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  • View in gallery

    Geographic distribution of the mean MHD for the period of 1980–2005 in the four regions of XUAR, IMAR, Hebei, and Guizhou in China. Locations of solid circles indicate the stations with hail size records.

  • View in gallery

    Scatterplot of the mean MHD (1980–2005) against corresponding station elevation in four regions (shown in Fig. 1).

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    PDV (refer to the definition in section 3) of the six ranks of the MHD for the four regions. The horizontal lines denote the mean PDV of the four regions for each rank.

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    (a) PDV of severe hail of four regions for months 1–12. (b) PDV of the MHD of the six ranks across the four regions for the entire year, the warm season, and the cold season.

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    Annual anomalies (bars) and long-term trend (solid line) in PDV of severe hail for 1980–2005 in (a) Guizhou, (b) Heibei, (c) IMAR, and (d) XUAR.

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    (left) Amount of melting during descent to the ground for different hail sizes in the cloud. (right) Final hail size as a function of hail size before melting. Dashed lines indicate the 5–15-mm MHD on the ground corresponding to the 15–20-mm MHD before melting.

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    (left) Sensitivity of hail size to Qm and (right) interannual variation (indicated by “CWV”) and linear long-term trend (indicated by “linear CWV” with p value given) in the annual mean CWV averaged over the stations shown in Fig. 8 during 1980–2005.

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    Geographic distribution of the simulated MHD based on elevation, mean FLH, and mean CWV at the selected 80 stations in China.

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    Sensitivity of the simulated variation and long-term trend of mean MHD to (a) CAPE, (b) CWV, and (c) FLH for the period 1980–2005. (d) The simulated variation of mean MHD based on the annual mean FLH, CWV, and CAPE and observations. The linear trends of mean MHD are indicated by the solid lines, and the p values are also given.

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Observed Characteristics of Hail Size in Four Regions in China during 1980–2005

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  • 1 Department of Atmospheric Science, School of Physics, Peking University, Beijing, China
  • 2 Department of Meteorology, and International Pacific Research Center, University of Hawaii at Manoa, Honolulu, Hawaii
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Abstract

The climatology and long-term trend of hail size in four regions of China are documented for the period of 1980–2005 using the maximum hail diameter (MHD) data obtained from the Meteorological Administrations of Xinjiang Uygur Autonomous Region (XUAR), the Inner Mongolia Autonomous Region (IMAR), Guizhou Province, and Hebei Province. The reported MHD is mainly around 10 mm in the four regions. Guizhou (in southwestern China) has the largest proportion of severe hail (MHD greater than 15 mm) among the four regions. Severe hail in southwestern China mainly occurs between February and June, while in northern China it occurs in summer (from May to August) with the peak in June. During the period studied, the size of severe hail shows a slight downtrend in Guizhou and IMAR, whereas it shows an uptrend and a flat trend in Hebei and XUAR, respectively. However, none of the trends is statistically significant. Results from sensitivity experiments using a one-dimensional numerical model show that hail size is sensitive to the freezing level height, the maximum updraft, and column cloud liquid water—all working together to determine the geographic distribution and long-term trend of the observed hail size in China.

Corresponding author address: Dr. Qinghong Zhang, Department of Atmospheric Science, School of Physics, Peking University, Beijing 100871, China. Email: qzhang@pku.edu.cn

Abstract

The climatology and long-term trend of hail size in four regions of China are documented for the period of 1980–2005 using the maximum hail diameter (MHD) data obtained from the Meteorological Administrations of Xinjiang Uygur Autonomous Region (XUAR), the Inner Mongolia Autonomous Region (IMAR), Guizhou Province, and Hebei Province. The reported MHD is mainly around 10 mm in the four regions. Guizhou (in southwestern China) has the largest proportion of severe hail (MHD greater than 15 mm) among the four regions. Severe hail in southwestern China mainly occurs between February and June, while in northern China it occurs in summer (from May to August) with the peak in June. During the period studied, the size of severe hail shows a slight downtrend in Guizhou and IMAR, whereas it shows an uptrend and a flat trend in Hebei and XUAR, respectively. However, none of the trends is statistically significant. Results from sensitivity experiments using a one-dimensional numerical model show that hail size is sensitive to the freezing level height, the maximum updraft, and column cloud liquid water—all working together to determine the geographic distribution and long-term trend of the observed hail size in China.

Corresponding author address: Dr. Qinghong Zhang, Department of Atmospheric Science, School of Physics, Peking University, Beijing 100871, China. Email: qzhang@pku.edu.cn

1. Introduction

Hail is one of the most extreme weather phenomena, causing great loss to agriculture every year in China (Han 1999). However, studies on hail climatology are quite few because of the difficulties of hail data collection. Liu and Tang (1966) were the first, showing the spatial and temporal distributions of hail storms in China for the 10-yr period during 1950–60. Recently, Zhang et al. (2008) studied the spatial distribution and seasonal variation of hail occurrence, an update of hail climatology in China. The long-term trend of hail frequency of occurrence in China was first documented by Xie et al. (2008), who showed the significant decreasing trend of hail frequency in most of China from the early 1980s based on 46 yr of data during 1960–2005. The decrease in annual hail frequency is attributed to the increase in freezing level height (FLH) below which hail stones would melt when falling (Xie et al. 2008). In addition to changes in hail frequency, changes in hail size are also an important aspect of hail climatology. Many studies in the other countries have documented the hail size distributions (Morgan 1973; Paul 1980; Dessens 1986; Giaiotti et al. 2001; Schaefer et al. 2004). However, none of these studies has focused on the trend of hail size during a long period so far. In China, Li and Ma (2001) conducted a qualitative analysis and showed that the maximum hail diameter in Heilongjiang Province in the 1990s was larger than that in 1980s, which implied the strengthening of hail intensity since the 1980s. However, the study covered only one province of China and the analysis was qualitative only. Tuovinen et al. (2009) studied the hail size distribution of severe hail cases in Finland in which the data covered 78 yr from 1930 to 2006. Much of the information about severe hail was reported from newspapers, mobile phones, networks, and so on. They attributed the increasing severe hail events [with large maximum hail diameter (MHD)] in recent years to the increased methods to report hail events. However, they did not discuss any connections between the trend of severe hail events and any other climate factors.

The question remains as to whether hail size has been changing in response to the warming climate. This study will focus on the climatology and changes in hail size in China since the 1980s (because of the availability of reliable hail size data) and will try to answer the question stated earlier. Observed hail size data analysis and sensitivity experiments with a one-dimensional hail growth model were combined to examine the likelihood of hail size changes in four regions of China for the period of 1980–2005. The rest of the paper is organized as follows. The data collection and analysis method are described in section 2. Section 3 shows the size distribution, geographic distribution, and seasonal variation of hail size in the four regions. Model experiments are shown in section 4, with a discussion on the possible controlling factors of hail size. Our main conclusions are drawn in the last section.

2. Dataset collection and analysis method

Observation of hail precipitation is regularly operated at meteorological observational stations in China. According to the observational guide, standard hail precipitation records include hail occurrence and the maximum hail diameter of hail collected by the rain container. However, hail size records were not recognized as reliable observations until 1980—when the new observational norm for meteorological stations was implemented in China. Therefore, this study is based on the data of 26 yr during 1980–2005. In addition, only hail occurrence records are collected by the National Meteorological Information Center (NMIC); hail size records are kept by meteorological bureaus of individual provinces and may not be complete in some stations or provinces. Fortunately, complete hail size records are found in the Xinjiang Uygur Autonomous Region (XUAR) in northwestern China, the Inner Mongolia Autonomous Region (IMAR) in northern China, Hebei Province in the central plain of China, and Guizhou Province in southwestern China (Fig. 1). According to Zhang et al. (2008), hail happens more frequently in northern China than in southern China and most frequently in the high mountainous areas and central plains. Therefore, hail size records used in the study may roughly represent the typical regions with hail precipitation in China.

The following quality control algorithms were implemented sequentially on the hail size dataset: 1) the records of hail occurrence have been double checked with the released hail occurrence dataset from NMIC; 2) if one station with the ratio of missing hail size records to hail occurrence records is greater than 50%, then the station is excluded from this initial raw data screening; 3) hail occurrence records without corresponding hail size records are discarded from the dataset; and 4) the records with either the “coins” or “beans” description (only found in the data of Guizhou Province) are reclassified into different ranks of hail diameter (e.g., “bean like” hail size record was grouped into the 2–5-mm rank and “coin like” into the 10–15-mm rank). Table 1 shows the number of conventional surface observational stations in the four regions (column 2), the number of stations taken into account in this study (column 3), and the proportion of the MHD records to number of hail occurrences in the four regions (column 4). Lastly, 138 stations were selected in this study, and their locations are shown in Fig. 1.

Since we focus on the seasonal variation and the long-term trend of the MHD, the MHD records were classified into six ranks (2–5, 5–10, 10–15, 15–20, 20–40, and >40 mm). The rank 15 mm was selected as the threshold value of the MHD for defining severe hail. Then we analyzed the mean characteristics of probability density of the MHD on each rank for the four regions. The severe hail frequency and its proportion to the total hail occurrence were examined to study the monthly characteristics and the long-term trend in each region.

To interpret the cause of the long-term trend in hail size, the one-dimensional numerical hail growth model described in Wu et al. (1997) was used to perform several sensitivity experiments with varying freezing level height, the maximum updraft, and column-integrated water vapor. A detailed description of the model used in this study is in the appendix. The input variables/parameters were derived from 80 radiosonde stations with complete 26-yr (from 1980 to 2005) sounding data.

3. Results

a. Geographic distribution of the MHD

Geographic distributions of the mean MHD are shown in Fig. 1 (solid circles). There are only two stations (in Guizhou Province) with a mean MHD that reaches the threshold value of severe hail (a mean MHD greater than 15 mm), implying that the two stations suffer greatly from hail every year. There are 14 stations with a mean MHD between 10 and 15 mm: 5 in Guizhou, 6 in Hebei, and 3 in XUAR. Interestingly, no station with a mean MHD greater than 10 mm occurred in IMAR; that is, 8 out of 9 stations with the mean MHD less than 5 mm are located northwest of IMAR and only one station in XUAR. Most of the stations show the mean MHD between 5 and 10 mm. This pattern roughly reflects the severe hail and nonsevere hail distributions. However, because of the limitation of the dataset, the pattern of severe hail is not clear. Since there are obvious differences in hail frequencies between southern and northern China (Xie et al. 2008), there should be some geographic characteristics of hail size distribution, especially in the concentrated regions with severe hail. A similar issue was examined by Schaefer et al. (2004) for the United States. They showed that severe hail activity mainly occurs in a north–south belt, corresponding to the “tornado alley” regions of the United States, with large hail being a typical by-product of tornadic supercell storms. In Britain and Ireland, severe hail closely correlates to the area of higher summer temperature in the Midlands and eastern England.

Zhang et al. (2008) found that hailstorms are closely related to topography and frequently occur in mountainous areas with high elevation in China. Observational evidence (Xie et al. 2008; Foote 1984) and model results (Brimelow et al. 2002) have confirmed that FLH is important to hail size. FLH is closely related to topographic elevation, since higher (lower) elevation corresponds to lower (higher) FLH. To examine the possible linkage between hail size and elevation stations, we show in Fig. 2 the scatterplots of the mean MHD versus station elevation. It shows no significant correlation between hail size and the elevation of the station. This may be because station elevation not only determines FLH to some degree but also reduces total column water vapor (CWV) that may be unfavorable for the production of large size hail.

b. Size distribution of the MHD

The probability density value (PDV), defined as the number of MHD records of a certain rank divided by the total number of MHD records, is shown in Fig. 3 for the four regions. PDVs of the four regions all have a single-peaked distribution, with a peak value at a MHD rank of 5–10 mm and an averaged value of 45.95%. This is similar to the hail size distribution in Finland (Tuovinen et al. 2009), which showed a hail size that is usually within the range of 5–10 mm. An MHD of 2–5 mm is the second most frequent hail size with the PDV of 31.28%. Ranks 10–15 and 15–20 mm, which are close in size to severe hail, have the PDV of 11.00% and 4.66%, respectively. Severe hail precipitation in the four regions accounts for 6.20% of the total hail precipitation.

In addition, the general characteristics of the PDV in the four regions are similar to the results obtained for all of China (Xie et al. 2008; Zhang et al. 2008). The PDV of nonsevere hail shows an overall increase from south to north. Guizhou and IMAR have the minimum and maximum PDV of nonsevere hail, respectively. As stations in IMAR and XUAR are at similar latitudes, there are no large differences in the PDV between the two regions. The PDV of severe hail in Guizhou Province is remarkably larger than that in the other three regions because more column-integrated water vapor and jet stream associated with southwesterly monsoon in southwestern China may favor larger size hail.

c. Seasonal variation of the MHD of severe hail

To examine the characteristics of the MHD of severe hail in different months, we show the monthly-mean PDV of severe hail for each region in Fig. 4a. Similar to the seasonal variation in hail frequency (Xie et al. 2008), severe hail in Guizhou Province starts in January, reaches its peak (30%) in April, and then descends to its lowest in November. The monthly-mean PDVs of severe hail in the other three regions are similar to each other. XUAR, IMAR, and Hebei all suffered from severe hail in the beginning of March and experienced the most frequent severe hail in June. In addition, the PDV of severe hail in Guizhou Province is a little bit higher than that in the other three regions, and severe hail lasts for the whole year in contrast to the other three regions in northern China, where severe hail occurs only between May and October.

To examine the variability of severe hail in different seasons, charts of the averaged seasonal PDV of the MHD on six ranks of hail size across the four regions were constructed. Figure 4b illustrates the PDV on six ranks for all areas for the whole year, the warm season (from May to October) and the cold season (from November to January). It is interesting to see that the proportion of severe hail in the cold season is greater than that in the warm season. This is consistent with previous analyses and is contributed mostly by the large proportion of severe hail in the cold season in Guizhou Province.

d. The long-term trend of the MHD

The characteristics of the MHD in different regions discussed earlier are determined by the regional climate, which may be subject to long-term changes and thus changes in the MHD may be expected. To reveal the long-term trend of hail size in China, changes in the MHD for the period of 1980–2005 were analyzed. Because the annual mean MHD could not reflect the long-term trend of hail size, we indirectly examined the hail size changes via the PDV of hail. The increase or decrease in the PDV would indicate the increase or decrease trend in hail size.

Figures 5a–d show the anomalies (defined as the deviation of the annual values from the 26-yr mean annual values) and trends (represented by the coefficient of the linear regression) of the PDV of severe hail in Guizhou, Hebei, IMAR, and XUAR. There are obvious large (small) PDV years of severe hail, which are indicated by positive (negative) anomalies. In Guizhou Province, in the first 10 yr, 6 yr of the anomalies in the PDV are positive (the year with large severe hail ratio) and 4 yr are negative. During the most recent 10 yr, the severe hail events are relatively rare in the first 6 yr and the remaining 4 yr show a slight increase of severe hail occurrences. In addition, the magnitudes of negative anomalies are larger than those of positive anomalies in the most recent 10 yr. This implies that severe hail ratio in Guizhou Province may have a nonsignificant declining trend in the most recent 30 yr, with a decreasing rate of about 1.41% 10 yr−1. In Hebei Province, the situation is nearly opposite to that in Guizhou. The PDV of severe hail shows a slightly upward trend (not significant at the 95% confidence level) in the most recent 11 yr. Although there are only 3 yr with severe hail in this positive phase, and 8 yr in the negative phase, the magnitude of positive anomalies (22.5%) is remarkably larger than that of negative anomalies (all less than 7%). Similar to Guizhou Province, IMAR shows an increasing trend (not significant at the 95% confidence level) in severe hail ratio, with 6 yr of negative severe hail ratios in the most recent 10 yr. However, there are no trends in the ratio of severe hail in XUAR. Correspondingly, the nonsevere hail (MHD < 15 mm) exhibited opposite changes to the severe hail. None of the linear trends in the PDV of severe hail in the four regions is significant at the 95% confidence level (statistical p values are also given in Figs. 5a–d).

Note that some increasing trends in severe hail have been reported in the United States (Schaefer et al. 2004), southeastern Australia (Schuster et al. 2005), Britain and Ireland (Webb et al. 2009), and Finland (Tuovinen et al. 2009). However, because of the inflation in the number of reports, the increasing trends in severe hail were attributed to changes in the reporting system. Here, we found no significant long-term trend in hail size based on the proportion of severe hail indirectly in the four regions in China, suggesting that hail size, as an important aspect of hail climatology, may not be sensitive to the intrinsic natural variability or climate change in the last 2–3 decades.

4. Modeling experiments

The observed evidence presented in the previous section suggests that hail size might not be sensitive to the present climate variability. In this section, we will give further explanation based on some sensitivity modeling experiments. The long-term trend of hail size is a complicated issue, since hail precipitation is influenced by many factors. Vertical wind shear, low-level jet stream, column water vapor, and FLH (Xie et al. 2008) may all play important roles in hail formation and precipitation. In particular, Xie et al. (2008) found that the increased FLH is the most important cause of the decrease in hail frequency in China, because the higher the FLH extends, the more the hail would melt. Questions arise as to whether and to what degree hail size has been changed because of the increased FLH and other factors. CWV is another factor that has an important effect on hail formation. Since the annual mean CWV has a nonsignificant decreasing trend in the studied regions during 1980–2005 (see Fig. 7b), it would be interesting to see the sensitivity of the maximum hail size to CWV. In addition, convective available potential energy (CAPE) is found to have an increasing trend over China (Xie et al. 2008). Since CAPE provides a good estimate of the maximum vertical velocity in buoyant convective updraft, it should be a factor that could affect the hail size too. It is our interest to use a numerical hail growth model to address the earlier-mentioned issues through sensitivity experiment. A simple one-dimensional hail formation model (Wu et al. 1997) was used here (see the details of the model in the appendix). We therefore conducted four sensitivity experiments to include the effects of FLH, CWV, and CAPE (maximum vertical velocity in the model) individually and as a whole on the trend of hail size in China.

a. Freezing level height

Since the typical FLH in China is 3000–5000 m and the mean increasing amount is about 200 m over the past 30 yr (Xie et al. 2008), we selected 4500 and 4725 m (increasing 4500 m by 5%) in the sensitivity experiment. Figure 6 compares the loss percentage (defined as the percentage of mass loss due to melt to the mass before melting) of mass of the same hail size for the FLHs of 4500 and 4725 m. It is clearly seen that the lower FLH favors larger hail size and that the smaller the hail, the larger the loss percentage of mass. Note that hail above the FLH with the maximum diameter less than 12 mm totally melts before reaching the ground. Increasing the FLH from 4500 to 4725 m hardly has any effect on extremely large hail—for example, a MHD greater than 40 mm—but significantly affects small hail with the maximum mass melted by about 15%. These results are consistent with Doppler radar observations (Foote 1984), which show that small hail always leads to rain rather than hail because it generally melts completely before reaching the ground. The final hail size falling to the ground and the corresponding hail size before melting are shown in Fig. 6b. Ground hail with 5–10-mm diameter, which is the most common MHD in observations, corresponds to the hail with a size of 15–20 mm before melting. Therefore, the increased FLH may modify the distribution of hail size to some degree when other factors are the same.

b. The maximum column cloud liquid water

In the one-dimensional hail growth numerical model, the maximum column cloud liquid water qm is important and determines the possible maximum diameter that hail could reach. Figure 7a shows the dependence of hail size on qm with the FLH of 4500 m together with the observed trend in the annual mean CWV in the studied regions during 1980–2005 (Fig. 7b). If qm increases by 150%, then the hail size correspondingly increases by 100%. In addition, smaller hail is more sensitive to the maximum column cloud liquid water than larger hail. Comparing the results from the two sensitivity experiments, we found that for the 15–20-mm hail the mass loss due to the increase in the FLH are comparable to the mass growth due to the increase in qm in a similar proportion.

c. Modeling geographic distribution of hail size

As hail size is sensitive to FLH and liquid water in a cloud, it is interesting to see to what degree the distribution of FLH and liquid water could determine the geographic distribution of hail size in China. Since there are no observations for qm, we simply assume that the CWV is completely condensed to form clouds. As a result, qm can be approximated by CWV. The distribution of CWV is thus considered as an approximation of column cloud liquid water in our calculations. We obtained the mean FLH and CWV from 80 sounding stations in China with complete 26-yr (1980–2005) data. In the modeling experiment, the hail size of each station is only a function of FLH and CWV, other variables are fixed. In addition, the station elevation is considered as an input parameter into the model to measure the melting height together with FLH. Lastly, the geographic distribution of hail size produced by the simple model experiment is given in Fig. 8. Compared with observations (Fig. 1), the simulated mean MHDs are a little bit larger. However, the model roughly reproduces the basic geographic distribution of hail size. The MHD in southern China is significantly larger than that in northern China, implying that abundant water vapor favors large hail with a given FLH.

d. Modeling trend of MHD

In this one-dimensional hail formation model, larger vertical updraft, higher water vapor content in a cloud, and lower cloud top all favor the larger MHD. It is hard to estimate changes in hail size due to climate change because of the uncertainties involved. Brimelow et al. (2002) showed that the maximum hail size is sensitive to the cloud-top height and freezing region (from 0°C to −40°C) in thunderstorms using a time-dependent hail growth model coupled with a one-dimensional steady-state cloud model (HAILCAST). On the other hand, Van den Heever and Cotton (2004) found that hail size has a significant effect on the simulated supercell storms in the Regional Atmospheric Modeling System (RAMS). They showed that increasing the number of smaller (lager) hail would weaken (strengthen) the hailstorm. This interaction between hail size and hailstorm makes the issue much more complicated. Nevertheless, the simple one-dimensional model may still provide some useful information regarding the trend of hail size in response to climate change.

Figure 9 shows variations of the mean MHD as functions of the annual mean updraft, CWV, and FLH from the one-dimensional hail formation model (see the details in the appendix). The maximum updraft is estimated from the CAPE. The hail size shows a clear upward trend in response to the increasing CAPE since 1980 (Fig. 9a) but a downward trend in response to either CWV or FLH (Figs. 9b,c).

With the annual mean CAPE, FLH, and CWV, we get the variation and long-term trend of the annual mean MHD from the model experiment for the period of 1980–2005 (Fig. 9d). Compared with the observations, though the variation of the simulated annual mean MHD is not strictly the same as the observed, the decadal variability and long-term trend of the two are consistent with each other. In section 3, we have shown that there are no obvious changes in hail size in the four regions in China (indicated by the proportion of severe hail). This could be a result of the compensation of the positive and negative effects on hail size. In our model experiments, CAPE, FLH, and CWV may roughly explain both the geographic distribution and long-term trend of the observed MHD to some degree.

5. Conclusions

Hail size data of four typical regions in China for the period of 1980–2005 are collected and analyzed to examine the mean distributions and potential changes of hail size. It is found that the MHD around 5–10 mm is the most common maximum hail size in the four regions. However, the ratio of severe hail in southern China is larger than that in northern China. Special attention has been given to severe hail and its seasonal variation. Similar to the distribution of hail frequency, severe hail in southern China mainly occurs from February to June, while in northern China, the high ratio of severe hail occurs mainly in summer with its peak in June.

The long-term trend of hail size, especially the MHD of severe hail, is also examined. Hail size shows a weak downward trend in Guizhou and IMAR and an upward trend in Hebei, whereas no trend in XUAR. However, none of these trends is statistically significant. The factors that may influence hail size are also discussed with the results from a one-dimensional hail formation model, which is used to examine the sensitivity of hail size to FLH and column cloud liquid water. The results show that CAPE, CWV, and FLH all play important roles in determining both the geographic distribution and long-term trend in hail size in China.

Acknowledgments

We thank the meteorology agency at XUAR, IMAR, Guizhou Province, and Hebei Province for allowing us to access their data. Comments by two anonymous reviewers helped improve the original manuscript. This study is partly supported by the Chinese Ministry of Science and Technology Project (Grant 2009CB421500) and by the Chinese National Science Foundation under Grants 40975059 and 40921160380. YW is partly supported by the Japan Agency for Marine-Earth Science and Technology (JAMSTEC), NASA, and NOAA through their sponsorship of the International Pacific Research Center (IPRC) at the University of Hawaii at Manoa.

REFERENCES

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    • Search Google Scholar
    • Export Citation
  • Dessens, J., 1986: Hail in southwestern France. I: Hailfall characteristics and hailstorm environment. J. Climate Appl. Meteor., 25 , 3547.

    • Search Google Scholar
    • Export Citation
  • Doswell III, C. A., , and E. N. Rasmussen, 1994: The effect of neglecting the virtual temperature correction on CAPE calculations. Wea. Forecasting, 9 , 625629.

    • Search Google Scholar
    • Export Citation
  • Foote, G. B., 1984: A study of hail growth utilizing observed storm conditions. J. Climate Appl. Meteor., 23 , 84101.

  • Giaiotti, D., , E. Gianesini, , and F. Stel, 2001: Heuristic considerations pertaining to hailstone distributions in the plain of Friuli-Venezia Giulia. Atmos. Res., 57 , 269288.

    • Search Google Scholar
    • Export Citation
  • Han, G. F., 1999: The analysis on the feathers of hail hazard in Hebei province (in Chinese). J. Catastr., 14 , 243246.

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APPENDIX

An Introduction to the One-Dimensional Numerical Hail Model

The one-dimensional numerical hail model introduced by Wu et al. (1997) was used for calculating the maximum hail size given the cloud properties. The model consists of two modules: one is the one-dimensional cumulus cloud model and the other is the hail growth model.

a. One-dimensional cumulus numerical model

According to Wu et al. (1997), water transformation in a quasi-steady one-dimensional cumulus cloud can be expressed as
i1520-0442-23-18-4973-ea1
i1520-0442-23-18-4973-ea2
where Qc is cloud water; λ is the threshold value (here set to 5 × 10−4; when Qc is greater than λ, rain begins forming); Qh is rainwater; Qs is water vapor in cloud; qs is saturated specific humidity in cloud; qe is specific humidity outside the cloud (namely of the environment); μ is the entrainment rate related to the initial radius of the cloud base; K1 and K2 are coefficients of autoconversion growth and aggregation growth of rain, respectively; K2 = EN00.125; N0 is the intercept parameter for rain; E is the aggregation coefficient for rain and is set to be 0.85; ρ is air density; W is updraft velocity in cloud; and z is height.
With the one-dimensional cumulus model, Wu et al. (1997) found that cloud water content and updraft velocity could be approximately written as linear functions of height:
i1520-0442-23-18-4973-eaq1
where c, c1, a, and b are constants; z1 and z2 are the initial height and end height of the maximum water vapor distribution, respectively; H is the cloud-top height; qm and Wm are assumed at the same height.

b. One-dimensional hail growth model

Assuming R to be the hail radius, the growth of hail is described by the equation
i1520-0442-23-18-4973-ea3
The solution of R as a function of height was given by Wu et al. (1997). In this model, hail melting is considered (see the details in Wu et al. 1997). Lastly, the maximum hail diameter (MHD) is a function of Wm, qm, H, z1, and z2.

c. Simulation of long-term trend of hail size

Some details in the simulation of the long-term trend of hail size are discussed here. Given column water vapor (CWV), freezing level height (FLH), and convective available potential energy (CAPE), we set the following arrangements and experiments:

1) CWV

In the hail model, the maximum water content qm is one of the key variables to the MHD. To find the sensitivity of the long-term trend of MHD to the long-term trend of CWV, qm was replaced by CWV with other variables fixed. The model was run with the annual value of CWV for each station. Although it is not perfect to replace qm with CWV, the model could roughly reflect the variation and trend of the MHD in response to the long-term trend in CWV.

2) FLH

In the model, hail melting is calculated from FLH to the ground. Thus, FLH is a key variable to hail size. The long-term trend and variation of the MHD were obtained by running the model with the annual mean FLH at each station.

3) CAPE

The maximum vertical motion in cloud is closely related to CAPE, which is roughly equal to half the square of the maximum vertical wind speed (Doswell and Rasmussen 1994). This allows us to estimate the maximum vertical wind speed based on the annual mean CAPE in the model.

Fig. 1.
Fig. 1.

Geographic distribution of the mean MHD for the period of 1980–2005 in the four regions of XUAR, IMAR, Hebei, and Guizhou in China. Locations of solid circles indicate the stations with hail size records.

Citation: Journal of Climate 23, 18; 10.1175/2010JCLI3600.1

Fig. 2.
Fig. 2.

Scatterplot of the mean MHD (1980–2005) against corresponding station elevation in four regions (shown in Fig. 1).

Citation: Journal of Climate 23, 18; 10.1175/2010JCLI3600.1

Fig. 3.
Fig. 3.

PDV (refer to the definition in section 3) of the six ranks of the MHD for the four regions. The horizontal lines denote the mean PDV of the four regions for each rank.

Citation: Journal of Climate 23, 18; 10.1175/2010JCLI3600.1

Fig. 4.
Fig. 4.

(a) PDV of severe hail of four regions for months 1–12. (b) PDV of the MHD of the six ranks across the four regions for the entire year, the warm season, and the cold season.

Citation: Journal of Climate 23, 18; 10.1175/2010JCLI3600.1

Fig. 5.
Fig. 5.

Annual anomalies (bars) and long-term trend (solid line) in PDV of severe hail for 1980–2005 in (a) Guizhou, (b) Heibei, (c) IMAR, and (d) XUAR.

Citation: Journal of Climate 23, 18; 10.1175/2010JCLI3600.1

Fig. 6.
Fig. 6.

(left) Amount of melting during descent to the ground for different hail sizes in the cloud. (right) Final hail size as a function of hail size before melting. Dashed lines indicate the 5–15-mm MHD on the ground corresponding to the 15–20-mm MHD before melting.

Citation: Journal of Climate 23, 18; 10.1175/2010JCLI3600.1

Fig. 7.
Fig. 7.

(left) Sensitivity of hail size to Qm and (right) interannual variation (indicated by “CWV”) and linear long-term trend (indicated by “linear CWV” with p value given) in the annual mean CWV averaged over the stations shown in Fig. 8 during 1980–2005.

Citation: Journal of Climate 23, 18; 10.1175/2010JCLI3600.1

Fig. 8.
Fig. 8.

Geographic distribution of the simulated MHD based on elevation, mean FLH, and mean CWV at the selected 80 stations in China.

Citation: Journal of Climate 23, 18; 10.1175/2010JCLI3600.1

Fig. 9.
Fig. 9.

Sensitivity of the simulated variation and long-term trend of mean MHD to (a) CAPE, (b) CWV, and (c) FLH for the period 1980–2005. (d) The simulated variation of mean MHD based on the annual mean FLH, CWV, and CAPE and observations. The linear trends of mean MHD are indicated by the solid lines, and the p values are also given.

Citation: Journal of Climate 23, 18; 10.1175/2010JCLI3600.1

Table 1.

Columns 2–7 are defined respectively as the number of first-order stations (Stations), number of stations qualified for being used (Used), Used/Stations (Percentage), number of hail days (HDs), number of hail size observations (HSOs), and HSOs/HDs (Percentage) in the four regions.

Table 1.
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