1. Introduction
Torrential rainfall that results in flash floods and landslides is often caused by a long-lived slow-moving quasi-linear convective system (QLCS). A class of QLCS in vertically sheared flows has a property of “back-building” (e.g., Bluestein and Jain 1985; Kato and Goda 2001; Schumacher and Johnson 2005; Parker 2007; Schumacher 2009; Kato 2020). In a back-building QLCS, new cumulus clouds repeatedly develop upstream of the preceding clouds. This type of QLCS may persist for several hours, longer than the life cycle of each cumulus cloud. If cumulus clouds continuously develop at the point almost fixed in ground-relative space, the precipitation beneath the QLCS may become large enough to cause flash flood disasters. Although such a quasi-stationary QLCS that caused torrential rain has been reproduced by numerical simulations after such events (e.g., Oizumi et al. 2018), it is still difficult for current operational models to precisely predict time and location of their occurrence and amount of precipitation (Kato 2020).
Unuma and Takemi (2016) analyzed operational weather radar data over the Japanese islands and detected more than 4000 quasi-stationary QLCSs in the warm seasons between 2005 and 2012. A large fraction of the quasi-stationary QLCSs occurred over Kyushu Island in the southwestern part of Japan (Fig. 1a). Kyushu Island is exposed to warm moist westerly or southwesterly flow from the East China Sea during the summer, especially in the baiu–mei-yu rainy season. In fact, there have been a number of case studies on back-building QLCSs on Kyushu Island (e.g., Davidson et al. 1998; Kato 1998, 2005; Yoshizaki et al. 2000),
Topography of regions around (a) Japan and (b) Kyushu Island and (c) 12-h accumulated precipitation at 2400 JST 5 Jul 2017 synthesized by radar and AMeDAS (surface observation network) of JMA. In (b), the red box indicates the area to be averaged for generating the sounding in Fig. 3, while the black line shows the position of a vertical cross section in Fig. 12b. The gray contours in (c) indicate elevations of 200, 400, 600, 800, and 1000 m.
Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-19-0150.1
Among many previous heavy precipitation events in Kyushu Island, the torrential precipitation over Kyushu-Hokubu on 5 July 2017 (hereafter denoted by the KH2017 event; e.g., Kato et al. 2018) was record-breaking: the accumulated rainfall over 12 h, from 1200 to 2400 Japan standard time (JST; JST = UTC +9 h) on the same day, reached 600 mm at the Asakura Automated Meteorological Data Acquisition System (AMeDAS) station (Fig. 1b) of the Japan Meteorological Agency (JMA). This rainfall is the Japanese record for the greatest 12-h accumulated precipitation that is not associated with a tropical cyclone. 1 Heavy rainfall was indeed forecasted for somewhere in the western part of Japan on this day. However, it was not forecasted that the record-breaking rainfall would occur in Kyushu. A torrential rain warning was issued only after the onset of the precipitation and was too late to allow the evacuation of residents. Landslides and floods caused 48 fatalities.
The heavy rainfall was localized in a small area covering only ~20 km in the west–east and ~5 km in the south–north directions (Fig. 1c). As is often the case for precipitation associated with a back-building system, the heavy precipitation area was line-shaped. There were a stationary front (baiu–mei-yu front) to the north of Kyushu Island and a humid southwesterly flow toward the front (Fig. 2a), which is a typical environment for torrential rainfall in the baiu–mei-yu season (Kato 2005). Moreover, this precipitation area was much smaller than that in several cases reported in the central United States (e.g., Schumacher and Johnson 2005), which are possibly linked to large-scale forcing (Schumacher and Johnson 2008; Schumacher 2015).
(a) Surface weather map at 0900 JST 5 Jul 2017 provided by JMA and (b) surface temperature (shading) and wind vectors at 1500 JST 5 Jul 2017 from the JMA hourly analysis in which both operational observations and numerical weather predictions are considered. The gray contours in (b) indicate elevations as in Fig. 1c but smoothed.
Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-19-0150.1
Because the maximum precipitation in the KH2017 event occurred at the valley bottom (Fig. 1), it is reasonable to suppose that the mountains with height of about 1 km to the west or east may have contributed to the development and maintenance of the QLCS. In fact, a previous study on a different case in Kyushu Island has shown that topography did trigger cumulus clouds to form a back-building system (Yoshizaki et al. 2000). There are several regions favorable for line-shaped heavy precipitation in Kyushu Island (e.g., the Koshikijima and Nagasaki lines; Kato 2005). However, the Asakura area is not one of these regions.
Takemi (2018) has suggested that including detailed topography in a numerical model may be a key to accurate prediction of the location and precipitation of the QLCS in the KH2017 event. However, other numerical studies on the KH2017 event found that the quasi-stationary QLCS formed even in the absence of the topography of northern Kyushu Island, so that the topography does not seem to be a critical factor for the present QLCS (Tsuguti 2019; Kawano and Kawamura 2020). They also indicated that a cold pool was not essential to maintain the quasi-stationary QLCS; a similar QLCS was reproduced in a sensitivity experiment in which evaporative cooling was switched off. Although it is generally considered that quasi-stationary QLCSs may be caused by larger-scale forcing such as a mesoscale convective vortex (e.g., Unuma and Takemi 2016), such forcing was absent in the KH2017 case.
The present study explores the causes of such a QLCS by means of idealized numerical simulations with a simplified configuration. We consider a zonally uniform belt of flat land sandwiched by seas to the north and south. In fact, surface temperature contrasts between land and sea were significant in the KH2017 event as seen in a JMA analysis based mostly on surface observations (Fig. 2b): the surface temperature over the land was at least 4 K higher than that over the sea due to daytime solar heating.
We will also put an additional focus on the resolution dependence of the simulated QLCS; the present numerical simulations employ various horizontal resolutions dx between 100 m and 2 km. The latest supercomputers allow even dx ~ 100 m to simulate a mesoscale convective system (e.g., Verrelle et al. 2017). Simulations with dx ~ 1 km may be marginal for resolving each cumulus cloud, and we address whether or not such dx values, which have recently been referred to as the “gray zone” (e.g., Field et al. 2017), can reasonably reproduce a quasi-stationary QLCS.
This paper is organized as follows: Section 2 describes the configuration of the numerical experiments conducted in the present study. Section 3 presents the results of the numerical experiments with dx = 100 m, and compares them with observations of the KH2017 event. Section 4 discusses the resolution dependence of the results and the mechanism for maintaining the present QLCS. Finally, section 5 gives the conclusions.
2. Numerical setup and data for initial and boundary conditions
The numerical model used in the present study is the JMA nonhydrostatic model (JMA-NHM; Saito et al. 2006, 2007). A horizontally explicit and vertically implicit (HE-VI) scheme is used, whereas numerical diffusion used in operational forecasts is switched off. A three-ice single-moment bulk scheme (Lin et al. 1983; modified by Ikawa and Saito, 1991) is used for microphysics parameterization. The turbulence parameterization employs a simple local closure (Deardorff 1971). The surface flux of momentum, sensible heat, and moisture are parameterized by the bulk method (Beljaars and Holtslag 1991). Coriolis force is not considered.
At the initial time, a one-dimensional sounding (Fig. 3 and Fig. S1 in the online supplemental material; U and V stand for velocity components in the x and y directions, respectively) is uniformly specified over the whole computational domain. 2 The same sounding is also used as lateral boundary conditions at later times. This one-dimensional sounding is obtained by averaging the JMA 5-km-mesh mesoscale analysis at the time of peak torrential rain (1500 JST 5 July 2017) over the red box in Fig. 1a around Asakura. The convective available potential energy (CAPE) for the most unstable parcel of this sounding is 2717 J kg−1, while the convective inhibition (CIN) for the parcel was negligibly small (~3 J kg−1). Such a high value of CAPE is occasionally observed in Kyushu Island but does not always lead to torrential rainfall. The lifting condensation level of the profile in Fig. 3 is 459 m, whereas the level of free convection is 689 m.
Skew T–logp plot of sounding employed for the idealized experiments. The black solid line shows temperature of a lifted air parcel, while red and green solid lines are temperature and dewpoint temperature of the environment, respectively. The long barbs denote 5 m s−1 (10 kt).
Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-19-0150.1
Figure 4 depicts the configuration of the numerical domain and surface boundary conditions. The size of the numerical domain is 225 km in the longitudinal (x), 135 km in the latitudinal (y), and 19.3 km in the vertical (z) directions. The central one-third of the whole domain in the y direction is assumed to be land, and other areas are assumed to be sea. This configuration crudely represents the peninsular shape of the northwest of Kyushu Island: the width of the land (45 km) roughly corresponds to the north–south span of the peninsula (Fig. 1b). To simulate the daytime situation, the sea surface temperature is fixed to the same temperature as that at the lowest level of the sounding, while the land surface temperature was set to 5 K warmer. Note that insolation is not considered for simplicity. A flat land surface (no topography) with roughness length of 0.1 m is assumed. The roughness length of the ocean surface depends on wind speeds (Beljaars 1995). The typical surface sensible and latent heat (moisture) fluxes diagnosed by the surface parameterization (Beljaars and Holtslag 1991) are ~50 and ~100 W m−2, respectively, over the land in the upstream area of the QLCS, while they are ~0 and ~50 W m−2, respectively, over the sea.
Schematic of the numerical domain. The hatched area is assigned as the lateral sponge layer.
Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-19-0150.1
Both lateral boundaries in the x and y directions are open. The grid points in lateral peripheries, which span 10% of the domain size in the x direction, constitute sponge layers. 3 In the vertical direction, the top 10 layers are also set as sponge layers.
We overview results of the experiment with dx = 100 m (hereafter the “control experiment”) in section 3. Experiments are also conducted with coarser dx such as 150, 300, 500 m, 1, 1.5, and 2 km to investigate resolution dependence, while various sensitivity experiments are run with dx = 150 m. The grid size in the vertical direction is 100 m for all dx. Time integration is performed for 12 h with a time step of 0.5 s.
3. Simulation results of the control experiment and comparison with observations
The control experiment succeeds in reproducing localized heavy precipitation (Fig. 5a). The maximum accumulated precipitation exceeds 1000 mm at the end of the time integration (t = 12 h) (orange line in Fig. 6a). The large accumulated precipitation (≥1000 mm) is localized in a small area of 20 km × 5 km in the x and y directions (Fig. 5a), respectively, which is as small as that in the KH2017 event (Fig. 1b).
Accumulated precipitation during 12 h of time integration for various values of dx. The gray solid lines at y = 45 and 90 km indicate the coastlines.
Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-19-0150.1
Time series of (a) maximum accumulated precipitation and (b) precipitation rate averaged over the land for various values of dx.
Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-19-0150.1
The time evolution of a spinup of a QLCS is shown in Fig. 7. Weak precipitation occurs both along the north and south coastlines soon after the start of the simulation (Fig. 7i). The intrusion of the sea breeze from the south is faster than that from the north because of the southerlies (V > 0) below z ~ 1 km in the sounding (Fig. 3 and Fig. S1b). These fronts collide at y ~ 75 km at t ~ 2.5 h (Figs. 7b,c). The height of upstream convective boundary layer reaches about 400 m. Cumulus clouds are triggered and cause precipitation along a zonal convergence zone where the intruding sea-breeze fronts collide (Fig. 7k). The precipitation associated with the cumulus clouds that are aligned along x axis dissipates because of downdrafts and resulting divergences in the lower heights accompanied by a cold pool (Figs. 7e,l). The averaged precipitation also weakens at around t = 5 h (Fig. 6b). Subsequently, the two convergence lines originated from the sea-breeze fronts upstream starts to develop downstream and intrudes into the cold pool (Figs. 7e–g,l–n). Note that the northern precipitation system is stronger than the southern one.
Time series of (a)–(g) divergence ( 10−4 s−1) (shading) and horizontal wind vectors at z = 100 m, (h)–(n) hourly precipitation, and (o)–(u) surface temperature from t = 1 to 7 h. The gray solid lines indicate the coastlines.
Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-19-0150.1
After t = 6 h, the convergence upstream is almost fixed (Figs. 7f,g), and a quasi-stationary QLCS, which is a back-building system, is established. Although each individual cumulus cloud is advected eastward by the westerly wind, succeeding cumulus clouds are repeatedly generated near sea-breeze fronts upstream. The convective system that originates from the north sea-breeze front is stronger. The maximum accumulated precipitation from the back-building system increases linearly at a rate exceeding 100 mm h−1 (Fig. 6a). Note that the grid point with maximum precipitation moves little with time after the quasi-stationary QLCS is formed. The average precipitation rate over the land is about ~13 mm h−1 and remains almost constant after t = 6 h (Fig. 6b).
Figure 8 shows a three-dimensional visualization of liquid and ice cloud water after the quasi-stationary QLCS has developed (t = 7.5 h). This figure seems to illustrate that the control simulation resolves each cumulus cloud in the QLCS and that even finer-scale structures are embedded in each cumulus cloud. Its top view looks like satellite images of the KH2017 event (not shown).
Three-dimensional view of simulated cloud water at t = 7.5 h. The entire domain except for the lateral sponge is shown, and land (sea) is shown in brown (light blue) at the bottom.
Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-19-0150.1
The QLCS consists of a train of updrafts (Fig. 9a). Surface winds converge toward the QLCS. Their wind speed exceeds 10 m s−1 and even reaches 20 m s−1 (Fig. 9b). Comparable wind speeds are also found in near-surface outflows from the QLCS (southeast corner of Fig. 9b). The temperature of the lowest level of the atmosphere is raised along with the convergence, while a cold pool with temperature ~2 K lower than the environment is formed downstream (Fig. 9c). These strong convergent surface winds toward the land, warmer surface temperature, and cold pool were also observed in the KH2017 event (Fig. 2b).
Horizontal cross sections of (a) vertical velocity (shading) and horizontal velocity (vectors) at z = 5 km and (b) horizontal velocity vector and its magnitude at z = 10 m (arrows and shading, respectively), (c) temperature at z = 2 m, and (d) pressure deviation (Pa) at the surface at t = 7.5 h for dx = 100 m. The vertical cross section along the purple line in (a) is shown in Figs. 10 and 11. The gray solid lines indicate the coastlines.
Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-19-0150.1
Moist plumes corresponding to cumulus clouds are periodically generated in the upstream edge as seen in equivalent potential temperature θ e in Fig. 10. 4 They are triggered at x ~ 80 km, which is about 40 km upstream of the location where accumulated precipitation is largest. The spacing between two adjacent moist plumes is about 5 km, and time intervals between their passage are ~10 min. Figure 11 shows a vertical cross section of vertical velocity and θ e along the QLCS. Updrafts in the moist plumes are accelerated from the cloud base up to the upper troposphere (e.g., indicated as “A” at x ~ 120 km in Fig. 11a). These updrafts are subject to the mean wind shear during their ascent. As a result, each updraft and corresponding cumulus cloud are significantly tilted (e.g., 45° in the x–z plane as seen in the difference in x between the bottom and top of updraft “A” in Fig. 11). Smaller-scale buoyant plumes are formed in the lower atmosphere (indicated by “B” at x ~ 90 km in Fig. 11b). These plumes merge as they ascend, and fewer plumes reach the tropopause downstream in the x direction.
Equivalent potential temperature in a zonal–time cross section at y = 82.5 km at 5 km height between t = 9 and 12 h. The path of this cross section is shown as the purple line in Fig. 9a.
Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-19-0150.1
(a) Vertical velocity and (b) equivalent potential temperature on a vertical cross section along the QLCS at y = 82.5 km (purple line in Fig. 9a) at t = 7.5 h.
Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-19-0150.1
Figure 12a shows vertical cross sections of radar reflectivity across the QLCS in the KH2017 event using the composite reflectivity 5 along the solid line in Figs. 1b and 12b, shows similar plot for the simulated radar reflectivity. Note that the observational data are plotted on a 1 km grid in both the horizontal and vertical directions (Fig. 12a), and is coarser than that of the simulation. The increasing height of the reflectivity top between x ~ 60 and 100 km looks similar between the observations and the simulation.
(a) Composite reflectivity of multiple radars provided by JMA along the latitudinal vertical plane in the Asakura area at 1500 JST 5 Jul 2018 (solid line in Fig. 1a) and (b) simulated reflectivity on a vertical section at y = 82.5 km at t = 7.5 h along the simulated QLCS.
Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-19-0150.1
4. Discussion
a. Horizontal resolution dependence
The almost linear increases exceeding 100 mm h−1 in the maximum accumulated precipitation occur after t = 6 h. The large localized accumulated precipitation exceeding 500 mm occurs only for dx ≤ 1 km (Figs. 5a–e and 6a). Among the experiments with dx ≤ 1 km in which the stationary systems appear to form, the one with dx = 150 m attains the largest accumulated precipitation after t = 8 h (Fig. 6a). The experiments with dx ≤ 300 m result in maximum accumulated precipitation larger than those with dx = 1 km and dx = 500 m. The average precipitation over the land is similar in the experiments with dx ≤ 1 km after t = 6 h (Fig. 6b). The area with moderately heavy precipitation (≥300 mm) is largest for the experiment with dx = 1 km (Fig. 5e).
Although the total precipitation is similar for experiments with dx ≤ 1 km, several systematic differences between various dx are found. In the following, these differences are presented in vertical profiles of several variables obtained by temporal averaging between t = 6 and 12 h when the stationary system has formed and also by spatial averaging over the cumulus developing area (75 < x < 150 km, 67.5 < y < 90 km) or over cumulus cloud cores defined by grid points with w > 3 m s−1 and mixing ratio of cloud water q c > 0 in the area of developing cumulus clouds.
The averaged updraft velocity for grid points with w > 0 tends to increase with decreasing dx (Fig. 13a). Such behavior is often seen in numerical models when resolution is increased (e.g., Ito et al. 2017). On the other hand, the maximum updraft during the averaging period varies little for dx ≤ 1 km (Fig. 13b). The maximum updrafts may be associated with the thermodynamical limit,
Vertical profiles of updrafts over the area of developing cumulus clouds for each value of dx. (a) Spatiotemporally averaged updraft velocity and (b) maximum updraft velocity.
Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-19-0150.1
A more significant difference due to dx is found in the characteristics of the clouds. Figure 14a shows the fraction of cloud area (q c > 0) and cumulus cores at each height in the area of developing cumulus. The fraction of cloud area is significantly different even between dx = 150 and 100 m: it decreases with decreasing dx. On the other hand, the fraction of cores changes little with dx for dx ≤ 300 m (Fig. 14a). The water vapor mixing ratio q υ in the core is about 10% higher than that of the sounding and the averages over the area of developing cumulus, and it changes little with dx (Fig. 14b). Potential temperature also changes little with dx above the lifting condensation level (Fig. S2).
Horizontal resolution dependence of (a) fraction of cloud area (dashed lines) and cumulus cores (thick lines) in the area of developing cumulus and spatiotemporally averaged mixing ratio of (b) water vapor over the cumulus cores (thick lines) and the entire area of developing cumulus (dashed lines), (c) hydrometeors, and (d) velocity of the cumulus cores in the x direction, U c . The black lines in (b) and (d) are those of the sounding displayed in Fig. 3.
Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-19-0150.1
The mixing ratio of hydrometeors is larger for smaller dx, particularly above the freezing level (z ~ 5 km; Fig. 14c). The larger mixing ratio of hydrometeors appears to be associated with stronger w for finer dx above z = 4.5 km (Fig. 13a).
The peak of the accumulated precipitation tends to shift upstream as dx becomes coarser (Fig. 5): the peaks for dx = 100 m and dx = 1 km are about 25 km apart. Such a difference may be significant when the results are used as an input to a hydrological simulation to forecast flooding. Several possible factors that could result in the dependence of zonal location of the QLCS on dx may be considered.
First, if a parcel in the cumulus cloud cores at the lower heights ascends while carrying its horizontal momentum in an environment with strong vertical shear (though it is more or less diffused by entrainment and dynamic pressure perturbations as the height increases), horizontal velocity of the cores at the middle heights may be slower than the surroundings. Kato (2006) has suggested that this process gives one reason for the convective system being slow moving. Previous studies (Lebo and Morrison 2015; Zhang et al. 2016; Verrelle et al. 2017) have suggested that the entrainment in numerical models may be underestimated for coarser dx. In fact, Fig. 14d shows that velocity in the x direction of the cumulus cores, U c , for experiments with coarser dx (dx = 1 km and 500 m) is slightly slower above z ~ 5 km than that for experiments with finer dx. Owing to the faster U c at middle heights with finer dx, the area of heavy precipitation may shift slightly downstream. However, the difference of U c between various dx at middle heights is not large enough to explain the shift of ~25 km.
Second, the resolution could also change the vertical profiles of converging winds and associated thermodynamic variables such as potential temperature and moisture through boundary layer processes (e.g., Fig. S3). These differences could affect the location of the QLCS.
Third, the cold pool and associated surface divergence could also affect the zonal location of the QLCS. In fact, the location of the cold pool moves downstream as dx is decreased (Fig. 15). Since the QLCS is accompanied simultaneously by the cold pool, however, it seems difficult to clarify the cause and effect relationship between the QLCS and the cold pool. A more detailed discussion about the effects of the cold pool is given in section 4c
Potential temperature profiles along the x direction for experiments with various resolution. These profiles are spatiotemporally averaged between t = 6 and 12 h and for 67.5 < y < 90 km at z = 200 m along x direction.
Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-19-0150.1
b. Mechanism for maintenance of the convective system
In the present idealized experiments, an intrinsic mechanism to trigger the convective system is the surface temperature heterogeneity due to the land–sea contrast. We made experiments in which topography (an isolated mountain) is included or a thermal bubble is forced initially without the land–sea contrast. The resulting convective system, however, did not show a stationary behavior and exhibited much smaller maximum accumulated precipitation (not shown). In addition to the land–sea contrast, however, surface pressure depression and vertical shear also appear to contribute to the organization of the system, which will be described in the following subsections.
1) Intensification of convergence due to surface pressure depression: Feedback from the convective system
A sensitivity test was conducted to examine the importance of the latent heating by excluding the moist processes. This dry experiment does produce a line-shaped region of convergence over the land (Fig. 16), similar to that in the spinup stage of the control experiment (Fig. 7c). However, the horizontal wind speed remains less than ~5 m s−1 at largest. In the control experiment, the maximum convergence of horizontal winds at z = 100 m is larger than ~300 × 10−4 s−1 in the spinup stage (Fig. 7c) and ~700 × 10−4 s−1 when the QLCS is settled (Fig. 7g), while that in the dry experiment reaches only ~120 × 10−4 s−1. The minimum surface pressure in the dry experiment is always higher than in the control experiment (not shown), showing that latent heating causes lower surface pressure depression and significantly enhances convergence near the surface. Thus, a positive feedback from the preceding cumulus clouds occurs in the present QLCS.
Horizontal wind vector (arrows) and its magnitude (shading) at z = 10 m in the dry experiment at t = 7.5 h.
Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-19-0150.1
2) Effects of vertical shear
The cumulus clouds with strong updrafts in their cores have a significant downshear tilt (Fig. 11). If an updraft occurs in an environment with a linear vertical shear, the dynamic pressure perturbation may decelerate the tilted updraft at the lower levels in the upshear side (Rotunno and Klemp 1982; Bluestein 2013). In spite of the opposing effect of the shear, however, buoyancy generated by latent heating enables the updrafts to penetrate into the upper troposphere.
We have conducted four sensitivity experiments with dx = 150 m to examine the importance of vertical shear. In three experiments, the environmental zonal wind speed U above z = 1 km is changed to 1.25, 0.5, or 0.1 times that in the control experiment; these experiments are referred to as experiments 1.25U, 0.5U, or 0.1U, respectively. Another experiment referred to as experiment 0V has no meridional wind component V while the zonal wind component U is the same as the control (i.e., the vertical shear is unidirectional).
The maximum accumulated rainfall after t = 6 h for experiment 1.25U is larger than that for experiment 1U (Fig. 17a), while the average precipitation is almost the same (Fig. 17b). In experiment 1.25U, the maximum accumulated precipitation occurs about ~20 km downstream of that for experiment 1U, and the area with large precipitation is more elongated in the x direction (Figs. 18a,b). Precipitation is weaker for the experiments with weaker vertical shear (experiments 0.5U and 0.1U; Figs. 17c,d).
As in Fig. 6, but showing results for experiments 1.25U, 1U, 0.5U, 0.1U, 0V, and NOEVP, where experiment 1U is the same as the control experiment, but with dx = 150 m.
Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-19-0150.1
(a) As in Fig. 5b (experiment 1U), but showing results for experiments (b) 1.25U, (c) 0.5U, (d) 0.1U, (e) 0V, and (f) a sensitivity experiment in which the evaporative cooling is excluded (experiment NOEVP).
Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-19-0150.1
The organized QLCS as seen in Fig. 8 is not generated for experiment 0.5U (Fig. 18c; precipitation is likely to occur rather near the coastlines) nor for experiment 0.1U (Fig. 18d). The precipitation rather looks similar to that occurs in the spinup stage of the control experiments (Fig. 7k). The maximum accumulated precipitation for experiment 0.1U is as small as in the experiments with dx = 2 km or 1.5 km (Fig. 6b) in which an organized convective system does not develop.
Convergence of sea-breeze fronts is known to trigger daytime thunderstorms over peninsulas (e.g., Nicholls et al. 1991; Warren et al. 2014; Comin et al. 2015), elliptical islands (e.g., Crook 2001), and coastal plains (e.g., Saito et al. 2018). In these cases, the vertical shear parallel to convergence lines was not considered (Nicholls et al. 1991), weak (Warren et al. 2014; Comin et al. 2015; Saito et al. 2018), or not important (Crook 2001). In the present experiments, the vertical shear plays an important role in organizing the QLCS, although a precipitation system along converged fronts as similar to those in the previous studies occurs at the spinup stage (Fig. 7k). Especially in experiment 0.1U with weak vertical shear, a large domain-averaged precipitation occurs at the early stage (Fig. 17b).
The sounding employed in the present study is accompanied by large vertical shear in U over the entire troposphere (Fig. S1a), and weak vertical shear in V (Fig. S1b). Therefore, its hodograph (not shown) has weak veering. Experiment 0V without the veering attains even larger precipitation than experiment 1U (Fig. 17a) and forms a back-building system, which is more symmetric in the y direction (Fig. 18e). This fact suggests that the veering wind, meridional shear, and associated helicity are not necessarily essential for organizing the present convective system.
Previous studies have pointed out that vertical shear contributes to organizing quasi-steady convective systems (e.g., Bluestein and Jain 1985; Rotunno et al. 1988; Fovell and Ogura 1989; Unuma and Takemi 2016). For squall lines, vertical shear can also play an important role but in a different way: the horizontal vorticity associated with the vertical shear causes erect updrafts when it balances with that baroclinically generated at the head of a gravity current extending from a cold pool [the Rotunno–Klemp–Weisman (RKW) theory; Rotunno et al. 1988]. As will be shown in the following subsection, however, it is not the case for the present experiments in which a cold pool does not play an essential role. In fact, the RKW theory suggests that the deepest lifting occur in the downshear side, while in the present case the lifting occurs the upshear side.
c. Effect of evaporation and the resulting cold pool
A cold pool caused by preceding precipitation is generally thought to help the development of new cumulus clouds by causing convergence at its upstream boundaries. To examine the effect of the cold pool, an additional sensitivity experiment in which evaporative cooling is suppressed (experiment NOEVP) is conducted. No cold pool is formed in this sensitivity experiment.
Figures 17 and 18f show that a stationary QLCS similar to the one in experiment 1U (Fig. 18a) is formed even in the absence of evaporative cooling and hence without a cold pool. Thus, the cold pool is not essential for the formation of the present stationary QLCS. In experiment NOEVP, however, the area with heavy precipitation extends farther downstream, possibly because the convergence near the surface downstream of the precipitation area is not intervened by the cold pool. The total amount of precipitation is larger than that of experiment 1U (Fig. 17).
Although experiment NOEVP eventually forms a stationary QLCS similar to the one in Exp. 1U, its temporal evolution at the spinup stage is very different from that in the control experiment (Fig. S4): the initially developed zonally aligned convection does not dissipates in experiment NOEVP at around t = 5 h and precipitation does not become weak (Fig. 17b). This is because the divergent flow near the surface of the initial convection does not develop in the experiment NOEVP.
The tilts of updrafts as similar to Fig. 11a indeed occur in experiment NOEVP due to the vertical shear (not shown). In the previous subsection, experiment 1.25U attains the even stronger precipitation. In experiment 1.25U, one can expect a weaker influence of the cold pool for the back-building system because the precipitation that causes the cold pool appears to occur further downstream (Bresson et al. 2012).
As was mentioned in section 4a, the location of the cold pool also varies with dx: the cold pool extends more upstream for coarser dx, although the temperature deficits downstream are almost the same (Fig. 15). However, this difference of the location seems to be merely a result of the difference in the location of the QLCS, since a similar difference of the QLCS with respect to the resolution is found even without an evaporative cooling. We have conducted an experiment that is the same as experiment NOEVP, but with dx = 500 m, and found that a QLCS forms more upstream as an experiment same as the control experiment, but with dx = 500 (Fig. S5).
The above results show that the cold pool is not essential for generation of the present QLCS. Since the initial convection at the spinup stage of the control experiments dissipates due to evaporative cooling and resulting divergence in the cold pool, the cold pool may be said to have a detrimental effect on the QLCS in the present environment.
5. Conclusions
The record-breaking precipitation concentrated in a small area in the KH2017 event was caused by a back-building QLCS. The present idealized experiments with a simple land–sea configuration reproduce a back-building QLCS similar to the observed one. The stationary QLCS becomes established about 6 h after the experiments are started, and cumulus clouds are repeatedly triggered where the sea breezes converge. The peak of the precipitation is located about 40 km downstream of the leading edge of the QLCS, and accumulated precipitation at this point increases linearly at a rate of ~100 mm h−1.
The present experiments demonstrate that a feedback from preceding cumulus clouds does exist. They generate a mesoscale pressure depression near the surface, which strengthens the near-surface convergence to the system. The sensitivity experiments show that the present convective system can develop even in the absence of topography, a cold pool, and larger-scale forcing, although these are in general thought to be essential for maintaining a back-building system. The present situation that the sea-breeze fronts and vertical shear nearly parallel to the fronts play important roles in the formation of the back-building QLCS may look similar to Houston and Wilhelmson (2012) in which an airmass boundary and vertical shear roughly parallel to the boundary played important roles. In their QLCS, however, the cold pool played an important role possibly because of the weak vertical shear environment. Figure 19 shows a schematic of the present quasi-stationary QLCS. Note that, though a weak cold pool is formed, it does not contribute to maintaining the QLCS.
Schematic picture of the present back-building convective system.
Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-19-0150.1
Due to the stationarity of the present QLCS, robust statistics of physical quantities in the QLCS may be obtained by taking temporal averages after the system is established. For example, investigating the statistics of turbulence, entrainment, detrainment, and so on in the fine resolution experiment would be useful for developing parameterizations for coarser resolution as has been done for a convective system by Verrelle et al. (2017). The present framework of the idealized experiments would enable investigation of the various processes involved in extreme phenomena. In the real world, however, a QLCS may dissipate or more rapidly develop owing to various factors such as diurnal variation or changes in synoptic conditions, 6 which are not considered in the present idealized experiments.
The present experiments show that the horizontal resolution dx has to be less than 1 km in order to reproduce the convective system: it appears that the effective resolution of the numerical model needs to be sufficiently fine to resolve each cumulus cloud. Although accumulated precipitation and distributions of hydrometeors almost converge at horizontal resolution finer than 300 m, the fractions of cloud areas do not converge even if dx is decreased to 100 m. Even for such fine dx, the location of the maximum precipitation can depend on dx. Furthermore, parameterizations of physical processes such as turbulence and cloud microphysics have room for improvements, which can more or less alter the simulation results. Therefore, uncertainties still remain in numerically predicting the precise location of extreme rainfall.
Acknowledgments
We thank Drs. Hiromu Seko and Wataru Mashiko for their advice and three anonymous reviewers for their helpful comments. This work was supported by JSPS KAKENHI Grants 19K03967 and 19H00815, by Advancement of Meteorological and Global Environmental Predictions Utilizing Observational Big Data of the Social and Scientific Priority Issues (Theme 4) to be tackled by using the Post K Computer of the FLAGSHIP2020 Project, and by Program for Promoting Researches on the Supercomputer Fugaku (Large Ensemble Atmospheric and Environmental Prediction for Disaster Prevention and Mitigation).
APPENDIX
Sensitivities to Initial Sounding
We have conducted additional experiments to confirm that the peculiarities in the sounding (the moist absolutely unstable layer and low dewpoint temperature at the lowest level) are insignificant for the present results. One experiment employs a profile for which relative humidity at each height is reduced to be less than 95% to eliminate the moist absolutely unstable layer (experiment No Sat.; Fig. A1a). To address the second point, another experiment in which the mixing ratio at the lowest level is set to be equal to the second lowest level (experiment 1st Layer Mod.; experiment A1b) is performed. These changes turn out to have little impact on the precipitation (Fig. A1c), and the stationary QLCS does form for each experiment.
Skew T–logp plots of sounding for experiments (a) No Sat. and (b) 1st Layer Mod., and (c) a time series of the maximum point accumulated precipitation for each experiment.
Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-19-0150.1
In the control experiment, we have examined vertical profiles in the area right upstream of the cumulus developing area (Fig. A2). Both of the moist absolutely unstable layer and low dewpoint temperature at the bottom are absent. These facts also suggest that the peculiarities do not directly influence the present results. The moist absolutely unstable layer disappears mainly due to adiabatic heating accompanied by weak downdrafts that prevail in the environment of the QLCS, but not due to convective mixing.
As in Fig. 3, but for a sounding averaged over the area just upstream of the cumulus developing area (56.25 < x < 75 km, 67.5 < y < 90 km) in the control experiment.
Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-19-0150.1
One may argue that the present sounding (Fig. 3) is significantly affected by the deep convection having developed in the region. We conducted additional sensitivity experiments which employ sounding before the occurrence of the QLCS in KH2017 event. It turns out that a similar QLCS develops in idealized experiments with the sounding obtained at 0900 and 1200 JST (Fig. S6) which are not significantly different from that in Fig. 3.
With sounding obtained at 3 h earlier, 0600 JST (Fig. S6a), the QLCS does not form in the idealized experiment, although the lower layer is still very humid. The sensitivity on the sounding is an interesting subject for future studies.
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Although the tropical cyclone 201703, Nanmadol, had passed through the region on 4 July, it had moved well off to the east and did not affect the rainstorm.
One may concern peculiarities of the sounding such as the moist absolutely unstable layer (cf. Bryan and Fritsch 2000) between 900 and 700 hPa and the significantly low dewpoint temperature at the lowest level, where the mixing ratio of the lowest level is lower than that of the second lowest level. However, these peculiarities disappear right upstream of the QLCS, so that they little affect the present results (see also appendix).
The sponge layer is used to adjust U, V, potential temperature, and water vapor mixing ratio of the sounding by the Rayleigh damping in order to prevent reflections of gravity waves.
We choose θ e to plot in Figs. 10 and 11b because it exhibits the best contrast between the inside and outside of the updrafts. The value of θ e indeed correlates well with larger w or mixing ratio of hydrometeors q w at each location, but w and q w vary considerably in space.
The composite reflectivity is based on observations by operational radars of JMA. If an area is covered by multiple radars, the maximum reflectivity is chosen.
In the KH2017 event, in fact, an upper-level short trough accompanying subsynoptic ascent may have affected the development of the QLCS.