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Asymmetric Structures of a Squall-Line MCS over Taiwan with Significant Hydraulic Jumps

Asymmetric Structures of a Squall-Line MCS over Taiwan with Significant Hydraulic Jumps On 19 April 2019, a mature squall-line mesoscale convective system (MCS) with the characteristics of a leading convective line and trailing stratiform landed on Taiwan, resulting in strong gust wind and heavy rainfall. This squall-line MCS became asymmetric after landfall on Taiwan. Two sets of idealized numerical simulations (mountain heights and low-level vertical wind shear) using the Weather Research and Forecasting (WRF) model were conducted to examine the impacts of realistic Taiwan topography on a squall-line MCS. Results showed numerous similarities between the idealized simulations and real-case observations. The low-level Froude number which considered the terrain height (F ) was calculated to examine mt the blocking effect of the Taiwan terrain, and the cold pool (determined by − 1.5 K isotherm) was found to be completely blocked by the 500-m height contour. The northeast-southwest orientation of the Snow Mountain Range (SMR), and the north–south orientation of the Central Mountain Range (CMR) led to the upwind side asymmetry. On the other hand, the lee-side asymmetry was associated with different intensities and occurrence locations of the hydraulic jump between the SMR and southern CMR, and the cold-pool Froude number (F ) indicated the flow-regime transition from subcritical to cp supercritical. Keywords Squall-line MCS · Taiwan topography · Froude number · Hydraulic jump 1 Introduction There are relatively few studies on the terrain effects to squall-line MCSs. Since Taiwan is a mountainous island, During the Mei-Yu season (from mid-May to mid-June) in the relation between a squall-line MCS and realistic Taiwan Taiwan, the squall-line type of mesoscale convective sys- terrain is worth investigating. One previous observational tems (MCSs) frequently form ahead of or along the Mei- study (Teng et al. 2000) investigated the impacts of Taiwan Yu fronts over southeastern China, which approach Taiwan terrain on a squall-line MCS during the Taiwan Area Mes- from the west and lead to heavy rainfall and fierce gust wind oscale experiment (TAMEX; Kuo and Chen 1990), and they (Fang 1985; Ninomiya et  al. 1988). Ahead of the squall found the orientation of squall-line MCS became parallel to line, the environment usually has substantial vertical wind 1000-m terrain contour line after the contacts with Taiwan shear (particularly at low level), and the interaction between topography. environmental wind shear and precipitation-induced cold The evolution of a squall-line MCS is strongly determined pool can make the squall-line MCS a self-organized system by cold-pool dynamics. Cold pool is a region with substan- (Fovell and Tan 1998; Lin et al. 1998; Lin and Joyce 2001). tial evaporative cooling produced by precipitation, a key feature to initiate new convective cells at the leading edge and sustain the MCS (Rotunno et al 1988; Weisman 1993; Yang and Houze 1995a, b; Weisman and Rotunno 2004). Communicated by Hyeyum Hailey Shin As a result, whether the cold pool is blocked by terrain or not affects the longevity of the squall-line MCS (Frame and * Ming-Jen Yang Markowski 2006; Letkewicz and Parker 2011). mingjen@as.ntu.edu.tw After the contact with the terrain, the squall-line MCS Department of Atmospheric Sciences, National Taiwan would either dissipate away or reinitiate convection on the University, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, lee side, depending on the hydraulic jump effect (Long Taiwan Korean MeteorologicalSociety Vol.:(0123456789) 1 3 416 Y.-T. Pan, M.-J. Yang 1953). Numerous modeling studies examined the relation and Lin 2007; Letkewicz and Parker 2011), which may not between the downslope motion and hydraulic jump effect be suitable for the complicated terrain on Taiwan. Hence, on the lee side (Durran 1986, 1990; Karyampudi et al. 1995; instead of using an idealized terrain, idealized WRF simu- Frame and Markowski 2006; Armi and Mayr 2011). The lations with realistic Taiwan topography are conducted to hydraulic jump occurs when the flow makes a transition examine the influences of complex Taiwan topography on from subcritical flow upstream to supercritical flow over the a squall line. The mature squall-line MCS case with a sym- mountain, and the Froude number which considered cold metric precipitation structure which landed over Taiwan on pool depth (F ) is utilized to decide whether the fluid is 19 April 2019 is a case for us to compare with the results cp supercritical (F > 1) or subcritical (F < 1). obtained from the idealized simulations. cp cp The objectives of this study are listed as follows. Firstly, This paper is organized as follows. Overview of the we use the mountain-height Froude number (F ) to clarify sqaull-line MCS event on 19 April 2019 is in Sect. 2. Meth- mt the asymmetric structure on the upwind side and the cold- odology is presented in Sect.  3. Results from idealized pool blocking effect due to Taiwan terrain. Secondly, the model simulations are discussed in Sect. 4. The conclusions cold-pool Froude number (F ) is applied to discuss the are summarized in Sect. 5. cp leeside asymmetry. The transition from subcritical flow (F < 1) upstream to supercritical flow (F > 1) at mountain cp cp peak favors the hydraulic jump effect, which can reinitiate 2 Case Overview convection on lee side. Lastly, the terrain-heights and low- level shear experiments are conducted to further examine the On 19 April 2019, a mature squall-line MCS formed over control simulation results. southeastern China and moved eastward to Taiwan, develop- Previous studies mainly applied a bell-shaped mountain ing its mature stage and remained symmetric before being in idealized simulations to discuss the impacts of the terrain affected by Taiwan terrain. Figure  1 illustrates the radar on squall-line MCS (Frame and Markowski 2006; Reeves reflectivity evolution of this squall-line system. Before (a)1400 LST (c)1610 LST (b)1500 LST (f)1840 LST (e)1800 LST (d)1700 LST Fig. 1 Composite of vertical-maximum (CV) radar reflectivity (in units of dB Z) maps on 19 April 2019: a 1400 LST, b 1500 LST, c 1610 LST, d 1700 LST, e 1800 LST, and f 1840 LST (Image source: Central Weather Bureau in Taiwan) Korean MeteorologicalSociety 1 3 Asymmetric Structures of a Squall-Line MCS over Taiwan with Significant Hydraulic Jumps 417 reaching Taiwan, the precipitation feature of this squall line line-type convective systems produced in 1-km simula- was mostly symmetric (Fig. 1a). Even when the squall line tions. Thus, a horizontal grid size of 2 km is used in this just touched Taiwan’s coast line, the precipitation structure study, based on the compromise between the limitation of did not alter significantly (Fig.  1b). available computational resources, numbers of numerical After landing on Taiwan’s mountainous area, this squall experiments, and the grid resolution required to resolve line changed its structure. It is clear from Fig. 1c that the deep convective cells. The cumulus parameterization is not orientation of the southern leading line became roughly used. Effects of Coriolis force and radiation are ignored north–south orientation, but the northern leading line in this study in order to emphasize the effects of Taiwan remained the same northwest-southeast orientation as pre- terrain. vious stage (Fig. 1b). The southern part of the squall line For the environmental setting, instead of using the also showed slightly stronger radar echoes than the northern observed sounding directly, we alternatively use a compos- counterpart (Fig. 1c, d). It is clear that the variation of the ite sounding. The reason is that we only have the observed squall-line orientation resulted from the impacts by Taiwan sounding data at 00 UTC (08 LST) and 12 UTC (20 LST), terrain. The different leading line orientation on the upwind but the squall-line MCS case occurred from 13 to 18 LST side of the mountain is called “upwind side asymmetry”. (see Fig. 1); as a result, both the 00 UTC and 12 UTC data Later, the squall line moved to the lee side of the mountain cannot be used to fully determine the environmental condi- (Fig.  1e). Notice that the southern part of the squall line tion before the arrival of MCS. In fact, the 00 UTC sound- moved faster than the northern part, and this asymmetry is ing in either Makong (a small island west of Taiwan; see its called “leeside asymmetry”. Finally, the squall-line system location in Fig. 3) or Panchiao (northern Taiwan; also shown progressed to the east of Taiwan and dissipated eventually in (Fig. 3) contained convective available potential energy −1 (Fig. 1f). (CAPE) of less than 200 J kg which did not favor squall- line initiation in an idealized model setting. This low-CAPE situation might result from earlier convective precipitation 3 Methodology occurring before the arrival of this squall line and the contri- bution from sea breeze from the surrounding ocean. 3.1 Model Design The pre-storm environment is horizontally homogeneous in the idealized model setting. A composite sounding with The Advanced Research version of the Weather Research a surface temperature of 301.5 K (28.5 °C) and a surface −1 and Forecasting model (WRF-ARW version 3.9; Skamarock mixing ratio of water vapor of 21.3 g  kg is given, and this −1 et al. 2008) was used to perform the idealized simulations in environment contains the CAPE of 2588 J  kg (Fig. 2a). this study. In a real-case WRF simulation, synoptic forcing, This thermodynamic sounding is a composite from several Coriolis force, radiation, and topography are all included, sounding stations in Taiwan with high CAPEs during the and these physical processes will all affect the symmetry Southwest Monsoon Experiment field project (SoWMEX; of a squall-line MCS, causing us difficult to isolate the ter - Jou et al. 2011) to represent the environmental character- rain effects on a squall line. As a result, we used the ideal - istic of Mei-Yu season. Although the SoWMEX campaign ized WRF simulation to exclusively investigate the terrain was conducted more than 10 years ago, it is still the most impacts on a squall-line MCS. recent field experiment which had the most complete intense The computational domain was 1400 km in the x direc- observations (including surface, sounding, radar, satellite, tion and 940 km in the y direction with a horizontal grid size and aircraft measurements) in Taiwan during the Mei-Yu of 2 km. Since a mature squall line can develop vertically season. Therefore, a composite sounding from SoWMEX up to 15 km in vertical, we set the domain vertical top to be can still show the representative theromydnamic profile in 30 km with 55 stretched vertical levels. A sponge layer with Taiwan during the Mei-Yu season. −2 a damping coefficient of 0.0003  s was applied to the top The observed wind profile at Makong (Fig.  2b) showed 5 km to prevent energy reflection from the upper boundary. that there was strong vertical shear at low levels (0–2.5 km). The open condition was imposed for the lateral boundaries, Recall that the squall-line longevity is most sensitive to the and the time step was 3 s. low-level (0–3 km AGL) vertical wind shear perpendicular The physical parameterization schemes used in the to squall-line orientation (Rotunno et al. 1988; Weisman model include the WDM6 microphysics parameterization and Rotunno 2004); as a result, we ignore the wind varia- (Lim and Hong 2010) and the Yonsei University (YSU) tions at middle to upper levels at Makong for simplification. planetary boundary layer (PBL) parameterization (Hong Thus, we only consider the horizontal wind perpendicular and Pan 1996). Weisman et al. (1997) indicated that res- to the squall line, namely, the zonal wind. The wind speed −1 olutions of 4 km might be sufficient to reproduce much increases linearly from zero at the surface to 10 m  s  at the of the mesoscale structure and evolution of the squall altitude of 2500 m (based on the observed wind profile in Korean MeteorologicalSociety 1 3 418 Y.-T. Pan, M.-J. Yang Fig. 2 a Composite sounding (a) Composite sounding adapted from soundings in the SoWMEX field project. The surface temperature is 28.5 °C and the mixing ratio of water −1 vapor is 23.3 g Kg near the surface. Black and blue lines represent temperature and dew- point temperature. b Observed zonal wind profile at Makong at 00 UTC 19 April 2019. c Zonal wind profiles in low-level wind- shear experiments. The wind- shear below 2.5-km height is 5, −1 7.5, 10.0, 12.5, and 15.0 m  s , respectively (b) (c) Z = 2.5 km Fig. 3 Realistic Taiwan terrain after 9-point moving aver- age. The Taiwan topography Taiwan is located at the center of the Panchiao computational domain. Terrain heights are contoured at 1, 500, Mount Snow 1500, 2500 and 3000 m, respec- tively. The upper (lower) blue 12 km average line is the horizontal position for the 12-km averaged vertical cross section in Fig. 11 (12), Makong and the red triangles indicate the locations of Panchiao and Makong CMR 12 km average Korean MeteorologicalSociety 1 3 419 Makong), and the wind velocity is assumed to be constant found that a warm bubble of 4 K, with the size of 200 km in above 2500 m (Fig. 2c). length (north–south), 25 km in width (east–west) and 1.5 km deep, added at the quarter of the x direction and half of the y 3.2 Experiment Design direction at model time of 4 h, can have minimal impacts of lee-side convection and precipitation. The size of the initial Most of previous studies (Frame and Markowski 2006; thermal was chosen to mimic the observed squall-line char- Reeves and Lin 2007; Letkewicz and Parker 2011) used a acteristics shown in Fig. 1a. bell-shaped topography to discuss the relation between ter- rain and squall-line MCS, but the idealized terrain is too 3.3 Froude Numbers Used in This Study simplified to represent the complicated topography like Taiwan. Since we plan to understand impacts of Taiwan ter- Two definitions of Froude number are used in this study. One rain on squall-line MCS, the realistic Taiwan topography is the Froude number considering mountain height (F ), and mt is necessary. Therefore, a high-resolution (30 m) Taiwan the other is Froude number considering the cold-pool depth topography data was used. We downscaled the raw topogra- (F ). The details are discussed as follows. cp phy data to the model grid with 2-km horizontal grid size, Froude number which considers the mountain height and located the Taiwan terrain at the center of computational (F ) is a useful non-dimensional parameter when we discuss mt domain. Additionally, a 9-point moving average was per- the flow impinging on the steep mountains and the block - formed to smooth the terrain to avoid numerical instability ing effect. Mechanically, whether the flow contains enough in the WRF model. The highest terrain peak is 3312 m and kinetic energy to overcome potential energy of the terrain the main characteristic of Taiwan topography is captured barrier (Reeves and Lin 2007) can be determined by F , mt (Fig. 3), including Mount Snow and the Central Mountain which is defined as Range (CMR). A long warm bubble was used to initiate the squall- avg F = , (1) mt line convection, and the lee side gravity-wave convection N × H avg mt was produced by the westerly flow over the Taiwan terrain (Fig. 4). This lee-side convection phenomenon is common when the prevailing wind flowed over topography (Chu and g N = × , (2) Lin 2000; Chen and Lin 2005; Reeves and Lin 2007; Migli- dz etta and Rotunno 2009). In order to reduce the influence of the lee side convection and precipitation on the squall-line where U is the averaged wind speed for air within the avg MCS, the line-type warm bubble was put into the model atmospheric volume below 1 km shown in Fig. 20, N is avg −1 sometime after the initialization. After trial and error, we the averaged Brunt–Väisälä frequency (s ) within the same Fig. 4 Simulated radar reflectivity CV plot at 5 h of model simulation. Red arrow denotes the lee-wave convec- tion discussed in the text, and Lee-wave precipitaon blue arrow denotes the embryo squall-line MCS initiated by the line-type warm thermal Squall-line MCS Korean MeteorologicalSociety 1 3 420 Y.-T. Pan, M.-J. Yang atmospheric volume, H is mountain peak height (m), g is (K). Please see Appendix for the procedure of calculating mt −2 gravitational acceleration (m s ) and  is virtual potential F . v cp temperature (K). Please see Appendix for the detailed pro-The F is used to identify whether the flow regime is sub - cp cedure of calculating F .critical (F < 1) or supercritical (F > 1). As mentioned in mt cp cp If F is greater than 1, low-level air flow can climb over the introduction, the hydraulic jump helps to reinitiate con- mt the mountain; on the other hand, if F is less than 1, low-level vection on the lee side, and it occurs when the flow makes mt airflow will turn around the mountain and converge on the lee a transition from subcritical at upstream to supercritical at side. To understand the blocking effect on air flow near Taiwan mountain peak (Durran 1986, 1990). terrain, we choose a specific location and timing to calculate the F as shown in Fig. 5. The timing and space are chosen 3.4 Spatial Correlation Coefficient mt when the simulated squall-line MCS just lands on Taiwan. For the Froude number which considers the cold-pool depth In our numerical experiments, the symmetry of a squall- (F ), the formula is similar as F except for H term, which line MCS is not easy to determine visually; thus, in order to cp mt cp follows that in Frame and Markowski (2006) objectively quantify the degree of symmetry of a squall line, a spatial correlation coefficient (SCC) is utilized (Tai et al. F = , 2017). The SCC is defined as cp (3) N × H cp � �� � x − x x − x n n s s SCC = , (5) � � � � 2 2 g d v (Σ x − x Σ x − x n n s s N = × , (4) dz where variable x denotes the value of radar reflectivity, sub - where U is the wind speed, N is Brunt-Väisälä frequency, H script n and s denote the north and south parts of the squall- cp is cold-pool depth (assumed to be 1.5 km), g is gravitational line MCS respectively, and the overbar (¯) is the average over −2 acceleration (m s ) and  is virtual potential temperature either the northern or southern region. Fig. 5 The spatial range chosen for calculating the mountain- height Froude number (F ). mt The time and space are chosen when the squall-line MCS just lands on Taiwan. The spatial range of the yellow region is: x = –90 ~ –100 km, y = –40 ~ + 40 km, z = 1 km above the surface Korean MeteorologicalSociety 1 3 Asymmetric Structures of a Squall-Line MCS over Taiwan with Significant Hydraulic Jumps 421 Figure  6 shows the calculation procedure. Firstly, we Table 1 Design of terrain-heights experiments designate the leading edge of the squall-line MCS as the Experiment Max terrain Wind shear Max Froude Reinitiate rightmost boundary of the given rectangle. Secondly, the height (m) below 2.5 km number (F ) on the lee mt −1 (m s ) side central line is defined as the line ( y = 0) to divide a sym- metric squall line into the northern part and the southern CTL 3312 10 0.43 N counterpart, and the rectangle area in both parts are 200 km TER56 2760 10 0.53 N in length and 120 km in width. Notice that we ignore the TER46 2208 10 0.67 N missing-value region (the default radar reflectivity is − 30 TER36 1656 10 0.98 Y dBZ) to avoid the overestimation of the SCC. Therefore, TER26 1104 10 1.40 Y the structure of a squall line is more symmetric as the SCC TER16 552 10 2.90 Y is closer to 1. People might argue whether the central line NTR 0 10 X X (y = 0) we chose is fair or not, because the rightmost lead- ing edge may not be always at the central line (y = 0). Thus, additional central-line uncertainty experiments are also con- ducted. We adjust the central-line position either 5 km north investigate the relation between Froude number (F ) and mt the structure of squall-line MCS. Note that for the no-terrain or south from y = 0 to represent the position uncertainty, and results indicate that the SCC percentage error is less than 5% experiment (NTR), the whole island of Taiwan was com- pletely removed. (not shown). Hence, regarding the axis at y = 0 as the central line to divide the squall-line system into the northern and southern part should be reasonable. 4 Model Results 3.5 Sensitivity Experiments 4.1 Idealized Model Results: Control Experiment (CTL) In addition to the control experiment, two sets of sensitiv- ity experiments are done. When we consider the impacts of Figure 7 displays radar-reflectivity evolution of the idealized Taiwan terrain on a squall-line MCS, Froude number F mt is a critical parameter which is dynamically controlled by squall-line MCS for the control run. At the model time of 240 min, convection and precipitation on the lee side is evi- the mountain peak height and the zonal wind. As a result, both the terrain-height (Table  1) and low-level wind- dent (Fig. 7a). The lee-wave convection appears at the first 30 min and then develops into a convective line (not shown). shear (Table  2) sensitivity experiments are performed to Right after 240 min, a long warm thermal is inserted into the model to mimic a squall line; at 300 min, this long warm thermal evolves to its embryo stage (Fig. 7b). Notice that 120 km instead of inserting a warm bubble at the model initial time, we delay the insertion time until 240 min to prevent from the interference between lee-wave convection and the squall- line MCS represented by the warm bubble. Figure 7c shows that the idealized squall line has developed its mature stage before encountering the Taiwan terrain; meanwhile, the lee- wave precipitation has moved eastward away from Taiwan terrain by the westerly wind. In addition, the north–south Table 2 Design of low-level wind-shear experiments Experiment Max terrain Wind shear Max Froude Reinitiate height (m) below 2.5 km number (F ) on the lee mt −1 (m s ) side WS15.0 3312 15.0 0.46 Y WS12.5 3312 12.5 0.45 N Fig. 6 Schematic diagram for calculating the spatial correlation coef- CTL 3312 10.0 0.43 N ficient (SCC). The center of bow echo ( y = 0) is regarded as the sym- metry axis, and the blue boxes at north and south sides are the coun- WS7.5 3312 7.5 0.39 N terparts. Note that the red box (missing value) is ignored to avoid the WS5.0 3312 5.0 0.28 N overestimation of SCC Korean MeteorologicalSociety 1 3 422 Y.-T. Pan, M.-J. Yang Fig. 7 Simulated radar CV (a) 240 min plot of the full computa- (b)300 min tional domain at a 240 min, b 300 min, c 660 min, d 900 min, and e 1080 min. Contour inter- val for terrain height is 750 m (c) 660min (d)900 min (e)1080min length of precipitation area of the idealized squall line is is manifested that the leading line of the squall-line MCS approximately the same as the north–south length of Taiwan evolves to an asymmetric structure with the southern lead- Island, similar to the case of the 19 April 2019 squall-line ing line showing the north–south orientation but the north- MCS (Fig. 1c). Later, the simulated squall line touches the ern leading line remaining the original northwest-southeast Taiwan terrain and dissipates later over the lee side (Fig. 7d, orientation. This simulation result resembles the precipita- e). tion pattern of the observed 19 April 2019 case (Fig. 1c). When we zoom in the region near Taiwan, the impacts Furthermore, if we scrutinize the radar-echo intensity of the of the terrain upon the squall line can be seen clearly, such squall line, we find that the southern part also has stronger as the upwind-side asymmetry and lee-side asymmetry as radar reflectivity as observed in the 19 April case. Eventu - the observed radar CV shown in Fig. 1. Figure 8a  displays ally, Fig. 8e displays that the squall-line MCS dissipates on that the radar reflectivity of the idealized squall-line MCS the lee side, and the leading edge of southern part moves develops a symmetric bow-echo shape before encountering faster than that of the northern part. This lee-side asymme- the terrain. The lee-wave precipitation moves away from try is also similar to what we have found in the observation Taiwan except for the northeast and southeast corners due (Fig. 1e). to the convergence of the detouring winds (Kirshbaum and The vertical cross section in Fig. 9 is used to examine the Schultz 2018). Figure 8b shows that the squall-line MCS evolution of the idealized squall-line MCS and the relation precipitation pattern still remains nearly symmetric when between the cold pool and terrain blocking effect. To make the leading edge touches the terrain-height contour of 500 m. the vertical cross section more representative, this cross sec- This is reasonable because the height over the western plain tion is averaged within a 12-km strip along the y direction. of Taiwan is not tall enough to block the movement of the Figure 9a illustrates the typical leading-convection region squall line at this time; hence, the precipitation structure of and trailing-stratiform region (with radar bright bands near the squall-line MCS does not alter significantly. The deci - the melting level at 4 km) as shown in the conceptual model sive transition occurs at later stage as shown in Fig. 8d. It of Houze et al. (1989; see their Fig. 1). A prominent cold Korean MeteorologicalSociety 1 3 423 (a)670 min (b)740 min (c)800 min (d)860 min (e)970 min Fig. 8 Simulated radar CV plot near Taiwan at a 670 min, b 740 min, c 800 min, d 860 min, and e 970 min. Blue dotted line is the − 2 K con- tour for perturbation potential temperature, and the black dotted stripe area in (a) corresponds to the vertical cross section in Fig. 9 Fig. 9 Vertical cross sections 760 min (a) 540 min (b) of radar reflectivity (colored; in units of dBZ) and perturbation potential temperature (dotted line; contoured from − 0.5 K to − 4.5 K by 1 K): a 540 min, b 760 min, c 810 min, d 930 min. The horizontal position of the 12-km averaged vertical cross section is shown in Fig. 8a (c) 810min (d) 930min Korean MeteorologicalSociety 1 3 424 Y.-T. Pan, M.-J. Yang pool (i.e. with negative potential-temperature perturbation) shown in Fig. 10e and f (before and after the landfall of the can be seen clearly below 2 km. Figure 9b displays that the southern leading line on Taiwan). The wind convergence is leading-line convection is intensified over the up-wind slope indeed increased after landfall. Thus, it is confirmed that the because the terrain provides an extra mechanical lifting to wind deflection at southern part of the leading line leads to enhance the upward motion at the leading edge (Teng et al. increased convergence, stronger vertical motion, and more 2000; Frame and Markowski 2006). Figure 9c shows that intense convection for the squall-line MCS. the cold pool is mostly blocked by the terrain except for the Figure 11 displays the 12-km averaged vertical cross sec- − 0.5 K isotherm, and this blocking effect causes the cold tion over Mount Snow. Firstly, when the squall-line MCS pool to mainly spread around the terrain, instead of climbing approaches the mountain, the upward motion is at the lead- over the hill. Consequently, the updraft at the leading edge ing edge of the system (Fig. 11a, c). While the squall-line is weakened by the downward motion on the lee side. The MCS climbs to the mountain top, the convection intensity mountain-height Froude number (F ) is only 0.43, consist- decreases immediately due to the terrain blocking effect and mt ent with the fact that the cold pool is mainly blocked by no new convection is initiated on the lee side (Fig.  11b). terrain. Afterward, only stratiform precipitation region is Figure 11d shows that the potential temperature isotherms remained (Fig. 9d). Notice that there is already cold air pro- (isentropes) only ascend slightly on the downslope (x ≈ duced by the initial lee-wave precipitation (Fig. 7d) on the 20  km), indicating a weaker and insignificant hydraulic lee side before the arrival of the squall-line MCS (Fig. 9c, jump (Durran 1986, 1990). Figure 11f shows that the F is cp d). This pre-existing cold air also debilitates the ability of below 1 (subcritical) on the upstream side (Fig. 11f) and at convection regeneration on the lee side (French and Parker the peak (Fig. 11f), not a favorable condition for hydraulic 2014; Lombardo and Kading 2018). jump to occur. Figure 12 shows the 12-km averaged vertical cross sec- 4.2 Upwind‑Side and Lee‑Side Asymmetries tion for southern Taiwan situation. When the squall line of the Squall‑Line MCS approaches the mountain (Fig. 12a), the upward motion also occur at the leading edge (Fig. 12c) as that in the northern After encountering Taiwan terrain, the southern (northern) part (Fig. 11c), but the scenario bifurcates later. Notice that leading line of the simulated squall-line MCS alters obvi- the stronger downward motion on the steeper lee-side slope ously (slightly) on the upwind side (Fig. 8). How does the (slope ≈ 0.111) leads to an effective hydraulic jump with Taiwan topography produce different structure changes significant lifting of the isentrope near the surface (Fig.  12d). over the northern and southern parts of the squall line? Fig- Figure 12e and f show that the F within the cold pool is cp ure 10a shows that the leading line of the simulated idealized less than 1 (subcritical) in upstream area, but it becomes squall line has a symmetric bow echo with the lowest-level greater than 1 (supercritical) at the peak because of strong wind perpendicular to the leading edge. Later, the cold pool airflows above the peak. As a result, these factors (steeper encounters the 500-m terrain contour. Note that different downwind slope and occurring at surface) for the south- terrain-ridge orientations of northern and southern Taiwan ern part favor convection initiation on lee side (Fig. 12b). make the cold pool to detour in various manners (Fig. 10b). Also notice the time is different between Figs.  8, 11 and For the northern (southern) side, the terrain ridge orienta- 12, because the asymmetries and hydraulic jumps occur at tion is mainly parallel (normal) to the wind direction. As a various time. result, the northern leading line remains its original direc- tion, and the surface wind accelerates (see northern box in 4.3 Terrain‑Heights Experiments Fig. 10b) possibly by the terrain channel effect (Skylling - stad et al. 2001; Hitzl et al. 2014). In contrast, the southern Terrain-height experiments include the no-terrain (NTR) to leading line changes the direction significantly due to the full-terrain (CTL) simulations, and the interval is one-sixth ridge orientation of the southern CMR (see southern box of actual terrain height (Table 1). Because the Froude num- in Fig. 10b). The wind behind the southern leading edge is ber (F ) for the TER36 experiment is about 1 (0.98; see mt almost deflected by 90°, so the southern leading line changes Table 1), for simplicity we separate the experiments into two its direction (Fig. 10c). groups: CTL-type and NTR-type groups. After the squall-line MCS moves to the lee side, the Figure 13 shows the radar-reflectivity evolution of three leading edge of southern part moves ahead of the northern terrain-height experiments. If Taiwan is completely removed part, because of the lee-side asymmetry (Fig. 10d). For the (NTR), the squall-line MCS is almost symmetric for the airflow in southern red box, it is hypothesize that the col - entire period (Fig. 13g, h), although the symmetry slightly lision between the cold pool and the deflected wind rein - decreases at 930 min (Fig. 13i). For TER36 experiment, the forces the movement of the southern squall line (Fig. 8d convection is reinitiated on the lee side, and the bow-shaped and 10c). To verify this hypothesis, the convergence field is leading edge is slightly affected by the terrain (Fig.  13f). Korean MeteorologicalSociety 1 3 425 Fig. 10 The position between the cold-pool leading edge and (a) 700 min (b) 820 min Taiwan terrain at − 700 min, b 820 min, c 850 min, d 930 min. Blue dotted line is the perturba- tion potential temperature (con- m/s toured by − 2 K); black solid arrow is for the surface wind at the lowest model level (at 198 m). Taiwan terrain height is contoured at 1, 500, 1500, 2500, and 3000 m. Vertical −1 velocity (in units of m s ) at 2-km height is colored in (a–d). The divergence field (colored; −1 in units of s ) before and after squall-line’s landing on south- ern Taiwan terrain is shown in (c) 850 min (d) 930 min (e) and (f), respectively (e) Before (f) Aer The TER36 experiment resembles the NTR experiment hence, we can classify these experiments as the CTL-type in the sense that the bow-shaped leading edge appears on group. the lee side, so we can categorize TER36 as the NTR-type Figure 14 shows the propagation of the leading line of group. The TER26 and TER16 experiments display simi- the simulated MCSs for three experiments. The structure lar structures as the TER36 experiment on the lee side, so is symmetric at the beginning (Fig. 14a, d, g), and the NTR we also classify them as the NTR-type group. We notice experiment remains symmetric until 930 min (Fig. 14i). For from Table 1 that the F is greater than 1 when the terrain TER36 experiment (Fig. 14f), its leading edge is not as con- mt height is below or equal to that for TER36 (i.e., TER26 and tinuous as that in NTR (Fig. 14i) owning to terrain effect. TER16), and that the squall lines in these experiments have The TER36 experiment is supposed to have the ability to the ability to reinitiate convection on the lee side. However, reinitiate new convection on the lee side, according to the if the terrain height is above that of TER36 (i.e., TER46, Froude number (F ~ 1), but it does not. It is because the mt TER56, and CTL), the Froude number is less than 1, and no cold air produced by lee-wave precipitation at the model ini- obvious convection is reinitiated on the lee side (Fig. 13c); tiation is accumulated on the lee side and inhibits convection Korean MeteorologicalSociety 1 3 426 Y.-T. Pan, M.-J. Yang Fig. 11 Vertical cross sec- (a) 870 min (b) 920 min tions of the radar reflectivity (colored) at a 870 min and b 920 min for northern Taiwan (Mount Snow); vertical cross sections of the vertical veloc- ity (colored) and potential temperature (contoured by 2 K) at c 870 min and d 920 min for northern Taiwan (Mount Snow); vertical cross sections of the F (colored) when the MCS (c) 870 min (d) 920 min cp system moves to e the upstream side and f mountain peak of the northern Taiwan (Mount Snow). The red arrows in b and d denote the locations of hydrau- lic jump. The dashed red boxes in e and f denote the leading- edge cold pool positions. The horizontal position of the 12-km averaged vertical cross section is shown in Fig. 3 (e) At upstream (f) At peak re-initiation. As a result, the leading line of the TER36 is blocking effect (TER26 and TER16 experiments). To some discontinuous. degree, TER36 experiment is like a flow-regime division Figure 15 shows the change of SCC at different stages. to separate two different flow regimes when the squall- Four stages are chosen: Stage A is when the location of line MCS enters the hills area, and this is the reason why leading line is at west of Taiwan; Stage B is when the we show the change of SCCs for all terrain sensitivity leading edge touches the 1-m height contour (border of experiments. From Stage C to Stage D, the SCCs for all Taiwan); Stage C is when the leading edge touches the experiments decrease significantly and the decreasing rate 500-m height contour; Stage D is the most asymmetric is approximately proportional to terrain height at stage stage on the upwind side. The SCC coefficient for NTR D. This implies that the terrain peak height is a critical run is nearly 0.9 and slightly decreases to 0.86 at Stage parameter for the squall-line symmetry, and higher terrain D, as expected in the absence of Taiwan terrain. From peak makes the squall-line MCS more asymmetric on the Stage A to Stage B, the squall-line MCS is approaching upwind side. the Taiwan border from the west, and all experiments For the CTL experiment, it is not as symmetric as other have high SCCs. For Stage B to Stage C, the squall-line experiments at first (Stage A), and the terrain might force MCS starts to “feel” the impacts of Taiwan hills (below the squall-line MCS to develop more asymmetric structures 500 m). Recall that the F for TER36 experiment is near at the upslope stage (Teng et al. 2000). The increasing SCC mt 1, so the terrain blocking effect is obvious for experiments (from Stage B to Stage C) does not match the regime for the with terrain heights equal to or above the peak of TER36 low Froude number, but it is acceptable because the degree experiment. As a result, in this period, the SCC coefficient of symmetry for the CTL at first is too low as comparing decreases for TER46 and TER56 experiments. In contrast, with other experiments. Later, the SCC coefficient of the for experiments with peaks below the terrain height of CTL drops significantly from Stage C to Stage D due to the TER36 experiment, the SCC coefficient either remains the steep terrain. Notice that radar observation of the squall-line same or increases slightly, because of the minor terrain MCS on 19 April 2019 has similar evolution of SCC from Korean MeteorologicalSociety 1 3 Asymmetric Structures of a Squall-Line MCS over Taiwan with Significant Hydraulic Jumps 427 Fig. 12 a, b As in Fig. 11a, b, (a)890 min (b) 940 min but for the southern Taiwan (Southern CMR) at 890 min and 940 min; c, d as in Fig. 11c, d, but for the southern Taiwan (Southern CMR) at 890 min and 940 min; e, f as in Fig. 11e, f, but for the southern Taiwan when the squall-line MCS sys- tem is at the upstream side and mountain peak. The red arrows (d) 940 min (c) 890 min in b, d denote the locations of hydraulic jump, and the blue arrows indicate the locations of strong downward motion. The horizontal position of the 12-km averaged vertical cross section is shown in Fig. 3 (e) At upstream (f) At peak Subcrical at upstream Stage B to Stage D as the CTL, as expected from the fact that e, h). The fact that the WS15.0 experiment can initiate the observed squall line experienced the same full degree of new convection on the lee side with low F (Fig. 16c and mt terrain effect as the CTL simulation. Table 2) is not consistent with the results in previous section that for small Froude number, and it is because the strong 4.4 Low‑Level Wind‑Shear Experiments hydraulic jumps produced by strong mid- and upper-level winds (to be shown in Fig. 17a, c). In these experiments, we change the wind speed systemati- Figure 17a and b show that the new convection exists on cally in order to examine its influence on the F and squall- the lee side in WS15.0 experiment but not in CTL experi- mt line MCS evolution (Table 2 and Fig. 2c). We may use the ment, and that the hydraulic jump effect for the WS15.0 RKW theory (Rotunno et al. 1988) to examine the results. experiment is significantly stronger than that for the CTL The RKW theory, which considers the balance between hori- run. The reason is the intensity of mid- and upper-level zontal vorticity created by the cold pool and the vorticity by winds. The wind below 1 km does not change significantly environmental low-level wind shear, can be used to explain among different shear experiments (Table  2 and Fig. 2c), so different evolution of the squall line before the influence of the Froude number (F ) is still small even we increase the mt Taiwan terrain (Fig. 16a, d, g). The leading-line convection low-level shear. However, the environmental wind between remains upright when the vorticity by wind shear is strong 2.5- and 5.0-km heights offers an extra dynamical force to enough to balance with that by the cold pool (WS15.0; help the flow to have a transition from subcritical (F < 1) cp Fig. 16a). On the other hand, the leading-line convection at upstream to supercritical (F > 1) at mountain peak cp becomes up-shear tilted and trailing stratiform precipitation (Durran 1986, 1990), which induces hydraulic jump on the is evident when the vertical shear is weak and the cold pool lee side (Fig. 17g). But the flow transition does not occur in dominates (WS5.0; Fig. 16g). Large variations in precipita- the CTL experiment; as a result, no obvious hydraulic jump tion occur among the experiment when the simulated squall is found (Fig. 17h). Therefore, only using mountain-height lines are on the upwind side of Taiwan terrain (Fig. 16b, Froude number (F ) to decide whether the convection will mt Korean MeteorologicalSociety 1 3 428 Y.-T. Pan, M.-J. Yang Fig. 13 As in Fig. 7, but for the 750 min8 (b) 20 min9 (c) 30 min (a) terrain experiments. Upper row is for CTL, middle row is for TER36, and lower row is for NTR experiment. Left column of panel a, d, g is for simulation time at 750 min; middle column of panel b, e, h is for simulation time at 820 min; right column of panel c, f, i is for simulation time at 930 min (f) (d) (e) (i) (g)(h) Fig. 14 As in Fig. 10, but for 660 min 800 min 930 min the terrain experiments. Upper (c) (a)(b) row is for CTL, middle row is for TER36, and lower row is for NTR experiments. Left column of panel a, d, g is for simulation time at 660 min; middle column of panel b, e, h is for simulation time at 800 min; right column of panel c, f, i is for simulation m/s time at 930 min (f) (d) (e) (h) (i) (g) Korean MeteorologicalSociety 1 3 NTR TER36 CTL NTR TER36 CTL 429 Fig. 15 The spatial correlation Spaal correlaon coefficient coefficient (SCC) of the squall- line MCS structures at four stages for the observation (OBS; black dotted), CTL (black solid), TER56 (orange solid), TER46 (blue solid), TER36 (red solid), TER26 (blue dotted), TER16 (orange dotted), and NTR (red dotted) experiments. Definitions for Stage A, B, C, and D are described in the text B D A C Fig. 16 As in Fig. 13, but Approaching (a)(b) LandingL (c) eaving for the low-level wind shear experiments. Different timings are chosen when the squall-line MCS is approaching (left col- umn), landing (middle column), and leaving (right column) the Taiwan mountain (e) (f) (d) (h) (g) (i) Korean MeteorologicalSociety 1 3 WS5.0 CTL (WS10) WS15.0 430 Y.-T. Pan, M.-J. Yang Fig. 17 Vertical cross sec- WS15.0 CTL (b) (a) tions of a the radar reflectiv - ity (colored) and along-plane vectors, c the vertical velocity (colored) and potential tem- perature (contoured by 2 K), e the Froude number (colord; F ) when the squall-line MCS cp is at the upstream side, and g the Froude number (colored; F ) when the squall-line MCS (d) cp (c) system is at the mountain peak of the southern CMR for the WS15.0 experiment. Panels b, d, f, h are similar to panels a, c, e, g but for the CTL experiment. The dashed red boxes in g and h denote the leading-edge cold pool positions (e)At upstream (f)At upstream (h)At peak (g)At peak be reinitiated on the lee side, where there is significant verti - the southern terrain (southern CMR) is in north–south orien- cal wind shear, may not be appropriate. tation, nearly normal to the wind direction behind the leading line. The south side of the northern leading line accelerates 4.5 Schematic Diagrams for Upwind‑Side because the wind is parallel to the ridge orientation. As a and Lee‑Side Asymmetries result, the leading line rotates counterclockwise (Step 3). But for the southern side, the central part of squall line deceler- Figure  18 is the schematic diagram for the evolution of ates because the wind behind the leading line is nearly nor- upwind-side asymmetry. Firstly, the squall-line MCS devel- mal to the terrain (Step 4). The different propagation speed ops its mature stage with the bow-shaped leading line (Step between different parts of the leading line leads to the asym - 1), remaining its symmetric structure before the encounter metry on the upwind side. Finally, Step 5 indicates that the with Taiwan terrain. The surface wind is nearly perpendicu- convection ahead of the southern squall line intensifies owing lar to the leading line (Step 2). If we focus on the ridge to the surface-wind convergence and cold-pool collision. orientation, the northern terrain (Mount Snow) is mainly in Figure  19 is the schematic diagram for the lee-side northeast-southwest orientation, approximately parallel to asymmetry in two vertical cross sections. For Mount the wind direction behind the leading edge. On the contrary, Snow, the horizontal width of the mountain is extensive Korean MeteorologicalSociety 1 3 431 Fig. 18 Schematic diagram for the five evolution steps for the upwind-side asymmetry of squall-line MCS. Five steps are explained in the text. Orange area is the convergence area. Black solid arrows near Taiwan denote the ridge orientation of Taiwan mountain range. The black dotted line separates the squall-line MCS into the north- ern and southern parts Fig. 19 Schematic diagram for the leeside asymmetry of the squall line at a the northern (Mount Snow) and b southern Taiwan (Southern CMR). The cloud outline is shown, gray shading indicates the radar reflectivity convective cores and the bright band in the stratiform region. Blue arrow represents the downward motion, red arrow is for hydraulic jump, and blue dotted line displays the cold air produced by the gravity-wave convection and precipitation (120 km), and the lee slope is moderate (0.067); the flow- 5 Conclusions regime transition from subcritical at upstream to super- critical at mountain peak does not occur and the lee-side A mature squall-line MCS developed a bow-echo shape subsidence is not strong at peak. The weak hydraulic jump and approached Taiwan from the west on 19 April 2019, −1 occurs over mountainous area, which would not favor con- causing fierce gust wind up to 20 m  s and heavy rain- vection re-initiation (Fig. 19a). However, the situation is fall with hailstones over several places in Taiwan. After different over the southern CMR. The horizontal width the contact with Taiwan terrain, the originally symmet- (40 km) is only a third of that for Mount Snow, and the ric structure of this squall line altered with significant slope on the lee-wind side is steeper (0.111); the crucial upwind-side and lee-side asymmetries, which are the main flow-regime transition does occur and the subsidence is scientific foci of this study. The idealized WRF simula - stronger on the lee side. Furthermore, the hydraulic jump tions with horizontal grid size of 2 km (in the absence occurs at near the surface. All these factors support the of the effects of Coriolis force, radiation and horizontal convection re-initiation on the lee side over southern CMR heterogeneity) were conducted in order to systematically (Fig. 19b). Korean MeteorologicalSociety 1 3 432 Y.-T. Pan, M.-J. Yang examine the relationships among the Froude numbers (F mt and F ), squall-line structure, and hydraulic jump. cp Idealized simulations show that the squall-line MCS develops its bow-echo shape with nearly symmetric struc- ture before the arrival on Taiwan, similar to the observed case on 19 April 2019. According to the mountain-height Froude number (F ), the low-level air at the leading edge mt of the squall-line MCS is blocked by the steep Taiwan ter- rain; as a result, the wind deflection is apparent. Different ridge orientations between northern (northeast-southwest) and southern (north–south) Taiwan terrain bring about the upwind-side asymmetry (Fig. 18). On the other hand, the different mountain width, downwind slope, and the transi - tion of the flow regime (i.e., hydraulic jump) from subcriti - cal at upstream to supercritical at mountain peak lead to the lee-side asymmetry. Also, the intensity and location of the hydraulic jumps depend on the width and downwind slope of mountain. To be specific, the southern (northern) terrain is narrower (wider) and the downwind slope is steeper (more Fig. 20 The atmospheric volume in the calculation of Froude number moderate). In addition, the southern CMR (Mount Snow) mt has (lacks of) the flow transition from subcritical at upstream to supercritical at peak, causing significant (weak) hydrau - lic jump which occurs over surface (mountainous area) and hydraulic-jump effects obtained in this study can be applied to other scenarios. Finally, more studies of the squall-line the convection can (cannot) be reinitiated on the lee side (Fig. 19). MCSs impinging on high mountains over other geographic regions should be conducted to verify the results obtained Terrain-height experiments were performed to inves- tigate the terrain blocking effect. The TER36 experiment from this study near Taiwan. separates these experiments into two groups. One is that the squall-line structure becomes more symmetric after the Appendix: Details for calculating the Froude squall-line’s arrival on lower terrain, and the other is that the squall line becomes asymmetric. It depends on whether the Numbers of  F and  F mt cp mountain-height Froude number (F ) ≥ 1 (TER36, TER26 mt and TER16 experiments) or not (TER46 and TER56 experi- We describe the procedures in calculating the Froude num- bers (F and F ) in this Appendix, in additional to the ments). The terrain blocking effect is the main reason for the mt cp asymmetric structure of the squall-line MCS after its arrival graphic illustration given in Fig. 5. For Froude number F , mt its definition is given in Eq. ( 1), where the variables U on the steep Taiwan terrain. avg Low-level wind shear experiments are also conducted to and N are averaged for the same atmospheric volume avg (shown in Fig. 20) at the leading edge of squall line (with investigate the asymmetry and hydraulic jump on the lee side. In low-level shear experiments, we find that the mid- to a zonal width of 10 km, a meridional length of 80 km for y = − 40 km ~ + 40 km, and a depth of 1 km for z = 0 ~ 1 km) high-level winds are also important for the hydraulic jump, because it offers an extra dynamic forcing to support flow- in a Lagrangian framework, and H is the highest mountain mt peak in the range of y = −  40  km ~ + 40  km. For Froude regime transition at peak. In summary, the idealized WRF simulations in this study number F , its definition is given in Eq. ( 3), where the vari- cp ables U and N are the values at grid points, and the cold-pool provide us an opportunity to clarify and explore the effects of Taiwan terrain on a squall-line MCS. Nevertheless, the depth is the depth of cold-air perturbation (as defined by the depth of the contour of  =−1.5 K ), which approximately squall line on 19 April 2019, which is an eastward mov- ing squall-line MCS, is not a frequent case during the Mei- remained constant at z = 1.5  km (i.e., H = 1.5  km) before cp the cold pool encountered Taiwan terrain. Yu season. Other progression directions of the squall-line system are more common, such as southeastward or north- Acknowledgements Constructive comments by two reviewers on eastward directions. For future studies, different impinging our manuscript are highly appreciated. 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Asymmetric Structures of a Squall-Line MCS over Taiwan with Significant Hydraulic Jumps

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Springer Journals
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1976-7633
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10.1007/s13143-021-00262-1
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Abstract

On 19 April 2019, a mature squall-line mesoscale convective system (MCS) with the characteristics of a leading convective line and trailing stratiform landed on Taiwan, resulting in strong gust wind and heavy rainfall. This squall-line MCS became asymmetric after landfall on Taiwan. Two sets of idealized numerical simulations (mountain heights and low-level vertical wind shear) using the Weather Research and Forecasting (WRF) model were conducted to examine the impacts of realistic Taiwan topography on a squall-line MCS. Results showed numerous similarities between the idealized simulations and real-case observations. The low-level Froude number which considered the terrain height (F ) was calculated to examine mt the blocking effect of the Taiwan terrain, and the cold pool (determined by − 1.5 K isotherm) was found to be completely blocked by the 500-m height contour. The northeast-southwest orientation of the Snow Mountain Range (SMR), and the north–south orientation of the Central Mountain Range (CMR) led to the upwind side asymmetry. On the other hand, the lee-side asymmetry was associated with different intensities and occurrence locations of the hydraulic jump between the SMR and southern CMR, and the cold-pool Froude number (F ) indicated the flow-regime transition from subcritical to cp supercritical. Keywords Squall-line MCS · Taiwan topography · Froude number · Hydraulic jump 1 Introduction There are relatively few studies on the terrain effects to squall-line MCSs. Since Taiwan is a mountainous island, During the Mei-Yu season (from mid-May to mid-June) in the relation between a squall-line MCS and realistic Taiwan Taiwan, the squall-line type of mesoscale convective sys- terrain is worth investigating. One previous observational tems (MCSs) frequently form ahead of or along the Mei- study (Teng et al. 2000) investigated the impacts of Taiwan Yu fronts over southeastern China, which approach Taiwan terrain on a squall-line MCS during the Taiwan Area Mes- from the west and lead to heavy rainfall and fierce gust wind oscale experiment (TAMEX; Kuo and Chen 1990), and they (Fang 1985; Ninomiya et  al. 1988). Ahead of the squall found the orientation of squall-line MCS became parallel to line, the environment usually has substantial vertical wind 1000-m terrain contour line after the contacts with Taiwan shear (particularly at low level), and the interaction between topography. environmental wind shear and precipitation-induced cold The evolution of a squall-line MCS is strongly determined pool can make the squall-line MCS a self-organized system by cold-pool dynamics. Cold pool is a region with substan- (Fovell and Tan 1998; Lin et al. 1998; Lin and Joyce 2001). tial evaporative cooling produced by precipitation, a key feature to initiate new convective cells at the leading edge and sustain the MCS (Rotunno et al 1988; Weisman 1993; Yang and Houze 1995a, b; Weisman and Rotunno 2004). Communicated by Hyeyum Hailey Shin As a result, whether the cold pool is blocked by terrain or not affects the longevity of the squall-line MCS (Frame and * Ming-Jen Yang Markowski 2006; Letkewicz and Parker 2011). mingjen@as.ntu.edu.tw After the contact with the terrain, the squall-line MCS Department of Atmospheric Sciences, National Taiwan would either dissipate away or reinitiate convection on the University, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, lee side, depending on the hydraulic jump effect (Long Taiwan Korean MeteorologicalSociety Vol.:(0123456789) 1 3 416 Y.-T. Pan, M.-J. Yang 1953). Numerous modeling studies examined the relation and Lin 2007; Letkewicz and Parker 2011), which may not between the downslope motion and hydraulic jump effect be suitable for the complicated terrain on Taiwan. Hence, on the lee side (Durran 1986, 1990; Karyampudi et al. 1995; instead of using an idealized terrain, idealized WRF simu- Frame and Markowski 2006; Armi and Mayr 2011). The lations with realistic Taiwan topography are conducted to hydraulic jump occurs when the flow makes a transition examine the influences of complex Taiwan topography on from subcritical flow upstream to supercritical flow over the a squall line. The mature squall-line MCS case with a sym- mountain, and the Froude number which considered cold metric precipitation structure which landed over Taiwan on pool depth (F ) is utilized to decide whether the fluid is 19 April 2019 is a case for us to compare with the results cp supercritical (F > 1) or subcritical (F < 1). obtained from the idealized simulations. cp cp The objectives of this study are listed as follows. Firstly, This paper is organized as follows. Overview of the we use the mountain-height Froude number (F ) to clarify sqaull-line MCS event on 19 April 2019 is in Sect. 2. Meth- mt the asymmetric structure on the upwind side and the cold- odology is presented in Sect.  3. Results from idealized pool blocking effect due to Taiwan terrain. Secondly, the model simulations are discussed in Sect. 4. The conclusions cold-pool Froude number (F ) is applied to discuss the are summarized in Sect. 5. cp leeside asymmetry. The transition from subcritical flow (F < 1) upstream to supercritical flow (F > 1) at mountain cp cp peak favors the hydraulic jump effect, which can reinitiate 2 Case Overview convection on lee side. Lastly, the terrain-heights and low- level shear experiments are conducted to further examine the On 19 April 2019, a mature squall-line MCS formed over control simulation results. southeastern China and moved eastward to Taiwan, develop- Previous studies mainly applied a bell-shaped mountain ing its mature stage and remained symmetric before being in idealized simulations to discuss the impacts of the terrain affected by Taiwan terrain. Figure  1 illustrates the radar on squall-line MCS (Frame and Markowski 2006; Reeves reflectivity evolution of this squall-line system. Before (a)1400 LST (c)1610 LST (b)1500 LST (f)1840 LST (e)1800 LST (d)1700 LST Fig. 1 Composite of vertical-maximum (CV) radar reflectivity (in units of dB Z) maps on 19 April 2019: a 1400 LST, b 1500 LST, c 1610 LST, d 1700 LST, e 1800 LST, and f 1840 LST (Image source: Central Weather Bureau in Taiwan) Korean MeteorologicalSociety 1 3 Asymmetric Structures of a Squall-Line MCS over Taiwan with Significant Hydraulic Jumps 417 reaching Taiwan, the precipitation feature of this squall line line-type convective systems produced in 1-km simula- was mostly symmetric (Fig. 1a). Even when the squall line tions. Thus, a horizontal grid size of 2 km is used in this just touched Taiwan’s coast line, the precipitation structure study, based on the compromise between the limitation of did not alter significantly (Fig.  1b). available computational resources, numbers of numerical After landing on Taiwan’s mountainous area, this squall experiments, and the grid resolution required to resolve line changed its structure. It is clear from Fig. 1c that the deep convective cells. The cumulus parameterization is not orientation of the southern leading line became roughly used. Effects of Coriolis force and radiation are ignored north–south orientation, but the northern leading line in this study in order to emphasize the effects of Taiwan remained the same northwest-southeast orientation as pre- terrain. vious stage (Fig. 1b). The southern part of the squall line For the environmental setting, instead of using the also showed slightly stronger radar echoes than the northern observed sounding directly, we alternatively use a compos- counterpart (Fig. 1c, d). It is clear that the variation of the ite sounding. The reason is that we only have the observed squall-line orientation resulted from the impacts by Taiwan sounding data at 00 UTC (08 LST) and 12 UTC (20 LST), terrain. The different leading line orientation on the upwind but the squall-line MCS case occurred from 13 to 18 LST side of the mountain is called “upwind side asymmetry”. (see Fig. 1); as a result, both the 00 UTC and 12 UTC data Later, the squall line moved to the lee side of the mountain cannot be used to fully determine the environmental condi- (Fig.  1e). Notice that the southern part of the squall line tion before the arrival of MCS. In fact, the 00 UTC sound- moved faster than the northern part, and this asymmetry is ing in either Makong (a small island west of Taiwan; see its called “leeside asymmetry”. Finally, the squall-line system location in Fig. 3) or Panchiao (northern Taiwan; also shown progressed to the east of Taiwan and dissipated eventually in (Fig. 3) contained convective available potential energy −1 (Fig. 1f). (CAPE) of less than 200 J kg which did not favor squall- line initiation in an idealized model setting. This low-CAPE situation might result from earlier convective precipitation 3 Methodology occurring before the arrival of this squall line and the contri- bution from sea breeze from the surrounding ocean. 3.1 Model Design The pre-storm environment is horizontally homogeneous in the idealized model setting. A composite sounding with The Advanced Research version of the Weather Research a surface temperature of 301.5 K (28.5 °C) and a surface −1 and Forecasting model (WRF-ARW version 3.9; Skamarock mixing ratio of water vapor of 21.3 g  kg is given, and this −1 et al. 2008) was used to perform the idealized simulations in environment contains the CAPE of 2588 J  kg (Fig. 2a). this study. In a real-case WRF simulation, synoptic forcing, This thermodynamic sounding is a composite from several Coriolis force, radiation, and topography are all included, sounding stations in Taiwan with high CAPEs during the and these physical processes will all affect the symmetry Southwest Monsoon Experiment field project (SoWMEX; of a squall-line MCS, causing us difficult to isolate the ter - Jou et al. 2011) to represent the environmental character- rain effects on a squall line. As a result, we used the ideal - istic of Mei-Yu season. Although the SoWMEX campaign ized WRF simulation to exclusively investigate the terrain was conducted more than 10 years ago, it is still the most impacts on a squall-line MCS. recent field experiment which had the most complete intense The computational domain was 1400 km in the x direc- observations (including surface, sounding, radar, satellite, tion and 940 km in the y direction with a horizontal grid size and aircraft measurements) in Taiwan during the Mei-Yu of 2 km. Since a mature squall line can develop vertically season. Therefore, a composite sounding from SoWMEX up to 15 km in vertical, we set the domain vertical top to be can still show the representative theromydnamic profile in 30 km with 55 stretched vertical levels. A sponge layer with Taiwan during the Mei-Yu season. −2 a damping coefficient of 0.0003  s was applied to the top The observed wind profile at Makong (Fig.  2b) showed 5 km to prevent energy reflection from the upper boundary. that there was strong vertical shear at low levels (0–2.5 km). The open condition was imposed for the lateral boundaries, Recall that the squall-line longevity is most sensitive to the and the time step was 3 s. low-level (0–3 km AGL) vertical wind shear perpendicular The physical parameterization schemes used in the to squall-line orientation (Rotunno et al. 1988; Weisman model include the WDM6 microphysics parameterization and Rotunno 2004); as a result, we ignore the wind varia- (Lim and Hong 2010) and the Yonsei University (YSU) tions at middle to upper levels at Makong for simplification. planetary boundary layer (PBL) parameterization (Hong Thus, we only consider the horizontal wind perpendicular and Pan 1996). Weisman et al. (1997) indicated that res- to the squall line, namely, the zonal wind. The wind speed −1 olutions of 4 km might be sufficient to reproduce much increases linearly from zero at the surface to 10 m  s  at the of the mesoscale structure and evolution of the squall altitude of 2500 m (based on the observed wind profile in Korean MeteorologicalSociety 1 3 418 Y.-T. Pan, M.-J. Yang Fig. 2 a Composite sounding (a) Composite sounding adapted from soundings in the SoWMEX field project. The surface temperature is 28.5 °C and the mixing ratio of water −1 vapor is 23.3 g Kg near the surface. Black and blue lines represent temperature and dew- point temperature. b Observed zonal wind profile at Makong at 00 UTC 19 April 2019. c Zonal wind profiles in low-level wind- shear experiments. The wind- shear below 2.5-km height is 5, −1 7.5, 10.0, 12.5, and 15.0 m  s , respectively (b) (c) Z = 2.5 km Fig. 3 Realistic Taiwan terrain after 9-point moving aver- age. The Taiwan topography Taiwan is located at the center of the Panchiao computational domain. Terrain heights are contoured at 1, 500, Mount Snow 1500, 2500 and 3000 m, respec- tively. The upper (lower) blue 12 km average line is the horizontal position for the 12-km averaged vertical cross section in Fig. 11 (12), Makong and the red triangles indicate the locations of Panchiao and Makong CMR 12 km average Korean MeteorologicalSociety 1 3 419 Makong), and the wind velocity is assumed to be constant found that a warm bubble of 4 K, with the size of 200 km in above 2500 m (Fig. 2c). length (north–south), 25 km in width (east–west) and 1.5 km deep, added at the quarter of the x direction and half of the y 3.2 Experiment Design direction at model time of 4 h, can have minimal impacts of lee-side convection and precipitation. The size of the initial Most of previous studies (Frame and Markowski 2006; thermal was chosen to mimic the observed squall-line char- Reeves and Lin 2007; Letkewicz and Parker 2011) used a acteristics shown in Fig. 1a. bell-shaped topography to discuss the relation between ter- rain and squall-line MCS, but the idealized terrain is too 3.3 Froude Numbers Used in This Study simplified to represent the complicated topography like Taiwan. Since we plan to understand impacts of Taiwan ter- Two definitions of Froude number are used in this study. One rain on squall-line MCS, the realistic Taiwan topography is the Froude number considering mountain height (F ), and mt is necessary. Therefore, a high-resolution (30 m) Taiwan the other is Froude number considering the cold-pool depth topography data was used. We downscaled the raw topogra- (F ). The details are discussed as follows. cp phy data to the model grid with 2-km horizontal grid size, Froude number which considers the mountain height and located the Taiwan terrain at the center of computational (F ) is a useful non-dimensional parameter when we discuss mt domain. Additionally, a 9-point moving average was per- the flow impinging on the steep mountains and the block - formed to smooth the terrain to avoid numerical instability ing effect. Mechanically, whether the flow contains enough in the WRF model. The highest terrain peak is 3312 m and kinetic energy to overcome potential energy of the terrain the main characteristic of Taiwan topography is captured barrier (Reeves and Lin 2007) can be determined by F , mt (Fig. 3), including Mount Snow and the Central Mountain which is defined as Range (CMR). A long warm bubble was used to initiate the squall- avg F = , (1) mt line convection, and the lee side gravity-wave convection N × H avg mt was produced by the westerly flow over the Taiwan terrain (Fig. 4). This lee-side convection phenomenon is common when the prevailing wind flowed over topography (Chu and g N = × , (2) Lin 2000; Chen and Lin 2005; Reeves and Lin 2007; Migli- dz etta and Rotunno 2009). In order to reduce the influence of the lee side convection and precipitation on the squall-line where U is the averaged wind speed for air within the avg MCS, the line-type warm bubble was put into the model atmospheric volume below 1 km shown in Fig. 20, N is avg −1 sometime after the initialization. After trial and error, we the averaged Brunt–Väisälä frequency (s ) within the same Fig. 4 Simulated radar reflectivity CV plot at 5 h of model simulation. Red arrow denotes the lee-wave convec- tion discussed in the text, and Lee-wave precipitaon blue arrow denotes the embryo squall-line MCS initiated by the line-type warm thermal Squall-line MCS Korean MeteorologicalSociety 1 3 420 Y.-T. Pan, M.-J. Yang atmospheric volume, H is mountain peak height (m), g is (K). Please see Appendix for the procedure of calculating mt −2 gravitational acceleration (m s ) and  is virtual potential F . v cp temperature (K). Please see Appendix for the detailed pro-The F is used to identify whether the flow regime is sub - cp cedure of calculating F .critical (F < 1) or supercritical (F > 1). As mentioned in mt cp cp If F is greater than 1, low-level air flow can climb over the introduction, the hydraulic jump helps to reinitiate con- mt the mountain; on the other hand, if F is less than 1, low-level vection on the lee side, and it occurs when the flow makes mt airflow will turn around the mountain and converge on the lee a transition from subcritical at upstream to supercritical at side. To understand the blocking effect on air flow near Taiwan mountain peak (Durran 1986, 1990). terrain, we choose a specific location and timing to calculate the F as shown in Fig. 5. The timing and space are chosen 3.4 Spatial Correlation Coefficient mt when the simulated squall-line MCS just lands on Taiwan. For the Froude number which considers the cold-pool depth In our numerical experiments, the symmetry of a squall- (F ), the formula is similar as F except for H term, which line MCS is not easy to determine visually; thus, in order to cp mt cp follows that in Frame and Markowski (2006) objectively quantify the degree of symmetry of a squall line, a spatial correlation coefficient (SCC) is utilized (Tai et al. F = , 2017). The SCC is defined as cp (3) N × H cp � �� � x − x x − x n n s s SCC = , (5) � � � � 2 2 g d v (Σ x − x Σ x − x n n s s N = × , (4) dz where variable x denotes the value of radar reflectivity, sub - where U is the wind speed, N is Brunt-Väisälä frequency, H script n and s denote the north and south parts of the squall- cp is cold-pool depth (assumed to be 1.5 km), g is gravitational line MCS respectively, and the overbar (¯) is the average over −2 acceleration (m s ) and  is virtual potential temperature either the northern or southern region. Fig. 5 The spatial range chosen for calculating the mountain- height Froude number (F ). mt The time and space are chosen when the squall-line MCS just lands on Taiwan. The spatial range of the yellow region is: x = –90 ~ –100 km, y = –40 ~ + 40 km, z = 1 km above the surface Korean MeteorologicalSociety 1 3 Asymmetric Structures of a Squall-Line MCS over Taiwan with Significant Hydraulic Jumps 421 Figure  6 shows the calculation procedure. Firstly, we Table 1 Design of terrain-heights experiments designate the leading edge of the squall-line MCS as the Experiment Max terrain Wind shear Max Froude Reinitiate rightmost boundary of the given rectangle. Secondly, the height (m) below 2.5 km number (F ) on the lee mt −1 (m s ) side central line is defined as the line ( y = 0) to divide a sym- metric squall line into the northern part and the southern CTL 3312 10 0.43 N counterpart, and the rectangle area in both parts are 200 km TER56 2760 10 0.53 N in length and 120 km in width. Notice that we ignore the TER46 2208 10 0.67 N missing-value region (the default radar reflectivity is − 30 TER36 1656 10 0.98 Y dBZ) to avoid the overestimation of the SCC. Therefore, TER26 1104 10 1.40 Y the structure of a squall line is more symmetric as the SCC TER16 552 10 2.90 Y is closer to 1. People might argue whether the central line NTR 0 10 X X (y = 0) we chose is fair or not, because the rightmost lead- ing edge may not be always at the central line (y = 0). Thus, additional central-line uncertainty experiments are also con- ducted. We adjust the central-line position either 5 km north investigate the relation between Froude number (F ) and mt the structure of squall-line MCS. Note that for the no-terrain or south from y = 0 to represent the position uncertainty, and results indicate that the SCC percentage error is less than 5% experiment (NTR), the whole island of Taiwan was com- pletely removed. (not shown). Hence, regarding the axis at y = 0 as the central line to divide the squall-line system into the northern and southern part should be reasonable. 4 Model Results 3.5 Sensitivity Experiments 4.1 Idealized Model Results: Control Experiment (CTL) In addition to the control experiment, two sets of sensitiv- ity experiments are done. When we consider the impacts of Figure 7 displays radar-reflectivity evolution of the idealized Taiwan terrain on a squall-line MCS, Froude number F mt is a critical parameter which is dynamically controlled by squall-line MCS for the control run. At the model time of 240 min, convection and precipitation on the lee side is evi- the mountain peak height and the zonal wind. As a result, both the terrain-height (Table  1) and low-level wind- dent (Fig. 7a). The lee-wave convection appears at the first 30 min and then develops into a convective line (not shown). shear (Table  2) sensitivity experiments are performed to Right after 240 min, a long warm thermal is inserted into the model to mimic a squall line; at 300 min, this long warm thermal evolves to its embryo stage (Fig. 7b). Notice that 120 km instead of inserting a warm bubble at the model initial time, we delay the insertion time until 240 min to prevent from the interference between lee-wave convection and the squall- line MCS represented by the warm bubble. Figure 7c shows that the idealized squall line has developed its mature stage before encountering the Taiwan terrain; meanwhile, the lee- wave precipitation has moved eastward away from Taiwan terrain by the westerly wind. In addition, the north–south Table 2 Design of low-level wind-shear experiments Experiment Max terrain Wind shear Max Froude Reinitiate height (m) below 2.5 km number (F ) on the lee mt −1 (m s ) side WS15.0 3312 15.0 0.46 Y WS12.5 3312 12.5 0.45 N Fig. 6 Schematic diagram for calculating the spatial correlation coef- CTL 3312 10.0 0.43 N ficient (SCC). The center of bow echo ( y = 0) is regarded as the sym- metry axis, and the blue boxes at north and south sides are the coun- WS7.5 3312 7.5 0.39 N terparts. Note that the red box (missing value) is ignored to avoid the WS5.0 3312 5.0 0.28 N overestimation of SCC Korean MeteorologicalSociety 1 3 422 Y.-T. Pan, M.-J. Yang Fig. 7 Simulated radar CV (a) 240 min plot of the full computa- (b)300 min tional domain at a 240 min, b 300 min, c 660 min, d 900 min, and e 1080 min. Contour inter- val for terrain height is 750 m (c) 660min (d)900 min (e)1080min length of precipitation area of the idealized squall line is is manifested that the leading line of the squall-line MCS approximately the same as the north–south length of Taiwan evolves to an asymmetric structure with the southern lead- Island, similar to the case of the 19 April 2019 squall-line ing line showing the north–south orientation but the north- MCS (Fig. 1c). Later, the simulated squall line touches the ern leading line remaining the original northwest-southeast Taiwan terrain and dissipates later over the lee side (Fig. 7d, orientation. This simulation result resembles the precipita- e). tion pattern of the observed 19 April 2019 case (Fig. 1c). When we zoom in the region near Taiwan, the impacts Furthermore, if we scrutinize the radar-echo intensity of the of the terrain upon the squall line can be seen clearly, such squall line, we find that the southern part also has stronger as the upwind-side asymmetry and lee-side asymmetry as radar reflectivity as observed in the 19 April case. Eventu - the observed radar CV shown in Fig. 1. Figure 8a  displays ally, Fig. 8e displays that the squall-line MCS dissipates on that the radar reflectivity of the idealized squall-line MCS the lee side, and the leading edge of southern part moves develops a symmetric bow-echo shape before encountering faster than that of the northern part. This lee-side asymme- the terrain. The lee-wave precipitation moves away from try is also similar to what we have found in the observation Taiwan except for the northeast and southeast corners due (Fig. 1e). to the convergence of the detouring winds (Kirshbaum and The vertical cross section in Fig. 9 is used to examine the Schultz 2018). Figure 8b shows that the squall-line MCS evolution of the idealized squall-line MCS and the relation precipitation pattern still remains nearly symmetric when between the cold pool and terrain blocking effect. To make the leading edge touches the terrain-height contour of 500 m. the vertical cross section more representative, this cross sec- This is reasonable because the height over the western plain tion is averaged within a 12-km strip along the y direction. of Taiwan is not tall enough to block the movement of the Figure 9a illustrates the typical leading-convection region squall line at this time; hence, the precipitation structure of and trailing-stratiform region (with radar bright bands near the squall-line MCS does not alter significantly. The deci - the melting level at 4 km) as shown in the conceptual model sive transition occurs at later stage as shown in Fig. 8d. It of Houze et al. (1989; see their Fig. 1). A prominent cold Korean MeteorologicalSociety 1 3 423 (a)670 min (b)740 min (c)800 min (d)860 min (e)970 min Fig. 8 Simulated radar CV plot near Taiwan at a 670 min, b 740 min, c 800 min, d 860 min, and e 970 min. Blue dotted line is the − 2 K con- tour for perturbation potential temperature, and the black dotted stripe area in (a) corresponds to the vertical cross section in Fig. 9 Fig. 9 Vertical cross sections 760 min (a) 540 min (b) of radar reflectivity (colored; in units of dBZ) and perturbation potential temperature (dotted line; contoured from − 0.5 K to − 4.5 K by 1 K): a 540 min, b 760 min, c 810 min, d 930 min. The horizontal position of the 12-km averaged vertical cross section is shown in Fig. 8a (c) 810min (d) 930min Korean MeteorologicalSociety 1 3 424 Y.-T. Pan, M.-J. Yang pool (i.e. with negative potential-temperature perturbation) shown in Fig. 10e and f (before and after the landfall of the can be seen clearly below 2 km. Figure 9b displays that the southern leading line on Taiwan). The wind convergence is leading-line convection is intensified over the up-wind slope indeed increased after landfall. Thus, it is confirmed that the because the terrain provides an extra mechanical lifting to wind deflection at southern part of the leading line leads to enhance the upward motion at the leading edge (Teng et al. increased convergence, stronger vertical motion, and more 2000; Frame and Markowski 2006). Figure 9c shows that intense convection for the squall-line MCS. the cold pool is mostly blocked by the terrain except for the Figure 11 displays the 12-km averaged vertical cross sec- − 0.5 K isotherm, and this blocking effect causes the cold tion over Mount Snow. Firstly, when the squall-line MCS pool to mainly spread around the terrain, instead of climbing approaches the mountain, the upward motion is at the lead- over the hill. Consequently, the updraft at the leading edge ing edge of the system (Fig. 11a, c). While the squall-line is weakened by the downward motion on the lee side. The MCS climbs to the mountain top, the convection intensity mountain-height Froude number (F ) is only 0.43, consist- decreases immediately due to the terrain blocking effect and mt ent with the fact that the cold pool is mainly blocked by no new convection is initiated on the lee side (Fig.  11b). terrain. Afterward, only stratiform precipitation region is Figure 11d shows that the potential temperature isotherms remained (Fig. 9d). Notice that there is already cold air pro- (isentropes) only ascend slightly on the downslope (x ≈ duced by the initial lee-wave precipitation (Fig. 7d) on the 20  km), indicating a weaker and insignificant hydraulic lee side before the arrival of the squall-line MCS (Fig. 9c, jump (Durran 1986, 1990). Figure 11f shows that the F is cp d). This pre-existing cold air also debilitates the ability of below 1 (subcritical) on the upstream side (Fig. 11f) and at convection regeneration on the lee side (French and Parker the peak (Fig. 11f), not a favorable condition for hydraulic 2014; Lombardo and Kading 2018). jump to occur. Figure 12 shows the 12-km averaged vertical cross sec- 4.2 Upwind‑Side and Lee‑Side Asymmetries tion for southern Taiwan situation. When the squall line of the Squall‑Line MCS approaches the mountain (Fig. 12a), the upward motion also occur at the leading edge (Fig. 12c) as that in the northern After encountering Taiwan terrain, the southern (northern) part (Fig. 11c), but the scenario bifurcates later. Notice that leading line of the simulated squall-line MCS alters obvi- the stronger downward motion on the steeper lee-side slope ously (slightly) on the upwind side (Fig. 8). How does the (slope ≈ 0.111) leads to an effective hydraulic jump with Taiwan topography produce different structure changes significant lifting of the isentrope near the surface (Fig.  12d). over the northern and southern parts of the squall line? Fig- Figure 12e and f show that the F within the cold pool is cp ure 10a shows that the leading line of the simulated idealized less than 1 (subcritical) in upstream area, but it becomes squall line has a symmetric bow echo with the lowest-level greater than 1 (supercritical) at the peak because of strong wind perpendicular to the leading edge. Later, the cold pool airflows above the peak. As a result, these factors (steeper encounters the 500-m terrain contour. Note that different downwind slope and occurring at surface) for the south- terrain-ridge orientations of northern and southern Taiwan ern part favor convection initiation on lee side (Fig. 12b). make the cold pool to detour in various manners (Fig. 10b). Also notice the time is different between Figs.  8, 11 and For the northern (southern) side, the terrain ridge orienta- 12, because the asymmetries and hydraulic jumps occur at tion is mainly parallel (normal) to the wind direction. As a various time. result, the northern leading line remains its original direc- tion, and the surface wind accelerates (see northern box in 4.3 Terrain‑Heights Experiments Fig. 10b) possibly by the terrain channel effect (Skylling - stad et al. 2001; Hitzl et al. 2014). In contrast, the southern Terrain-height experiments include the no-terrain (NTR) to leading line changes the direction significantly due to the full-terrain (CTL) simulations, and the interval is one-sixth ridge orientation of the southern CMR (see southern box of actual terrain height (Table 1). Because the Froude num- in Fig. 10b). The wind behind the southern leading edge is ber (F ) for the TER36 experiment is about 1 (0.98; see mt almost deflected by 90°, so the southern leading line changes Table 1), for simplicity we separate the experiments into two its direction (Fig. 10c). groups: CTL-type and NTR-type groups. After the squall-line MCS moves to the lee side, the Figure 13 shows the radar-reflectivity evolution of three leading edge of southern part moves ahead of the northern terrain-height experiments. If Taiwan is completely removed part, because of the lee-side asymmetry (Fig. 10d). For the (NTR), the squall-line MCS is almost symmetric for the airflow in southern red box, it is hypothesize that the col - entire period (Fig. 13g, h), although the symmetry slightly lision between the cold pool and the deflected wind rein - decreases at 930 min (Fig. 13i). For TER36 experiment, the forces the movement of the southern squall line (Fig. 8d convection is reinitiated on the lee side, and the bow-shaped and 10c). To verify this hypothesis, the convergence field is leading edge is slightly affected by the terrain (Fig.  13f). Korean MeteorologicalSociety 1 3 425 Fig. 10 The position between the cold-pool leading edge and (a) 700 min (b) 820 min Taiwan terrain at − 700 min, b 820 min, c 850 min, d 930 min. Blue dotted line is the perturba- tion potential temperature (con- m/s toured by − 2 K); black solid arrow is for the surface wind at the lowest model level (at 198 m). Taiwan terrain height is contoured at 1, 500, 1500, 2500, and 3000 m. Vertical −1 velocity (in units of m s ) at 2-km height is colored in (a–d). The divergence field (colored; −1 in units of s ) before and after squall-line’s landing on south- ern Taiwan terrain is shown in (c) 850 min (d) 930 min (e) and (f), respectively (e) Before (f) Aer The TER36 experiment resembles the NTR experiment hence, we can classify these experiments as the CTL-type in the sense that the bow-shaped leading edge appears on group. the lee side, so we can categorize TER36 as the NTR-type Figure 14 shows the propagation of the leading line of group. The TER26 and TER16 experiments display simi- the simulated MCSs for three experiments. The structure lar structures as the TER36 experiment on the lee side, so is symmetric at the beginning (Fig. 14a, d, g), and the NTR we also classify them as the NTR-type group. We notice experiment remains symmetric until 930 min (Fig. 14i). For from Table 1 that the F is greater than 1 when the terrain TER36 experiment (Fig. 14f), its leading edge is not as con- mt height is below or equal to that for TER36 (i.e., TER26 and tinuous as that in NTR (Fig. 14i) owning to terrain effect. TER16), and that the squall lines in these experiments have The TER36 experiment is supposed to have the ability to the ability to reinitiate convection on the lee side. However, reinitiate new convection on the lee side, according to the if the terrain height is above that of TER36 (i.e., TER46, Froude number (F ~ 1), but it does not. It is because the mt TER56, and CTL), the Froude number is less than 1, and no cold air produced by lee-wave precipitation at the model ini- obvious convection is reinitiated on the lee side (Fig. 13c); tiation is accumulated on the lee side and inhibits convection Korean MeteorologicalSociety 1 3 426 Y.-T. Pan, M.-J. Yang Fig. 11 Vertical cross sec- (a) 870 min (b) 920 min tions of the radar reflectivity (colored) at a 870 min and b 920 min for northern Taiwan (Mount Snow); vertical cross sections of the vertical veloc- ity (colored) and potential temperature (contoured by 2 K) at c 870 min and d 920 min for northern Taiwan (Mount Snow); vertical cross sections of the F (colored) when the MCS (c) 870 min (d) 920 min cp system moves to e the upstream side and f mountain peak of the northern Taiwan (Mount Snow). The red arrows in b and d denote the locations of hydrau- lic jump. The dashed red boxes in e and f denote the leading- edge cold pool positions. The horizontal position of the 12-km averaged vertical cross section is shown in Fig. 3 (e) At upstream (f) At peak re-initiation. As a result, the leading line of the TER36 is blocking effect (TER26 and TER16 experiments). To some discontinuous. degree, TER36 experiment is like a flow-regime division Figure 15 shows the change of SCC at different stages. to separate two different flow regimes when the squall- Four stages are chosen: Stage A is when the location of line MCS enters the hills area, and this is the reason why leading line is at west of Taiwan; Stage B is when the we show the change of SCCs for all terrain sensitivity leading edge touches the 1-m height contour (border of experiments. From Stage C to Stage D, the SCCs for all Taiwan); Stage C is when the leading edge touches the experiments decrease significantly and the decreasing rate 500-m height contour; Stage D is the most asymmetric is approximately proportional to terrain height at stage stage on the upwind side. The SCC coefficient for NTR D. This implies that the terrain peak height is a critical run is nearly 0.9 and slightly decreases to 0.86 at Stage parameter for the squall-line symmetry, and higher terrain D, as expected in the absence of Taiwan terrain. From peak makes the squall-line MCS more asymmetric on the Stage A to Stage B, the squall-line MCS is approaching upwind side. the Taiwan border from the west, and all experiments For the CTL experiment, it is not as symmetric as other have high SCCs. For Stage B to Stage C, the squall-line experiments at first (Stage A), and the terrain might force MCS starts to “feel” the impacts of Taiwan hills (below the squall-line MCS to develop more asymmetric structures 500 m). Recall that the F for TER36 experiment is near at the upslope stage (Teng et al. 2000). The increasing SCC mt 1, so the terrain blocking effect is obvious for experiments (from Stage B to Stage C) does not match the regime for the with terrain heights equal to or above the peak of TER36 low Froude number, but it is acceptable because the degree experiment. As a result, in this period, the SCC coefficient of symmetry for the CTL at first is too low as comparing decreases for TER46 and TER56 experiments. In contrast, with other experiments. Later, the SCC coefficient of the for experiments with peaks below the terrain height of CTL drops significantly from Stage C to Stage D due to the TER36 experiment, the SCC coefficient either remains the steep terrain. Notice that radar observation of the squall-line same or increases slightly, because of the minor terrain MCS on 19 April 2019 has similar evolution of SCC from Korean MeteorologicalSociety 1 3 Asymmetric Structures of a Squall-Line MCS over Taiwan with Significant Hydraulic Jumps 427 Fig. 12 a, b As in Fig. 11a, b, (a)890 min (b) 940 min but for the southern Taiwan (Southern CMR) at 890 min and 940 min; c, d as in Fig. 11c, d, but for the southern Taiwan (Southern CMR) at 890 min and 940 min; e, f as in Fig. 11e, f, but for the southern Taiwan when the squall-line MCS sys- tem is at the upstream side and mountain peak. The red arrows (d) 940 min (c) 890 min in b, d denote the locations of hydraulic jump, and the blue arrows indicate the locations of strong downward motion. The horizontal position of the 12-km averaged vertical cross section is shown in Fig. 3 (e) At upstream (f) At peak Subcrical at upstream Stage B to Stage D as the CTL, as expected from the fact that e, h). The fact that the WS15.0 experiment can initiate the observed squall line experienced the same full degree of new convection on the lee side with low F (Fig. 16c and mt terrain effect as the CTL simulation. Table 2) is not consistent with the results in previous section that for small Froude number, and it is because the strong 4.4 Low‑Level Wind‑Shear Experiments hydraulic jumps produced by strong mid- and upper-level winds (to be shown in Fig. 17a, c). In these experiments, we change the wind speed systemati- Figure 17a and b show that the new convection exists on cally in order to examine its influence on the F and squall- the lee side in WS15.0 experiment but not in CTL experi- mt line MCS evolution (Table 2 and Fig. 2c). We may use the ment, and that the hydraulic jump effect for the WS15.0 RKW theory (Rotunno et al. 1988) to examine the results. experiment is significantly stronger than that for the CTL The RKW theory, which considers the balance between hori- run. The reason is the intensity of mid- and upper-level zontal vorticity created by the cold pool and the vorticity by winds. The wind below 1 km does not change significantly environmental low-level wind shear, can be used to explain among different shear experiments (Table  2 and Fig. 2c), so different evolution of the squall line before the influence of the Froude number (F ) is still small even we increase the mt Taiwan terrain (Fig. 16a, d, g). The leading-line convection low-level shear. However, the environmental wind between remains upright when the vorticity by wind shear is strong 2.5- and 5.0-km heights offers an extra dynamical force to enough to balance with that by the cold pool (WS15.0; help the flow to have a transition from subcritical (F < 1) cp Fig. 16a). On the other hand, the leading-line convection at upstream to supercritical (F > 1) at mountain peak cp becomes up-shear tilted and trailing stratiform precipitation (Durran 1986, 1990), which induces hydraulic jump on the is evident when the vertical shear is weak and the cold pool lee side (Fig. 17g). But the flow transition does not occur in dominates (WS5.0; Fig. 16g). Large variations in precipita- the CTL experiment; as a result, no obvious hydraulic jump tion occur among the experiment when the simulated squall is found (Fig. 17h). Therefore, only using mountain-height lines are on the upwind side of Taiwan terrain (Fig. 16b, Froude number (F ) to decide whether the convection will mt Korean MeteorologicalSociety 1 3 428 Y.-T. Pan, M.-J. Yang Fig. 13 As in Fig. 7, but for the 750 min8 (b) 20 min9 (c) 30 min (a) terrain experiments. Upper row is for CTL, middle row is for TER36, and lower row is for NTR experiment. Left column of panel a, d, g is for simulation time at 750 min; middle column of panel b, e, h is for simulation time at 820 min; right column of panel c, f, i is for simulation time at 930 min (f) (d) (e) (i) (g)(h) Fig. 14 As in Fig. 10, but for 660 min 800 min 930 min the terrain experiments. Upper (c) (a)(b) row is for CTL, middle row is for TER36, and lower row is for NTR experiments. Left column of panel a, d, g is for simulation time at 660 min; middle column of panel b, e, h is for simulation time at 800 min; right column of panel c, f, i is for simulation m/s time at 930 min (f) (d) (e) (h) (i) (g) Korean MeteorologicalSociety 1 3 NTR TER36 CTL NTR TER36 CTL 429 Fig. 15 The spatial correlation Spaal correlaon coefficient coefficient (SCC) of the squall- line MCS structures at four stages for the observation (OBS; black dotted), CTL (black solid), TER56 (orange solid), TER46 (blue solid), TER36 (red solid), TER26 (blue dotted), TER16 (orange dotted), and NTR (red dotted) experiments. Definitions for Stage A, B, C, and D are described in the text B D A C Fig. 16 As in Fig. 13, but Approaching (a)(b) LandingL (c) eaving for the low-level wind shear experiments. Different timings are chosen when the squall-line MCS is approaching (left col- umn), landing (middle column), and leaving (right column) the Taiwan mountain (e) (f) (d) (h) (g) (i) Korean MeteorologicalSociety 1 3 WS5.0 CTL (WS10) WS15.0 430 Y.-T. Pan, M.-J. Yang Fig. 17 Vertical cross sec- WS15.0 CTL (b) (a) tions of a the radar reflectiv - ity (colored) and along-plane vectors, c the vertical velocity (colored) and potential tem- perature (contoured by 2 K), e the Froude number (colord; F ) when the squall-line MCS cp is at the upstream side, and g the Froude number (colored; F ) when the squall-line MCS (d) cp (c) system is at the mountain peak of the southern CMR for the WS15.0 experiment. Panels b, d, f, h are similar to panels a, c, e, g but for the CTL experiment. The dashed red boxes in g and h denote the leading-edge cold pool positions (e)At upstream (f)At upstream (h)At peak (g)At peak be reinitiated on the lee side, where there is significant verti - the southern terrain (southern CMR) is in north–south orien- cal wind shear, may not be appropriate. tation, nearly normal to the wind direction behind the leading line. The south side of the northern leading line accelerates 4.5 Schematic Diagrams for Upwind‑Side because the wind is parallel to the ridge orientation. As a and Lee‑Side Asymmetries result, the leading line rotates counterclockwise (Step 3). But for the southern side, the central part of squall line deceler- Figure  18 is the schematic diagram for the evolution of ates because the wind behind the leading line is nearly nor- upwind-side asymmetry. Firstly, the squall-line MCS devel- mal to the terrain (Step 4). The different propagation speed ops its mature stage with the bow-shaped leading line (Step between different parts of the leading line leads to the asym - 1), remaining its symmetric structure before the encounter metry on the upwind side. Finally, Step 5 indicates that the with Taiwan terrain. The surface wind is nearly perpendicu- convection ahead of the southern squall line intensifies owing lar to the leading line (Step 2). If we focus on the ridge to the surface-wind convergence and cold-pool collision. orientation, the northern terrain (Mount Snow) is mainly in Figure  19 is the schematic diagram for the lee-side northeast-southwest orientation, approximately parallel to asymmetry in two vertical cross sections. For Mount the wind direction behind the leading edge. On the contrary, Snow, the horizontal width of the mountain is extensive Korean MeteorologicalSociety 1 3 431 Fig. 18 Schematic diagram for the five evolution steps for the upwind-side asymmetry of squall-line MCS. Five steps are explained in the text. Orange area is the convergence area. Black solid arrows near Taiwan denote the ridge orientation of Taiwan mountain range. The black dotted line separates the squall-line MCS into the north- ern and southern parts Fig. 19 Schematic diagram for the leeside asymmetry of the squall line at a the northern (Mount Snow) and b southern Taiwan (Southern CMR). The cloud outline is shown, gray shading indicates the radar reflectivity convective cores and the bright band in the stratiform region. Blue arrow represents the downward motion, red arrow is for hydraulic jump, and blue dotted line displays the cold air produced by the gravity-wave convection and precipitation (120 km), and the lee slope is moderate (0.067); the flow- 5 Conclusions regime transition from subcritical at upstream to super- critical at mountain peak does not occur and the lee-side A mature squall-line MCS developed a bow-echo shape subsidence is not strong at peak. The weak hydraulic jump and approached Taiwan from the west on 19 April 2019, −1 occurs over mountainous area, which would not favor con- causing fierce gust wind up to 20 m  s and heavy rain- vection re-initiation (Fig. 19a). However, the situation is fall with hailstones over several places in Taiwan. After different over the southern CMR. The horizontal width the contact with Taiwan terrain, the originally symmet- (40 km) is only a third of that for Mount Snow, and the ric structure of this squall line altered with significant slope on the lee-wind side is steeper (0.111); the crucial upwind-side and lee-side asymmetries, which are the main flow-regime transition does occur and the subsidence is scientific foci of this study. The idealized WRF simula - stronger on the lee side. Furthermore, the hydraulic jump tions with horizontal grid size of 2 km (in the absence occurs at near the surface. All these factors support the of the effects of Coriolis force, radiation and horizontal convection re-initiation on the lee side over southern CMR heterogeneity) were conducted in order to systematically (Fig. 19b). Korean MeteorologicalSociety 1 3 432 Y.-T. Pan, M.-J. Yang examine the relationships among the Froude numbers (F mt and F ), squall-line structure, and hydraulic jump. cp Idealized simulations show that the squall-line MCS develops its bow-echo shape with nearly symmetric struc- ture before the arrival on Taiwan, similar to the observed case on 19 April 2019. According to the mountain-height Froude number (F ), the low-level air at the leading edge mt of the squall-line MCS is blocked by the steep Taiwan ter- rain; as a result, the wind deflection is apparent. Different ridge orientations between northern (northeast-southwest) and southern (north–south) Taiwan terrain bring about the upwind-side asymmetry (Fig. 18). On the other hand, the different mountain width, downwind slope, and the transi - tion of the flow regime (i.e., hydraulic jump) from subcriti - cal at upstream to supercritical at mountain peak lead to the lee-side asymmetry. Also, the intensity and location of the hydraulic jumps depend on the width and downwind slope of mountain. To be specific, the southern (northern) terrain is narrower (wider) and the downwind slope is steeper (more Fig. 20 The atmospheric volume in the calculation of Froude number moderate). In addition, the southern CMR (Mount Snow) mt has (lacks of) the flow transition from subcritical at upstream to supercritical at peak, causing significant (weak) hydrau - lic jump which occurs over surface (mountainous area) and hydraulic-jump effects obtained in this study can be applied to other scenarios. Finally, more studies of the squall-line the convection can (cannot) be reinitiated on the lee side (Fig. 19). MCSs impinging on high mountains over other geographic regions should be conducted to verify the results obtained Terrain-height experiments were performed to inves- tigate the terrain blocking effect. The TER36 experiment from this study near Taiwan. separates these experiments into two groups. One is that the squall-line structure becomes more symmetric after the Appendix: Details for calculating the Froude squall-line’s arrival on lower terrain, and the other is that the squall line becomes asymmetric. It depends on whether the Numbers of  F and  F mt cp mountain-height Froude number (F ) ≥ 1 (TER36, TER26 mt and TER16 experiments) or not (TER46 and TER56 experi- We describe the procedures in calculating the Froude num- bers (F and F ) in this Appendix, in additional to the ments). The terrain blocking effect is the main reason for the mt cp asymmetric structure of the squall-line MCS after its arrival graphic illustration given in Fig. 5. For Froude number F , mt its definition is given in Eq. ( 1), where the variables U on the steep Taiwan terrain. avg Low-level wind shear experiments are also conducted to and N are averaged for the same atmospheric volume avg (shown in Fig. 20) at the leading edge of squall line (with investigate the asymmetry and hydraulic jump on the lee side. In low-level shear experiments, we find that the mid- to a zonal width of 10 km, a meridional length of 80 km for y = − 40 km ~ + 40 km, and a depth of 1 km for z = 0 ~ 1 km) high-level winds are also important for the hydraulic jump, because it offers an extra dynamic forcing to support flow- in a Lagrangian framework, and H is the highest mountain mt peak in the range of y = −  40  km ~ + 40  km. For Froude regime transition at peak. In summary, the idealized WRF simulations in this study number F , its definition is given in Eq. ( 3), where the vari- cp ables U and N are the values at grid points, and the cold-pool provide us an opportunity to clarify and explore the effects of Taiwan terrain on a squall-line MCS. Nevertheless, the depth is the depth of cold-air perturbation (as defined by the depth of the contour of  =−1.5 K ), which approximately squall line on 19 April 2019, which is an eastward mov- ing squall-line MCS, is not a frequent case during the Mei- remained constant at z = 1.5  km (i.e., H = 1.5  km) before cp the cold pool encountered Taiwan terrain. Yu season. Other progression directions of the squall-line system are more common, such as southeastward or north- Acknowledgements Constructive comments by two reviewers on eastward directions. For future studies, different impinging our manuscript are highly appreciated. 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Journal

Asia-Pacific Journal of Atmospheric Sciences – Springer Journals

Published: Aug 1, 2022

Keywords: Squall-line MCS; Taiwan topography; Froude number; Hydraulic jump

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