Representative Height of the Low-Level Water Vapor Field for Examining the Initiation of Moist Convection Leading to Heavy Rainfall in East Asia

This study investigated the representative height of low-level water vapor field that can be used to examine the occurrence possibility of heavy rainfall in East Asia. First, cloud base heights (CBHs) of moist convection were statistically examined by performing simulations with a 1-km-resolution numerical model during April–August 2008, with a focus on Kyushu and Shikoku Islands, western Japan. CBHs of moist convection with strong updrafts were simulated mainly around 500 and 300 m heights above sea level over land and over the ocean, respectively. This result indicates that low-level humid air below a height of 500 m is very important for the initiation of strong moist convection. Moreover, the equivalent potential temperature θ e at the CBHs was examined to clarify θ e values of lifted air parcels initiating cumulonimbus development. This result showed that, below the CBHs, θ e was usually around 355 K. Given these results for the CBHs, θ e at 500 m height from 10-km-resolution objective analysis data was statistically compared with θ e at various heights and pressure levels over the ocean south of 35°N in East Asia during June–September 2008. These comparisons showed that analyses at the 850-hPa level could not represent the low-level water vapor field, while the θ e field at 850 hPa in the Baiu season was strongly influenced by convective activity over the Baiu frontal zone. The θ e field at 925 hPa also could not adequately represent the low-level water vapor field, but the difference in θ e between heights of 250 and 500 m was very small. Because high θ e layers must have some thickness, data at 500 m height can be considered representative of the low-level water vapor field in analyses examining the initiation of moist convection leading to heavy rainfall.


Introduction
Most heavy rainfall observed in East Asia, especially in the vicinity of the Japanese Islands, is caused by the inflow of low-level humid air from over the ocean (Kato and Goda 2001;Kato 2006;Tsuguti and Kato 2014;Jeong et al. 2016).This humid air accumulates in the convective mixed layer, which develops over the ocean at a height close to 1 km.One of the major processes driving the development of the mixed layer over the ocean is water vapor buoyancy.Over the North Pacific Ocean, where subsidence is predominant owing to the presence of North Pacific high-pressure systems, atmospheric layers above the 800-hPa level are notably dry.As a result, there is a large vertical difference in the mixing ratio of water vapor q v , and this difference frequently exceeds 10 g kg −1 at low levels.For example, a time-height cross section of observed q v in the 2015 warm season over Minamidaitojima (Figs. 1,2a), a small island (25°50′N, 131°14′E; area 30.57km 2 ) in the Pacific Ocean south of Kyushu, shows that q v frequently exceeded 22 g kg −1 near the surface and was less than 12 g kg −1 at a height of about 1 km; thus, the vertical difference in q v often exceeded 10 g kg −1 .Moreover, a convective mixed layer was roughly estimated from the virtual potential temperature (see the Appendix) to have developed above 500 m height.
A number of numerical studies have successfully reproduced many heavy rainfall events in the vicinity of the Japanese Islands (e.g., Watanabe and Ogura 1987;Nagata and Ogura 1991;Kato and Goda 2001;Kato 2006;Kawabata et al. 2011;Tsuguti and Kato 2014;Hirota et al. 2016;Jeong et al. 2016).Some numerical studies (Kato and Goda 2001;Kato 2006;Tsuguti and Kato 2014) have shown that cumulonimbi, which cause heavy rainfall, form by the lifting of air parcels from the layer below 500 m height to above that height.Others (e.g., Hirota et al. 2016;Jeong et al. 2016) have examined the effect of vertically integrated water vapor transport on the formation of heavy rainfall.However, researchers and forecasters in operational meteorological centers often use the water vapor field at the 850-or 925-hPa level to characterize environmental conditions when estimating the possibility of heavy rainfall occurrence (e.g., Ninomiya et al. 1984;Nagata and Ogura 1991).For example, the Showalter Stability Index, which represents conditional instability, is calculated by lifting an air parcel from the 850-hPa level and comparing its temperature with that of ambient atmosphere at 500 hPa.In addition, the forecasters of the Japan Meteorological Agency (JMA) usually characterize the Baiu front as a stationary front in a region with a large meridional gradient of equivalent potential temperature θ e at 850 hPa.The Baiu season, when the Baiu front often appears around the Japanese Islands, usually lasts from early June to late July.During the Baiu season, large amounts of rainfall are observed in the Japanese Islands, and heavy rainfall events frequently occur.
One of the most important indices for examining the possibility of heavy rainfall occurrence is the θ e of the lifted air parcels that initiate cumulonimbi because the conditional instability necessary for the initiation of moist convection is estimated from the θ e of lifted air parcels and the vertical profile of saturated θ e in the ambient atmosphere.Because θ e can be treated as a conserved quantity even in the moist atmosphere when no mixing with ambient air occurs, the θ e of lifted air parcels initiating moist convection can be estimated by examining θ e values at the cloud base height (CBH).
The goal of this study is to clarify the low-level water vapor field height that can be considered representative for examining the initiation of moist convection, which is the major precursor to heavy rainfall in East Asia.First, to find the originating height of a lifted low-level humid air parcel initiating cumulonimbus development, the CBH appearance frequency of cumulonimbi is statistically examined using the simulation results of a cloud-resolving model with a horizontal resolution of 1 km (1km-CRM; detailed in Section 2).Second, the characteristic features of the water vapor fields at the 925-and 850-hPa levels over the ocean during the warm season are statistically examined and compared with those at 500 m height by the JMA mesoscale objective analysis data with a horizontal resolution of 10 km (JMA-MA; JMA 2007).
This paper is organized as follows.Section 2 describes the data and numerical models used in this study as well as the method used to detect CBHs.In Section 3, statistical results for CBHs simulated by the 1km-CRM are presented, and θ e at the CBHs is examined to clarify θ e values of lifted air parcels initiating cumulonimbi.In Section 4, water vapor fields at different vertical height and pressure levels (i.e., at 200 m height and the 925-and 850-hPa levels) are statistically compared with the water vapor field at 500 m height.In Section 5, the characteristic features of the 850-hPa θ e field during the Baiu season are examined.The last section includes a summary and discussion.

Data, numerical models, and the CBH detection method
In this study, two types of the JMA-MA, produced operationally every 3 hours from 00 UTC (eight times a day), are used to examine the low-level water vapor field and to produce the initial and boundary conditions for the two numerical models described below.The first type is coordinated with 20 vertical pressure levels (1000, 950, 925, 900, 850, 800, 700, 600, 500, 400, 300, 250, 200, 150, 100, 70, 50, 30, 20, and 10 hPa), and the second type has 40 hybrid sigma-pressure (σ-p) vertical levels, given as a function of surface pressure.The vertical resolution of the lowest level is about 5 hPa.The height fields (relative to sea level) examined in this study (i.e., 250 and 500 m) are interpolated from JMA-MA with 40 hybrid σ-p vertical levels.
The JMA-MA domain (3610 km × 2890 km) covers a large part of East Asia (Fig. 2a); however, the analyses in Sections 4 and 5 consider only the part of the domain over the ocean south of 35°N, which includes part of the western North Pacific Ocean and the East China Sea.This area was selected because the humid air leading to heavy rainfall targeted in this study flows mainly from the warm ocean to the Japanese Islands.Upper-air sounding data observed at 11 stations (triangles in Fig. 2a) during the warm seasons of 1989 -2016 were also used to characterize statistically the water vapor field during the 2008 warm season (June-September) examined using the JMA-MA.The 2008 warm season was selected for this study because heavy rainfall was observed more frequently in 2008 than in other recent years.
This study used two nested models: the JMA nonhydrostatic model (JMANHM; Saito et al. 2006) with a horizontal resolution of 5 km (5km-NHM) and a domain (bold rectangle in Fig. 2a; 2500 km × 2000 km) covering most of the Japanese Islands and the Korean Peninsula, and the 1km-CRM, nested within the 5km-NHM, with a domain (Fig. 2b; 600 km × 500 km) covering the area around Kyushu and Shikoku Islands.Both models use 50 vertical levels with variable thicknesses, from 40 m near the surface to 886 m at the top of the domain (height 21.8 km), and the same dynamical and physical processes, except those for precipitation.For precipitation, the 1km-CRM uses only a bulk-type cloud microphysics scheme (Murakami 1990), whereas the 5km-NHM additionally uses the Kain-Fritsch convection parameterization scheme (Kain 2004).The bulk-type microphysics scheme predicts both the mixing ratio and number density of ice hydrometeors (i.e., cloud ice, snow, and graupel) but only the mixing ratio of liquid hydrometeors (i.e., cloud water and rain).See Saito et al. (2006Saito et al. ( , 2007) ) for details of other model specifications.
The initial and 3-hourly linearly interpolated boundary conditions of the 5km-NHM were obtained from the JMA-MA with hybrid 40 σ-p vertical levels at initial times of 00, 06, 12, and 18 UTC every day.The forecast time is 12 hours.The 1km-CRM was oneway nested within the hourly output of the 3-hourly forecast of the 5km-NHM.This study used the hourly output of the 1km-CRM between the 4-hourly and 9-hourly forecasts; previous forecasts were not used for spin-up data.The statistical period of each model included 612 numerical integrations (= 153 days × 4) covering the 2008 warm season (April-August).The warm seasons of 2007 and 2009 were also examined.Note that the warm season was defi ned differently between the low-level water vapor fi eld (defi ned as June-September) and CBH examinations.The period of the CBH examinations includes late spring (i.e., April and May) because heavy rainfall can occur around the Japanese Islands during those months and because low-level θ e values change greatly between late spring and summer.However, statistical results on the CBHs changed little when late spring was excluded from the statistical period.
The method used to detect CBHs from the 1km-CRM simulations is schematically displayed in Fig. 3. Previous studies (e.g., Auer and Sand 1966;LeMone and Zipser 1980;Mecikalski et al. 2016) have shown that, in developed moist convective cells observed by airplanes and satellites, updrafts exceed 4.0 m s −1 .In this study, however, so that strong moist convection could be compared with weak moist convection, moist convection was judged to exist when simulated updrafts exceeded 1.0 m s −1 in each vertical core.It should be noted that stronger updrafts tend to produce stronger rainfall, owing to larger vertical transport of water vapor, but updraft speed does not necessarily correspond to rainfall intensity.
Because the vertical profi le of moist convection is often slanted, the CBH was detected by searching upward in the three-dimensional domain from the surface under the grid point with the maximum updraft in each vertical core, using a threshold value of simulated specifi c humidity of cloud water equal to 0.1 g kg −1 .The horizontal displacement between the grid with the maximum updraft (D in Fig. 3) and that with the detected CBH could be up to 33 % of the vertical distance between the two grids (H in Fig. 3).Thus, the CBH was often detected in a different vertical core from that with the maximum updraft, as shown in Fig. 3.

Comparison with observed rainfall
The ability of the 1km-CRM to reproduce observed rainfall during April-August 2008 was confi rmed by comparing the simulated rainfall distribution with the distribution of 5-month accumulated radar/rain-gaugeanalyzed (R-A) precipitation (horizontal resolution of 1 km), which is produced every 30 min by JMA (Nagata 2011) (Fig. 4).R-A precipitation is estimated hourly from radar observations and calibrated by rain gauge observations.In this study, the hourly data were integrated over April-August.Large R-A precipitation amounts were observed in the mountainous areas of Kyushu Island and in the coastal regions on the Pacifi c Ocean side of Shikoku Island.Over the Pacifi c Ocean south of Shikoku Island, there was a clear discontinuity because, over areas covered by two radars, the maximum value is chosen for the R-A dataset, and the radar-estimated precipitation cannot be calibrated by rain gauge observations.As a result, the accuracy of R-A precipitation over the ocean is not high.
The characteristic features of the simulated 5-month accumulated rainfall distribution (Fig. 4b) mostly agree with those of the R-A precipitation distribution (Fig. 4a), although simulated precipitation amounts were slightly underestimated.The simulated hourly rainfall distribution also showed good agreement with the observed data, though the model sometimes failed to predict a precipitation event (not shown).
The accumulated probability distribution frequency (PDF) of hourly accumulated precipitation amounts simulated by the 1km-CRM was also compared with rain gauge observations of the JMA Automated Meteorological Data Acquisition System (AMeDAS).The 1km-CRM model domain (Fig. 2b) includes 317 rain gauge observation sites.Hourly rainfall amounts of less than 0.5 mm simulated by the 1km-CRM were disregarded (treated the same as no rain) because the minimum unit of AMeDAS observations is 0.5 mm.PDFs simulated by the 1km-CRM at the 317 grid points nearest AMeDAS sites (thin line in Fig. 5) slightly overestimated the PDFs of the AMeDAS observations (bold line), and when all terrestrial grid points were used in the simulation, the result slightly

Moist convection
Cloud water = 0.1 g kg -1 Grid with maximum updraft (Wmax) exceeding 1 m s -1 in each vertical core

< 33%
Cloud base is detected for moist convection slanting by 33 % in vertical.underestimated AMeDAS precipitation amounts between 10 and 60 mm (broken line).Because these discrepancies are small, the 1km-CRM simulation results were considered adequate for examining the CBHs of moist convection.

Cloud base heights of moist convection
Some numerical studies (e.g., Kato and Goda 2001;Kato 2006) have reported that cumulonimbi causing heavy rainfall form when air parcels are lifted from a layer below 500 m height to above that height; however, the originating height of low-level humid air parcels lifted during the initiation of cumulonimbus development has never been examined statistically.Because the height of the lifted low-level air parcel is necessarily lower than the lifting condensation level (i.e., the CBH), the CBH appearance frequency of cumulonimbi in the area around Kyushu and Shikoku Islands (Fig. 2b) was statistically examined using hourly output of the 1km-CRM during April-August 2008 to clarify the height from which most low-level air parcels that initiated cumulonimbi were lifted.It should be noted that heights over land examined in this study are relative to sea level.
First, the appearance frequency of maximum updrafts (W max ) exceeding 1.0 m s −1 in relation to height in vertical cores, simulated by the 1km-CRM, was examined over the ocean and over land (Fig. 6).Here, W max refers to maximum updrafts (m s −1 ) in vertical cores exceeding the values shown on the abscissa of Fig. 6.Over the ocean, the appearance frequency of W max exceeding 1.0 m s −1 was 1.50 %, and over land, it was 3.44 %.Over both the ocean and land, the appearance frequency of W max exceeding 10.0 m s −1 was more than two orders of magnitude lower than that of W max exceeding 1.0 m s −1 (bold curves in Fig. 6).This result means that few cumulonimbi with strong updrafts exceeding 10.0 m s −1 were simulated by the 1km-CRM.Moreover, the appearance frequency of W max ≥ 4.0 m s −1 was an order of magnitude lower than that of W max ≥ 1.0 m s −1 ; therefore, the features of W max 500 750 1000 1250 1500 2000 (mm/153d) ≥ 1.0 m s −1 roughly correspond to those of W max ranging from 1.0 to 3.0 m s −1 .Over the ocean, the height of the peak appearance frequency of W max (Fig. 6a) became higher as W max increased; for W max ≥ 1.0 m s −1 , the peak appearance frequency height was around 4 km, and for W max ≥ 10.0 m s −1 , it was around 7 km.
The trend was similar over land (Fig. 6b), although the peak appearance frequency height for W max ≥ 1.0 m s −1 was only ~2 km over land.This lower peak height may be due to terrain-forced updrafts.
Next, the upward cumulative appearance frequency of the CBHs from the surface was examined in relation to W max (Fig. 7).The CBHs tended to become lower as W max increased.This tendency was examined by focusing on a cumulative appearance frequency of 0.8 (CAF0.8),that is, the height below which 80 % of the CBHs are found.CAF0.8 was lower over the ocean than over land; for W max ≥ 1.0 m s −1 , it was about 1.75 km over the ocean and 1.9 km over land, whereas, for W max ≥ 10.0 m s −1 , it was around 500 m over the ocean and 700 m over land.Moreover, for W max ≥ 4.0 m s −1 , the most frequent appearance height of the CBHs (i.e., the region of closely spaced contours between 0.2 and 0.4 in Fig. 7) was around 300 m over the ocean and 500 m over land.These results indicate that most moist convection causing heavy rainfall was initiated by the lifting of air parcels from below a height of 500 m, particularly considering that most heavy rainfall is likely to be caused by moist convection associated with stronger updrafts.Finally, the monthly variation in the CBHs relative to W max was examined by focusing on the variation of CAF0.8 during April-August 2008 (Fig. 8).For W max < 3.0 m s −1 , the monthly variation in CAF0.8 could exceed 500 m; however, for W max ≥ 5.0 m s −1 , the monthly variation was small over both the ocean and land.Moreover, almost the same statistical results were obtained when the monthly variation during the warm seasons of 2007 and 2009 was examined (not shown).These results suggest that the low-level water vapor field below 500 m height is representative for examining the initiation of moist convection leading to heavy rainfall, particularly considering that the most frequent appearance height of the CBHs is 500 m over land when W max ≥ 4.0 m s −1 (Fig. 7b).

Equivalent potential temperature at cloud base heights
Because θ e of lifted air parcels is an index of the occurrence possibility of heavy rainfall (see Section 1), the distribution of the appearance frequency of θ e of lifted air parcels at the CBHs over the ocean and over land, simulated by the 1km-CRM during June-August 2008, was examined in relation to W max (Fig. 9).The temperature of the peak appearance frequency of CBH θ e became higher as W max increased; it was about 355 K over the ocean and 356 K over land for W max ≥ 10.0 m s −1 .However, the change in the peak temperature was small for W max ≥ 4.0 m s −1 (~1 K).This result indicates that θ e of around 355 K occurs most frequently below the CBHs when judging the low-level water vapor field for the initiation of moist convection leading to heavy rainfall over Kyushu and Shikoku Islands.
The monthly variation of the CBH θ e in the vicinity of the Japanese Islands strongly depends on that of sea surface temperature (SST), even over land, because most humid air initiating cumulonimbi flows from over the ocean.In April and May 2008, the temperature of the peak CBH θ e appearance frequency for W max ≥ 10.0 m s −1 was less than 340 and 350 K, respectively (not shown).This result indicates that the CBH θ e is strongly influenced by SST, and CBH θ e values of around 355 K are observed mainly during months with high SST (i.e., June-September in the study area of 1km-CRM).

Comparisons of water vapor fields among different vertical levels
To determine the most representative height of the low-level water vapor field for examining the initiation of moist convection leading to heavy rainfall, the water vapor fields at 850, 925, and 950 hPa and at 250 m height, depicted from the JMA-MA, were statistically compared with the water vapor field at 500 m height during June-September 2008. Figure 10 shows the appearance frequency distribution of θ e at these pressure levels and heights over the ocean south of 35°N in the JMA-MA domain (Fig. 2a).At low heights and pressure levels, the fact that θ e tended to decrease as height increased indicates that the low-level atmosphere was fundamentally in a state of convective instability (∂θ e /∂z < 0).At 850 hPa (~1500 m), θ e with the maximum appearance frequency was about 10 K less than θ e with the peak appearance frequency at 500 m height or 950 hPa.Moreover, the θ e variance became larger as height increased.It is notable that the θ e appearance frequency distribution at 500 m height is very close to that at 950 hPa because the 950-hPa surface is distributed at a height of around 540 m with a standard deviation of 30.8 m.This deviation is not small relative to the absolute height of the 950-hPa surface (~ 540 m) because the 950-hPa level is sometimes absent around developed depressions and typhoons.Therefore, the absolute height of 500 m above sea level was adopted for statistical examination in this study.
Next, the θ e appearance frequency distributions at 250 m height and at 850 and 925 hPa were compared with the θ e appearance frequency distribution at 500 m height (Fig. 11).In particular, to judge the low-level water vapor field for examining the initiation of moist convection leading to heavy rainfall, the appearance frequency of θ e of 355 K at 500 m height was compared with the appearance frequencies of θ e at the other height and pressure levels because, as shown in Section 3.3, θ e of 355 K was distributed most frequently below the CBHs.The 850-hPa θ e with an appearance frequency exceeding 0.2 of the maximum value (within the contour labeled 0.2 in Fig. 11a) was distributed from 338 to 354 K (along the ordinate) when the 500-m θ e was 355 K (on the abscissa).This large variance, which exceeds 15 K, indicates that θ e at 850 hPa was not necessarily high, even when the 500-m θ e was high.Therefore, the 850-hPa level was not representative of the low-level water vapor field for examining the initiation of moist convection leading to heavy rainfall.
The variance of the 925-hPa θ e appearance frequen- Appearance frequency cy distribution at 355 K on the abscissa (Fig. 11b) was considerably smaller than that of the 850-hPa θ e distribution (Fig. 11a), and the 925-hPa θ e was relatively high when the 500-m θ e was high.However, because the appearance frequency of the 925-hPa θ e exceeding 0.2 relative to the maximum value varied from 349 to 355 K at 355 K on the abscissa, the 925-hPa level cannot adequately represent the low-level water vapor field.In contrast, the variance of the appearance frequency distribution of the 250-m θ e at 355 K on the abscissa (Fig. 11c) was very small.These results indicate that it is not necessary to use the low height of 250 m as the representative height for examining the low-level water vapor field; the height of 500 m can adequately represent the low-level water vapor field.Moreover, Kato and Goda (2001) and Kato (2006) showed that the thickness of the high-θ e layer must be at least 500 m for heavy rainfall to occur.Taken together, these results suggest that it is appropriate to use data from 500 m as representative of the low-level water vapor field in analyses examining the initiation of moist convection leading to heavy rainfall.The characteristic features of the above comparisons were confirmed using upper-air sounding observations during the 25 warm seasons from 1989 to 2016 (the sounding station locations are shown in Fig. 2a).These observations were strongly influenced by atmospheric conditions over the ocean because all of the stations are near the coast or on small islands.Comparison of the θ e appearance frequency between 500 m height and 850 hPa (Fig. 12) showed that θ e with an appearance frequency exceeding 0.2 of the maximum value at 850 hPa ranged from 338 to 352 K when the 500-m θ e was equal to 355 K.This variance is slightly smaller than that estimated from the JMA-MA for the 2008 warm season (Fig. 11a), but it is still too large for the data at 850 hPa to be considered representative of the low-level water vapor field.The results of a comparison of the θ e appearance frequency between 500 m height and 925 hPa (not shown) were also almost the same as those obtained by the analysis based on the JMA-MA (Fig. 11b).

Comparison over the Baiu frontal zone
The Baiu front is usually identified by JMA forecasters by the presence of a large meridional θ e gradient at 850 hPa, as mentioned in Section 1.Thus, the analysis of the Baiu front is not made at the representative height of the low-level water vapor field for the initiation of moist convection that was determined in this study (i.e., 500 m height).In this section, the distribution of the θ e appearance frequency in regions with clouds was examined to clarify the relationship between θ e at 500 m height and at 850 hPa in the Baiu frontal zone.Regions with clouds were detected by Multi-functional Transport Satellite (MTSAT) as regions where brightness temperatures of less than 270 K were observed; the 270 K threshold was selected so that developed moist convective cells with a top higher than 500 hPa and accompanying cirrus clouds would be detected.It should be noted that, around the Baiu frontal zone, the temperature of 270 K mostly corresponds to the temperature at 500 hPa.
The cloud appearance frequency, detected by a brightness temperature of less than 270 K during June-September 2008 around the Japanese Islands, was 30 -40 % (Fig. 13a), but in June 2008, during the Baiu season (Fig. 13b), the cloud appearance frequency exceeded 70 % at around latitude 32°N, which corresponds to the Baiu frontal zone.This high frequency reflects the very frequent occurrence of convective activity in the Baiu frontal zone.
Comparison of the θ e appearance frequency between 500 m height and 850 hPa in regions with and without clouds during June-September 2008, based on the analysis with JMA-MA (Fig. 14), showed that the variance of the 850-hPa θ e where θ e at 500 m was equal to 355 K was large in regions both with and without clouds.However, in regions with clouds, a relatively high appearance frequency was observed in 850-hPa θ e , where the 850-hPa θ e was close to the 500-m θ e (around the dotted line in Fig. 14a), whereas this was not the case in regions without clouds (Fig. 14b).
Moreover, in regions with clouds during the Baiu season (June 2008), the high appearance frequency distributions where the 850-hPa θ e was equal to the 500-m θ e were more pronounced (Fig. 15).Regions where the 850-hPa θ e is close to the 500-m θ e are expected to have high convective activity because, where the vertical change of θ e is small, such as in the Baiu frontal zone, little mixing with the ambient atmosphere occurs (Kato et al. 2003); thus, θ e is mostly conserved in updrafts where moist convection is occurring.These results indicate that the high 850-hPa θ e over the Baiu frontal zone was mainly caused by convective activity; thus, the 850-hPa θ e field is not appropriate to use as a standard reference for the initiation of convective activity.These characteristic features of the 850-hPa θ e over the Baiu frontal zone were demonstrated by a heavy rainfall event that occurred during 19 -21 June 2008 on Kyushu Island.Around the Baiu frontal zone, convective activity produces a humid region, called a "moist tongue", in the middle layers of the atmosphere.In the Baiu season, a moist tongue extending from the Asian continent and the East China Sea to the Japanese Islands can usually be recognized between 700 and 500 hPa (Kato et al. 2003).Therefore, the presence of this moist tongue was examined next.
During 19 -21 June 2008, a cloud band extended over the Baiu frontal zone from the Chinese coast across the Japanese Islands (Fig. 16a), and in the area corresponding to the cloud band, the 700-hPa relative humidity (Fig. 16b) was higher than it was in surrounding areas.Over Kyushu Island, in particular, it exceeded 80 % as a result of convective activity.This high humidity zone is the moist tongue.The 500-m θ e distribution (Fig. 16c) shows that southwesterlies with θ e exceeding 345 K were blowing from the East China Sea to Kyushu Island.This high θ e inflow caused heavy rainfall on Kyushu Island.In addition, an 850-hPa θ e exceeding 345 K was observed mainly around Kyushu Island (Fig. 16d), possibly as a result of upward transport by convective activity.At the 850-hPa level, moreover, westerlies were dominant in the area corresponding to the Baiu frontal zone, and a high-θ e region extended from the Asian continent to the Japanese Islands; this high-θ e region did not correspond to the high-θ e inflow from the East China Sea observed at 500 m height.These characteristic features observed at the 850-hPa level are similar to those of the moist tongue produced by convective activity (Fig. 16b).
In the Baiu season, the 850-hPa θ e distribution, but not the θ e distribution at 500 m height, is close to the distribution of the moist tongue, and the Baiu front is usually considered to correspond to the northern edge of the moist tongue, where the meridional θ e gradient is large.At the northern edge of the moist tongue, however, the meridional θ e gradient is almost the same as the gradient at 500 m height (Fig. 16c).Therefore, use of the 850-hPa θ e field to analyze the Baiu front does not raise any difficulties because the analysis around 355 K was most frequent below a height of 500 m when judging the initiation of moist convection leading to heavy rainfall.Comparisons of θ e at various heights and pressure levels showed that 850-hPa analyses, although they have been used by many forecasters and researchers, cannot represent the low-level water vapor field for examination of the initiation of moist convection leading to heavy rainfall.However, in the Baiu season, the 850-hPa θ e field is strongly influenced by convective activity over the Baiu frontal zone, and its distribution is close to that of the moist tongue found in the 700-hPa relative humidity field.θ e at 850 hPa has a variance exceeding 10 K for θ e equal to 355 K at 500 m height, which is dominantly associated with the development of moist convection in East Asia in summer.Similarly, the variance of the 925-hPa θ e field was too large for that field to be able to represent the low-level water vapor field.However, the difference in θ e between heights of 250 and 500 m was very small.Considering that high-θ e layers must have some thickness, these results suggest that data at 500 m can be used to represent low-level water vapor fields for examining the initiation of moist convection leading to heavy rainfall.
For this reason, the JMA has been operationally using 500-m-height data (Table 1) to forecast the occurrence of heavy rainfall since May 2011.These data are produced from 84-hour forecasts of the Global Spectral Model, 39-hour forecasts of the Meso-Scale Model, and 9-hour forecasts of the Local Forecast Model (JMA 2013).The data are also used in many studies performed by forecasters and other JMA staff members.Special treatments are applied in areas at elevations exceeding 300 m to produce 500-m-height data.Nakano et al. (2012) separately examined CBHs over coastal (elevation < 100 m) and mountainous areas (elevation > 300 m) using the same 1km-CRM output as was used in this study, and they showed that CBHs over mountainous areas are very low, whereas those over coastal areas agreed with the results of this study.On the basis of their results, the 500-m height data shown in Table 1, except pressure, are produced from data at 500 m above sea level for model terrain elevations lower than or equal to 300 m and from data at model terrain elevations +200 m when model terrain elevations are higher than 300 m.
The applicability of the 500 m representative height was also examined for a region over the ocean south of the Japanese Islands (analysis domain, 15 -25°N, 110 -130°E), including the South China Sea and the area surrounding Taiwan.As analysis data, 6-hourly available JMA global analysis data with a horizontal resolution of about 20 km (JMA 2013) were used instead of the JMA-MA.The JMA global analysis data yielded almost the same statistical results for the  analysis domain in this study (Fig. 2a) as were obtained with the JMA-MA (not shown).Comparison of the θ e appearance frequency distributions between 500 m height and 850 hPa (Fig. 17) showed little relation between them because the variation of the 500-m θ e is small in the regions south of the Japanese Islands.This result indicates that a 500-m-height analysis is important in areas of East Asia where southerlies transport the humid air that causes heavy rainfall.
In this study, the low-level water vapor field was statistically examined only at the representative height of 500 m.Heavy rainfall is, however, caused by the inflow of low-level humid air with some depth.Therefore, the depth of humid air should also be examined statistically by the future studies.Moreover, other factors that cause heavy rainfall (e.g., moist advection) should also be examined by future studies.

Appendix: Estimation of the developed height of the convective mixed layer due to water vapor buoyancy
The developed height of the convective mixed layer due to water vapor buoyancy can be roughly estimated from the virtual potential temperature θ v ≡ (1 + 0.61q v )θ, where q v is specific humidity and θ is the potential temperature.θ increases with altitude at a rate of 3.3 K km −1 in the International Standard Atmosphere with a lapse rate of 6.5°C km −1 , calculated as follows: where Γ d is the dry adiabatic lapse rate (9.8°C km −1 ) and z is height (km).Because q v is considerably smaller than 1, at constant specific humidity q vo , θ v increases with altitude at a rate nearly equal to that of θ (~3.3 K km −1 ).Hereafter, it is assumed that q v = q vo , but q v = q vo + ∆q v near the surface.The difference between θ v near the surface and that in the upper layer is roughly estimated to be 0.61∆q v θ sfc because θ does not change greatly with altitude.Here, θ sfc is θ near the surface.Water vapor buoyancy, therefore, develops a convective mixed layer up to a height of 0.61∆q v θ sfc / 3.3 K km −1 to remove the unstable layer (∂q v /∂z < 0) (Fig. A1).
In the case shown in Fig. 1, where q v ranged from more than 22 g kg −1 near the surface to less than 12 g kg −1 at a height of around 1 km, the vertical difference of q v often exceeded 10 g kg −1 .From this difference and θ = 300 K (the mean observed near-surface θ over Minamidaitojima), the depth of the convective mixed layer can be estimated to be about 550 m, which corresponds approximately to the most frequent top height of large q v in Fig. 1. creases with altitude at a rate of 3.3 K km −1 , and the thick line shows the vertical profile of virtual potential temperature θ v at constant spe- cific humidity q vo .θ sfc represents θ near the sur- face, and ∆q v is the difference between q v near the surface and that in the upper layer.

Fig. 1 .
Fig. 1.Time-height cross section of the mixing ratio of water vapor, observed four times a day over the Minamidaitojima upper-air sounding station, between 12 UTC 24 June and 06 UTC 09 July 2015.The location of Minamidaitojima is shown in Fig. 2a.

Fig. 3 .
Fig. 3. Schematic diagram of the detection of cloud base heights.

Fig. 6 .Fig. 7 .
Fig. 6.Height distributions (shading and contours) of the appearance frequency of maximum updrafts (W max ) (a) over the ocean and (b) over land during April-August 2008, simulated by the 1km-CRM.Heights are relative to sea level.W max refers to maximum updrafts (m s −1 ) in vertical cores exceeding the values shown on the abscissa.The frequencies shown on the left ordinate are normalized by the maximum frequency in each ordinate.The appearance frequencies of W max are also shown by the bold curves (right ordinate).The overall appearance frequency of W max > 1 m s −1 is shown at the bottom right of each panel.

Fig. 8 .
Fig. 8. Same as Fig. 7 but showing monthly variation during April-August 2008 at the height below which 80 % of the CBHs simulated by the 1km-CRM occur: (a) over the ocean and (b) over land.CBHs are relative to sea level.

Fig. 10 .Fig. 9 .
Fig. 10.Appearance frequency distributions of equivalent potential temperature (K) at heights of 250 and 500 m and at 950, 925, and 850 hPa over the ocean south of 35°N in the JMA-MA domain during June-September 2008, statistically analyzed from the JMA-MA.The amplitudes are normalized by the maximum value among the bins, which are partitioned at 0.5 K intervals.

Fig. 11 .
Fig. 11.Appearance frequency distributions of equivalent potential temperature (K) at (a) 850 hPa and (b) 925 hPa and (c) 250 m height relative to that at 500 m height.Statistics are based on the JMA-MA over the ocean south of 35°N during June-September 2008.The amplitudes are normalized by the maximum value among the bins, which are partitioned at 0.5 K intervals.

Fig. 12 .Fig. 13 .
Fig. 12. Same as Fig. 11a but based on upper-air sounding data for June-September during the 25 years from 1989 to 2016.Sounding station locations are shown in Fig. 2a.

Fig. 14 .Fig. 15 .
Fig. 14.Same as Fig. 11c but for regions (a) with and (b) without clouds, detected by a brightness temperature of less than 270 K observed by MTSAT.

Fig. 17 .
Fig. 17.Same as Fig. 11a but over the ocean in the region of 15-25°N and 110-130°E based on 6-hourly available JMA global analysis data with a horizontal resolution of about 20 km.

Fig
Fig. A1.Schematic diagram showing the estimation of the developed height of the convective mixed layer.The thin line shows the vertical profile of potential temperature θ, which in-creases with altitude at a rate of 3.3 K km −1 , and the thick line shows the vertical profile of virtual potential temperature θ v at constant spe- cific humidity q vo .θ sfc represents θ near the sur- face, and ∆q v is the difference between q v near the surface and that in the upper layer.

Table 1 .
Five-hundred-meter height data used operationally by JMA.All elements except pressure are derived from data at 500 m above sea level for model terrain elevations lower than or equal to 300 m and from data at