Climatological characteristics of raindrop size distributions within a topographically complex area

Introduction Conclusions References Tables Figures

To further investigate natural DSD variations, Ulbrich (1983) developed a gamma DSD that permitted changing the dimension of the intercept parameter of N 0 (m −3 mm −1−µ ) with (N(D) = N 0 D µ exp(−ΛD)).In addition, to enable the quantitative analysis of different rainfall events, the development of a normalized gamma DSD model that accounted for the independent spread of DSD from the disdrometer channel interval enabled a better representation of the actual DSD (Willis, 1984;Dou et al., 1999;Testud et al., 2001).
DSDs depend on the rainfall type, geographical and atmospheric conditions, and observation time, and are closely linked to microphysical characteristics that control rainfall development mechanisms.The microphysical structures of rainfall are more complicated in the middle and high latitudes than in the low latitudes (Leinonen et al., 2012).
In the case of stratiform rainfall, raindrops grow by accretion because of the relatively long residence time in weak updrafts, in which almost all water droplets are changed to ice particles.With time, the ice particles grow sufficiently and fall to ground.The raindrop size of stratiform rainfall observed at ground level is larger than that of convective rainfall, due to the resistance of the ice particles to break-up mechanisms.In contrast to stratiform rainfall, in convective rainfall raindrops grow by the collision-coalescence mechanism associated with relatively strong vertical wind speeds and short residence time in the cloud.Fully-grown raindrops are smaller in diameter than those in stratiform rainfall due to the break-up mechanism (Mapes and Houze Jr, 1993;Tokay and Short, Introduction Conclusions References Tables Figures

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Full  1996).Convective rainfall can be classified into two types based on the origin and direction of movement.Rainfall systems occurring over ocean and land are referred to as maritime and continental rainfall, respectively (Göke et al., 2007).Continental rainfall is related to a cold-rain mechanism whereby raindrops grow in the form of ice particles.In contrast, maritime rainfall is related to a warm-rain mechanism whereby raindrops grow by the collision-coalescence mechanism.Therefore, the mass-weighted drop diameter (D m ) of continental rainfall observed on the ground is larger than that of maritime rainfall, and a smaller normalized intercept parameter (N w ) is observed in continental rainfall (Bringi et al., 2003).Specific heat is a major climatological feature that creates differences between DSDs in maritime and continental regions.These two regions have different thermal capacities and thus display different temperature variations with time.The surface temperature of the ocean changes slowly because of the water's high thermal capacity, while the continental regions, which have comparatively lower thermal capacity, display greater diurnal variability.Sea breezes generally occur in the evening when the temperature gradient between the sea and land becomes negative, which is the opposite of the gradient in the daytime (DT).In coastal regions, the land-sea breeze effect causes a pronounced difference between the DT and nighttime (NT) DSD characteristics.When mountains are located near the coast, the difference is intensified by mountain and valley winds (Qian, 2008).
In the present study, we analyzed a four-year dataset spanning from 2001 to 2004, collected from Busan, Korea (35.12 • N, 129.10 • E) using a Precipitation Occurrence Sensor System (POSS) disdrometer, to investigate the characteristics of DSDs in this complex mid-latitude region comprising both land and ocean.To quantify the effect of land-sea breeze on these characteristics, we also analyzed diurnal variations in DSDs.The remainder of the manuscript is organized as follows.In Sect. 2 we review the normalized gamma model and explain the DSD quality control method and the classification of rainfall.In Sect. 3 we report the results of DSD analysis with respect to Figures

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Full stratiform/convective and continental/maritime rainfall, and discuss diurnal variations.
Finally, a summary of the results and the main conclusions are presented in Sect. 4.

Normalized gamma DSD
The DSD reflects the microphysical characteristics of rainfall.Normalization is used to define the DSD and to solve the non-independence of each DSD parameter (Willis, 1984;Dou et al., 1999;Testud et al., 2001).Furthermore, a normalized gamma DSD enables the comparison of quantitative estimations for cases of rainfall events that have different time scales and rain rates.Here, we use the DSD model designed by Testud et al. (2001): where N(D) is the number concentration (m −3 mm −1 ), D is raindrop size (mm), and f (µ) is defined using the shape parameter (µ) and gamma function (Γ) as follows: From the value of N(D), the median volume diameter D 0 can be obtained as follows: Full Mass-weighted mean diameter (D m ) is calculated as the ratio of the fourth to the third moment of the DSD: The normalized intercept parameter (N w ) is calculated as follows: The shape of the DSD is calculated as the ratio of D m to the SD of D m (Ulbrich and Atlas, 1998;Bringi et al., 2003;Leinonen et al., 2012): In addition, σ m /D m is related to µ as follows: Liquid water content (LWC) and rainrate (R) can be defined from the estimated DSD: where ρ w is water density (gm −3 ).Similarly, R can be defined as follows: where v(D) is the fall velocity for each raindrop size.The relationship between fall velocity (m s −1 ) and raindrop size (D) is given by Atlas et al. (1973) who developed an empirical formula based on the data reported by Gunn and Kinzer (1949):

Quality control of POSS data
POSS was used to measure the number of raindrops within the diameter range of 0.34-5.34mm, using bistatic, continuous wave X-band Doppler radar across 34 channels (Fig. 1; Sheppard and Joe, 2008).
A POSS disdrometer was installed in Busan, Korea, along with other atmospheric instruments, the locations of which are shown in Fig. 2. Estimating raindrop size correctly is challenging and care should be taken to ensure reliable data are collected.We performed the following quality controls to optimize the accuracy of the disdrometer estimates.(i) Snow event data detected by POSS were excluded, to focus only on liquid state rainfall.(ii) Non-atmospheric data were removed from the analysis if the DSD spectra was smaller than five consecutive channels, or smaller (larger) than the 5th (10th) channel.(iii) Only data recorded in more than 10 complete channels were considered.(iv) To compensate for the reduced capability to detect raindrops smaller than 1 mm when R > 200 mm h −1 (as recorded by the disdrometer), data collected when R > 200 mm h −1 were not included in the analyses.(v) To eliminate wind and acoustic noise, data collected when R < 0.1 mm h −1 were removed (Tokay and Short, 1996).
Because the correlation coefficient between D 0 and D m was 0.985 for the whole study period, we considered that D m could be used for the analysis instead of D 0 .After performing all quality control procedures, 114 155 spectra were left from an original total of 166 682.Accumulated rainfall amount from POSS during the entire period was about Introduction

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Radar Parameters
To derive the rainfall relations, polarimetric parameters were computed by a T-matrix scattering simulation (Waterman, 1971;Zhang et al., 2001).The radar reflectivity factor (z, mm 6 m −3 ) and horizontal polarized radar reflectivity (Z h , dBZ) were computed using the DSD data collected by POSS, as follows: Axis ratios of raindrops differ with atmospheric conditions and rainfall type.To derive the drop shape relation from the drop diameter, we performed numerical simulations and wind tunnel tests employing a forth-polynomial equation, as in many previous studies (Beard and Chuang, 1987;Pruppacher and Beard, 1970;Andsager et al., 1999;Brandes et al., 2002).The drop-shape relation used in the present study is a combination of those from Andsager et al. (1999) and Beard and Chuang (1987) for three raindrop size ranges (Bringi et al., 2003).
The raindrop axis ratio relation of Andsager et al. (1999) is applied in the range of 1 < D(mm) < 4, as follows: The drop-shape relation of Beard and Chuang (1987) is applied in the range of D < 1 mm and D > 4 mm, as follows: We assumed the SD and the mean canting angle of raindrops as 7 and 0 • , respectively.The refractive indices of liquid water at 20 • C were used (Ray, 1972).We calculated dual Introduction

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Full polarized radar parameters based on these conditions.The parameters of differential reflectivity, Z dr (dB), specific differential phase, K dp (deg km −1 ), and attenuation, A h (dB km −1 ), using one-minute resolution DSD data were calculated and analyzed.

Classification of rainfall types and rainfall events
Rainfall systems can be classified as stratiform or convective in nature, via analysis of the following microphysical characteristics: (i) DSD, using relationships between N 0 and R (N 0 = 4 × 10 9 R 4.3 ) (Tokay and Short, 1996;Testud et al., 2001), (ii) radar reflectivity, where, according to Gamadre and Houze (1982), a rainfall system that displays radar reflectivity larger than 38 dBZ is considered to be convective, and (iii) rainfall rate, where average 5 min R > 0.5 mm h −1 is considered convective rainfall (Hamilton, 1988).
Alternatively, rainfall that has 1 min R > 5 mm h −1 and a SD of R > 1.5 is considered as convective type (Bringi et al., 2003).The rainfall classification method proposed by Bringi et al. (2003) is applied in the present study.
It is necessary to categorize different rainfall systems because their microphysical characteristics show great variation depending on the type of rainfall, as well as the type of rainfall event; e.g., typhoon, changma, heavy rainfall and seasonally discrete rainfall.To investigate the temporal variation in DSDs, we analyzed daily and seasonal DSDs.Likewise, to investigate diurnal variability in DSD, DT and NT data were considered by using the sunrise and sunset time in Busan (provided by the Korea Astronomy and Space Science Institute (KASI)).In the middle latitudes, and especially Busan, the timings of sunrise and sunset vary due to solar culminating height.The earliest and latest sunrise (sunset) time is 05:09 KST (17:12 KST) and 07:33 KST (19:42 KST), respectively.DT (NT) is defined as the period from the latest sunrise (sunset) time to the earliest sunset (sunrise) time (Table 1).To analyze the predominant characteristics of DSDs for typhoon rainfall, nine typhoon events were selected from throughout the entire study period.Introduction

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Full This study utilizes the Korea Meteorological Administration (KMA) rainfall warning regulations to identify heavy rainfall events.The KMA issues a warning if the accumulated rain amount is expected to be > 70 mm h −1 within a 6 h period, or > 110 mm h −1 within a 12 h period.Rainfall events classified as changma and typhoon were not included in the classification "heavy rainfall".
Changma is the rainfall system or rainy season that is usually present over the Korean Peninsula between mid-June and mid-July.The selected dates and periods of each rainfall category are summarized in Table 1.

DSD and radar parameters
Figure 4 shows the Probability Density Function (PDF) and Cumulative Distribution Function (CDF) of DSDs and radar parameters with respect to stratiform and convective rainfall.The PDFs of DSD and radar parameters were calculated using the non-parameterization kernel estimation to identify the dominant distribution of each parameter recorded in Busan.Non-parameterization kernel estimation was also used to identify continuous distributions of DSDs.The PDF of stratiform rainfall is similar to that of the dataset for the entire analysis period due to the dominant contribution of stratiform rainfall (about 90.6 %) to the overall rainfall.However, the PDF for convective rainfall is significantly different from that of the entire analysis period, and as the convective rainfall contributes only 5.8 % of the overall rainfall (Table 4).When µ < 0 the distribution of µ for convective rain is more frequent than that for stratiform rain (Fig. 4a).Alternatively, the frequency of µ for stratiform rainfall is higher than that of convective rainfall when 0 < µ > 5.The value of µ for convective rainfall is higher than that for stratiform rainfall because the break-up mechanism reduces the number concentration of large raindrops.As the result, the number concentrations of mid-size raindrops increased due to the decrease in the number concentration of relatively large Introduction

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Full raindrops (Hu and Srivastava, 1995;Sauvageot and Lacaux, 1995).However, we observed a higher frequency of convective rainfall than stratiform rainfall in the negative µ range.The PDF of D m displays two peaks around 0.7 and 1.2 mm for stratiform rainfall and the entire rainfall dataset, respectively.We note that a gentle peak exists around 0.7 mm for both stratiform and convective rainfall datasets (Fig. 4b).These features are similar to the distribution of D m observed in a high-latitude region at Järvenpää, Finland (Fig. 4 of Leinonen et al., 2012).For D m values > 1.5 mm, the PDF for convective rainfall is higher than stratiform rainfall.Accordingly, the frequency of stratiform rainfall is higher than that of convective rainfall when D m < 1.5 mm.Generally, stratiform rainfall that develops by the cold rain process displays weaker upward winds and less efficient break-up of raindrops.Therefore, stratiform rainfall tends to produce larger raindrops than convective rainfall that develops by the warm rain process.In contrast to this general concept, the average D m values for convective and stratiform rain are approximately 1.6 and 1.3 mm, respectively.This finding is consistent with the results of Atlas et al. (1999) who found that the D m of convective rainfall is larger than that of stratiform rainfall on Kapingamarangi Island, Micronesia.
The PDF of log 10 (N w ) for the entire rainfall dataset was evenly distributed between 1.5 and 5.5 m −3 mm −1 , with a peak at N w = 3.3 m −3 mm −1 (Fig. 4c).The PDF of log 10 (N w ) for stratiform rainfall is rarely > 5.5 m −3 mm −1 , while for convective rainfall it is often > 5.5 m −3 mm −1 .There is a similar frequency in the stratiform and convective rainfall at 4.4 m −3 mm −1 .
The PDF distributions for log 10 (R) and log 10 (LWC) are similar (Fig. 4d and e).The PDF of log 10 (R) for the entire rainfall dataset ranged between −1 and 2 mm h −1 .A peak exists at 0.3 mm h −1 and the PDF rapidly decreases from the peak value as R increases.The PDF for stratiform rainfall has a higher frequency than that of the entire rainfall when log(R) < 0.5 mm h −1 , while the PDF for convective rainfall is denser between 0.4 and 2 mm h −1 .Furthermore, at the peak value of 0.9 mm h −1 , the fre-Introduction

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Full quency of the PDF for convective rainfall was higher than that of stratiform rainfall when log 10 (R) > 0.65 mm h −1 .The PDF and CDF for horizontal reflectivity (Z h ), differential reflectivity (Z dr ), specific differential phase (K dp ), and specific attenuation of horizontal reflectivity (A h ) are shown in Fig. 4f-i.The PDF of Z h for stratiform rainfall (Fig. 4f) is widely spread between 6 and 50 dBZ with the peak at approximately 30 dBZ.Conversely, for convective rainfall, frequencies lie between 25 and 55 dBZ and the peak frequency value at approximately 40 dBZ.The frequency value of reflectivity is higher for convective rainfall than for stratiform rainfall in the range of ∼> 34 dBZ.Furthermore, the shape of the PDF for convective rainfall is similar to that reported for Darwin, Australia (Steiner et al., 1995); however, for stratiform rainfall there are significant differences between Busan and Darwin in terms of the shape of the frequency distribution.The method of classifying rainfall as convective when radar reflectivity is > 38 dBZ, as proposed by Gamache and Houze Jr. (1982), is therefore not suitable in this instance because of the distribution of stratiform and convective rainfall types in Busan.
The PDF of Z dr primarily exists between 0 and 2 dB, and the peaks are at 0.3 and 0.8 dB (Fig. 4g).The distribution of Z dr for convective and stratiform rainfall is concentrated between 0.5 and 1.4 dB, and between 0.7 and 2 dB, respectively.The frequency of Z dr for convective (stratiform) rainfall exists in ranges higher (lower) than 0.7 dB.
The dominant distribution of K dp for the entire dataset and for stratiform rainfall lies between 0 and 0.14 deg km −1 , with a peak value of 5.0 × 10 −3 deg km −1 .However, for convective rainfall the PDF of K dp is evenly spread between 0.01 and 0.15 deg km −1 .
Furthermore, when K dp > 5.0 × 10 −2 deg km −1 , the frequency of the PDF for convective rainfall is higher than that of stratiform rainfall (Fig. 4h).The PDF of A h is similar to that of K dp and is spread between 0 and 1.0 × 10 −2 dB km −1 .For the case of the entire rainfall dataset and for stratiform rainfall, the PDF of A h is concentrated between 0 and 2.0×10 −3 dB km −1 and that of convective rainfall is strongly concentrated between 1.0 × 10 −3 and 8.0 × 10 −3 dB km −1 (Fig. 4i).Unlike Introduction

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Full the PDF of A h for convective rainfall, the PDF for stratiform rainfall shows a strong peak at about 2.0 × 10 −3 dB km −1 .Based on the PDF analysis, DSDs in Busan exhibit larger R and N w , and smaller µ and D m than those observed in Järvenpää (Table 2).

Climatological characteristics of DSD in Busan
The climatological characteristics of DSDs for 10 rainfall categories are analyzed in this study.Sample size and ratio rainfall for each category are summarized in Table 3. Figure 5a illustrates the distribution of all 1 min stratiform rainfall data, and Fig. 5b shows scatter plots of averaged D m and log 10 (N w ) for all 10 rainfall categories for stratiform rainfall data.Figure 5a displays a remarkably clear boundary in the bottom sector and shows that most of the data lie below the reference line used by Bringi et al. (2003) to classify convective and stratiform rainfall.The average value of D m and N w for all rainfall categories, except for heavy rainfall, spreads between 1.2 and 1.5 mm and between 3.2 to 3.5 m −3 mm −1 , respectively (Fig. 5b).These values are relatively small compared with the reference line presented by Bringi et al. (2003).However, the average line of N w for each rainfall type extends beyond the reference line when D m is greater than 1.7 mm (figure not shown), which is similar to the results from Järvenpää (Fig. 15 of Leinonen et al., 2012).The distribution of 1 min convective rainfall data is displayed in Fig. 6a and the distribution of average values of D m and N w for the 10 rainfall categories in the case of convective rainfall in Fig. 6b.The blue and red cross symbols represent maritime and continental rainfall, respectively, as defined by Bringi et al. (2003).The scatter plot of 1 min convective rainfall data shows more spread in the continental cluster than the maritime cluster; however, the average values for the 10 rainfall categories are all located around the maritime cluster, except for the typhoon category.By considering the average value of typhoon (Fig. 6b), we can induce the simple linear equation using D m and N w as follows: N w = 10 exp[−1.8Dm + 6.9] (15) Introduction

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Full The D m (N w ) value for the typhoon category was considerably smaller (larger) than that of the other categories.This result does not agree with that reported by Chang et al. (2009), who noted that the D m of convective rainfall typhoon showed a large value compared with that associated with stratiform rainfall.

Diurnal variations in DSDs
Figure 7a shows a histogram of normalized frequency of 16 wind directions recorded by the AWS, which is the same instrument as that used to collect the data shown in Fig. 3. To establish the existence of a land-sea breeze, the difference in wind direction frequencies between DT and NT were analyzed.Figure 7b shows the difference between DT and NT in terms of the normalized frequency of 16 wind directions.Positive (negative) values indicate that the frequency of wind is higher in the DT (NT).The frequency of wind direction in the DT (NT), between 205.5 • (22.5 • ) and 22.5 • (205.5 • ), is higher than that in the NT (DT) (Fig. 7b).The observation site where the POSS was installed is located 611 m from the coast line, suggesting that the effect of the land-sea breeze would have been recorded.To understand the effects of the land-sea breeze on DSD characteristics, we analyzed the PDF and 2 h averaged DSD parameters for DT and NT. Figure 8 illustrates the distributions of µ, D m , log 10 (N w ), log 10 (LWC), log 10 (R), and Z h .There were large variations of µ with time.The µ values varied from 2.628 to 3.366 and the minimum and maximum µ values occurred at 08:00 KST and 22:00 KST, respectively (Fig. 8a).A D m larger than 1.3 mm dominated from 00:00 KST to 12:00 KST, before decreasing dramatically between 12:00 and 14:00 KST.The minimum and maximum D m appeared at 14:00 KST and 08:00 KST, respectively (Fig. 8b).N w generally varies inversely to D m ; however, no inverse relationship was identified between D m and N w in our study (Fig. 8c).The maximum and minimum values of N w were found at 06:00 KST and 22:00 KST.Introduction

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Full Variability through time was similar for R, LWC, and Z h .There was an increasing trend from 00:00 KST to 08:00 KST followed by a dramatically decreasing trend from 08:00 KST to 14:00 KST (Figs. 8d,11e and f).Note that the time of the sharp decline for R between 12:00 KST and 14:00 KST is simultaneous with a D m decrease.Larger (smaller) drops would contribute to higher R in the morning (afternoon).
The PDF distribution of µ between −2 and 0 is more concentrated for NT than for DT.Furthermore, when µ > 0, DT and NT frequency distributions are similar (Fig. 9a).A larger number of smaller and larger raindrops would be expected in NT than in DT.
The distribution of DT D m < 0.7 mm is wider than that of the NT.However, between 0.7 and 1.5 mm the frequency for NT is higher than that for DT, whereas the distribution in the range > 1.5 mm is similar for both DT and NT (Fig. 9b).We note that the smaller peak of D m around 0.6 mm for the entire rainfall dataset (Fig. 4b) was observed only in DT.
The distribution of log 10 (N w ) for DT (NT) is narrower than that of NT (DT) between 4 and 5.2 m −3 mm −1 (2.8 and 4 m −3 mm −1 ) (Fig. 9c).Bringi et al. (2003) noted that the maritime climatology displayed larger N w and smaller D m values than the continental climatology, based on observed DSDs in the low and middle latitude.Also, Göke et al. (2007) emphasized that rainfall type can be defined by the origin location and movement direction.In accordance with these previous results, we consider NT rainfall in the Busan region to be more likely caused by a continental convective system.Kozu et al. (2006) analyzed the diurnal variation in R at Gadanki (South India), Singapore, and Kototabang (West Sumatra) during the summer monsoon season.All regions displayed maximum R at approximately 16:00 KST, except for Gadanki.Qian (2008) also examined the diurnal variation of accumulated rain amount on Java Island, Indonesia, for 30 years from 1971 to 2000.Rainfall occurred mainly on land areas (over the ocean) in the DT (NT) when the sea (land) breeze was dominant.
In the present study, the shape of the PDF of LWC and R for DT and NT are similar.LWC and R distributions during the DT (NT) are higher (lower) than in the NT (DT) Introduction

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Full when LWC and R are smaller (greater) than 6.3×10 −3 g m −3 and 1 mm h −1 , respectively (Fig. 9d and e).The positive relationship between horizontal radar reflectivity and LWC and R during the DT (NT) was higher (lower) than in the NT (DT) in the range below (above) about 27 dBZ (Fig. 9f).

Diurnal variations of DSDs with respect to season
Busan experiences distinct atmospheric conditions that are caused by the different frequencies and magnitudes of land-sea breezes in response to variable sunrise and sunset times.To identify seasonal variations of DSDs with respect to the effect of the land-sea breeze, we analyzed the DT and NT PDF of D m and N w in the summer and winter.The start and end times of DT (NT) were sorted using the latest sunrise (sunset) and the earliest sunset (sunrise) time for each season (Table 4).
Figure 10 shows a histogram of wind directions in summer and winter for the entire period.The frequencies of summer and winter wind directions are similar to each other.However, in Fig. 11, the DT and NT distributions of winter wind direction display opposing frequencies between 0 and 45 • , which is a land and ocean area, and between 90 and 225 • , which is an ocean area.In other words, in contrast to the summer, the frequency of land breeze increased (decreased) during the DT (NT) in winter.
To identify the variability of DSDs caused by the land-sea breeze in summer and winter, a 2 h interval time series of D m , N w and R was analyzed.In the summer, the time series of D m displays considerably large values between 00:00 KST and 12:00 KST, compared with the period between 14:00 KST and 22:00 KST (Fig. 12a).The mean value of D m decreases dramatically between 12:00 KST and 14:00 KST.N w generally has a negative relationship with D m , except at 18:00 KST and 20:00 KST (Fig. 12b).A time series of D m for the Busan area shows a relatively large value from 00:00 KST to 12:00 KST and a relatively small value from 14:00 KST to 22:00 KST.In the case of N w , however, the value was relatively small from 00:00 KST to 12:00 KST and there was no clear pattern for larger values.There are two peaks of log 10 (N w ), at 06:00 KST and Introduction

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Full 20:00 KST (Fig. 12b).The rainfall rate tends to increase gradually from 00:00 KST to 08:00 KST and decrease from 08:00 KST to 14:00 KST, which is similar to the pattern of R (Fig. 12c).The D m time series is similar to results from Qian (2008), who analyzed the diurnal variability of wind direction and R on Java Island during the summer season using 30 years (from 1971 to 2000) of NCEP/NCAR reanalyzed data.They found that a land-breeze occurred from 01:00 KST to 10:00 KST and a sea-breeze from 13:00 KST to 22:00 KST (Fig. 7 of Qian, 2008).
Variability of the winter D m time series is the inverse of the summer time series (Fig. 13a).The mean value of D m steadily increases from 00:00 KST to 16:00 KST and then decreases from 16:00 KST to 22:00 KST.The winter N w time series displays a clear inverse pattern compared with the D m variation with time (Fig. 13b).The mean value of log 10 (N w ) increases from 16:00 KST to 04:00 KST and then steadily decreases from 04:00 KST to 16:00 KST.The peak occurs at 04:00 KST (Fig. 13c).
The PDF distribution of summer D m displays a relatively large DT frequency compared with NT when D m < 1.65 mm, except for the range between 0.7 and 1 mm.However, in the range of D m > 1.65 mm, the NT PDF displays a larger frequency (Fig. 14a).The PDF of log 10 (N w ) for NT has a larger frequency than the DT when log 10 (N w ) < 3.3 m −3 mm −1 but smaller frequency when log 10 (N w ) > 3.3 m −3 mm −1 (Fig. 14b).
The DT and NT PDFs of D m and log 10 (N w ) during winter display an inverse distribution.For the PDF of D m , there is a considerable frequency for NT (DT) when D m < (>) 1.6 mm (Fig. 15a).The PDF of log 10 (N w ) during summer display an inverse distribution to that of the winter.The PDF frequency of summer season for NT (DT) is larger than that of the DT(NT) when log 10 (N w ) < (>) 3.3 m −3 mm −1 (Fig. 14b).However, during the winter DT (NT) a relatively large frequency exists when log 10 (N w ) < (>) 3.5 m −3 mm −1 (Fig. 15b).Relatively large (small) D m and small (large) log 10 (N w ) are displayed during the NT (DT) when a land-breeze (sea-breeze) occurs.Introduction

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Summary and conclusion
Climatological characteristics of DSDs in Busan were analyzed using the DSD data observed by POSS over a four-year period from 24 February 2001 to 24 December 2004.Observed DSDs were filtered to remove error by performing several quality control measures, and an AWS rain gauge installed nearby was used to verify the rainfall amount recorded by the POSS.We analyzed DSD characteristics of convective and stratiform rainfall types, as defined by Bringi et al. (2003).The rainfall dataset was thus divided into stratiform and convective rainfall and their contributions to the total rainfall were 90.6 and 5.8 %, respectively.
In the comparison of DSD parameters observed between Busan and Järvenpää, the averaged rainfall rate in Busan was higher than in Järvenpää.D 0 was smaller and N w larger in Busan compared with Järvenpää and there was a considerable difference in µ between the two cities.We consider that the greater number of smaller drops contributes to the higher rainfall rate in the mid latitudes.According to the study by Bringi et al. (2003), the rainfall in Busan has more maritime climatological DSD characteristics.
The mean values of D m and N w for stratiform rainfall are relatively small compared with the average line of stratiform rainfall produced by Bringi et al. (2003), except for heavy rainfall events.The mean values of D m and N w for convective type for all rainfall categories converged around the maritime cluster, except for the typhoon category.
The convective rainfall associated with a typhoon has considerably smaller D m and larger N w values compared with the other rainfall categories.This is likely caused by increased raindrop break-up as a result of strong wind effects.Furthermore, the distributions of mean D m and N w values for all rainfall categories associated with convective rainfall display a linear relationship, apart from the typhoon category.
The analysis of diurnal variation in DSD yielded the following results: first, in the negative range of µ, the frequency of µ is higher at night than during the DT.The PDF of R is higher at NT than during the DT when log 10 (R) > 0.6 mm h −1 .A gentle Introduction

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Full peak of D m was identified during the DT at approximately 0.6 mm for both stratiform and convective rainfall.Additionally, the frequency of D m is higher at NT than during the DT when D m > 0.65 mm h −1 .For N w , which tends to be inversely related to D m , its frequency is higher at NT than during the DT when log 10 (N w ) > 3.9 m −3 mm −1 .At NT, D m is higher and R, µ, and N w values are lower compared with the DT.In other words, maritime characteristics are observed in the DT more often than in the NT, based on the results of Bringi et al. (2003).The above-mentioned DSD characteristics are likely due to the land-sea breeze caused by differences in specific heat between the land and ocean.These features are also apparent in the seasonal diurnal distribution.The PDF of DT and NT during the summer is similar to the PDF of the entire period; however, the PDF of DT and NT in the winter displays the inverse distribution because of seasonal differences in wind direction.8.31 5.29,6.19,8.7,8.19,6.30,6.27,6.30,7.1,7.1,Full  Full  Full  Full Distribution (DSD) controls microphysical processes of rainfall and therefore plays an important role in the development of quantitative rainfall estimation algorithms based on forward scattering simulations of radar measurements Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Author contributions.C.-H.You designed the study.S.-H.Suh modified the original study theme and performed the study.C.-H.You and S.-H.Suh performed research, obtained the results and prepared the manuscript along with contributions from all of the co-authors.D.-I. Lee examined the results and checked the manuscript.Discussion Paper | Discussion Paper | Discussion Paper | Ulbrich, C. W. and Atlas, D.: Rainfall microphysics and radar properties: analysis methods for drop size spectra, J. Appl.Meteorol., 37, 912-923, 1998.Waldvogel, A.: The N 0 jump of raindrop spectra, J. Atmos.Sci., 31, 1067-1078, 1974.Waterman, P.: Symmetry, unitarity, and geometry in electromagnetic scattering, Phys.Rev. DDiscussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Table 1 .
Designated date with respect to the source of rainfall.

Table 2 .
Mean value of DSDs for Busan and Järvenpää.

Table 3 .
Rainfall rate for each rainfall category and the number of sample size for 1 min data.

Table 4 .
DT and NT (KST)in summer and winter season.