP ex- are the sum of vertically and azimuthally averaged wind periment than in the control experiment. Therefore, and anomalies around the front, tend to be along the water loading has no significant impact on the downdraft concentric circles. formation and evaporative cooling is a major factor for it. It is noteworthy that in the NOWL experiment radially d. Maintenance mechanism of rainbands outward-propagating rainbands are reproduced. Some rainbands are maintained for about 10 h or Occurrence of strong updrafts (.2ms21) at both more despite a short lifetime of individual convective 1.14- and 4.22-km height is quite less in the NOEVP cells (about 1 h or less). The cross-band propagation experiment than in the control and NOWL experiments,

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2 FIG. 6. Horizontal structure of rainbands at 64 h 30 min in the control experiment over a domain of 36 3 36 km . The shaded area depicts the cold pool. The value is 21 K of potential temperature anomaly from an azimuthally averaged potential temperature at 20-m height. Contour shows (a) precipitation, (b) vertical motion at 620-m height, (c) pressure anomaly from azimuthally averaged pressure at 20-m height, and (d) horizontal divergence at 20-m height. Dashed lines are negative values. Vectors present wind anomaly from azimuthally averaged wind at 260-m height at greater than 2 m s21. Gray circles depict a distance from the TC center with an interval of 10 km. because in the NOEVP experiment rainbands are ab- development. Rainbands also rotate in the counterclock- sent. At 1.14-km height, occurrence of strong updrafts wise direction around the TC center through cross-band (.5ms21) is somewhat greater in the NOWL experi- propagation, which is a key factor for the maintenance of ment than in the control experiment. This is considered rainbands. Here, whether features of simulated rainbands due to the lack of a suppressing effect resulting from are consistent with those of observational results in the water loading. previous studies is discussed. The spiral shape of rainbands by upstream devel- 3. Discussion opment is consistent with the spiral shape of radar echo patterns associated with an observed TC (Tatehira a. Comparison with observed rainbands 1961). The evidence of propagation of observed radar Simulated rainbands under an idealized environment echo patterns by his study, which propagates radially are organized into a spiral shape along low-level stream- outward and rotates in the counterclockwise direction, lines and propagate radially outward through upstream also closely resembles features of simulated rainbands.

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FIG. 8. Histogram of vertical wind velocity at each grid within a radius from 50 to 300 km for T 5 72–96 h at (a) z 5 4.22 km and (b) z 5 1.14 km in the control (thick solid line), the NOEVP (thin solid line), and the NOWL (dashed line) experiments.

FIG. 7. Vertical structures of the rainband along line A1–A2 (cross maintaining rainbands from airborne observation, which band) in Fig. 6 at 64 h 30 min. (a) Vertical motion (contour) and is consistent with the results of numerical experiments. potential temperature anomaly from azimuthally averaged tem- A decrease of temperature is observed during rainband perature (shaded), (b) rainwater mixing ratio (thick solid line) with contour intervals of 1 g kg21, cloud water mixing ratio (shaded), and passing from surface weather elements (Ushijima 1958; equivalent potential temperature with contour intervals of 1 K Tatehira 1962), and especially airborne observations larger than 350 K (thin solid line), and (c) diabatic heating (thick (Barnes et al. 1983; Powell 1990b). However, the de- 2 solid line) with contour values of 10, 30, 50, 100, and 150 K h 1,the crease of surface temperature with the passage of rain- 21 cooling with contour values of 215, 210, 25Kh (dashedlineand bands is hardly observed in some cases (Tatehira 1961; shaded), and relative humidity (thin solid line) with contour intervals of 24%, starting from 80%, are shown. Thick dashed lines at Ishihara et al. 1986; Shimazu 1997). Ishihara et al. (1986) each panel depict the melting layer (Tc 5 08C). indicated that this might be because of the lack of a dry layer at the middle and lower layer. To clarify the detailed structure of cold pools, an observation of a near-surface Moving the direction of each convective cell in simulated thermodynamic ﬁeld is required. rainbands is supported by the ﬁndings of Powell (1990a), b. Comparison with previous studies on rainband which showed that cells move along almost a concentric formation and propagation circle at a speed of about 85% of the 0.2–6-km density- weighted mean wind. The counterclockwise motion of In this study, evaporative cooling–induced cold pools simulated rainbands is similar to moving bands catego- play essential roles in the formation and propagation of rized by Willoughby et al. (1984) and Shimazu (1997). rainbands. The importance of a cold pool for the rain- It is found that cold pools are essential for the or- bands’ behavior is highlighted by Yamasaki (1983), using a ganization of simulated rainbands. Barnes et al. (1991) two-dimensional axisymmetric model; however, there are remarked that cold pools play an important role in differences between his study and this study. Yamasaki’s

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(1983) simulation shows at the mature stage that rainbands condensation heating of precipitation outside the eye- propagate inward and convective activity becomes quite wall. Radially outward-propagating precipitation is at- weak outside the eyewall; whereas in this study, 3D sim- tributed to the behaviors of rainbands, while they are ulations show the radially outward-propagating rainbands hardly observed in the experiment without evaporative and convective cells are actively formed even outside cooling. At very least, the features of rainbands in this the eyewall, as shown in the observational studies. This study seem to be more closely related to cold pool dy- is because 3D models can express axially asymmetric namics than the proposed mechanisms for rainband behavior, so that upstream development forms radially formation and propagation by previous studies (internal outward-propagating rainbands with a realistic spiral gravity waves and vortex Rossby waves). Cold pools shape and cross-band propagation inhibits rainbands lead to upstream development of rainbands, which is from being drawn into the eyewall. defined as an extension of the rainband at its upstream Some previous studies indicate that internal gravity end and cross-band propagation, which is defined as waves are possibly responsible for the formation and a movement of rainband normal to its rainband. Rain- propagation of rainbands (Kurihara 1976; Willoughby band behaviors result from upstream development and 1977, 1978). To examine whether simulated rainbands cross-band propagation, which are quite similar to those can be characterized as internal gravity waves, temporal of the observed radar echo patterns (Tatehira 1961). changes of pressure anomalies from azimuthally aver- Upstream development originates from horizontal aged pressure at 1.82-km height, and vertically accumu- convergence between the upstream of a cold pool and lated rainwater in the control and NOEVP experiments low-level inflows with high equivalent potential tem- are shown in Fig. 9. In both experiments, spiral-shaped perature (EPT). The lifting successively generates new patterns of pressure anomalies, which seem to be a result convective cells at the upstream end of a cold pool and of internal gravity waves, propagate radially outward; organizes spiral-shaped rainbands along azimuthally however, these anomalies do not accompany band-like averaged streamlines from the surface to the top of the cloud structures. An outward propagation speed of pres- PBL and propagates them radially outward. sure anomalies is 25–40 m s21, which is much faster than Cross-band propagation is caused by asymmetric flows that of the simulated rainbands (1–4 m s21). Therefore, from azimuthally averaged wind at the PBL. Asymmetric internal gravity waves do not organize convective cells flows are driven by a positive pressure anomaly resulting into rainbands, at least in this simulation; however, they from downdrafts and become normal to the rainband at might trigger a formation of convective cells. the cold pool front (outer side). The cross-band propa- Franklin et al. (2006) explains the dynamics of outer gation deflects movement of each cell away from the rainbands with a theory of VRWs, whose restoring low-level streamlines. Actual movement is the vectorial mechanism is associated with the radial gradient of po- sum of azimuthally averaged flows and axially asym- tential vorticity (PV) similar to Rossby waves at the metric flows, and it rotates counterclockwise almost midlatitude (Guinn and Schubert 1993; Montgomery and along concentric circles. Kallenbach 1997) from 3D simulations. In our simula- Also, cross-band propagation is essential for the tions, rainbands propagate across the stagnation radius, maintenance of rainbands. The advancing cold pool whereas the radial gradient of basic-state PV becomes fronts lift up the high EPT air mass slantwise and make nearly zero, indicating that it is not reasonable to explain condensation. As a result of evaporation from rain- the rainbands as VRW. Differences between their and our drops, heavy precipitation induces downdrafts and gives simulations are considered to be attributed to the different a feedback to the enhancement of cold pools. The environmental setting and different models; however, the structures of simulated rainbands are consistent with precise causes are not clear yet. The understanding of the those observed (Barnes et al. 1991). In addition, down- relationship between VRW and rainbands is desirable. drafts are mainly produced by evaporative cooling but have less contribution by water loading. As mentioned in Part I, the enhanced secondary cir- 4. Conclusions culation by condensation heating of rainbands increases Cloud-resolving simulations of a tropical cyclone kinetic energy of the TC and enlarge its size. Namely, (TC) are performed to investigate the impacts of evap- radially outward-propagating rainbands with counter- orative cooling on the formation, propagation, and clockwise motion resulting from cold pools have signif- maintenance of rainbands under an idealized environ- icant impacts on TC size. Cold pool dynamics may be ment. Evaporative cooling produces radially outward important for TC-track forecasts as well as intensity propagation of precipitation, which expands the TC size forecasts. The track forecast is sensitive to its size through through enhanced secondary circulation associated with its interaction with environmental flows (Iwasaki et al.

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2 FIG. 9. Propagation of internal gravity waves from 66 h 40 min to 67 h with 10-min intervals over a domain of 600 3 600 km in the (left) control and (right) NOEVP experiments. Shaded areas show positive pressure anomaly from azimuthally averaged pressure and thin dashed contours are negative at 1.82-km height. Thick contours depict vertically accumulated rainwater with a value of 1 kg m22.

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1987). Toward an accurate TC forecast, it is desired to Iwasaki, T., H. Nakano, and H. Sugi, 1987: The performance of operate a high-resolution model with appropriate cloud a typhoon track prediction model with cumulus parameteri- microphysics. zation. J. Meteor. Soc. Japan, 65, 555–570. Jones, R. W., 1977: A nested grid for a three-dimensional model of This is an idealized experiment with an initial axi- a tropical cyclone. J. Atmos. Sci., 34, 1528–1553. symmetric vortex under a horizontally uniform envi- Kurihara, Y., 1976: On the development of spiral bands in a tropi- ronment. In nature, including wind shear, baroclinicity, cal cyclone. J. Atmos. Sci., 33, 940–958. and beta effect, some observational studies demonstrate ——, and R. E. Tuleya, 1974: Structure of a tropical cyclone de- not only propagating rainbands but also stationary veloped in a three-dimensional numerical simulation model. J. Atmos. Sci., 31, 891–919. rainbands, which stay around a fixed location with re- MacDonald, N. J., 1968: The evidence for the existence of Rossby- spect to the TC center (Willoughby et al. 1984; Shimazu like waves in the hurricane vortex. Tellus, 20, 138–150. 1997). Hence, investigations of the impacts of cloud Malkus, J. S., C. Ronne, and M. Chaffee, 1961: Cloud patterns in microphysics on stationary rainbands and of relation- Hurricane Daisy, 1958. Tellus, 13, 8–30. ships between propagating and stationary rainbands are Montgomery, M. T., and R. J. Kallenbach, 1997: A theory for vortex Rossby waves and its application to spiral bands and of great interest. Further understanding of rainbands is intensity changes in hurricanes. Quart. J. Roy. Meteor. Soc., explored from cloud-resolving simulations of rainbands 123, 435–465. under a realistic condition. Powell, M. D., 1990a: Boundary layer structure and dynamics in outer hurricane rainbands. Part I: Mesoscale rainall and ki- Acknowledgments. 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