Figure 5 shows the observed and simulated vertical profiles of potential temperature, water vapor mass density, u-wind speed, and v-wind speed, which represent meteorological fields. Radiosonde data as observation data are averaged over observation sites in the domain and the simulation period, while simulated meteorological fields are averaged over the domain and the simulation period to obtain the profiles. Positive (negative) u-wind speed represents eastward (westward) wind speed, while positive (negative) v-wind speed represents northward (southward) wind speed. Comparisons between the observed profiles and the simulated counterparts show that overall differences between them are within ∼10 % of observed values. Hence, with confidence, it can be considered that the simulation of meteorological fields is performed reasonably well.

The area-mean precipitation rate at the surface smoothed over 3 h for the control run and the low-aerosol run is depicted by solid lines in Fig. 6. Dotted lines in Fig. 6 depict the precipitation rate for the repeated control run and low-aerosol run and will be discussed in Sect. 4.3. The simulated precipitation rate in the control run follows the observed counterpart well, which demonstrates that simulations perform reasonably well. Here, observed precipitation is obtained from measurement by rain gauges that are parts of the automatic weather station (AWS) at the surface. The AWS has a spatial resolution of ∼3 km. Also, the temporal evolution of the mean precipitation rate in the control run is very similar to that in the low-aerosol run. Associated with this similarity, the averaged cumulative precipitation over the domain at the last time step for the control run is 154.7 mm, which is just ∼3 % greater than 150.2 mm for the low-aerosol run.

Figure 7a, b, and c show frequency distributions of precipitation rates that are collected over all time steps and all grid points at the surface in the simulations. In Fig. 7, solid lines represent frequency distributions for the control run and the low-aerosol run, while dashed lines represent those for the repeated control run and low-aerosol run, which will be described in Sect. 4.3. Figure 7a, d, g, j, and m show frequency distributions only for the control run and the low-aerosol run. The other panels in Fig. 7 are supposed to show distributions only for the repeated control run and low aerosol run; however, for comparisons among the control run, the low-aerosol run, and the repeated runs, the control run and the low-aerosol run are displayed as well in those panels.

In Fig. 7a, b, and c, frequency distributions of observed precipitation rates that are interpolated to grid points and time steps in the simulations are also shown. The observed maximum precipitation rate is ∼180 mm h-1, which is similar to that in the control run. Also, observed frequency distribution is consistent with the simulated counterpart in the control run, although it appears that particularly for heavy precipitation with rates above 60 mm h-1, the simulated frequency is underestimated compared to the observed counterpart. The overall difference in frequency distributions between observation and the control run is much smaller than those between the control run and the low-aerosol run. Hence, we assume that the difference between observation and the control run is considered negligible compared to that among the runs. Based on this, when it comes to a discussion about the difference between the control run and the low-aerosol run, results in the control run can be assumed to be benchmark results against which the effect of decreases in the spatial variability and concentrations of aerosol on results in the low-aerosol run can be assessed.

While we do not see a large difference in cumulative precipitation between the control run (154.7 mm) and the low-aerosol run (150.2 mm), the frequency distribution of precipitation rates shows distinctively different features between the control run and the low-aerosol run (Fig. 7a). For precipitation with rates above 60 mm h-1 or heavy precipitation, cumulative frequency is ∼60 % higher for the control run. For certain ranges of precipitation rates above 60 mm h-1, there are increases in cumulative frequency by a factor of as much as ∼10 to ∼100. Moreover, for precipitation rates above 120 mm h-1, while there is the presence of precipitation in the control run, there is no precipitation in the low-aerosol run. Hence, we see that there are significant increases in the frequency of heavy precipitation in the control run compared to that in the low-aerosol run.

Figure 8 shows spatial distributions of precipitation rates at the surface. Purple lines in Fig. 8 mark the eastern part of where there is substantial transition from high-value aerosol concentrations to low-value aerosol concentrations as in Fig. 4. In this transition part, as explained in Fig. 4, there is reduction in aerosol concentrations by more than a factor of 10. Figure 8a and b show those distributions at 17:00 LST 27 July 2011 corresponding to initial stages of the precipitating system in the control run and the low-aerosol run, respectively. At 17:00 LST, there is a small area of precipitation around the northwest corner of the domain in both the control run and the low-aerosol run. This implies that a small cloud system develops around the northwest corner of the domain at 17:00 LST. The size of the system and its precipitation area grow with time and at 19:00 LST, the size is much larger (Fig. 8c and d). The maximum precipitation rate reaches ∼100 mm h-1 when time progresses to 19:00 LST (Fig. 7d). Heavy precipitation is concentrated in a specific area (surrounded by the green rectangle) in both of the runs (Fig. 8c and d). The green rectangle surrounds a specific area where more than 90 % of the events of heavy precipitation (over the domain) with rates above 60 mm h-1 occur in each of the runs at 19:00 LST. Since heavy precipitation starts to form around 19:00 LST, the green rectangle starts to be identified around 19:00 LST. Contrast in precipitation between the green rectangle and the other areas in the domain generates an inhomogeneity in the spatial distribution of precipitation. The location of the specific area in the control run is consistent with the location of heavy precipitation in observation as seen in comparisons between Figs. 4a, 8c, and 9a. Figure 9a shows the blue contour, which surrounds areas with observed heavy precipitation in Fig. 4a, and the green rectangle, which surrounds the specific area where more than 90 % of the events of heavy precipitation occur in Fig. 8c. In Fig. 9a, the purple line, which marks a substantial transition in aerosol concentrations in Fig. 4a, is also shown. The good consistency among the locations demonstrates that the simulation of the spatial distribution of heavy precipitation is performed reasonably well. Between 17:00 and 19:00 LST, we do not see significant differences in the frequency distribution of precipitation rates, particularly in heavy precipitation with rates above 60 mm h-1 between the control run and the low-aerosol run (Fig. 7d).

By 20:00 LST, the maximum rate of torrential rain reaches ∼130 mm h-1 for the control run and ∼110 mm h-1 for the low-aerosol run (Fig. 7g). Associated with this, between 19:00 and 20:00 LST, significant differences in frequency distributions, particularly for heavy precipitation between the control run and the low-aerosol run, start to appear (Fig. 7g). At 20:00 LST as seen in Fig. 8e and in the previous hours, in the control run more than 90 % of heavy precipitation events are concentrated in a specific area that is surrounded by the green rectangle. Note that only in this specific area, does extremely heavy precipitation with rates above 100 mm h-1 occur. In the low-aerosol run, the extremely heavy precipitation with rates above 100 mm h-1 also occurs only in a particular area, which is surrounded by the green rectangle, at 20:00 LST (Fig. 8f). At 20:00 LST, as seen in Fig. 4b, observation shows that there are five spots of heavy precipitation. The location of the largest spot where most heavy precipitation events occur is similar to that of the specific area that is surrounded by the green rectangle in the control run as seen in comparisons between Figs. 4b, 8e, and 9b. Figure 9b shows the blue contour and the purple line from Fig. 4b and the green rectangle from Fig. 8e. This again demonstrates that the simulation of the spatial distribution of heavy precipitation is performed with fairly good confidence.

The system propagates eastwards after 20:00 LST in a way that its easternmost part is closer to the east boundary of the domain as seen in comparisons between Fig. 8e (Fig. 8f) and Fig. 8g (Fig. 8h) for the control (low-aerosol) run. As seen in Fig. 8g and in the previous hours, for the control run more than 90 % of heavy precipitation events are concentrated in a specific area (surrounded by the green rectangle) at 23:00 LST. However, in the low-aerosol run, heavy precipitation is not concentrated in a specific area at 23:00 LST. Unlike the green rectangle in the control run at 23:00 LST, the green rectangle at 23:00 LST in the low-aerosol run surrounds an area where ∼50 % of heavy precipitation events are located, although the rectangle surrounds the largest area with heavy precipitation among heavy precipitation areas in the low-aerosol run. For a period between 20:00 and 23:00 LST compared to that between 19:00 and 20:00 LST, the maximum precipitation rate rises up to ∼180 mm h-1 in the control run; however, in the low-aerosol run, the maximum precipitation rate stays at ∼120 mm h-1 (Fig. 7g and j). Hence, there is the presence of precipitation rates between ∼120 and ∼180 mm h-1 in the control run, while there is their absence in the low-aerosol run for the period between 20:00 and 23:00 LST. This reflects that increases in the frequency of torrential rain, which are induced by increases in the spatial variability and loading of aerosol, enhance as the system evolves from its initial stage before 20:00 LST to its mature stage between 20:00 and 23:00 LST.

Of interest is that the green rectangle is included in an area which is surrounded by the purple line in all panels with different times in Fig. 8 and further discussion for this matter is provided in Sect. 4.2. After 23:00 LST 27 July 2011, the precipitating system enters its decaying stage. Figure 7m shows precipitation-rate frequency in the control run and the low-aerosol run for a period between 04:00 and 05:00 LST 28 July 2011. As seen in Fig. 7m, with the progress of the decaying stage, the maximum precipitation rate reduces down to ∼25 mm h-1 as an indication that heavy precipitation disappears and the system is nearly at the end of its life cycle.

For the examination of condensation which is the main source of precipitation, convergence fields at the surface, where updrafts that produce condensation originate, are obtained and the column-averaged condensation rates are superimposed on them. Other processes such as deposition and freezing produce the mass of solid hydrometeors and act as sources of precipitation; however, their contribution to precipitation is ∼ 1 order of magnitude smaller than that by condensation in the control run and the low-aerosol run. Hence, here, among sources of precipitation, we focus on condensation. Convergence and condensation fields are again superimposed on shaded precipitation fields as shown in Fig. 10. In Fig. 10, convergence and condensation fields are represented by white and yellow contours, respectively. When it comes to the convergence field in the green rectangle in Fig. 10, which starts to be formed around 19:00 LST and is composed of convergence lines, the field in the rectangle in the control run is stronger than that in the low-aerosol run. The averaged intensity of the convergence field over an area with non-zero convergence in the green rectangle and over the simulation period is 0.013 s-1 in the control run, while the averaged intensity is 0.007 s-1 in the low-aerosol run. The convergence field in the green rectangle is strongest among convergence lines over the whole domain and, associated with this, stronger updrafts and greater condensation develop over that field in the green rectangle than in the other lines over the whole domain in each of the runs.

Figure 11 shows horizontal distributions of wind vector field (arrows) superimposed upon fields of convergence, condensation, and precipitation. In general, particularly from 19:00 LST on, in the area with high-value aerosol concentrations to the west of the strong convergence field (surrounded by the green rectangle), there are greater horizontal wind speeds than in the area with low-value aerosol concentrations to the east of the strong convergence field in the control run. As seen in comparisons between the location of the rectangle and that of the purple line, which mark the transition zone for aerosol concentrations, the area to the west of the rectangle has higher aerosol concentrations than that to the east. In the area with high-value aerosol concentrations, there is greater cloud liquid evaporation occurring than in the area with low-value aerosol concentrations in the control run as shown in Fig. 12a. Figure 12a shows the vertical distribution of the time- and domain-averaged cloud liquid and rain evaporation rates over each of the areas to the west and east of the strong convergence field, which is surrounded by the green rectangle, and over the period between 17:00 and 19:00 LST for the control run and the low-aerosol run. For the calculation of the averaged values in Fig. 12, the area to the west (east) of the strong convergence field is set to include all parts of the north–south direction, which is the y direction, and the vertical domains but only a portion of the east–west direction domain, which is the x-direction domain that extends from the western boundary of Domain 3 to 90 km where the western boundary of the green rectangle at 19:00 LST is located (from 110 km where the eastern boundary of the green rectangle at 19:00 LST is located to the eastern boundary of Domain 3) in Domain 3 for the control run. For the low-aerosol run, the area to the west (east) of the strong convergence field is identical to that in the control run except for the fact that the area includes a portion of the x-direction domain that extends from the western boundary of Domain 3 to 70 km where the western boundary of the green rectangle at 19:00 LST is located (from 90 km where the eastern boundary of the green rectangle at 19:00 LST is located to the eastern boundary of Domain 3) in Domain 3.

High-value aerosol concentrations reduce autoconversion and in turn increase cloud liquid as a source of evaporation and thus increase cloud liquid evaporation compared to low-value aerosol concentrations. In addition, high-value aerosol concentrations produce high-value cloud droplet number concentration and the associated high-value surface areas of droplets. The surface of droplets is where condensation occurs and as shown by Lee et al. (2009) and a recent study by Fan et al. (2018), the high-value surface areas cause higher-value condensation compared to the situation with low-value aerosol concentrations that lead to lower-value condensation. The averaged condensation rate over the abovementioned area to the west (east) of the strong convergence field and over the period between 17:00 and 19:00 LST is 1.28 (0.97) g m-3 h-1 in the control run. This further increases cloud liquid (as a source of evaporation) and thus its evaporation in the area with high-value aerosol concentrations. Also, with high-value aerosol concentrations, there is an increase in the surface-to-volume ratio of cloud droplets and this increases evaporation efficiency and thus cloud liquid evaporation compared to the situation with low-value aerosol concentrations. However, mainly due to an increase in the size of raindrops and their associated decrease in the surface-to-volume ratio, which is induced by high-value aerosol concentrations, rain evaporation reduces compared to the situation with low-value aerosol concentrations as also shown in van den Heever et al. (2011). Increases in cloud liquid evaporation in turn enhance negative buoyancy, which induces stronger downdrafts in the area with high-value aerosol concentrations than in the area with low-value aerosol concentrations in the control run particularly between 17:00 and 19:00 LST as seen in Fig. 12b. Sublimation and melting also enhance negative buoyancy; however, their contribution is ∼ 1 order of magnitude smaller than the contribution by cloud liquid evaporation. Hence, here, we focus on cloud liquid evaporation. Figure 12b shows the vertical distribution of the time- and domain-averaged downdraft mass fluxes over each of the areas to the west and east of the strong convergence field (surrounded by the green rectangle) for the control run and the low-aerosol run over the period between 17:00 and 19:00 LST. Previous studies have shown that aerosol-induced increases in cloud liquid evaporation are closely linked to the enhancement of the intensity of downdrafts (Lee et al., 2008a, b, 2013; Lee, 2017). Cloud liquid or droplets in downdrafts move together with downdrafts; thus, when downdrafts descend, cloud liquid descends while being included in downdrafts. Cloud liquid in the descending downdrafts evaporates. More evaporation of cloud liquid provides greater negative buoyancy to downdrafts so that they accelerate more (Byers and Braham, 1949; Grenci and Nese, 2001).

After reaching the near-surface altitudes below ∼3 km, in the control run, stronger downdrafts spread out as stronger outflow or horizontal movement, as seen in the area with high-value aerosol concentrations, compared to those in the area with low-value aerosol concentrations around 19:00 LST in Fig. 11c. The outflow in the area with high-value aerosol concentrations accelerates, due to evaporation on its path, as it moves southeastwards from the northern and western boundaries of the domain. The outflow accelerates until it collides with surrounding air that has weaker horizontal movement in the area with low-value aerosol concentrations. This collision mainly occurs in the places where the transition between high-value aerosol concentrations and low-value aerosol concentrations is located (surrounded by the purple line) as seen in Fig. 11c. This collision creates the strong convergence field around 19:00 LST, which is surrounded by the green rectangle in those places in the control run as seen in Fig. 11c. Hence, most of the strong convergence field (surrounded by the green rectangle) is included in the transition zone between high-value and low-value aerosol concentrations (which is surrounded by the purple line) in the control run (Fig. 11c). The strong convergence field in the green rectangle generates a large amount of condensation and cloud liquid and this large amount of cloud liquid produces not only heavy precipitation but also high-degree of evaporation. Then, high-degree of evaporation in turn contributes to the occurrence of a stronger convergence field in the green rectangle, which establishes feedbacks between the convergence field, condensation, heavy precipitation, and evaporation. This enables the intensification of downdrafts and horizontal wind to the west of the convergence field shown in the green rectangle, the convergence field, and the increases in heavy precipitation with time, while the convergence field shown in the green rectangle is advected eastwards in the control run as seen in Figs. 7g, j and 11e and g. As seen in Fig. 11e and g, even after 19:00 LST, the convergence field shown in the green rectangle stays within the transition zone between the high-value and low-value aerosol concentrations (which is surrounded by the purple line) during its eastward advection. This indicates that the collision explained above between strong outflow and surrounding weak wind, which is essential for the formation of the convergence field shown in the green rectangle, continuously occurs in the transition zone even after 19:00 LST.

Note that, associated with aerosol concentrations in the western part of the domain, which are 2 times greater in the control run than in the low-aerosol run, there are differences in aerosol concentrations 2 times greater between the area with high-value aerosol concentrations and that with low-value aerosol concentrations in the control run than in the low-aerosol run. This leads to a transition in aerosol concentrations 2 times greater , particularly in the transition zone surrounded by the purple line in the control run than in the low-aerosol run (Fig. 4). Associated with this, there is a greater reduction in autoconversion and increases in cloud liquid and surface-to-volume ratio of cloud droplets in the area with high-value aerosol concentrations in the control run than in the low-aerosol run. Then, there is greater evaporation, intensity of downdrafts, and associated outflow and its acceleration during its southeastward movement around the surface in that area in the control run than in the low-aerosol run (Figs. 11 and 12). This means that there is stronger collision between outflow and the surrounding air in the control run than in the low-aerosol run, and stronger collision forms the strong convergence field (in the green rectangle), which is much more intense in the control run than in the low-aerosol run as seen in Figs. 10 and 11. Over this much more intense convergence field, there is the formation of stronger updrafts that are able to form stronger convection, which is in turn able to produce more events of heavy precipitation in the control run than in the low-aerosol run (Fig. 7). The more intense strong convergence field in the green rectangle establishes stronger feedbacks between the convergence field, condensation, heavy precipitation, and evaporation in the control run than in the low-aerosol run. Hence, differences in intensity of the convergence field shown in the green rectangle and in the heavy precipitation between the runs become greater as time progresses (Figs. 7, 10, and 11).

It is discussed that cloud liquid evaporative cooling plays an important role in the formation of the strong convergence field where most of heavy precipitation occurs (surrounded by the green rectangle) in the control run. To confirm this role, we repeat the control run and the low-aerosol run with cooling from cloud liquid evaporation turned off and cooling from rain evaporation left on. The repeated control run and the low-aerosol run are referred to as the control-noevp run and the low-aerosol-noevp run, respectively. In these repeated runs, cloud liquid mass reduces due to cloud liquid evaporation, although cloud liquid evaporation does not affect temperature.

The temporal evolution of precipitation rates in the control-noevp run and the low-aerosol-noevp run is similar to that in the control run and the low-aerosol run (Fig. 6a). However, due to the absence of cloud liquid evaporative cooling, there is no formation of strong outflow and convergence field (as seen in wind field and the green rectangle in the control run and the low-aerosol run) in these repeated runs as shown in Fig. 13a and b. Figure 13a and b show wind vector and convergence fields at the surface over the whole domain in the control-noevp run and the low-aerosol-noevp run, respectively, at 23:00 LST, which corresponds to the mature stage of the system. Note that the strong convergence field is clearly distinguishable in its intensity and length from any other convergence lines in each of the control run and the low-aerosol run as seen in Figs. 10 and 11. However, there is no field in each of the repeated runs that is distinguishable in its intensity and length from other lines as seen in Fig. 13a and b. This leads to the situation in which there is no particular convergence field in the control-noevp run that produces many more events of heavy precipitation than in the low-aerosol-noevp run. As seen in Fig. 7h and k, associated with this, differences in the frequency of heavy precipitation with rates above 60 mm h-1 between the repeated runs are much smaller than those between the control run and the low-aerosol run, particularly for the period between 19:00 and 23:00 LST, although the control-noevp run shows a greater frequency of heavy precipitation than the low-aerosol-noevp run. This results in much smaller differences in heavy precipitation between the repeated runs than between the control run and the low-aerosol run for the whole simulation period as seen in Fig. 7b. This demonstrates that cloud liquid evaporative cooling and its differences between the control run and the low-aerosol run play a key role in many more events of heavy precipitation in the control run than in the low-aerosol run.

Note that between the control run and the low-aerosol run, there are changes not only in the spatial variability in aerosol concentrations but also in aerosol concentrations. This means that differences between those runs are caused not only by changes in the variability but also by changes in aerosol concentrations. Although there have been many studies on the effects of changes in aerosol concentrations on heavy precipitation, studies on those effects of changes in the variability have been rare. Motivated by this, as a preliminary step to the understanding of those effects of changes in the variability, here, we attempt to isolate the effects of changes in the variability on heavy precipitation from those in aerosol concentrations or vice versa. For this purpose, the control run and the low-aerosol run are repeated with homogeneous spatial distributions of background aerosol concentrations. These repeated runs are referred to as the control-homoge run and the low-aerosol-homoge run. In the control-homoge run (low-aerosol-homoge run), aerosol concentrations over the domain are fixed at one value, which is the domain-averaged concentration of the background aerosol in the control run (the low-aerosol run), at each time step. Hence, in the control-homoge run and the low-aerosol-homoge run, the variability (or contrast) in the spatial distribution of aerosol concentrations between the area with high-value aerosol concentrations and that with low-value aerosol concentrations is removed, which achieves homogeneous spatial distributions.

The temporal evolution of precipitation rates in the control-homoge run and the low-aerosol-homoge run is similar to that in the control run and the low-aerosol run (Fig. 6b). However, with the homogeneity in the spatial distribution of aerosol concentrations, there is no formation of strong outflow and thus strong convergence field that is distinguishable from any other convergence lines in the control-homoge run and low-aerosol-homoge run as seen in Fig. 13c and d. Figure 13c and d show wind vector and convergence fields over the whole domain at 23:00 LST in the control-homoge run and the low-aerosol-homoge run, respectively. In the absence of the variability between the area with high-value aerosol concentrations and that with low-value aerosol concentrations, there are no differences in evaporative cooling between those areas and thus there is no strong outflow or convergence field which is distinguishable from any other lines.

Comparisons between the control run and the control-homoge run (the low-aerosol run and the low-aerosol-homoge run) isolate the effects of the variability on heavy precipitation from those of aerosol concentrations whose averaged value is set at an identical value at each time step in the runs. Due to the absence of the variability in the spatial distribution of aerosol concentrations and the associated strong convergence field, the frequency of heavy precipitation in the control-homoge run and in the low-aerosol-homoge run is, on average, just ∼18 % and ∼13 % of that in the control run and in the low-aerosol run, respectively, for the whole simulation period (Fig. 7c). Hence, the presence of the variability alone (in the absence of changes in aerosol concentrations) increases the number of the heavy precipitation events by a factor of ∼5 or ∼10. This presence alone also results in a substantial increase in the maximum precipitation rate in the control run and the low-aerosol run compared to the repeated runs. Between the low-aerosol run and the low-aerosol-homoge run, the increase is from 80 mm h-1 in the low-aerosol-homoge run to 120 mm h-1 in the low-aerosol run, while between the control run and the control-homoge run, the increase is significant and from 90 mm h-1 in the control-homoge run to 180 mm h-1 in the control run (Fig. 7c). Here, we see that even without the effects of changes in aerosol concentrations, the presence of the variability alone is able to cause significant enhancement of heavy precipitation in terms of its frequency and maximum value.

Remember that there is an identical domain-averaged background aerosol concentration at each time step between the control run and the control-homoge run and between the low-aerosol run and the low-aerosol-homoge run. Hence, changes in the averaged aerosol concentration between the control-homoge run and the low-aerosol-homoge run are identical to those between the control run and the low-aerosol run. With these identical changes in the averaged aerosol concentration, between the control run and the low-aerosol run, there are additional changes in the variability in aerosol distributions. There is a larger frequency of heavy precipitation in the control-homoge run than in the low-aerosol-homoge run (Fig. 7c). However, as mentioned above, there is no strong convergence field which is distinguishable from any other lines in the control-homoge run, as seen in Fig. 13c. Associated with this, differences in the frequency of heavy precipitation between the control-homoge run and the low-aerosol-homoge run are much smaller than those between the control run and the low-aerosol run, particularly during the period between 19:00 and 23:00 LST, as seen in Fig. 7i and l. This results in a situation in which differences in the frequency of heavy precipitation between the control-homoge run and the low-aerosol-homoge run are, on average, just ∼15 % of those between the control run and the low-aerosol run for the whole simulation period (Fig. 7c). With identical changes in the averaged aerosol concentration between a pair of the control run and the low-aerosol run and a pair of the control-homoge run and the low-aerosol-homoge run, this demonstrates that additional changes in the variability in aerosol distributions play a much more important role in aerosol-induced increases in the occurrence of heavy precipitation than changes in the averaged aerosol concentrations.