atmosphere

Article Effect of -Generated Cold Wake on the Subsequent and Its Sensitivity to Horizontal Resolutions

Mincheol Moon 1,2 and Kyung-Ja Ha 1,2,3,*

1 Center for Climate Physics, Institute for Basic Science (IBS), 46241, ; [email protected] 2 Department of Climate System, Pusan National University, Busan 46241, Korea 3 Department of Atmospheric Science, Pusan National University, Busan 46241, Korea * Correspondence: [email protected]; Tel.: +82-051-510-7860

 Received: 27 September 2019; Accepted: 22 October 2019; Published: 24 October 2019 

Abstract: Weather research models have been used to investigate the sensitivity of simulations of Typhoon Tembin (1214) to changes in three horizontal grid spacings and the effect of the cold wake generated by (1215). We used modified (SST) to simulate Tembin as it approached after Bolaven had passed through the Ieodo Ocean Research Station and the buoy in Korea. In the (TC) tracking experiments, a higher resolution showed the faster and more eastward movement of TCs in all SST conditions. TCs tend to move more eastward at all resolutions particularly when there is a cold wake in their western regions. When there is no cold wake, the intensity of TC is very sensitive to the resolution of the experiment. If a cold wake is maintained on the western and eastern sides, TC intensity is less sensitive to differences in resolution. The precipitation from TCs in the cold wake of the eastern (western) region is lower (higher) than when there is no wake. The TC-generated cold wake significantly affects intensity and movement in cold wake cases in the western region, regardless of horizontal grid, for various reasons.

Keywords: cold wake; potential vorticity; tropical cyclone; typhoon; horizontal grid; potential vorticity tendency

1. Introduction are significant causes of disasters such as floods and building collapses through their strong winds and heavy rains. Of the approximately 80 global tropical cyclones (TCs) that occurred from 1981–2010, 30% occurred in the Western North Pacific (WNP) basin annually. To improve TC simulation and to understand TC track dynamics, previous studies have conducted sensitivity tests on the horizontal and vertical grids and physical processes [1–4]. Although many variables affect tropical cyclone development, sea surface temperatures (SSTs) majorly impact their paths and intensities [5–8]. In particular, the higher the latitude, the stronger the SST gradient becomes; environmental factors also have more of an influence on the typhoon [9]. Previous work attempted to understand the structure of typhoons using satellite data, statistical approaches, and parameters [10–14]. Many typhoons occur from July to October, with about 5.8 typhoons occurring on average in August; thus, the occurrence of simultaneous typhoons leads to the systems directly or indirectly affecting one another. Previous research has been conducted via tank experiments [15–17], observations [18–22], and modeling studies [23–28], with most focusing on the direct effects of binary interaction between typhoons. The Fujiwhara effect, in particular, is a binary interaction in which direct interaction between typhoons directly affects adjacent typhoons through merging, rotation, and other processes. These direct interaction studies are significant, but indirect interactions have been underrepresented in the

Atmosphere 2019, 10, 644; doi:10.3390/atmos10110644 www.mdpi.com/journal/atmosphere Atmosphere 2019, 10, 644 2 of 18 literature, despite their importance. For example, typhoon-generated cold wakes have been shown to cool SSTs from ~3 to 8 ◦C[29–32]. In Dare and McBride [33], the cooling effect of an initial typhoon was recovered by just 44% approximately five days following the cooling, and by 88% after 30 days. This cold wake effect impacts the direction and intensity of other typhoons [28,34–38]. Jeong et al. [34] also considered how the typhoon-induced cold wake of (0603; the third typhoon of 2006) inhibited the development of Typhoon Billis (0604; the fourth typhoon of 2006). Typhoon Bolaven (1215) resulted in a decrease of about 10 ◦C along the coast of Jeollanam-do in the Yellow Sea, and the intensity of Typhoon Tembin (1214) was weakened by the rapidly cooled sea surface [35]. However, Kim et al. [35] only noted the weakened intensity of Tembin in response to the cooling from Bolaven without investigating the processes that led to this weakening. Moon et al. [37] and Heo et al. [38] also studied the change in the track of the following and weakening of Tembin via the cold wake using Bolaven and Tembin and focusing on 10 m wind and changes in the waves caused by a typhoon. The previous studies [34–38] investigated the impact of the changed SST on around region of the following TC. However, there is a lack of understanding of the mechanisms by which the track, intensity, and precipitation of a TC is affected by the SST gradient generated by a typhoon that occurred before it. In this study, we investigate the effect of the Typhoon Bolaven-generated cold wake on the track, intensity, and precipitation of Typhoon Tembin using the potential vorticity tendency (PVT) and vertical structure of potential vorticity (PV). The typhoon was simulated from 27 to 30 August, before Typhoon Tembin made landfall on the Korean Peninsula, using the Weather Research and Forecasting (WRF) model (version 3.2). We prescribed the SST field that modified the location of the SST gradient using the observed SST change and the three horizontal grid spacings of 12 km, 8 km, and 6 km, which were based on high-resolution data and experiments with the WRF. This study is composed of five Sections: Section2 introduces the characteristics of the model, the initial data, and case selection. In Section3, we review the experimental design and results of the track intensity and vertical structure of TC in model experiments; in Section4, we analyze variables associated with the physical processes on the surface and top of the TC and how they affect changes in the typhoon and the temporal change in the precipitation rate. In Section5, we summarize and discuss the main results.

2. Model Experiment and Case Selection

2.1. Model Experiment WRF version 3.2 is used to simulate Typhoons Tembin (1214) and Bolaven (1215); the details of these TCs are included in the following section [39]. The model domain consists of 240 240 (360 × 360 and 480 480) grid points with a uniform horizontal resolution of 12 km (8 km and 6 km) × × and 27 vertical levels, with the top model level at 50 hPa. All experiments are conducted through 72-h integration with a 60-s (48-s and 36-s) time step. The Kain-Fritsch scheme [40] is used for the cumulus parameterization. The details of the model physics have been documented by Yun et al. (2012) and Choi et al. (2013) [41,42]. National Centers for Environmental Prediction (NCEP) Final (FNL) Operational Global Analysis 6-hourly data with 1.0 1.0 resolution, and SST data obtained at ◦ × ◦ the daily interval from the Optimal Interpolation Sea Surface Temperature version 2 (OISST.v2) with 0.25 0.25 resolution, are used as initial and boundary conditions [43]. The best-track datasets are ◦ × ◦ from the Joint Typhoon Warning Center (JTWC). Atmosphere 2019, 10, 644 3 of 18

Difficulties in numerical model initialization are a major obstacle in accurate TC forecasting. Therefore, a simple bogussing scheme used in the Mesoscale Model Fifth Generation (MM5) [44] is employed to insert a bogus vortex onto a background field to improve the simulation performance. Briefly, the bogussing procedure consists of identifying an initial TC vortex relative to the best-track data and removing the vortex from the first-guess field. Finally, the bogus Rankine vortex is inserted into the removed region to generate the vortex, which is an improvement over the initial vortex. The bogus vortex has a radius of maximum wind of 45 km with a maximum wind speed of 50 m/s considering the best track data.

2.2. Case Selection: Typhoon Tembin (1214) and Typhoon Bolaven (1215) One of the major challenges in predicting typhoons is handling changes in the track and intensity due to the interaction between typhoons. This is particularly important since successive impacts on a particular area from subsequent typhoons will increase the damage in the region. For this reason, we selected Bolaven and Tembin for this study; this case is significant in Korea due to the forecasting errors that resulted in damage from both of the typhoons occurring back-to-back. According to the forecast preceding landfall on the Korean peninsula by the Korea Meteorological Administration, the first system was expected to move north along the coast of on 27 August; Tembin, however, deflected northeastward and made landfall on the Korean peninsula. Bolaven, a relative larger typhoon (radius is 550 km), directly interacted with Tembin, a relative smaller typhoon (radius is 350 km), after the former’s first landfall in , which changed the track of Tembin. After the interaction between typhoons, Tembin passed through the track of Bolaven, which deflected eastward and minimized its development thereafter (Figure1a,b). The 200 hPa and 500 hPa weather maps (Figure1c–f) show the relationship between Tembin and synoptic phenomena such as jets and troughs on 29 and 30 August 2012. The jet, marked with a thick red arrow, blows along with the geopotential height on 29 August and exits on 30, weakening Tembin at 200 hPa. At 500 hPa, Tembin is weakened by interaction with the trough generated by typhoon Bolaven and the existing mid-latitude trough. We analyze Tembin when it approaches the Korean Peninsula and Bolaven passes through the Ieodo Ocean Research Station (IORS) and Yellow Sea (YS) buoy observation points. According to the time series of the observed SST, Bolaven approached the IORS and started to decrease its SST observations at 00 UTC on 27 August [45]; the SSTs decreased by about 3 ◦C, but, after 12 UTC on 27 August, data were missing. At 00 UTC on 29 August, YS buoy SST data indicate an SST reduction of 7 ◦C and a subsequent recovery of 2 ◦C (Figure2a). Using the OISST.v2 data, we defined ∆SST (the Bolaven-generated cold wake) as the difference of SST between SSTs on 27 August over 0.5 ◦C (Figure2b), before Bolaven passed through, and on 28 August, after its passage. The forcing of the Bolaven-generated cold wake was controlled using the observed SST evolution at each station. The OISST.v2 data is underestimated three times compared to YS buoy data. Therefore, we force ∆SST three times to change the SST gradient. Atmosphere 2019, 10, 644 4 of 18 Atmosphere 2019, 10, x FOR PEER REVIEW 4 of 18

FigureFigure 1.1. (a) Best track of Typhoon Tembin (red(red solidsolid line)line) and Typhoon BolavenBolaven (black solid line), greengreen triangletriangle (orange (orange triangle) triangle) represent represent YS buoyYS buoy (IORS), (IORS), and (b and) the ( meanb) the sea mean level pressuresea level (unit:hPa) pressure changes(unit:hPa) in changes Typhoon in Tembin Typhoon (red Tembin solid line) (red and soli Typhoond line) and Bolaven Typhoon (black Bolaven solid line) (black obtained solid fromline) JTWC.obtained A three-dayfrom JTWC. integration A three-day is conducted integration from is conducted 00 UTC 27 from August 00 UTC 2012 to27 00August UTC 302012 August to 00 2012.UTC The30 August weather 2012. charts The during weather approach charts Tembinduring approach to Korea at Tembin (c,d) 200 to hPaKorea and at ( e(c,f–)d 500) 200 hPa hPa from and 00UTC (e–f) 500 29 AugusthPa from 2012 00UTC to 00UTC 29th Aug 30 August 2012 to 2012. 00UTC 30th Aug 2012.

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Figure 2. (a) Time evolution of the Sea Surface Temperature (SST, unit: ◦C) of observed station and Figure 2. (a) Time evolution of the Sea Surface Temperature (SST, unit: °C) of observed station and OISST.v2, and green solid (dashed) line indicates the SST located at YS buoy (OISST.v2 at YS buoy OISST.v2, and green solid(dashed) line indicates the SST located at YS buoy (OISST.v2 at YS buoy point), and orange solid (dashed) line indicates the SST located at the IORS (OISST.v2 at the IORS point). point), and orange solid(dashed) line indicates the SST located at the IORS((OISST.v2 at the IORS The orange (green) vertical line means when Typhoon Bolaven passes through the IORS (YS buoy). point). The orange(green) vertical line means when Typhoon Bolaven passes through the IORS (YS (b) Spatial distribution of the difference in SST between 27 August and 28 August. The left box is the buoy). (b) Spatial distribution of the difference in SST between 27 August and 28 August. The left box defined western region of Tembin (WT); the right box is the defined eastern region of Tembin (ET). is the defined western region of Tembin (WT); the right box is the defined eastern region of Tembin 2.3. Experimental(ET). Design This study used nine experiments as time series during the approach of Tembin towards the 2.3. Experimental Design Korean peninsula; the experiments used three different SST conditions and three horizontal grid spacings.This Westudy prescribed used nine the experiments effects of the as cold time wake series caused during by the typhoon approach and recoveredof Tembin SSTtowards after thethe typhoonKorean peninsula; passed through the experiments specific regions. used OISST.v2 three diffe datarent was SST underestimated conditions and compared three horizontal to the observed grid SSTspacings. change We and prescribed did not showthe effects recovery of the in cold terms wake of SST caused after by the typhoon typhoon and passed recovered through SST a after specific the regiontyphoon as thepassed observed through SST. Inspecific the No_CW regions. experiment, OISST.v2 we data not considerwas underestimated the typhoon Bolaven-generatedcompared to the coldobserved wake; SST we change use the and SST did on 27not August. show recovery In ET_CW in terms experiment, of SST after we prescribed the typhoon the passed cold wake through effect a whenspecific typhoon region as Bolaven the observed passed SST. through In the theNo_CW IORS. experiment, Subsequently, we not we consider considered the thetyphoon change Bolaven- in the observedgenerated SST, cold added wake; three we use times the the SST underestimated on 27 August.∆ InSST ET_CW to the SSTexperiment, in the ET we region, prescribed and subtracted the cold ∆wakeSST ineffect the WTwhen region. typhoon We prescribed Bolaven passed the cold thro wakeugh after the theIORS. Bolaven Subsequently, passed through we considered the YS region the inchange the WT_CW in the observed experiment. SST, Thenadded we three were times then the forced underestimated to add three times∆SST to the the∆SST SST inin thethe WTET region, region andand subtractsubtracted∆SST ∆SST in thein ETthe regionWT region. as SST We change prescribed of YS buoy. the cold We simulatedwake after experiments the Bolaven with passed the smoothedthrough the∆SST YS forregion the double-checkin the WT_CW boundary experiment. of the Then box atwe WT were and then ET; theforced result to wasadd consistentthree times with the non-smoothed∆SST in the WT∆ regionSST experiments. and subtract The ∆SST more in detailedthe ET region experimental as SST change design of is shownYS buoy. in TableWe simulated1. experiments with the smoothed ∆SST for the double-check boundary of the box at WT and ET; the result was consistent with Tablenon-smoothed 1. The experimental ∆SST experiments. design used The in this more study. detailed experimental design is shown in TableSST 1. No_CW ET_CW WT_CW Res Table 1. The experimental design used in this study. 12 km SSTNo_CW : Using SSTET = SSTWT = SST 00 UTC 27 August SSTNo_CW + ∆SST 3 SSTNo_CW + ∆SST 3 No_CW ET_CW × WT_CW × Res SST SSTWT = SSTNo_CW ∆SST SSTET = SSTNo_CW ∆SST 8 km − − : (No Cold Wake)SST:= (Eastern SST_ region+ ∆SST of × Tembin 3 SST: (Western = SST region_ + of∆SST Tembin × 3 12 km SST_: Using 00 UTC 27 ex) SST: No_CW, SST = SSTCold_ Wake)− ∆SST SST = Cold SST_ Wake)− ∆SST August SST 6 km Res: 6 km, EXP:: (Easternex) region SST: ET_CW,of Tembin Res: Cold 8 km, : (Westernex) SST: region WT_CW, of Tembin Res: Cold 12 8 km : (No Cold Wake) No_CW_6 km EXP:Wake) No_CW_8 km km, EXP:Wake) WT_CW_12 km ex) SST: No_CW, Res: 6 km, EXP: ex) SST: ET_CW, Res: 8 km, EXP: ex) SST: WT_CW, Res: 12 km, EXP: 6 km No_CW_6 km The difference of area-averaged SST betweenNo_CW_8 WT region km and ET region (SSTWT_CW_12SST km ) in each WT − ET experimentThe difference is 2.60 ofC area-averaged in No_CW, 0.40 SST betweenC in ET_CW, WT region and and5.94 ETC region for the (SST WT_CW − SST condition in each in − ◦ ◦ − ◦ theexperiment initial data. is −2.60 Moon °C etin al.No_CW, [33] investigated 0.40 °C in ET_CW, how the and Bolaven-generated −5.94 °C for the coldWT_CW wake condition influenced in thethe initial data. Moon et al. [33] investigated how the Bolaven-generated cold wake influenced the change in the track of Tembin using the same experimental design and found the main factors from the

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Atmosphere 2019, 10, x FOR PEER REVIEW 6 of 18 change in the track of Tembin using the same experimental design and found the main factors from the synopticsynoptic patternpattern aroundaround the the typhoon typhoon and and asymmetric asymmetric flow withflow only with a 12only km grida 12 spacingkm grid experiment; spacing experiment;however, it didhowever, not reveal it did the not characteristics reveal the characteristics of 3-D structure of of3-D PV structure and precipitation of PV and with precipitation change of withgrid spacing.change of grid spacing. ForFor the the simulation simulation reliability reliability of of the the model, model, the the mo modeldel test test the the result result and and comparative comparative verification verification werewere conducted conducted using using 10 10 min min data data of of IORS. IORS. The The time time was was compared compared between between Sea Sea Level Level Pressure Pressure (SLP (SLP andand 10 10 m m wind wind intensity intensity for for 72 72 h h from from 00 00 UTC UTC 27 27 August, August, to to 00 00 UTC UTC 30 30 August August (Figure (Figure 33).). Figure3 3aa showsshows the the time time evolution evolution in in IORS, IORS, and and when when lookin lookingg at at the the time time evolution, evolution, Bolaven Bolaven passed passed the the IORS IORS afterafter 12 12 UTC UTC 27 27 August. August. At At this this ti time,me, the the sea sea level level air air pressure pressure was was about about 945 945 hPa, hPa, and and the the 10 10 m m wind wind waswas a a strong strong wind wind of of 35 35 m/s. m/s. Tembin Tembin passed passed on on 21 21UTC UTC 29 29August, August, when when the thesea sealevel level was wasabout about 980 hPa,980 hPa,and the and 10 the m 10 wind m wind was 30 was m/s. 30 mFigure/s. Figure 3b,c 3showb,c show SLP and SLP 10 and m 10wind m wind of the of location the location even evenin each in experiment.each experiment. Compared Compared with the with observations, the observations, SLP was SLP about was 955 about hPa 955 and hPa the and 10 them wind 10 m was wind about was 30about m/s 30in m12/s km in 12 and km 6 andkm 6experiments, km experiments, and they and theyare underestimated are underestimated than than Bolaven Bolaven at the at thetime time of passingof passing through through the the Bolaven. Bolaven. The The TC TC approached approached IORS IORS later later than than the the observation observation in in the the 12 12 km km experimentexperiment and and confirmed confirmed that that the the observations observations a approachedpproached a a similar similar time time in in the the 6 6 km km experiment. experiment. However,However, SLP and 10 m wind is underestimated than the observation data.

FigureFigure 3. 3. TimeTime series series of of sea sea level level pressure pressure (right (right y-ax y-axis,is, orange,unit:hPa) orange, unit: hPa) and and 10 10m wind m wind speed speed (left (left y- axis,y-axis, blue, blue, unit:m/s) unit:m/ ats) at(a) ( aIORS,) IORS, (b) ( bNo_CW_12) No_CW_12 km km experiment, experiment, and and (c) ( cNo_CW_6) No_CW_6 km km experiment. experiment. 3. Effect of the Location of the Cold Wake Generated by Bolaven on the Simulated Tembin 3. Effect of the Location of the Cold Wake Generated by Bolaven on the Simulated Tembin To understand the effects of the Bolaven-generated cold wake on Tembin, we simulated the To understand the effects of the Bolaven-generated cold wake on Tembin, we simulated the events from 00 UTC 27 August to 00 UTC 30 August. Figure4a–c show the SST distribution of each events from 00 UTC 27 August to 00 UTC 30 August. Figure 4a–c show the SST distribution of each experiment, denoted No_CW, ET_CW, and WT_CW in Table1. The No_CW indicates that SSTs are experiment, denoted No_CW, ET_CW, and WT_CW in Table 1. The No_CW indicates that SSTs are maintained as SSTs before the passage of Typhoon Bolaven so as to ignore the effect of the cold wake, maintained as SSTs before the passage of Typhoon Bolaven so as to ignore the effect of the cold wake, the ET_CW experiment defines the eastern cold wake from the IORS observation as 28 August minus the ET_CW experiment defines the eastern cold wake from the IORS observation as 28 August minus 27 August, and the WT_CW experiment is the opposite of the ET_CW. The track of the TC is a different 27 August, and the WT_CW experiment is the opposite of the ET_CW. The track of the TC is a response, depending on the SST condition and horizontal grid spacing (Figure4d), as the SST gradient different response, depending on the SST condition and horizontal grid spacing (Figure 4d), as the affects the direction of TC motion in all horizontal grid spacing. In comparison with No_CW and SST gradient affects the direction of TC motion in all horizontal grid spacing. In comparison with ET_CW, which are similar, the TC in the ET_CW moves faster and more westward than that in No_CW. No_CW and ET_CW, which are similar, the TC in the ET_CW moves faster and more westward than The movement of the TC of the WT_CW is slower than that of No_CW and is deflected more eastward. that in No_CW. The movement of the TC of the WT_CW is slower than that of No_CW and is The higher resolution experiment results in the faster and more eastward movement. deflected more eastward. The higher resolution experiment results in the faster and more eastward movement. Based on the results of previous studies that indicated that the typhoon-generated cold wake affects the intensity of the subsequent typhoon [34,35], we examined the change in intensity in the TC between experiments with mean sea level pressure. In terms of TC intensity, the results show that TCs in the SST condition No_CW show largely different responses at the 6 km resolutions. In the SST of ET_CW, the TC at the 6 km resolution weakens earlier compared to the other two resolutions (Figure 4e). In the SST of WT_CW, TC tends to maintain the intensity for all resolutions.

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FigureFigure 4. 4. SpatialSpatial patterns patterns of of SST(unit: SST(unit: °C)◦C) in in(a) ( aNo_CW,) No_CW, (b ()b ET_CW,) ET_CW, and and (c ()c WT_CW) WT_CW adapted adapted from from thethe initial initial condition condition of of Moon etet al.al. 2016; 2016; ( d()d The) The track track of Typhoonof Typhoon Tembin Tembin (black (black solid solid line: OBS,line: OBS, dotted dottedline with line brown(greenwith brown(green and blue):and blue): No_CW_12 No_CW_12 km (8km km(8 km and and 6 km), 6 km), solid solid line line with with brown(green brown(green and andblue) blue) ET_CW_12 ET_CW_12 km km(8 (8 km km and and 6km), 6 km), dashed dashed line line with with brown(green brown(green and and blue): blue): WT_CW_12 WT_CW_12 km km(8 (8 km kmand and 6 km))6 km)) and and contour contour is geopotentialis geopotential height heig atht 500 at 500 hPa hPa in No_CW_12 in No_CW_12 km experiment;km experiment; (e) the (e) mean the meansea level sea level pressure pressure changes changes in Typhoon in Typhoon Tembin. Temb Thein. two-day The two-day integration integration is conducted is conducted from 00 from UTC 00 28 UTCAugust 28 August 2012 to 2012 00 UTC to 00 30 UTC August 30 August 2012. 2012.

ToBased analyze on thethe results TC track, of previous asymmetric studies flow that analysis indicated using that the typhoon-generatedpotential vorticity tendency cold wake equationaffects the and intensity the asymmetric of the subsequent component typhoon with [the34, 35symmetric], we examined component the change removed in intensity from the in wind the TC fieldbetween was performed. experiments The with definition mean sea of level PV used pressure. in the In study terms is of the TC definition intensity, theof PV results in the show sigma that coordinateTCs in the system, SST condition as follows: No_CW show largely different responses at the 6 km resolutions. In the SST of ET_CW, the TC at the 6 km resolution weakens earlier compared to the other two resolutions PV = − 𝜉+𝑓 + − , (1) (Figure4e). In the SST of WT_CW, TC tends to maintain the intensity for all resolutions. To analyze the TC track, asymmetric flow analysis using the potential vorticity tendency equation PV 𝑔 𝑝 𝜉 𝑓 whereand the asymmetric, , , component, and arewith potential the symmetric vorticity, componentgravitational removed acceleration, from thesurface wind pressure, field was relativeperformed. vorticity, The and definition the Cori ofolis PV parameter, used in the respectively. study is the definition of PV in the sigma coordinate system,To divides as follows: PVT of TC into symmetric and asymmetric components, we use Fourier transform as " # follows: g ∂θ ∂u ∂θ ∂v ∂θ = ( + f ) + PV ξ , (1) −ps f c ∂σ ∂σ ∂y − ∂σ ∂x PV = PV +𝑎 𝑐𝑜𝑠 𝑛∅ +𝑏 𝑠𝑖𝑛 𝑛∅ (2) where PV, g, Psfc, ξ, and f are potential vorticity, gravitational acceleration, surface pressure, relative vorticity, and the Coriolis parameter, respectively. 1 𝑎 = PV𝑐𝑜𝑠∅𝑑∅ (3) 𝜋

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To divides PVT of TC into symmetric and asymmetric components, we use Fourier transform as follows: XN PV = PVwn0 + (ancosn∅ + bnsinn∅) (2) n=1 Z 1 2π an = PVcos∅d∅ (3) π 0 Z 1 2π bn = PVsin∅d∅ (4) π 0 an and bn are Fourier coefficients, n is a wavenumber, and PVwn0 is a symmetric component. Wavenumber 0 of PV is the symmetric component and represents the circulation based on the center of TC. Wavenumber 1 and more wavenumbers of PV are asymmetric components, especially the wavenumber 1 component is known as beta gyre. the components of wavenumber 2 and above number show the circulation of opposite phases in the advancing direction, and the magnitude thereof is smaller than that of the wavenumber 1 component. Therefore, we examine the Wavenumber 1 component associated with the track of TC. The PVT equation used in this study is defined as follows [46,47]:

!   . . .  ∂PV  ∂PV ∂PV . ∂PV g   ∂θ ∂u ∂θ ∂v ∂θ =  u v σ +  ξ + f +  (5) 1   ∂t 1 ∧ − ∂x − ∂y − ∂σ ps − ∂σ − ∂σ ∂y ∂σ ∂x  where a left side is wavenumber 1 component of PVT, is the operator of wavenumber 1, u ∂PV v ∂PV ∧1 − ∂x − ∂y . ∂PV is the horizontal advection (HA) included in beta effect and asymmetric flow, σ ∂σ is the vertical  . .− .  g  advection (VA) included vertical wind shear effect, and ξ + f ∂θ ∂u ∂θ + ∂v ∂θ is diabatic ps − ∂σ − ∂σ ∂y ∂σ ∂x heating (DH) included in vertical shear and precipitation. PVT is particularly sensitive to level; we vertical averaged from 0.9 to 0.55 sigma level because straight-moving TCs are affected by the low-mid layer in previous work [42,48]. In the asymmetrical flow, the symmetrical components that can be represented by typhoons in the same region are removed from the wind field of a 720 km radius from the center of the typhoon. Since Tembin is a small typhoon, the range used for the actual analysis is based on the asymmetry of a 250 km radius from its center. The asymmetric flows include the asymmetrical components of the direct currents and typhoons that are affected at the center of the TC. The magnitude of each term in the PVT in the 6 km resolution experiment is stronger than in the 12 km resolution experiment (Figure5). HA does not show the di fference in the direction according to SST at 12 km, while it is headed north in No_CW and ET_CW at 6 km and northeast at WT_CW. VA is similarly oriented in ET_CW, in the direction opposite No_CW and WT_CW, compared to 12 km and 6 km. However, the VA term is too small compared to the other terms in the two resolutions. DH does not show much difference in the direction depending on the resolution, but the strength of No_CW and WT_CW is greatly developed and offset with HA. However, although there is an offset between HA and DH, the former is the dominant role of the movement of TC because of its magnitude. Based on the PVT analysis, we analyzed the asymmetric flow associated with the HA term. In all SST conditions, the higher resolution experiments showed a faster asymmetric flow than the coarse resolution experiment. These results support the difference in the magnitude of the horizontal advection term of the wavenumber-1 component of PVT. In the region northeast from the center of typhoon (Quadrant 1), in particular, there are many differences in resolution (Figure6). However, the asymmetric flow in the center of the TC is strong in the 12 km resolution experiment; it seems to overestimate asymmetric flow in the center of TC. According to the SST conditions, the direction of asymmetric flow is more inclined at WT_CW and moves eastward compared to No_CW and ET_CW, Atmosphere 2019, 10, x FOR PEER REVIEW 9 of 18 while PV intensity is weakened overall and maximum value shifts to the lower layer (Figure 7). TC in WT_CW does not develop vertically compared to the other two SSTs, and it is inferred that it will be affected by synoptic phenomena. Comparing 48–60 h and 36–48 h, closer distance to the SST gradient, TC is weaker in WT_CW and stronger TC in No_CW and ET_CW. Through the difference in the vertical structure of PV, it is confirmed that the change in intensity according to the SST condition is more sensitive than the difference in intensity of PV according to the resolution. In addition to the vertical structural change, the analysis is performed using moisture static energy (MSE) to examine the effect on the intensity of TC. SST conditions and horizontal resolution are affected when looking at the MSE averaged vertically from sigma level 0.99 to 0.85. First, when comparing SST condition, ET_CW has the weak MSE at the center of the TC and WT_CW has the strong MSE at the center and northeast of the TC (Figure 8) even if the resolution is changed. As the resolution in each experiment, MSE at the center of TC does not change; however, it does decreases at the periphery of TC, which results in the asymmetric MSE. Then enhance the asymmetry of MSE areAtmosphere strong2019 in ,TC10, 644as finer horizontal grid spacing. 9 of 18 When vertically averaged from 0.85 to 0.55 sigma level, the difference in resolution is attenuated in the periphery of TC, similar to the results at the lower level. In WT_CW, MSE develops more widelywhich isthan consistent the other with two an SSTs. earlier In studyall experiments, [37]. In this MSE study, plays SST a gradientrole in the changes development the direction of TC ofat the centerTC and of the TC. horizontal grid spacing changes the translating speed of the TC.

Figure 5. Wavenumber-1Wavenumber-1 components components of of ( (aa––cc)) total total potential potential vorticity vorticity tendency, tendency, ( d–f) horizontal advection, ((gg––ii)) verticalvertical advection, advection, and and (j –(jl–)l diabatic) diabatic heating, heating, which which are are 12-h 12-h composites composites of lower-level of lower- level(0.9 (0.9σ ≥ σ0.55) ≥ 0.55) averages averages during during 48–60 48–60 h h in in (left) (left) No_CW, No_CW, (middle) (middle) ET-CW,ET-CW, andand (right) WT-CW ≥ ≥ experiment ofof Tembin.Tembin. TheThe left left panel panel is is for for 12 12 km km grid grid experiments experiments and and the the right right panel panel is for is 6for km 6 gridkm gridexperiments. experiments. Positive Positive values values are shaded. are shaded. The contour The contour interval interval is 3.0 inis (3.0a–f ),in 0.5(a– inf), ( g0.5–i ),in and (g–i 1.0), and in ( j1.0–l). 4 6 2 1 1 in[Unit: (j– 10l).− potential[Unit: vorticity10 potential unit (PVU) vorticity per seconds unit (PVU, (PVU) where PVU:10per seconds− m s− Kkg(PVU,− ).]. where 1 PVU: 10 msKkg).]. In order to confirm whether the difference in intensity is caused by the vertical structure change within the typhoon, the difference in intensity between 48 and 60 h (from 00 UTC 29 August to 12 UTC 29 August) and the averaged zonal cross-sections of PV in each experiment are examined to see how they differed from No_CW. When looking at the zonal cross-section of the vertical potential, there is little difference in resolution. However, there is a difference between the potential and the SST condition. At No_CW and ET_CW, the maximum potential intensity and asymmetry appear above the 0.5 sigma level. In WT_CW, the maximum value of PV is under 7 PVU and asymmetry shows above 0.5 sigma level, while PV intensity is weakened overall and maximum value shifts to the lower layer (Figure7). TC in WT_CW does not develop vertically compared to the other two SSTs, and it is inferred that it will be affected by synoptic phenomena. Comparing 48–60 h and 36–48 h, closer distance to the SST gradient, TC is weaker in WT_CW and stronger TC in No_CW and ET_CW. Through the difference in the vertical structure of PV, it is confirmed that the change in intensity according to the SST condition is more sensitive than the difference in intensity of PV according to the resolution. Atmosphere 2019, 10, 644 10 of 18

Atmosphere 2019, 10, x FOR PEER REVIEW 10 of 18 Atmosphere 2019, 10, x FOR PEER REVIEW 10 of 18

Figure 6. The 12-h averaged lower-level (900 hPa–550 hPa) asymmetric flow in the Typhoon Tembin Figure 6. The 12-h averaged lower-level (900 hPa–550 hPa) asymmetric flow in the Typhoon Tembin core coreFigure region 6. The (250 12-h km averaged × 250 km) lower-level over periods (900 hPa–550(48–60 h) hP ina) ( aasymmetric) No_CW_12 flow km, in ( bthe) No_CW_8 Typhoon Tembinkm, (c) region (250 km 250 km) over periods (48–60 h) in (a) No_CW_12 km, (b) No_CW_8 km, (c) No_CW_6 No_CW_6core region× km, (250 ( dkm) ET_CW_12 × 250 km) overkm, (periodse) ET_CW_8 (48–60 km, h) in (f )( aET_CW_6) No_CW_12 km, km, (g )( bWT_CW_12) No_CW_8 km,km, ((hc) km, (d) ET_CW_12WT_CW_8No_CW_6 km,km and( (de)) (ET_CW_12i ET_CW_8) WT_CW_6 km, km,km ( experimente () fET_CW_8) ET_CW_6 of km,Typhoon km, (f) ET_CW_6 ( gTembin.) WT_CW_12 km, (g) WT_CW_12 km, (h) WT_CW_8 km, (h) km and (i) WT_CW_6WT_CW_8 km experiment km and (i) WT_CW_6 of Typhoon km experiment Tembin. of Typhoon Tembin.

Figure 7. 12-h averaged zonal cross-section of PV at the center of TC during 48–60 h in (a) No_CW_12 km, (b) No_CW_8 km, (c) No_CW_6 km, (d) ET_CW_12 km, (e) ET_CW_8 km, (f) ET_CW_6 km, (g) WT_CW_12 km, (h) WT_CW_8 km and (i) WT_CW_6 km.Shaded is the PV magnitude in No_CW (top), ET_CW (middle), and WT_CW (bottom), the shading denotes the magnitude of PV and contour 6 2 1 1 denotes wavenumber 1 component of PV(shaded interval is 1 PVU:10− m s− Kkg− and the contour interval is 0.5 PVU). Atmosphere 2019, 10, 644 11 of 18

In addition to the vertical structural change, the analysis is performed using moisture static energy (MSE)Atmosphere to examine2019, 10, x theFOR e PEERffect REVIEW on the intensity of TC. SST conditions and horizontal resolution are aff11ected of 18 when looking at the MSE averaged vertically from sigma level 0.99 to 0.85. First, when comparing SST condition,Figure ET_CW7. 12-h averaged has the zonal weak cross-section MSE at the of center PV at ofthe the center TC of and TC WT_CW during 48–60 has h the in ( stronga) No_CW_12 MSE at the centerkm, and (b) northeast No_CW_8 ofkm, the (c) TC No_CW_6 (Figure 8km,) even (d) ET_CW_12 if the resolution km, (e) isET_CW_8 changed. km, As (f the) ET_CW_6 resolution km, in(g) each experiment,WT_CW_12 MSE km, at the(h) WT_CW_8 center ofTC km does and ( noti) WT_CW_6 change;however, km.Shaded it is does the decreasesPV magnitude at the in peripheryNo_CW of TC, which(top), ET_CW results (middle), in the asymmetric and WT_CW MSE. (bottom), Then the enhance shading thedenotes asymmetry the magnitude of MSE of arePV and strong contour in TC as 1 PVU: 10 msKkg finerdenotes horizontal wavenumber grid spacing. 1 component of PV(shaded interval is and the contour interval is 0.5 PVU).

Figure 8. TheThe spatial spatial pattern pattern of of the the vertical vertical averaged averaged MSE MSE during during 48–60 48–60 h in h ( ina) No_CW_12 (a) No_CW_12 km, km,(b) (No_CW_8b) No_CW_8 km, km, (c) (No_CW_6c) No_CW_6 km, km, (d) ( dET_CW_12) ET_CW_12 km, km, (e ()e )ET_CW_8 ET_CW_8 km, km, (f ()f )ET_CW_6 ET_CW_6 km, km, ( (g)) WT_CW_12 km, (h) WT_CW_8 km and (i) WT_CW_6 km. left panel is lower layer(0.99 to 0.85 sigma level) and right panel is middle layer(0.85 toto 0.550.55 sigmasigma level).level).

AlthoughWhen vertically the MSE averaged of ET_CW from is 0.85 relatively to 0.55 small sigma and level, the the MSE diff oference WT_CW in resolution is relatively is attenuated large, the intensityin the periphery of TC is, of conversely, TC, similar strong to the in results ET_CW at the and lower weak level. in WT_CW. In WT_CW, The cause MSE develops of this is investigated more widely throughthan the shear other between two SSTs. 200 In hPa all experiments, and 850 hPa. MSE No_C playsW and a role ET_CW in the have development the wind shear of TC under at the 10 center m/s atof TC.the center of TC, and the strength of the surrounding wind shear is less than 25 m/s. However, WT_CWAlthough has a stronger the MSE wind of ET_CW shear than is relatively that in two small SSTs and in thethe MSEcenter of and WT_CW south-east is relatively of the TC large, (Figure the 9).intensity There is of little TC is, difference conversely, in wind strong shear in ET_CW according and to weak the horizontal in WT_CW. resolution The cause experiment. of this is investigated The weak MSEthrough acts shear as a betweensource in 200 ET_CW, hPa and but 850 the hPa. energy No_CW loss in and the ET_CW TC is low have due the to wind the shearlow wind under shear; 10 m /buts at inthe WT_CW, center of although TC, and the the strength relatively of thestrong surrounding MSE acts wind as a shearsource is in less the than TC, 25 the m /energys. However, loss increases WT_CW duehas ato stronger the strong wind wind shear shear. than that in two SSTs in the center and south-east of the TC (Figure9). There is little difference in wind shear according to the horizontal resolution experiment. The weak MSE acts as a source in ET_CW, but the energy loss in the TC is low due to the low wind shear; but in WT_CW, although the relatively strong MSE acts as a source in the TC, the energy loss increases due to the strong wind shear.

Atmosphere 2019, 10, 644 12 of 18 Atmosphere 2019, 10, x FOR PEER REVIEW 12 of 18

Figure 9. TheThe 12-h 12-h averaged averaged wind wind shear(200 shear(200 hPa–850 hPa–850 hPa) hPa) in inthe the inner inner region region of TC of TC(250 (250 km × km 250 km)250 × overkm) overperiods periods (48~60 (48~60 h) in h)(a) in No_CW_12 (a) No_CW_12 km, ( km,b) No_CW_8 (b) No_CW_8 km, ( km,c) No_CW_6 (c) No_CW_6 km, ( km,d) ET_CW_12 (d) ET_CW_12 km, (km,e) ET_CW_8 (e) ET_CW_8 km, km,(f) ET_CW_6 (f) ET_CW_6 km, km, (g) (gWT_CW_12) WT_CW_12 km, km, (h ()h WT_CW_8) WT_CW_8 km km and and ( (ii)) WT_CW_6 WT_CW_6 km experiment of Typhoon Tembin.Tembin.

4. The Physical Response in the Surface and the Top of TC as SST and Horizontal Grid Spacing 4. The Physical Response in the Surface and the Top of TC as SST and Horizontal Grid Spacing We examined the changes in the physical processes at the top of the surface of TC in response to We examined the changes in the physical processes at the top of the surface of TC in response to SST forcing and horizontal grid spacing. We examine latent heat at the surface of 250 km from the SST forcing and horizontal grid spacing. We examine latent heat at the surface of 250 km from the center of TC. In each SST, the latent heat flux is released more strongly as the horizontal grid spacing center of TC. In each SST, the latent heat flux is released more strongly as the horizontal grid spacing becomes finer (Figure 10). In contrast, each SST shows a different spatial pattern of latent heat flux. becomes finer (Figure 10). In contrast, each SST shows a different spatial pattern of latent heat flux. Latent heat flux is sensitive to the horizontal grid spacing in No_CW. The maximum of latent heat flux Latent heat flux is sensitive to the horizontal grid spacing in No_CW. The maximum of latent heat shows the south-east region of TC in the No_CW_12 km experiment. In the 8 km experiment, the latent flux shows the south-east region of TC in the No_CW_12 km experiment. In the 8 km experiment, the 2 latentheat flux heat are flux separated are separated western western side and side eastern andside eastern of TC side under of TC 400 under Wm− 400. However, Wm. theHowever, latent heat the 2 latentflux in heat the 6flux km experimentin the 6 km developsexperiment in thedevelops western in side the ofwestern TC meridionally side of TC over meridionally 500 Wm− over. 500 Wm. In ET_CW, circular latent heat release in the 12 km experiment is less than 400 Wm and expands along the meridional in the 8 km and 6 km experiments. In WT_CW, the maximum value is over 500 Wm regardless of the resolution, and a lot of latent heat is released from the south to the east of the TC. At 8 km and 6 km, more latent heat flux than in the 12 km resolution is also enhanced west of the TC over 300 Wm. The latent heat dissipation from the surface area of TC is strong in the 6 km resolution experiment, the maximum value of latent heat flux at No_CW and ET_CW is shown to the west of TC, and the direction of TC movement is also shown. In WT_CW there is a great release in latent heat flux southeast of the TC. The top temperature (CTT) was investigated to confirm the change in the intensity and structure on the top of the TC (Figure 11). Looking at the SST conditions, CTTs in the No_CW and ET_CW show meridional, not zonal, expansion of the cloud structure. In WT_CW, the cloud structure shifts to the west compared to the other two SST conditions; thus, it is inferred that the typhoon is tilted. Compared to WT_CW, which has a lower PV vertical structure than it under other SST

Atmosphere 2019, 10, x FOR PEER REVIEW 13 of 18 conditions, CTT is similar to the other two SST conditions; thus, we infer that the cloud is developed toAtmosphere a similar2019 ,altitude.10, 644 In terms of the sensitivity to resolution, the cloud in the finer resolution13 of 18 experiment is more developed in the periphery than that in the coarse resolution experiment.

Figure 10. TheThe 12-h 12-h averaged averaged latent latent heat flux flux in the i innernner region of TC (250 km × 250250 km) km) over over periods periods × (48~60h)(48~60 h) in in (a (a) )No_CW_12 No_CW_12 km, km, ( (bb)) No_CW_8 No_CW_8 km, km, ( (cc)) No_CW_6 No_CW_6 km, km, ( (dd)) ET_CW_12 ET_CW_12 km, km, ( (ee)) ET_CW_8 ET_CW_8 km, ( f) ET_CW_6 km, ( g) WT_CW_12 km, ( h) WT_CW_8 km and ( i) WT_CW_6 km experiment of Typhoon Tembin.

2 In ET_CW, circular latent heat release in the 12 km experiment is less than 400 Wm− and expands along the meridional in the 8 km and 6 km experiments. In WT_CW, the maximum value is over 500 2 Wm− regardless of the resolution, and a lot of latent heat is released from the south to the east of the TC. At 8 km and 6 km, more latent heat flux than in the 12 km resolution is also enhanced west of 2 the TC over 300 Wm− . The latent heat dissipation from the surface area of TC is strong in the 6 km resolution experiment, the maximum value of latent heat flux at No_CW and ET_CW is shown to the west of TC, and the direction of TC movement is also shown. In WT_CW there is a great release in latent heat flux southeast of the TC. The cloud top temperature (CTT) was investigated to confirm the change in the intensity and structure on the top of the TC (Figure 11). Looking at the SST conditions, CTTs in the No_CW and ET_CW show meridional, not zonal, expansion of the cloud structure. In WT_CW, the cloud structure shifts to the west compared to the other two SST conditions; thus, it is inferred that the typhoon is tilted. Compared to WT_CW, which has a lower PV vertical structure than it under other SST conditions, CTT is similar to the other two SST conditions; thus, we infer that the cloud is developed to a similar altitude. In terms of the sensitivity to resolution, the cloud in the finer resolution experiment is more developed in the periphery than that in the coarse resolution experiment.

Atmosphere 2019, 10, 644 14 of 18 Atmosphere 2019, 10, x FOR PEER REVIEW 14 of 18

Figure 11. TheThe 12-h 12-h averaged averaged CTT CTT in in the the inner inner region region of of TC TC (250 (250 km km × 250250 km) km) over over periods periods (48~60 (48~60 h) × inh) ( ina) No_CW_12 (a) No_CW_12 km, km,(b) No_CW_8 (b) No_CW_8 km, ( km,c) No_CW_6 (c) No_CW_6 km, (d km,) ET_CW_12 (d) ET_CW_12 km, (e) km, ET_CW_8 (e) ET_CW_8 km, (f) ET_CW_6km, (f) ET_CW_6 km, (g) WT_CW_12 km, (g) WT_CW_12 km, (h) WT_CW_8 km, (h) WT_CW_8 km and ( kmi) WT_CW_6 and (i) WT_CW_6 km experiment km experiment of Typhoon of Tembin.Typhoon Tembin.

To examine the change of precipitation rate calculated calculated through through the the following following physical physical processes, processes, the timetime variationsvariations of of the the area-averaged area-averaged precipitation precipitation rate fromrate from the center the center of TC toof 500 TC km to are500 analyzed. km are analyzed.First, when First, the e ffwhenects of the the effects SST condition of the onSST the condition same resolution on the aresame examined, resolution the precipitationare examined, rate the in precipitationET_CW is weaker rate in than ET_CW that of is No_CWweaker than (Figure that 12 ofa). No_CW The decrease (Figure in 12a). precipitation The decrease rate accordingin precipitation to the rateSST conditionaccording isto particularly the SST condition great after is particularly 60 h in the 6great km experiment. after 60 h in However, the 6 km theexperiment. precipitation However, rate in theWT_CW precipitation is stronger rate than in No_CW.WT_CWThe is stronger 12 km experiment than No_CW. shows The that 12 the km di ffexperimenterence in precipitation shows that ratethe differenceincreases to in 60 precipitation h integration. rate In theincreases 6 km experiment to 60 h integration. the maximum In the positive 6 km experiment precipitation the rate maximum anomaly positiveappears precipitation before 48 h, andrate theanomaly 72 h precipitation appears before rate 48 is h, more and thanthe 72 that h precipitation in No_CW. Thisrate is di ffmoreerence than in thatprecipitation in No_CW. rate This indicates difference a diff erencein precipitation of less than rate 2 mmindicates/h before a difference TC until 36of h,less but than the 2 di mm/hfference before then TCincreases until 36 to h, as but much the asdifference 6 mm/h. then increases to as much as 6 mm/h. We compared the response of precipitation rate according to the resolution under the same SST condition (Figure 1212b).b). InIn thethe 88 kmkm experiment,experiment, the the strongest strongest precipitation precipitation rate rate di differencefference is shownis shown in inWT_CW WT_CW and and the weakestthe weakest precipitation precipitation ratein rate the in ET_CW the ET_CW is in the is 12 in km the experiment. 12 km experiment. This difference This differenceis particularly is particularly large after large 66 h af thanter 66 before h than 66 before h. In the66 h. 6 In km the experiment, 6 km experiment, the precipitation the precipitation rate of rateNo_CW of No_CW and WT_CW and WT_CW is usually is enhanced. usually enhanced. In the No_CW In the and No_CW WT_CW and experiment, WT_CW experiment, the difference the in differencethe precipitation in the precipitation rate increased rate until increased 51 h and until increased 51 h and again increased after 60 again h. In after ET_CW, 60 h. the In diET_CW,fference the in differenceprecipitation in precipitation rate increased rate up increased to 51 h, like up into No_CW,51 h, like butin No_CW, it then decreases but it then and decreases becomes and negative becomes at negative72 h. The at di 72fference h. The in difference precipitation in precipitation rate is similar rate to the is similar difference to the inSST difference condition, in SST but condition, TC is less than but TC2 mm is less/h until than 36 2 h.mm/h The until difference 36 h. increasesThe difference after theincreases maximum after 7the mm maximum/h. 7 mm/h.

Atmosphere 2019, 10, 644 15 of 18 Atmosphere 2019, 10, x FOR PEER REVIEW 15 of 18

Figure 12. Comparison of area-averaged precipitation rate from the center of TC to 500 km between (a) Figure 12. Comparison of area-averaged precipitation rate from the center of TC to 500 km between regional cold wake and Non-wake (b) higher resolution (8 km and 6 km) and 12 km. Blue (ET_CW) (a) regional cold wake and Non-wake (b) higher resolution (8 km and 6 km) and 12 km. Blue (ET_CW) -solid: 12 km, dotted: 8 km, and hatched: 6 km same with red (WT_CW) and green (8 km)—solid: -solid: 12 km, dotted: 8 km, and hatched: 6 km same with red (WT_CW) and green (8 km)—solid: No_CW, dotted: ET_CW, and hatched: WT_CW same with orange (6 km) bar is the difference between No_CW, dotted: ET_CW, and hatched: WT_CW same with orange (6 km) bar is the difference each experiment and (a) No_CW and (b) 12 km. between each experiment and (a) No_CW and (b) 12 km. 5. Summary and Discussion 5. Summary and Discussion In this study, we examine the effects of the location of the Typhoon Bolaven-generated cold wake on TyphoonIn this study, Tembin we and examine examine the theeffects sensitivity of the loca oftion three of (6, the 8, Typhoon and 12 km) Bolaven-generated horizontal grid spacings cold wake of onthe Typhoon numerical Tembin model throughand examine PVT, the asymmetric sensitivity flow, of th andree the (6, vertical8, and 12 structure km) horizontal of PV using grid WRF. spacings The ofSST the gradient numerical affects model the through direction PVT, and asymmetric intensity of theflow, TC and and the the vertical horizontal structure grid spacingof PV using affects WRF. the Thetranslation SST gradient speed affects of the TC.the direction and intensity of the TC and the horizontal grid spacing affects the translation speed of the TC.

Atmosphere 2019, 10, 644 16 of 18

First, the track of TC, when examined through the wavenumber 1 component of PVT, shows a strong asymmetry at 6 km compared to 12 km, according to the direction of TC. As seen through the asymmetric flow, all horizontal grid spacings show movements northeastward in WT_CW (western cooling) and northward in No_CW and ET_CW. In all SST conditions, the asymmetric flow is mainly characterized by the model resolution. The asymmetric flow in finer resolution experiments has a stronger magnitude than that in coarse resolution experiments. Second, the intensity of TC is examined by the vertical structure of PV, MSE, and wind shear. The intensity of TC has little difference in resolution and is greatly influenced by the SST gradient. In No_CW and ET_CW, the zonal cross-section of PV develops to about 0.2 sigma level and the maximum intensity appears at 0.5 sigma level. The asymmetry is the smallest for ET_CW. However, WT_CW has a weak maximum strength, with a maximum value that shifted down to 0.8 sigma level, and the asymmetry is strong in the upper layer. MSE is strong in WT_CW and weak in ET_CW at all resolutions, but TC becomes weaker in WT_CW, due to strong wind shear, and stronger in ET_CW. To consider the physical process of the reaction of TC, the surface latent heat flux and CTT on the top of TC were investigated. Latent heat flux is greatly affected by SST and the horizontal grid. The spatial distribution of latent heat and CTT are mainly determined with SST. No_CW and ET_CW maintain symmetry in the zonal direction, whereas in WT_CW, there is cloud development on the west side of the TC, increasing asymmetry. In all experiments, the altitudes of the CTTs are similar. Comparisons of the temporal evolution of precipitation rate show that WT_CW is strong while ET_CW is weak. The precipitation rate in the 8 and 6 km experiments increased compared to the 12 km experiments. The present study intends to focus on the effect of the SST gradient changed by typhoon-generated cold wake and its sensitivity to the horizontal grid spacing. However, the limitations of this work are that there is only one case study, SST is fixed, and that there is no finer resolution than 6 km can be the limitation of this study. Therefore, further case studies on the impact of adjacent typhoon-generated cold wake on TCs and model experiments with cloud-resolving scale resolutions and coupled simulations are needed. To study the typhoons that have recently affected the Korean Peninsula, more practical case studies can be conducted based on the data from the IORS and the Ocean Research Stations that have been built since 2012 [45]. Studies of the dynamic factor and thermodynamics are particularly required in the context of a moistened environment given the global climate.

Author Contributions: Conceptualization, K.-J.H.; Formal analysis, M.M.; Investigation, M.M.; Methodology, M.M.; Visualization, M.M.; Writing—original draft, M.M. and K.-J.H.; Writing—review & editing, M.M. and K.-J.H. Funding: This study was supported by the Institute for Basic Science (IBS), Republic of Korea, under IBS-R028-D1 and the Korea Ministry of Environment (MOE) as “Graduate School specialized in Climate Change” (M.M., and K.-J.H.). Acknowledgments: WRF model can be found at http://www2.mmm.ucar.edu/wrf/users/downloads.html. FNL data can be found at https://rda.ucar.edu/datasets/ds083.2/. Observation (IORS and YS buoy) data can be found at http://kors.kiost.ac.kr/en/data/sub1.php(More details of the research facilities, maintenance, observations and scientific achievements of KORS. OISST.v2 daily data can be found at https://www.esrl.noaa.gov/psd/cgi-bin/db_ search/DBListFiles.pl?did=132&tid=75. Best track data can be found at https://www.metoc.navy.mil/jtwc/jtwc. html?western-pacific. Conflicts of Interest: The authors declare no conflicts of interest.

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