Journal of the Meteorological Society of Japan, Vol. 85, No. 2, pp. 115--136, 2007 115

Observational Analysis and Numerical Evaluation of the Effects of Vertical Wind Shear on the Rainfall Asymmetry in the Typhoon Inner-Core Region

Mitsuru UENO

Typhoon Research Department, Meteorological Research Institute, Tsukuba, Japan

(Manuscript received 7 July 2006, in final form 13 November 2006)

Abstract

A number of observational and modeling studies have shown a tendency for typhoon strength vortices to develop upward motion and produce precipitation, particularly in the eyewall, on the downshear to downshear-left side of the tropical cyclones (TCs). However, the directional relationships obtained from the observational studies have been mostly confined to the TC cases in the Atlantic basin. Furthermore, little evidence has been presented so far for the relationship in magnitude, between shear and rainfall asymmetry. In the former part of the present study, the observational analysis on TC rainfall asymmetries is extended to the western North Pacific TCs in 2004, using the two types of rain-rate data, the Radar- AMeDAS precipitation data, and satellite-based rainfall estimates, such as TMI and AMSR-E rain rates. It is well demonstrated from the analysis that rainfall in the inner-core region of a TC tends to occur on the downshear to downshear-left side, irrespective of data type used and latitudes where TCs are lo- cated. However, as far as the relationship between shear and storm motion is concerned, a sharp con- trast is found between low and middle latitudes. In middle latitudes TCs have a tendency to move to the left of the shear, consistent with previous studies, while in low latitudes they tend to move to the right of the shear. The contrasting shear-relative storm heading between the two latitudes is attributed to the difference in vertical structure of the ambient wind. In the latter part of the study, to explore the quantitative relationship between shear and rainfall asymmetry, a formula for the shear-induced vertical motion is derived from the thermal wind balance equation for TC-like vortices. The formula states that the shear-induced vertical motion should be a function not only of shear magnitude, but also of vortex strength. To validate the formula a set of ideal- ized numerical experiments are conducted, with realistic wind profiles, in which the initial environmen- tal winds are specified from the 6-hourly JMA global analyses for two major typhoon cases in 2004. It is found from the numerical study that the magnitude of wavenumber-one vertical motion, predicted by the formula, is much more strongly correlated with that of model-produced rainfall asymmetry, than the shear alone, suggesting that the vortex strength is one of the main factors determining the magnitude of shear-induced rainfall asymmetry. The results from the idealized simulations also suggest that vortex tilt would have only a minor contribution to the rainfall asymmetry in the inner-core region, at least for well-developed TCs.

1. Introduction

Corresponding author: Mitsuru Ueno, Typhoon It is well known that strong tropical cyclones Research Department, Meteorological Research (TCs) exhibit highly axially symmetric struc- Institute, 1-1 Nagamine, Tsukuba, Ibaraki 305- ture in the core (defined as the region within a 0052, Japan. E-mail: [email protected] radius of about 100 km from the cyclone cen- ( 2007, Meteorological Society of Japan ter). However, radar observations, as well as 116 Journal of the Meteorological Society of Japan Vol. 85, No. 2 model simulations, have often shown azimuthal diabatic heating on the behavior of a typhoon- rainfall (or vertical motion) asymmetries in the like vortex embedded in a unidirectional verti- inner core of TCs (e.g., Kurihara and Bender cal shear. In the simulations strong wavenum- 1982; Marks and Houze 1987; Marks et al. ber-one asymmetries in TC rainfall are pro- 1992). Some theoretical studies have attempted duced, which are detectable, not only in the to explore the relationship between such asym- hourly model output, but also in 36-hour storm- metries and TC motion. For example, Shapiro relative composites. Consistent with the above- (1983) showed that a translating TC develops cited other modeling studies, the maximum asymmetries in frictional convergence within rainfall tends to occur somewhere on the down- the boundary layer, which induces asymme- shear to the left side of the initial shear vector. tries in the upward motion and rainfall pat- The relationship between asymmetries in terns. The calculation using a slab boundary rainfall, and vertical wind shear or storm mo- layer model suggests that maximum convection tion, obtained by most previous observational preferably occurs in the front to right-front studies are based on only a few cases. The first quadrants of the storm, in no shear situations. study that has extensively investigated the re- Although the results presented by Shapiro are lationship is Corbosiero and Molinari (2002, consistent with some observational studies, re- 2003 hereafter referred to as CMs). Using cent observational works (e.g., Franklin et al. ground-based lightning data during 1985–99, 1993; Black et al. 2002) suggest that the trans- CMs examined the relative importance of lation is not the sole cause of convective asym- asymmetric friction, and vertical wind shear, metries in the inner-core region of TCs. on the azimuthal asymmetry of convection, From airborne Doppler radar observations of and provided some observational evidence for a the eyewall of Hurricane Jimena of 1991, and stronger linkage between vertical wind shear, Olivia of 1994, Black et al. (2002) found that and convective asymmetries in TCs. CMs ar- the wavenumber-one asymmetries in radar re- gued that a systematic relationship between flectivity are enhanced when it encounters a storm motion and convective asymmetries, strong shear. In most cases the reflectivity which is well-documented in previous studies, maxima is located in the downshear left quad- is largely a reflection of the much stronger ver- rant of the TCs. Typically the radar echoes are tical shear effect, or an artifact stemmed from formed on the downshear side, and then moved the fact that storm motion is closely coupled to cyclonically around the center at a speed less vertical wind shear. than the local mean tangential wind. On the Previous observational studies on TC rainfall other hand, using an idealized hurricane model, asymmetries, including CMs, have focused on Bender (1997) showed that the maxima in low- the Atlantic basin. One of the purposes of the level convergence, upward motion and precipi- present paper is to extend the observational tation are located downshear of the center, analysis to the western North Pacific TCs. In whether the latitudinal variation of the Coriolis the former part of this study we examine the parameter is considered, or not in the numer- relationship between ambient vertical wind ical experiments. In a full-physics simulation of shear and rainfall asymmetry in the typhoons a hurricane in 5 m s1 vertical shear, through which made landfall on mainland Japan in the depth of the troposphere, Frank and Ritchie 2004. For the purpose we use one hour precipi- (2001) found that the maximum upward vertical tation data, derived from radar echo inten- motion occurs in the downshear-left quadrant, sities observed by JMA (Japan Meteorological in the inner core. They speculated that differen- Agency) Radar network, which is calibrated by tial advection of the axisymmetric vorticity by the rain gauge observations by JMA automated the shearing storm-relative flow, induces up- surface measurement system, AMeDAS. This ward vertical motion on the downshear side, synthesized precipitation data from Radar and the ascending air rise in a cyclonic spiral echo intensities and AMeDAS rain gauges on the left side of shear vector, producing maxi- (hereafter referred to as RAD data) covers the mum latent heat release and rainfall on that entire Japanese Islands and the surrounding side. Ueno (2003) also performed a set of ideal- sea area, about 200 km off the coasts with a ized simulations to investigate the impact of resolution of 0.025 degree latitude and 0.03125 April 2007 M. UENO 117 degree longitude. Although the RAD data pro- to as AM1) is relevant to the time tendency of vides a reliable gridded estimation of precipita- the tilt magnitude, due to vertical wind shear, tion, it is available only in the mid-latitudes it is only active for the period during which the in and around Japan, possibly limiting the vortex tilt increases with time. After that, as il- generality of the obtained statistical results. lustrated by dry model simulations performed Therefore we concurrently perform a similar by Jones, the created potential temperature analysis, using microwave imager rain esti- anomalies begin to play a significant role in mates from both TRMM/TMI and Aqua/ producing vertical motion asymmetry. While AMSR-E (hereafter referred to as SAT data), the contribution of this mechanism (hereafter extending the target typhoons to other than referred to as AM2) is considered rather pro- the landfalling ones in the same year. As shown portional to the magnitude of vortex tilt, that below, the extension of the analysis reveals of AM1 is more closely related to the tilt ten- that the relationship between storm motion dency. In a realistic situation, however, the and vertical wind shear in low latitudes is quite adiabatic cooling produced by upward motion different from that in the mid-latitudes. As a on the downtilt side, would be largely canceled result, a stronger linkage of rainfall asymmetry out by diabatic heating in the near-saturated to vertical wind shear than storm motion is TC core region, suppressing the growth of the demonstrated in a more generalized manner. cold anomaly there, and thereby helping the Satellite-based rainfall estimates are also used vortex resist the tilting by shear. Indeed, air- in previous observational studies (e.g., Alliss borne Doppler radar observations of well- et al. 1992; Lonfat et al. 2004) to examine the developed TCs (e.g., Marks et al. 1992; Frank- rainfall distribution around TCs. For example, lin et al. 1993; Roux and Marks 1996; Reasor Lonfat et al. (2004) examined the relationship et al. 2000) show only very small variations of between storm intensity, geographical location the center position with height, even in verti- of storms, and rainfall distribution including cally sheared environmental flow. Therefore, it asymmetry. In their study, however, the asym- is conceivable that the AM2 plays only a minor metric component of rainfall distribution is de- role in producing vertical motion asymmetry, at fined relative only to the storm motion. least in well-developed TCs. Although the observational studies suggest Most theoretical and numerical modeling that ambient vertical shear is the primary fac- studies (e.g., Jones 1995; Bender 1997; Frank tor in the wavenumber-one rainfall asymmetry, and Ritchie 2001; Ueno 2003; Wu et al. 2006) the mechanism governing the development of of the influence of vertical wind shear on the the azimuthal asymmetries is not well estab- azimuthal distribution of convection in TCs, lished, at least within the diabatic framework. have mainly focused on the directional relation- As recently summarized in Wu et al. (2006), ships between vertical shear, vortex tilt, and several mechanisms have been proposed by convective asymmetries, with one exception of which vertical wind shear produces asymme- Rogers et al. (2003), who showed that changes tries in vertical motions in adiabatic vortices. in convection, evaluated by the ratio between One of them is that a balanced response to the the wavenumber-one and wavenumber-zero shear-induced tilt of a vortex produces upward Fourier coefficients of model-simulated reflec- motion in the downtilt direction. According to tivity, are well correlated with changes in the the theoretical work of Jones (1995) a vortex vertical shear. In the latter part of the present that is initially upright and in gradient balance study, to make the relationship between shear tilts downshear after a shear flow is imposed. and rainfall asymmetry more quantitative, we In order for the vortex to remain balanced, a will attempt to derive a simple formula for the negative potential temperature anomaly occurs magnitude of wavenumber-one vertical motion, downtilt, and a positive anomaly uptilt. This due to AM1 based on the thermal wind balance effect is accomplished by upward (downward) consideration. Meanwhile, to examine the va- motion on the downtilt (uptilt) side of the vor- lidity of the formula, we perform a set of ideal- tex, and has been confirmed by numerical sim- ized simulations employing vertical shear pro- ulations (e.g., Jones 1995; Wang and Holland files obtained from the JMA global analyses, 1996). Since this mechanism (hereafter referred which include the contribution of veering or 118 Journal of the Meteorological Society of Japan Vol. 85, No. 2 backing of wind direction, as well as change in numbers from 0 to 250, and can be converted wind speed. into rain rates in units of mm h1 by multiply- ing it by 0.1. Consequently it covers rain rate 2. Observational analysis only within the range of 0 to 25 mm h1, limit- 2.1 Data and methodology ing its applicability to some degree. The data used for investigating the influence In the analysis using the RAD data, only the of vertical wind shear on the convective asym- case which meets the following three require- metry in CMs is ground-based lightning data ments is utilized; (i) the RSMC-Tokyo best- during 1985–99. In the study the area around track storm position is available at the data each storm is divided into two regions, with a time, (ii) a tropical cyclone is of tropical storm separation radius of 100 km, and the inner one strength or greater at the data time, (iii) rain is referred to as the inner core. The choice of rate is fully available over the area within the radius is made based on the previous obser- 100 km of the storm center. These require- vational study of Molinari et al. (1999), who ex- ments lead to a total of 121 one-hour TC precip- amined the radial distribution of lightning in itation observations for 10 typhoons, which Atlantic basin hurricanes, and found a clear made landfall on mainland Japan in 2004. The minimum in flash density, somewhere between first requirement is introduced to avoid a deg- the 60- and 140-km radii. In the present study radation of the analysis by using interpolated, we evaluate the rainfall asymmetry in the therefore less accurate storm positions for the inner-core region using the rainfall data within azimuthal decomposition of rain rate. However 100 km of the storm center after CMs. this requirement is not imposed on the analysis In the current study, to quantify the azimu- using the SAT data, since it is usually available thal distribution of rainfall in TCs, two kinds at asynoptic times. In the analysis using SAT of data, RAD and SAT data, are used sepa- data, therefore, only the last two requirements rately. RAD is one-hour precipitation estimates are considered, which leads to a total of 204 ob- from ground-based C-band radar, calibrated servations for 21 typhoons occurred from 1 with the AMeDAS rain gauge data. On the June–31 October 2004. Table 2 lists the 21 ty- other hand, SAT is microwave imager rain esti- phoons examined in the study. The storm posi- mates from both TRMM/TMI and Aqua/AMSR- tion at each SAT observation time is deter- E. While the RAD data is available only in the mined by linear interpolation of the two closest mid-latitudes in and around Japan, the SAT best track reports to the observation time. Use data covers mainly ocean area in low-latitudes of such an interpolated storm position could (see Table 1). In this sense they have somewhat introduce an additional uncertainty in the anal- complementary coverage, providing totally a ysis results. As shown below, however, the re- comprehensive dataset for the analysis of rain- sults from the SAT analysis are consistent to fall asymmetries in typhoons. both those from the RAD analysis and CMs, The SAT data used in the study is obtained possibly demonstrating the usefulness of such from the web site of Remote Sensing Systems. an asynoptic data to the analysis of the near- The data consists of 0.25 by 0.25 gridded core asymmetries in TCs. The circular area of maps, including observation time, sea surface 100 km radius centered on the storm position temperature (only for TMI), wind speed, total is divided into sixteen sectors (or half-octants), water vapor, cloud liquid water, and rain rate by meridional lines with 22.5 degree azimuthal for ascending and descending orbits separately. spacing, on a polar coordinates, located at the The original SAT rain rate data is coded with storm center. After the RAD or SAT gridded

Table 1. Number of cases in each 5-degree latitude band examined in the study. Latitude band –10 N 10–15 N 15–20 N 20–25 N 25–30 N 30–35 N 35–40 N 40 N– RA data 0 0 0 3 37 56 18 7 SAT data 4 38 51 46 27 29 8 1 April 2007 M. UENO 119

Table 2. List of storms and ‘‘Hours,’’ they were of tropical storm strength or greater, starting at ‘‘Be- gin time’’. ‘‘LPS’’ refers to the lowest pressure attained for each storm. The numbers of RAD- and SAT-samples are self-explanatorily given in two columns. The last column indicates whether each storm made landfall on mainland Japan or not. Storm Begin time Hours LPS (hPa) RAD-samples SAT-samples Landfall or not CONSON 1800 UTC 06 Jun 109 960 16 4 Yes CHANTHU 1800 UTC 10 Jun 54 975 0 3 No DIANMU 1200 UTC 13 Jun 195 915 14 15 Yes MINDULLE 0600 UTC 23 Jun 252 940 0 12 No TINGTING 0000 UTC 26 Jun 192 955 0 20 No KOMPASU 0000 UTC 14 Jul 54 992 0 3 No NAMTHEUN 0000 UTC 25 Jul 186 935 12 13 Yes MALOU 0000 UTC 04 Aug 18 996 6 0 Yes MERANTI 1200 UTC 04 Aug 108 960 0 14 No RANANIM 1200 UTC 08 Aug 102 950 0 5 No MALAKAS 0000 UTC 11 Aug 60 990 0 10 No MEGI 0600 UTC 16 Aug 96 970 7 8 Yes CHABA 1200 UTC 19 Aug 279 910 18 21 Yes AERE 0000 UTC 20 Aug 144 955 0 7 No SONGDA 0000 UTC 28 Aug 261 925 11 15 Yes SARIKA 1800 UTC 04 Sep 54 980 0 6 No HAIMA 0000 UTC 11 Sep 48 996 0 1 No MEARI 1800 UTC 20 Sep 219 940 16 11 Yes MA-ON 0600 UTC 04 Oct 135 920 6 9 Yes TOKAGE 0000 UTC 13 Oct 183 940 15 11 Yes NOCK-TEN 1200 UTC 16 Oct 228 945 0 16 No rain data is averaged over each sector, and the use of bogus observations helps to minimize stored in an array of size 16, a Fourier decom- the difference in center position between the position routine is applied to the array to best real-time operational estimates, and the determine the amplitude and phase angle of global analyses, it could also help to prevent wavenumber-one asymmetry of rainfall rates. aliasing of the symmetric wind components In the study, vertical wind shear is defined as onto the asymmetric components in the shear the vector difference between the average 200- calculation. As shown below, the vertical shear hPa, and 850-hPa winds (i.e., 200 hPa minus could vary with time, sometimes as large as 850 hPa), within a radius of 500 km from the 5ms1 in magnitude, and 60 degrees in direc- cyclone center, and calculated from 6-hourly tion per 6 h. Therefore the vertical shears ob- JMA global analyses (23 pressure levels, tained at 6-hourly intervals are linearly inter- 1:25 1:25 grids). The choice of the larger polated to the observation time of rainfall data, averaging radius (i.e., 500 km), compared to to avoid mismatches in the time between shear the radius for rain data analysis (i.e., 100 km) and rainfall asymmetry. is just after CMs. Unlike the ECMWF (Euro- pean Centre for Medium-Range Weather Fore- 2.2 Analysis results casts) analyses CMs used, bogus TC observa- Figure 1 shows the number of cases that the tions are assimilated into the JMA global first-order asymmetry phase maximum is lo- model. The bogus observations are constructed, cated, per octant, with respect to vertical wind based on available vortex information (e.g., po- shear. As suggested in the figure, regardless of sition, central pressure, and radius of 15 m s1 the rain data sources, the rain rate tends to be winds), so as to retain the asymmetric wind enhanced downshear, with a leftward prefer- components developed in the model such as ence, consistent with CMs. This downshear-left beta gyres (a pair of counterrotating gyres due preference of the asymmetry is more pro- to Rossby wave dispersion) (Ueno 1995). Since nounced in the RAD dataset, partly because a 120 Journal of the Meteorological Society of Japan Vol. 85, No. 2

CMs examined the relative importance of the vertical wind shear and storm motion effects, on convective distribution by stratifying the ob- servational data by the separation angle be- tween shear and motion, and found a much stronger shear signal. They also examined the distribution of the angle between shear and motion vectors (measured counterclockwise from the shear to motion vector), and found that a substantial fraction of the total cases studied (specifically, 78%), have a left-of-shear motion vector. For their study, however, only Fig. 1. The number of cases the highest the TCs that are over land, or come within rainfall rate was analyzed, per octant, 400 km of the United States coastline are con- within a radius of 100 km from the sidered, limiting the cases mostly to the mid- storm center, with respect to shear vec- latitudes. The relationship between shear and tor (arrow), obtained from (a) RAD- and motion can be established without rainfall (b) SAT-datasets. The octants which at- data, so in this paper, we extend the work of tained the largest and the second larg- est number are dark- and light-shaded, CMs by sampling shear and storm motion data respectively. every 6 hours throughout most of the lifetime of the typhoons, listed in Table 2. This sampling of data yields a total of 514 cases, including a relatively larger number of strong shear cases sufficient number of low-latitude cases. Figure (>10 m s1) are included in the dataset. Recall 2 shows the directional relationship between here that the RAD dataset mostly consists of storm motion and shear, stratifying all the mid-latitude cases, where the shear is gener- cases into three latitude groups, according to ally larger. Indeed, when the SAT dataset is the latitude of the storm center. It is clear stratified by shear strength into three groups from Fig. 2 that TCs in the westerly (easterly) (i.e., weak-, medium-, and strong-shear groups), shear zone tend to move leftward (rightward) after CMs, the strength of the directional rela- relative to the shear vector, and the shear is tionship between shear and rainfall asymmetry predominantly westerly (easterly) in the middle is found to increase with shear strength, consis- (low) latitudes. The latitudinal change of the tent with CMs, although such a shear strength zonal component of the vertical wind shear in dependency is not very clear in the RAD data- the western North Pacific is qualitatively con- set (Ueno 2005). sistent with the earlier work of Gray (1968), It might be argued that the RAD samples are who portrayed the climatological distribution significantly affected by the landmass, because of tropospheric shear of the horizontal wind, be- of their proximity to the mainland of Japan. A tween 200 hPa and 850 hPa. The result sug- quick way to evaluate the influence of land- gests that the left-of-shear preference of the mass on the above-mentioned result, is to di- storm motion, as discussed in CMs, is rather vide all the RAD samples into two groups, that confined to the middle latitudes, and the situa- is, ‘‘landmass-area’’ group (58 samples in total), tion is reverse in the low latitudes at least in and ‘‘landmass-free’’ one (63 ditto), and apply the western North Pacific. For the readers’ ref- the same statistical procedure, as above, to erence, 127 of the 187 mid-latitude cases (68%) each of the groups. Here a sample is classified have a left-of-shear motion vector, while 170 of as ‘‘landmass-free’’ if it does not contain any the 209 low-latitude cases (81%), have a right- piece of landmass within the area concerned of-shear motion vector. (i.e., within 100 km of the storm center). The In order to clarify the differences in the direc- result is consistent with the above one (Fig. 1), tional relationship of storm motion and shear and does not exhibit any noteworthy difference between, in the low- and mid-latitudes, we ex- between the two groups, suggesting a minimal amine the direction of 200-hPa wind relative to impact of the landmass on the above statistics. that of 850-hPa one. Figure 3 shows the distri- April 2007 M. UENO 121

Fig. 2. Directional relationship between storm motion and environmental shear. Vertical axis de- notes the direction (in degree) of storm motion vector relative to that of shear one with positive (negative) values for the motion to the left (right) of the shear, while horizontal one represents the direction (in degree) of shear measured counterclockwise from due east. The sampled cases are stratified by the latitude of storm center into three groups with the specified thresholds, 20 and 25 degrees north latitude, and indicated by different symbols as in the legend at the top of figure. The less-than-20 (larger-than-25) degrees north latitude group is referred to as low-latitude (midlatitude) one in the text. bution of the said quantity, comparing the two equal to a vertically integrated tropospheric latitude groups. As shown in the figure, the flow around the storm (Ueno 2003), the rela- upper-level wind tends to point somewhere to tionship between vertical shear and storm the left (right) of the low-level wind in the low- motion may be illustrated schematically, as in latitudes (mid-latitudes), suggesting that the Fig. 4. hodograph tends to rotate cyclonically (anticy- To determine the relative importance of ver- clonically) with height in the low-latitudes tical wind shear, and storm motion on the con- (mid-latitudes). This result, combined with the vective asymmetries in TCs, CMs examined the common understanding that the TC motion is location of the convective maximum for differ- a steering-type process, with the steering flow ent angles of separation, between shear and 122 Journal of the Meteorological Society of Japan Vol. 85, No. 2

Fig. 3. Distribution of 200-hPa wind direction minus 850-hPa one for two latitude zones as indicated in the legend. Labels along the horizontal axis denote the range of the values, with plus (minus) signs indicating measured counterclockwise (clockwise). motion. For the purpose the total samples used of-shear motion group), to 8 for 270-group, (or in their study are stratified into four groups, ac- right-of-shear motion group). This is the case cording to the angles between the shear and when the RAD dataset alone is used in our motion vectors (i.e., 0,90, 180, and 270, study. Here, in this study, we perform the each G45). Since the samples are confined same analysis as CMs, but for using the com- to the middle latitudes in their study, how- bined RAD and SAT dataset, so that no one of ever, the number of cases significantly varied the four groups consists of an extremely small with the angle, from 48 for 90-group (or left- number of cases. Figure 5 shows the number of cases that the first-order asymmetry phase maximum is located, per quadrant, with re- spect to both shear, and storm motion, for each of the four groups. The shear vector (S)ineach quadrant diagram is plotted towards the north, and the motion vector (M) is drawn at the appropriate angle, counterclockwise from the shear. Since the rearrangement of the motion vector, and the shear for the diagram is done, keeping both of their directional relationships to the rainfall asymmetry unchanged for every case, a case does not always drop in a single quadrant unequivocally in the diagram. For this reason the number of cases is given sepa- Fig. 4. Simplified schematic showing re- rately for each of the two vectors in each dia- lationship between shear and storm gram. As shown in the figure, the shear-related heading for the low-latitude type (left), maximum extends to the downshear left quad- and mid-latitude type (right). rant, irrespective of the separation angle be- April 2007 M. UENO 123

(a) Contribution of other factors to rainfall asymmetry, (e.g., asymmetry in boundary layer frictional drag, etc.) (b) An active role of internal dynamical, and thermodynamic processes in determining the final rainfall distribution in the inner- core region, (e.g., contribution of vortex Rossby wave, vortex structure-dependent advection of condensate by the tangential flow, etc.) (c) Insufficient accuracy of data, and/or some deficiencies in the methodology, including inadequate definition of the parameters used in the study, (e.g., use of ill-defined vertical wind shear, contamination of the results by weak-shear cases, etc.)

Although previous studies have shown the Fig. 5. The number of cases the highest rainfall rate was analyzed, per quad- importance of vertical shear on wavenumber- rant, within a radius of 100 km from one asymmetry in TC structure, there has the storm center, with respect to ver- been a considerable variety among them in the tical wind shear (upper figures in each definition of vertical wind shear as a single quadrant), and storm motion (lower value parameter (Rhome et al. 2006). It is ones) for different angles of separation likely that such a single value parameter does between shear and motion (0,90, 180 not always appropriately stand for the environ- and 270, all G45). The shear and mo- mental forcing responsible for the asymmetry, tion vectors are drawn in light black ar- since generally the environmental winds vary rows, and labeled S and M, respectively. nonlinearly with height in a realistic situation. Based on these considerations, it seems that to tackle with the last item, has the first priority tween shear and motion. On the contrary, the over the other items, on the way toward estab- quadrants where the storm motion-related lishing a clearer, and more quantitative rela- maximum occurs, are all different in the four tionship, if any, between vertical shear and quadrant diagrams, with the maximum in the rainfall asymmetry. To confirm how much the left-front, right-front, right-rear, and left-rear detailed vertical wind structure is responsible quadrants of storm motion, for 0,90, 180, for the spread in the preferred direction rela- and 270-groups, respectively. The result sug- tive to shear vector in a realistic situation, a gests a greater dominance of the shear signal, set of idealized numerical experiments are ac- supporting that of CMs. complished, in which environmental wind com- ponents are extracted from the JMA global 3. Numerical evaluation analyses during all life cycle stages of some Although the results from the observational selected typhoons. Braun et al. (2006) pointed study presented in the previous section suggest out that idealized simulations, employing more a strong contribution of vertical shear to rain- complex vertical shear profiles (i.e., those other fall asymmetry, there is still a large variance than unidirectional ones), are needed to de- in the directional relationship between the scribe more clearly the relationships between two. Furthermore, the correlation coefficient vertical shear, convective asymmetries and so between the magnitude of vertical shear, and on. In this section, we will attempt to examine that of wavenumber-one rainfall asymmetry, the validity of the conventional shear defini- calculated over the entire RAD (SAT) dataset, tion, as a predictor of rainfall asymmetry in is as small as 0.18 (0.04). Possible reasons for terms of magnitude, as well as direction. these are as follows: Rogers et al. (2003) showed that changes in 124 Journal of the Meteorological Society of Japan Vol. 85, No. 2 convection, evaluated by the ratio between the gas constant for dry air, respectively, and the wavenumber-one, and wavenumber-zero tangential wind speed v and temperature T Fourier coefficients of reflectivity between 20- are expressed as a function of distance from and 40-km radius, are well correlated with the storm center r, and pressure p for a given changes in the vertical shear. The result sug- time. The subscript p on the right-hand side of gests that the magnitude of rainfall asymmetry the equation denotes that pressure is held con- as a response to vertical wind shear depends stant. Now we consider a middle-troposphere not only on the shear itself, but also on some level (say 500 hPa level and denoted by pM), at symmetric aspects of the vortex structure, such the radius of maximum tangential wind down- as vortex strength. In the next subsection, we shear of the vortex center, where upward mo- will derive a formula for the magnitude of tion caused by vertical wind shear would be asymmetric vertical motion generated by AM1 nearly strongest, at least shortly after the in TC vortices embedded in vertical shear, as a shear is imposed. Note that generally such a function not only of shear magnitude, but also level is expected to be located midway between of vortex strength, and show from a set of nu- 850 hPa and 200 hPa levels, over which the merical experiments, that it is a good measure shear is typically calculated. of the magnitude of rainfall asymmetry. When a vertical shear flow is imposed on an initially upright vortex, the vortex would be 3.1 Analytical expression for the magnitude of vertically tilted (or sheared apart) in the direc- asymmetric vertical motion tion of the vertical shear, without any restoring In this subsection, we attempt to relate the mechanism. Now consider a situation in which magnitude of wavenumber-one rainfall asym- both the upper ðp Þ and lower ðp Þ portions of metry, to that of vertical wind shear. Jones U L a vortex are being separated from its middle (1995, hereafter referred to as J95), having ex- portion ðp Þ at a speed of U, but in the oppo- amined the behavior of dry vortices in vertical M site directions to each other. Then the change shear, showed that the vertical circulation de- in the vertical shear of the azimuthal flow, velops in a manner which is consistent with evaluated at the p level, and at a point on the model flow remaining balanced. As illus- M the downtilt side of the vortex center, during a trated by J95, in the situation that the vertical time period dt, may be approximated as shear tends to tilt the vortex in the vertical, the "# vertical shear of the azimuthal flow tends to qv qv Udt change in the opposite sense, between the loca- þ : ð2Þ qr p qr p pL pU tions of maximum tangential wind and else- L U where, since the vortex flow varies with radius A similar expression, which is equal in magni- such that the tangential wind speed increases tude, but of opposite sign to (2), can be obtained 1 from the center to a radius then decreases. on the uptilt side. By letting S 2U/ðpL pUÞ, and assuming Then consistency with thermal wind balance "# requires that a pair of temperature anomalies 1 qv qv qv of opposite sign is generated, with a positive þ G ; 2 qr qr qr (negative) anomaly on the upshear (downshear) pL pU pM side. This temperature perturbation should be (2) may be rewritten as achieved by vertical circulation. Based on these considerations, the vertical motion, due to ver- qv Sdt: ð3Þ tical wind shear, may be quantified in the fol- qr pM lowing manner. By definition, S has the same dimension as The thermal wind balance equation for an vertical wind shear, and could be approximated axisymmetric typhoon-like vortex may be writ- by ambient vertical shear, to the extent that ten in pressure coordinates as the separation between upper- and lower- 2v qv R qT portions of the vortex can be accounted for the f þ ¼ ; ð1Þ r qp p qr ambient shear. If the thermal wind balance ap- p proximation in the form of Eq. (1) is still valid where f and R are the Coriolis parameter and for the vortex being tilted, followed by a change April 2007 M. UENO 125 in the vertical shear of azimuthal wind as Eq. p o ¼ v (3), we may then obtain the following relation m; pM R m; pM from Eq. (1); 2v kT qT f þ m; pM S ; ð6Þ 2v qv R qdT rm; p p qp f þ Sdt ¼ , ð4Þ M m; pM r qr p qr pM pM where the subscript m denotes that the quan- where dT is a temperature change needed for tity is evaluated at the radius of maximum the achievement of a newly balanced state, and wind rm. Likewise, we get a similar expression considered as a function of azimuthal angle y, for vertical p velocity on the uptilt side. It is as well as r and p, since the change in the ver- noteworthy that Eq. (6) is a time-independent tical shear of azimuthal wind sharply depends solution, and gives an amplitude of vertical mo- on the angle relative to the tilt direction. In tion asymmetry. It will be shown below that the this sense the derivation of Eq. (4) assumes magnitude of vertical motion asymmetry ob- that the thermal wind equation for a balanced tained from the formula is well correlated with vortex Eq. (1) can be applied, not only for an that of simulated rainfall asymmetry in the upright vortex, but also for a tilted one. The va- inner-core region, suggesting a strong depen- lidity of this assumption will be demonstrated dence of rainfall asymmetry, on the vortex in- in a later subsection. Note again here that Eq. tensity, as well as the shear magnitude. (4) is a formulation valid in the downtilt direc- 3.2 Outline of experiment tion. a. Model used As an immediate consequence of Eq. (4), we The model used in the study is an f-plane get a temperature tendency due to ambient ver- version of the previous JMA typhoon model, tical shear in the downtilt direction, which is and essentially the same as that used in Ueno equivalent to the downshear direction here, as (2003), except for increased horizontal and ver- q qT p 2v qv tical resolutions. It is a three-dimensional, hy- ¼ f þ S: qr qt R r qr drostatic, primitive equation, spectral limited- pM pM area model, with physical parameterizations of Assuming that the temperature tendency is to- the boundary layer and cumulus convection. tally accounted for by the temperature change The model has 109 109 transform grid points due to vertical motion within the framework of on each of 13 sigma levels (s ¼ 0:98, 0.925, dry adiabatic dynamics, the above equation 0.85, 0.75, 0.625, 0.5, 0.4, 0.325, 0.26, 0.2, 0.15, may be rewritten as 0.1 and 0.035), at an interval of 20 km in the x and y directions on a Mercator map projection, q kT qT o and its whole domain is entirely over the sea. qr p qp pM The model prognostic variables then consist of p 2v qv both zonal and meridional winds, surface pres- ¼ f þ S; ð5Þ R r qr sure, virtual temperature, and mixing ratio of pM water vapor. The truncation at wavenumber where o is the vertical p velocity, and k 1 R/cp, 70, is applied to all the prognostic variables. with cp the specific heat at constant pressure. By this truncation the model has a shortest For simplicity here in this study we assume resolved half-wavelength of about 30 km. The solid-body rotation to characterize the winds model is integrated, both with and without the inside the radius of maximum wind though pre- moist physics from identical initial conditions, vious observational studies suggest that the va- to 6 h for all the selected cases described below. lidity of the assumption may depend on the The results from the dry integrations are main- stages of TC development (Yau et al. 2004). ly used for the verification of the analytical Under the aforementioned assumption, we may solution of wavenumber-one vertical motion integrate Eq. (5) with respect to r from the cy- asymmetry, derived in the previous subsection. clone center to the radius of maximum wind, to On the other hand, the moist simulations are get an azimuthal wavenumber-one component utilized to further understand the relationship of vertical velocity as between vertical shear and rainfall asymmetry. 126 Journal of the Meteorological Society of Japan Vol. 85, No. 2

In the moist runs diabatic heating is evaluated Ueno (2003), which allows only for the environ- by the so-called large-scale condensation, evap- ments with unidirectional shear. The initial TC oration of raindrops, and moist convective ad- environment, is specified from the JMA global justment scheme, proposed by Gadd and Keers analyses at the corresponding time. The hori- (1970). In the model it is assumed that the zontal wind components, at the storm center, large-scale condensation occurs when the mix- are obtained by averaging those over a circular ing ratio of water vapor exceeds the saturation region, within 500 km of the storm center, at value, and the temperature and mixing ratio, each mandatory pressure level. While the wind are adjusted to their saturation values, and direction is kept the same as that at the center that all the condensate falls directly to the throughout the model domain, the wind speed ground, without both horizontal and vertical V is varied in the manner below. advections. This adjustment is done before the cumulus convection scheme is affected. 1 px VðxÞ¼ V0 cos þ 1 ; The convective adjustment scheme is a moist 2 L scheme that keeps the vertical lapse rate below where x is the perpendicular distance between a critical value, inversely proportional to the each grid point and a straight line crossing the relative humidity, without changing the rela- storm center, and oriented along the wind di- tive humidity at each level. Due to the condi- rection there. V is the wind speed at the cen- tion set on the relative humidity, the rainfall 0 ter, and L is a length parameter to govern the amounts produced by the scheme, are usually horizontal variation of the environmental very small. winds. The parameter is set to 2700 km in the b. Initial conditions study. The virtual temperature fields are de- The purpose of the numerical experiments, rived from the geopotential height fields is to examine the validity not only of the ana- through the hydrostatic relation, after the lat- lytical expression for the AM1-produced ver- ter is determined so as to be in geostrophic tical motion asymmetry, but also of the conven- balance, on isobaric surfaces with the above- tional shear definition, within a realistic range mentioned horizontal wind components. The of environmental wind profiles and vortex geopotential heights at the storm center loca- strengths. Therefore it is a natural choice to tion, are derived from the JMA global analyses, construct the initial conditions based on some by spatially averaging geopotential over an an- real TC cases, and focus on the very early stage nulus surrounding the cyclone center. Simi- of the simulations. In the present numerical larly, the initial environmental specific humid- study, the two typhoon cases, Chaba and Tok- ities, for the moist integrations, are specified age in 2004, are selected for this purpose from from the gridded global analyses of dewpoint among the cases used for the observational depression. The bound radii of the annulus de- analysis. Although the environmental fields pend on the radius of gale force wind, in the are defined from the corresponding JMA global same way as those used for the definition of en- analyses, their horizontal variations are mini- vironment, in the JMA numerical typhoon mized, through the procedure described below, model (Ueno 1989). Sea surface temperatures to focus on the vertical shear effect. Moreover, are based on the daily global SST analyses because the disturbance in the analyses is usu- from JMA (0.25 grid), and are held constant ally much weaker in strength than the best throughout the simulation. Finally, all the track record, it is replaced by one with a more prognostic variables, but for surface pressure, realistic strength, by use of a bogussing are vertically interpolated onto the model method. Some more details, on the preparation sigma surfaces. method for the initial environment and vortex, Vortex will be separately given in the following para- The initial typhoon vortex for the experi- graphs. ments is provided by the JMA operational Environment bogussing scheme (Iwasaki et al. 1987), based The construction method of initial environ- on the best-track vortex information (e.g., cen- ment presented here, is an extension of that in tral pressure, and radius of gale force winds), April 2007 M. UENO 127 with the Coriolis parameter evaluated at the both Chaba’s, and Tokage’s, evolution is pro- respective storm position. The resulting vortex vided below. is implanted into the above-mentioned environ- Storm history of Chaba ments, with the storm center at the center of The post-analysis track of Chaba is presented the model domain. In all the moist experiments in Fig. 6, along with the vertical wind shear the relative humidity is modified to be 90% vectors at 6-hourly intervals. According to the in the near-core region through the depth of RSMC-Tokyo post-seasonal analysis, Chaba is the troposphere, in order to reduce the spin-up one of the most long-lived, and most-developed time for precipitation, as in the operational typhoons in 2004. It formed as a tropical de- bogussing scheme. pression in a very active low-latitude monsoon c. Cases studied trough, near the Caroline Islands. The cyclone A number of consecutive experiments at attained to tropical storm strength at 1200 6-hourly intervals, though idealized, are con- UTC on 19 August, when it was located approx- ducted with different vortices and shear condi- imately 900 nm east of Guam. Chaba continued tions, which cover almost all life cycle stages of to slowly intensify in an easterly-sheared envi- Typhoon Chaba, and Tokage in 2004. In total, ronment, as it moved westward on the 19th and 47 integrations are made for Chaba, and 31 for 20th. At 1800 UTC on the 21st, the cyclone Tokage, with and without the moist physics reached typhoon-strength. On the day intensifi- from identical initial conditions. The experi- cation began to accelerate, and the central ments are expected to give us some improved pressure dropped by 45 hPa in 24 hours, be- knowledge on how vertical wind shear produces tween 1200 UTC on the 21st and 1200 UTC on asymmetries in vertical motion, and therefore the 22nd, exceeding the 24-hour minimum cri- in rainfall in TC vortices. A brief description of terion for rapid deepening (42 hPa/day). The

Fig. 6. Post-analysis track (thin solid line with typhoon symbols) of (a) Typhoon Chaba and (b) Typhoon Tokage, overlaid by the large-scale 850–200-hPa vertical wind shear vectors at 6-hourly intervals (arrow), with the vector scale indicated above the upper-right corner. Typhoon symbols are given for 0000 UTC on each day (numerals attached to the symbols) during the period when each typhoon is of tropical storm strength or greater. 128 Journal of the Meteorological Society of Japan Vol. 85, No. 2 maximum sustained wind (10-minute average) the 16th, Tokage reached its peak intensity of reached a peak of 110 kts at 1800 UTC on the 85 kts, with a minimum central pressure of 22nd, and remained at that level until 1800 940 hPa. At this time, the radius of gales lay UTC on the 25th. The minimum central pres- up to 325 nm in all but the south quadrant, sure, estimated by the JMA, was 910 hPa. where they reached as far as 600 nm. Tokage Chaba’s track became increasingly north- turned northward at 1800 UTC on the 18th, fol- northwesterly on 25 August, as it tracked lowed by an acceleration to the north-east, with around the western periphery of the subtrop- the intensity down to 75 kts by 0400 UTC on ical ridge. A 25/2018 UTC QuikSCAT winds re- the 20th, when it made landfall near the south- vealed that Chaba had developed asymmetries, ern tip of Shikoku, Japan. The system weak- in the inner-core wind fields. By 1800 UTC ened quickly as it began to be affected by high on the 26th, deep convection was confined vertical wind shear. Tokage was declared extra- mainly to the southern and eastern sides of the tropical at 1800 UTC on the 20th, shortly after system. The cyclone continued tracking north- it was downgraded below typhoon-intensity at northwestward up to 28 August, then it began 1200 UTC. to track more to the west-northwest. Slow weakening ensued on the 29th, due to dry air 3.3 Comparison of analytical and simulated intrusion, and land interaction. By 0000 UTC asymmetries on the 30th the typhoon was accelerating to In this subsection we first attempt to validate the north-northeast, as it made landfall over the analytical solution obtained in Subsection extreme southeastern Kyushu. The weakening 3.1, by comparing it with the numerical model cyclone was downgraded below typhoon- results. Even if the environmental flow fields intensity, before declared extratropical at 0600 are horizontally uniform, and the vortex is ax- UTC on the 31st, over the northernmost Japa- ially symmetric at the initial time, as in this nese island of Hokkaido. study, subsequent nonlinear interactions be- tween vortex and environment would distort Storm history of Tokage both more and more with time, making it diffi- The post-analysis track of Tokage is pre- cult to clearly define the vertical wind shear, sented in Fig. 6, along with the vertical wind therefore to relate the induced asymmetries to shear vectors at 6-hourly intervals. Tokage is a the shear in a quantitative manner. Thus, in typhoon of the largest storm-size in 2004, such this study, the very early stage of the model in- that at the cyclone’s peak intensity gales ex- tegration is focused on. Of course the model tended outward 600 nm to the south of the undergoes the so-called spinup process in the center, and 325 nm elsewhere (based on the early stage of integration. Indeed, the ampli- RSMC-Tokyo post-seasonal analysis). The pre- tude of the Fourier coefficients of wavenumber- cursory cloud system of the cyclone developed zero rainfall fields is very small initially, and into a tropical depression at 0000 UTC 12 Octo- grows rapidly with time, suggesting a serious ber, in an area of low wind shear approximately spinup problem. In contrast, however, the 480 nm east-southeast of Guam. The system adverse effects from the model spin-up on subsequently moved westward, passing very wavenumber-one component, seem to be kept near Rota, and then away from the islands. At minimal, as suggested by Fig. 7. 0000 UTC on the 13th, the system was pro- Figure 7 shows a time series of the magni- moted to tropical storm intensity. It moved tude of azimuthal wavenumber-one vertical westward further, and attained typhoon- motion, comparing the analytical solutions intensity at 1200 UTC on the 14th, when cen- with the results from the dry integrations. The tered some 500 nm west of Guam. The storm’s calculation of the analytical omega, given by path then gradually curved onto a northwest- Eq. (6), needs the azimuthal-mean values of erly heading at 1800 UTC on the 14th. Typhoon the tangential wind, temperature and vertical Tokage continued moving in a general north- gradient of temperature evaluated at 500 hPa, westerly fashion, reaching a position 200 nm and at the radius of maximum wind (RMW), as south-southwest of Okinawa, Japan at 1200 well as RMW value, and some other parame- UTC on the 18th. Meanwhile, at 1200 UTC on ters, including the shear value. Those values April 2007 M. UENO 129

Fig. 7. Comparison of ‘‘analytical’’ (thick solid line) and model-simulated (thin solid line with open squares) wavenumber-one omega (i.e., vertical p-velocity in units of Pa s1) at RMW, and at 1 h of the consecutive 6-hourly dry integrations for (a) Typhoon Chaba and (b) Typhoon Tokage. The hor- izontal axis denotes the initial time of the integrations, with numbers indicating day of the month located at 00 UTC.

can be obtained from the output of consecutive and model-produced omega, are 0.44 and 0.39, 6-hourly dry integrations, after the variables respectively. on sigma levels are vertically interpolated, One of the assumptions made in the deriva- with a cubic spline onto pressure surfaces. In tion of Eq. (6), is that the thermal wind equa- this study, the output at 1 h of each integration tion for a balanced vortex as in the form of Eq. is utilized for the purpose. The storm center for (1) can be applied not only for an upright one, the RMW calculation is defined as that which but also for a tilted one. To confirm the validity maximizes the symmetric tangential wind. of the assumption, both the left-hand, and This definition minimizes aliasing of the sym- right-hand sides of Eq. (1) are calculated from metric wind component onto the asymmetric the 1-h dry model integrations for 16 different component (Wu et al. 2006). The vertical gradi- points at the 500-hPa level, which are equally ent of temperature is calculated as the differ- spaced, in the azimuthal direction along a circle ence between 300 hPa and 700 hPa, to be cen- of 100 km radius from the storm center at the tered differencing in the vertical. The use of level. It should be noted that even a medium another combination of the two levels, such as shear of 7@8m s1 would yield a distance of 400 hPa and 600 hPa, provides a similar result 25@30 km of separation (i.e., vortex tilt), be- to Fig. 7. The amplitude of model-produced tween 200- and 850-hPa level centers only in a wavenumber-one omega at RMW, is obtained 1-h period, without any restoring mechanism. from the same output, by applying a Fourier The choice of 100 km radius for the calculation, decomposition routine to the model-produced results in a separation distance of about 40 km omega fields. Considering that a number of as- between adjacent two points, which is well sumptions are made, in the derivation of Eq. larger than the model’s shortest resolved half- (6), the analytical omega obtained as a function wavelength. The vertical gradient of tangential of shear, compares remarkably well with the wind on the left-hand side of Eq. (1) is calcu- model-produced one. The correlation coeffi- lated as the difference between 400 hPa and cients between the two, computed for Chaba 600 hPa, to be centered differencing in the ver- and Tokage cases, are 0.94 and 0.91, respec- tical. On the other hand, the horizontal gradi- tively, while those between vertical wind shear, ent of temperature on the right-hand side is 130 Journal of the Meteorological Society of Japan Vol. 85, No. 2

components about the storm center, before it is used in the above calculation. Although the cal- culation is performed for all the Chaba and Tokage cases presented in Fig. 7, here in Fig. 8 we show the result for one of the Chaba cases in which the largest shear is observed. Figure 8 clearly demonstrates that the thermal wind balance as in the form of Eq. (1) is locally achieved in a tilted vortex. The azimuth at which the two curves take minimum values cor- responds to the shear direction in the specific case. The result explains why the analytical solution for omega, which is derived based on Fig. 8. Comparison of left-hand side (solid Eq. (1), is in good agreement with the model- line with open squares) and right-hand simulated one. side (solid line with closed circles) of Hereafter, we show some results from the Eq. (1), evaluated at a radius of 100 km moist integrations which is concurrently con- and at every 22.5 degrees of azimuth. ducted with the same initial conditions as the The azimuthal angle (abscissa) is mea- dry counterparts except for the moisture fields sured counterclockwise from due east, specified additionally. An example of rainfall and the ordinate is scaled appropriately. distribution after 1 h of integration is shown in Fig. 9 along with the corresponding RAD rain- rate distribution. The selected case is one of calculated as the difference between r ¼ 60 km, the Tokage cases that the inner-core region of and r ¼ 140 km, in the azimuthal direction of the storm is well covered by the RAD data and each of the 16 points. In the above calculations a relatively large wavenumber-one omega is local values are assigned to all the dependent obtained from Eq. (6) (see Fig. 7). Both the si- variables, instead of tangential means, so that mulated and observed storms exhibit marked azimuthal variations are allowed. As for the wavenumber-one asymmetries in the inner- tangential wind, asymmetric wind, defined as core region in this case, reflecting a relatively the mean current crossing the circle of 100-km large shear of about 14 m s1. Note that the radius, is subtracted from the tangential wind purpose of the idealized experiments in this

Fig. 9. Rain-rate distribution (mm h1) obtained by model integration (left), and Radar-Amedas (right) for 1800 UTC 19 October. Contours are drawn at 5 mm h1 intervals, and typhoon symbol denotes storm center position. Plotted domain is 150 km 150 km in size. North is up. April 2007 M. UENO 131

value parameter and the latter might introduce a strong vortex structure dependency into the phase of rainfall asymmetry. Note that all the condensate is assumed to fall directly to the ground in the present study, allowing a more straightforward interpretation of the re- sults. The results from the observational study, presented in the previous section, suggest a large correlation between shear and rainfall asymmetry. As far as their magnitudes are con- cerned, however, the correlation coefficient be- tween the two remains as small as 0.18 for the RAD dataset, and 0.04 for the SAT one, sug- gesting that some factors other than shear should be considered as well to quantitatively relate the shear to the rainfall asymmetry. Fig. 10. Scatter diagram of shear direc- From this viewpoint, Eq. (6) suggests both TC tion (abscissa) versus phase angle of strength, and static stability as possible candi- wavenumber-one rainfall asymmetry dates for such factors. To verify this speculation (ordinate) obtained from 1-h moist inte- against the observational datasets, the TC grations for Typhoon Chaba and Tok- strength-related parameter is approximately age. Both the direction and angle are derived from the RSMC-Tokyo best-track ar- measured counterclockwise from due chived by the JMA, and the static stability east. Each case is indicated by a closed from the JMA global analyses. When the corre- triangle or an open one. Open triangles lation coefficient is computed, taking into con- correspond to extremely weak shear sideration these two parameters, it increased cases (i.e., 1 m s1 or so). to 0.39 for the RAD dataset, although almost unchanged for the SAT dataset. The rather low values of correlation coefficient for the observa- study is to deepen our knowledge on the rela- tional datasets may be due in part to the dy- tionship between rainfall asymmetry and ver- namical inconsistencies, between the quantities tical wind shear rather than correctly repro- used in the calculation, since all the central duce the observed rainfall distribution. quantities, shear, TC strength and rainfall Figure 10 shows the directional relationship asymmetry are obtained from different data between initially specified vertical wind shear sources. Unlike the observational datasets, and model-produced rainfall asymmetry. Ac- model outputs can provide a dynamically con- cording to the conventional approach the 200– sistent dataset. In this sense numerical models 850-hPa layer is used to determine the shear might be considered as a powerful tool to un- for the figure. The phase of rainfall asymmetry derstand the physical mechanisms underlying is determined by the same method as used for the development of rainfall asymmetries the observational analysis described in Section around TCs. Figure 11 compares the analytical 2. The close correspondence in direction be- omega obtained from Eq. (6), with the tween shear and rainfall asymmetry suggests wavenumber-one asymmetry of the first 1-h that the rainfall in the inner-core region is rainfall amounts from the moist integrations. forced to occur downshear and the conventional The magnitude of initially specified shear, 200–850-hPa shear is a fairly good measure of which is used in the calculation of the analyt- such a forcing at least in the absence of compli- ical omega, is also presented in the same figure cated flow structure and/or horizontal advec- for comparison. The correlation coefficients, be- tion of condensate. The former would make it tween analytical omega and rainfall asymme- more difficult to define the environmental forc- try, are as high as 0.94 and 0.92 for Chaba, ing responsible for the asymmetry as a single and Tokage cases, respectively, while those be- 132 Journal of the Meteorological Society of Japan Vol. 85, No. 2

Fig. 11. Same as Fig. 7 but for comparison of ‘‘analytical’’ omega (thick solid line, in units of Pa s1) with magnitude of wavenumber-one rainfall asymmetry (thin solid line with open squares, mm h1), and vertical wind shear (dashed line, m s1). For plotting purposes, the magnitude of wavenumber-one rainfall asymmetry, and shear are divided by 3 and 7, respectively. tween shear, and rainfall asymmetry are 0.31 coverage, their statistics are confined to the TC and 0.37, respectively. Considering that the cases in the Atlantic basin. averaging radius for the rainfall amounts is set In the former part of the current study, we constant at 100 km, while the radius of maxi- carry out an observational analysis of the TC mum wind can largely vary with the initial rainfall asymmetry using the two types of rain- time, and the vertical levels over which the rate data, RAD and SAT data, for typhoons in shear is calculated is somewhat arbitrary, the 2004. Although the RAD data provides a reli- close correspondence between rainfall asymme- able gridded estimation of rain-rate, its cover- try, and analytical omega, is remarkable. age is mostly confined to the mid-latitudes, in the western North Pacific. On the other hand, 4. Summary and discussion although the SAT data is likely biased to lower A number of observational (e.g., Franklin values at higher rain-rate, it can cover the low et al. 1993; Gamache et al. 1997; Black et al. latitudes as well as the mid-latitudes. It is well 2002; Corbosiero and Molinari 2002, 2003), demonstrated, from the analysis, that rainfall and modeling (e.g., Bender 1997; Frank and in the inner-core region of TC tends to occur on Ritchie 2001; Rogers et al. 2003; Ueno 2003) the downshear-left side, irrespective of the data studies have shown a tendency for typhoon- type used in any latitudes. However, as far as strength vortices to develop upward motion, the relationship between shear and storm mo- and/or produce precipitation, particularly in tion is concerned, a sharp contrast is found be- the eyewall, on the down-shear to downshear- tween low and middle latitudes. In middle lati- left side of the storm. Among the observational tudes TCs have a tendency to move to the left of studies, the most extensive one is the work of the shear, consistent with the discussion by Wu Corbosiero and Molinari, that used ground- and Emanuel (1993), and Dengler and Reeder based lightning data to evaluate the convec- (1997). In low latitudes, however, TCs have the tive activities around TCs. Due to the non- opposite motion tendency, with respect to the convertible-to-rain character of the data, shear. A statistical investigation of the environ- however, the rainfall asymmetries are not eval- mental winds reveals that the wind vector uated within the framework of their works. tends to rotate counterclockwise (clockwise), Furthermore, due to the limitation of the data with height in middle (low) latitudes. Then the April 2007 M. UENO 133 notable difference in the shear-relative storm It is assumed in the moist experiments that heading, between the two latitudes is accounted the condensate is immediately removed to the for by the difference in vertical structure of the surface via precipitation. This assumption al- ambient winds, with the help of the common lows a more straightforward interpretation of understanding that the motion of typhoons is the directional relationship, if any, between approximated by the deep-layer mean of the en- model-produced rainfall asymmetry, and ver- vironmental flow. This result does not neces- tical wind shear. The results from the experi- sarily support the theory of a broad upper-level ments show that the maximum rainfall tends anticyclone advected downshear, of the low- to occur right downshear, rather than on the level center, and inducing motion to the left of downshear-left side as observed, except for ex- the shear, as discussed by Wu and Emanuel tremely low shear cases. The absence of left- (1993). Anyhow, use of the combined RAD and ward preference in model-produced rainfall, as SAT dataset, which totally covers both lati- compared to observed one, may be due in part tudes, clearly shows that the rainfall asymme- to the lack of advective processes of condensate try is much more intimately tied to the ambient in the model. Indeed, the previous observatio- wind shear, than the storm motion. nal studies (e.g., Franklin et al. 1993) shows Numerical models can be considered as a that the maximum in radar reflectivity occurs promising tool to investigate the physical mech- azimuthally downwind of the enhanced updraft anisms underlying the development of the region. Anyhow, the close correspondence in di- shear-induced rainfall asymmetry, because it rection between shear and rainfall asymmetry, provides the dataset possessing dynamical con- obtained under the realistic shear conditions, sistency between various quantities, such as suggests that the conventional 200–850-hPa shear, storm motion and rainfall asymmetry. shear is a good measure of the environmental In the latter part of the study, a formula for forcing responsible for the rainfall asymmetry. the shear-induced vertical motion is derived Some recent numerical studies (Braun et al. from the thermal wind balance equation for 2006; Wu et al. 2006), attempted to attribute TC-like vortices. The formula states that the the vertical motion asymmetries, obtained shear-induced vertical motion would be a func- from high resolution real-case experiments, to tion not only of shear magnitude, but also of the vortex tilt rather than the shear itself. To vortex strength, when it is evaluated at the ra- determine the relative importance of vortex tilt dius of maximum wind in the middle tropo- versus shear, in the development of such asym- sphere. To validate the formula, a set of ideal- metries, the shear as a forcing parameter ized experiments are conducted, with realistic should be suitably defined, as well as the vortex wind profiles in which the shear is specified tilt. Yet there is no consensus for an appropri- from the JMA global analyses for the two ty- ate way to define the shear forcing. In the pres- phoon cases, Chaba and Tokage in 2004, there- ent numerical study the shear forcing is defined fore it is due not only to change in speed, but as a single value parameter from horizontally also to veering or backing of direction. It is uniform environmental flow, with a minimal found from the numerical study, that the mag- ambiguity in the horizontal. However, as the nitude of wavenumber-one vertical motion from flow fields become more realistic, the shear the formula, agrees very well with the dry forcing needs to be more carefully determined, model-produced one, with correlation coeffi- in particular for the inner-core region, since cients of 0.94 and 0.91, for Chaba and Tokage the horizontal domain is taken smaller, then cases, respectively. It is also found that the the winds defined as the average over a single magnitude of rainfall asymmetry, produced by storm centered domain are increasingly af- the moist integration, correlates much better fected by the vortex tilt, if any. It is noteworthy with that of the analytical vertical motion that the tilt-generated shear vector points 90 (0.94 and 0.92, ditto), than that of the shear right of the tilt vector for a cyclonic vortex. alone (0.31 and 0.37, ditto), suggesting that the This arrangement of two vectors is just the vortex strength is one of the main factors deter- same as that reached by an initially upright mining the magnitude of shear-induced rainfall vortex at its maximum tilt (Reasor et al. 2004). asymmetry. Furthermore, the direction of tilt-generated 134 Journal of the Meteorological Society of Japan Vol. 85, No. 2 shear vector, misleadingly coincides with the fall asymmetry in the near-core region, at least expected direction of upward motion, due to for the said period, during which the actual the tilt (Jones 1995), hindering the unequivocal storm maintained typhoon-strength (64 kts or separation of the shear and tilt contributions to greater in maximum wind). The thermal wind the vertical motion asymmetry. balance consideration discussed in Section 3 re- Figure 12 shows a time series of the magni- quires that vortices are dynamically forced to tude of vortex tilt, diagnosed at 6 h both in the keep the vertical shear of azimuthal winds, dry, and moist simulations for the Chaba cases. less changed in the moist cases, since the latent As seen from Fig. 12, the magnitude of vortex heating almost exactly balances the adiabatic tilt in the moist simulations remains as small cooling in eyewall updrafts. This means that as half the model grid length of 20 km for the the vertical shear-induced diabatic heating initial times from 0000 UTC 22 August through could help vortices resist tilting by the shear. 0000 UTC 30 August, although much larger This speculation is consistent with the result tilts are diagnosed in the dry simulations for from idealized model simulations, performed the same period. Meanwhile, the amplitude of by Ueno (2003), in which diabatic heating is wavenumber-one rain rate at 6 h, greatly rather artificially imposed on the vortex in changes with the initial time during the period, vertically sheared environment, irrespective of with a maximum of 32.3 mm h1 (22/0600 water vapor distribution. The vortex could UTC), and a minimum of 1.4 mm h1 (26/1800 maintain highly consistent vertical structure, UTC). These results suggest that vortex tilt during the whole integration period of 72 hours may have only a minor contribution to the rain- in the experiment, when heat is imposed only at the grid points temperature decreases, so as to keep the temperature anomalies in the core as similar as possible to the initial ones.

Implications for tropical cyclone track forecast It is found from the observational analysis in Section 2 that the ambient shear is predomi- nantly westerly in mid-latitudes, while easterly in low latitudes. It follows from the result that the rainfall asymmetry phase maximum tends to be located in the northeastern quadrant of the storm in mid-latitudes, while in the south- western quadrant in low latitudes. This means that the locations of rainfall asymmetry phase maximum are somewhat fixed, with respect to the storm motion, both in low and middle lati- tudes, considering that a typhoon typically con- tinues to move westward in low latitudes, and then northeastward once it recurves into west- Fig. 12. Vortex tilt magnitude diagnosed erlies in mid-latitudes. The geographically fixed at 6 h in the idealized simulations arrangement of storm motion, and rainfall for Chaba. The magnitude is defined asymmetries, (roughly equivalent to diabatic as the distance between geopotential heating asymmetries) in TCs raises the follow- height minima at 850 hPa and 200 hPa, ing question: then does it affect TC movement and normalized by the model grid in any systematic way? However, the role of length. Solid line with closed circles is nonbarotropic processes, such as diabatic one for adiabatic vortices, and open squares for diabatic vortices. Since the geopo- in TC movement, has not been well understood tential height minimum at 200 hPa (Chan et al. 2002). The numerical study of could not be defined for the two initial Ueno (2003) for a long-term motion of TC-like times, 30/1800 UTC and 31/0000 UTC. vortices in vertical shear, suggests that asym- They are not shown in the figure. metric diabatic heating contribute to the ver- April 2007 M. UENO 135 tical coherency of the storm, rather than its Wada and Shunsuke Hoshino at MRI for their motion. help in handling the archived data used in the Recently, the importance of the precipitation study. mass sink in TCs is discussed by Lackmann and Yablonsky (2004). Although their study fo- References cuses on the role of the mass sink in the evolu- Alliss, R.J., S. Raman, and S.W. Chang, 1992: Spe- tion of axisymmetric surface pressure fields, cial Sensor Microwave/Imager (SSM/I) obser- the asymmetric mass loss, associated with vations of Hurricane Fugo (1989). Mon. Wea. asymmetric rainfall, is likely to affect the Rev., 120, 2723–2737. storm motion through its contribution to the Bender, M.A., 1997: The effect of relative flow on the wavenumber-one surface pressure tendency. asymmetric structure in the interior of hurri- Using the method to convert the surface pres- canes. J. Atmos. Sci., 54, 703–724. sure tendency into the equivalent storm motion Black, M.L., J.F. Gamache, F.D. Marks Jr., C.E. Samsury, and H.E. Willoughby, 2002: Eastern described in Ueno (2003), together with the Pacific Hurricane Jimena of 1991 and Olivia of pressure equivalent of the precipitation mass 1994: The effect of vertical shear on structure sink, found by Lackmann and Yablonsky and intensity. Mon. Wea. Rev., 130, 2291– (2004), the storm motion components, due to 2312. the mass sink, can be easily calculated from Braun, S.A., M.T. Montgomery, and Z. Pu, 2006: the asymmetric rain rate data. It is found by High-resolution simulation of Hurricane Bon- applying the conversion procedure to the RAD nie (1998). Part I: The organization of eyewall rain rate, that the mass sink-related storm mo- vertical motion. J. Atmos. Sci., 63, 19–42. tion speed strongly depends on the magnitude Chan, J.C.L., F.M.F. Ko, and Y.M. Lei, 2002: Rela- of wavenumber-one rainfall asymmetry, and tionship between potential vorticity tendency the ratio of it to the total storm speed reaches and tropical cyclone motion. J. Atmos. Sci., 59, 1317–1336. more than 0.3 in some cases. As discussed by Corbosiero, K.L. and J. Molinari, 2002: The effects of Lackmann and Yablonsky, the pressure reduc- vertical wind shear on the distribution of con- tion due to the mass sink would not be fully vection in tropical cyclones. Mon. Wea. Rev., realized, because the resulting unbalanced 130, 2110–2123. pressure gradient would drive compensating Corbosiero, K.L. and J. Molinari, 2003: The Rela- horizontal mass convergence. Anyhow, the pre- tionship between storm motion, vertical wind liminary quantification of the mass sink contri- shear, and convective asymmetries in tropical bution to storm motion suggests that the track cyclones. J. Atmos. Sci., 60, 366–376. forecasts produced by the numerical weather Dengler, K. and M.J. 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