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國 立 中 央 大 學
大 氣 科 學 學 系 碩 士 論 文
台灣北部地區長期統計不同季節與不同降雨型
態之雨滴粒徑微物理特徵分析
Microphysical characteristics of raindrop size distribution in
different seasons and precipitation type in Northern Taiwan
研 究 生：李孟澤 (M.-T. Lee)
指導教授：林沛練 博士 (Dr. P.-L. Lin)
中 華 民 國 一 o五 年 六 月
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研究生簽名: 李孟澤 學號： 103621017
論文名稱: 台灣北部地區長期統計之不同季節與不同降雨型態
之雨滴粒徑微物理特徵分析
指導教授姓名： 林沛練 博士
系所 ： 大氣物理 所 �博士班 ;碩士班
填單日期：____105年 8月 31號_____
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i
摘要
台灣位於太平洋西側、歐亞大陸東側的熱帶與副熱帶季風地區，春夏季轉換時、梅雨
鋒面、夏季的颱風和午後熱對流常常帶來豪大雨，在加上台灣地形陡峭，容易造成水災、
土石流，因此準確預估降水對防災有極大的幫助。雷達回波與降雨率的關係廣泛被用來
估計降水的方法之一，可以用在大範圍降水估計;缺點則是空間上的雨滴粒徑變化太大，
相同的回波值對應的降雨率範圍很廣， 兩者並非一對一的關係，因此了解雨滴粒徑分
佈的特性將有助於改善降水估計。不同的地區、不同的降水型態，都有可能造成雨滴粒
徑分佈不同，以及分析比較降水積分參數有助於了解不同的降水特性。
本研究使用的資料來源為中央大學 Joss-Waldvogel disdrometer(JWD)觀測資料與中央
氣象局(CWB)三維雷達回波合成資料(QPESUMS)，統計的區間為 2005年 1月至 2014年
12月間。由標準化的 gamma分布顯示,平均直徑 Dm (Mass-weighted average diameter)於
夏季有最高值，而平均 Nw(normalized intercept parameter)最高值則出現在冬季; 透過雷
達回波在高度上的變化得知垂直發展影響 DSD (drop size distribution)在不同季節的結果。
此外，台灣北部降雨率多集中於 20mm/hr以下(層狀性降水)，本篇研究使用雷達回波區
分對流性與層狀性降雨，移除層狀性降水主導的因素。所有季節的層狀降雨皆有相近的
DSD分布結構，但對流降雨的 DSD則是偏向海洋型對流; 平均 Dm在對流降雨系統有較
高值，而平均 log10Nw 在層狀系統內有較高值，透過 Contoured frequency by altitude
diagrams (CFADs)發現垂直發展主導 DSD的變異性。
ii
Abstract
Drop size distribution (DSD) is a metric widely used in meteorology and hydrology. Taiwan
is located in a subtropical monsoon area in the west Pacific Ocean off the coast of East Asia.
Enormous quantities of rainfall during the transition season often cause flooding and mudslides.
Accurate rainfall prediction can help to alleviate the effects of such rainfall events. DSD varies
with regard to the type of rain as well as its spatial distribution. Radar reflectivity-rate of rainfall
(Z-R) relations are strongly dependent on DSD variations, which means that it is important to
analyze the DSD in various seasons as well as in various types of rain.
Between January 2005 and December 2014, DSD data was collected using a Joss-
Waldvogel Disdrometer (JWD) to analyze variations in the Gamma parameters of raindrop
spectra at NCU (24°58'6"N 121°11'27"E). The normalized Gamma distribution of DSD
revealed that the highest mean Dm (Mass-Weighted Average Diameter) values were in summer,
whereas the highest mean log10Nw (normalized intercept parameter) values were in winter.
Vertical structures detected in radar reflectivity profiles dominate the results of seasonal DSD.
Furthermore, most of the rain falling at less than 20 mm/hr (stratiform precipitation) occurs in
Northern Taiwan. In this study, we used radar reflectivity to differentiate between convective
and stratiform systems. It was discovered that the mean Dm value is higher in convective
systems, whereas the mean log10Nw value is higher in stratiform systems. The structure of DSD
in stratiform systems remains constant in all seasons; however, convection is similar to
maritime type. Contoured Frequency by Altitude Diagrams (CFADs) revealed that vertical
structures dominate DSD in various types of precipitation.
iii
致謝
首先，要先感謝林沛練老師，有一個像家的實驗室，也給予我很大的學習空間，特別
是對自己想做的題目，給予目標與方向，朝著標竿前進，雖然路途上總是跌跌撞撞，不
過還是給我很大的支持與指導。另外，陳台琦老師、張偉裕老師總是不斷地被我打擾，
只要老師們一有空，總會抓住機會跟老師討論，老師們也會給予細心的督導，謝謝你們。
特別感謝保亮老師和志誠老師，在我大學的時候引薦我去做觀測的研究，引起我對大氣
的熱誠，也感謝老師百忙之中擔任我的口試委員，蒞臨指導。
實驗室的學長姐更是我學習的楷模，育真、盈臻學姊總是不厭其煩的回答我的研究上問
題;姚姚、忠剛、冠冠給我勇氣能和其他老師討論;昀靖、牧群、崇穎和秀秀也給我研究
上的建議;思翰、書維和柏儀在程式上的極力協助;學弟妹昭昭、炫慶、柿柿和怡真解決
實驗室中的小任務;暐晴、皓群更是實驗室的好室友，一共度實驗室好時光;另外還要特
別感謝印度博士生 Balaji Kumar和遠在英國的明葳,協助我完成英文論文的撰寫。
在碩士班的時光，總是獲得許多協助，特別是剛踏入中央的時候，市北的好同學們:奕
辰、紫萱、慧淳和宥璇一起篳路藍縷。之後加入了中大弦樂團，感謝你們:建安老師、昌
樺、慧文、心怡、遠山、柏頡、柏宇、敬元、嘉均、復戎、貫中、舒宇、謝寬、政熹…
等，再給我學習音樂的環境與動力，精彩我的研究生活。當然，我的同班同學更是支持
我繼續做研究的目標，承绮、秉儒、承勳、自宥、張幼、凱翊、俊寓、依涵、俊偉、如
瑜、簾傑、佑晟、立源和柏翰，在研究上的督促與討論，一定還少不了課餘的瘋狂且臨
時活動、大太陽下的運動以及每次都不揪的吃飯團。
最後要感謝的就是一直很支持、栽培我的家人、陪著我從懵懂的大學生漸漸有自己目
標與方向的郁欣、加油打氣團陪伴的依璇跟詩軒、還有很多很多身邊的好朋友，謝謝你
們一路上的支持，造就現在的我。
iv
Table of Contents
摘要 ........................................................................................................................ i
Abstract ................................................................................................................ ii
致謝 ...................................................................................................................... iii
Table of Contents ................................................................................................ iv
List of Tables ....................................................................................................... vi
List of Figures .................................................................................................... vii
Chapter 1 Introduction ....................................................................................... 1
1.1 Geographical environment in Taiwan ......................................................... 1
1.2 Seasons in Taiwan ........................................................................................ 1
1.3 Precipitation processes ................................................................................. 2
1.3.1 Rain types: warm rain and cold rain ..................................................... 3
1.3.2 Microphysical process ........................................................................... 4
1.4 Main objective of the study ......................................................................... 7
Chapter 2 Data and Methods ............................................................................. 8
2.1 Disdrometer ................................................................................................. 8
2.1.1 Data collection ....................................................................................... 8
2.1.2 Instrument .............................................................................................. 8
2.1.3 Data quality control ............................................................................... 9
2.1.4 Calculation of drop size distribution ..................................................... 9
2.1.5 Gamma distribution ............................................................................. 10
2.1.6 Normalization of Gamma distribution ................................................ 11
v
2.2 Z-R relation............................................................................................ 13
2.3 Radar data .............................................................................................. 13
2.4 Classification of stratiform and convective precipitation ..................... 16
2.5 Radiosonde data: ................................................................................... 17
Chapter 3 Results and discussion .................................................................... 18
3.1 Overview of DSD ...................................................................................... 19
3.2 Seasonal variation ...................................................................................... 21
3.3 Comparison of stratiform and convective systems .................................... 23
3.4 Rainfall integral parameter Z-R ................................................................. 25
Chapter 4 Conclusions and future work ......................................................... 27
4.1 Conclusions ................................................................................................ 27
4.2 Future work ................................................................................................ 28
References .......................................................................................................... 29
Table .................................................................................................................... 33
Figure .................................................................................................................. 39
vi
List of Tables Table 2. 1 Drop size classes of JWD .................................................................. 33
Table 2. 2 Coefficient of precipitation integral parameters of Gamma distribution
...................................................................................................................... 34
Table 3. 1 Statistics of DSD parameters derived from disdrometer data (Jan 1992-
Dec 1994,1 min rain data, total number of data=61384.) in Malaysia. (Hong
et al.2014) ..................................................................................................... 34
Table 3. 2 Statistics of DSD parameters derived from disdrometer data (Jan 2005-
Dec 2014,10 min rain data) in Northern Taiwan. ......................................... 34
Table 3. 3 Statistics of overall DSD parameters derived from disdrometer data
(Jan 2005- Dec 2014,10 min rain data) in different seasons in Northern
Taiwan. ......................................................................................................... 35
Table 3. 4 Statistics of stratiform DSD parameters derived from disdrometer data
(Jan 2005- Dec 2014,10 min rain data) in different seasons in Northern
Taiwan. ......................................................................................................... 36
Table 3. 5 Statistics of convection DSD parameters derived from disdrometer data
(Jan 2005- Dec 2014,10 min rain data) in different seasons in Northern
Taiwan. ......................................................................................................... 37
Table 3. 6 Coefficient of Z=aRb in different season and different precipitation
type. .............................................................................................................. 38
vii
List of Figures
Figure 2. 1 Appearance of JWD and receiver. ................................................... 39
Figure 2. 2 Distribution of radar and JWD. Location of radar sites are marked
with black “ X ” (Wu-Fan San (RCWF), Hua-Lien (RCHL), Chi-Gu
(RCCG), Ken-Ting (RCKT), Ma-Kung (RCMK) and Ching-Chuan-Kang
(RCCK)、JWD and automatic weather station of CWB (C0C520) are marked
with red “ * ”, and meteorological observation stations are marked with blue
“o” . ............................................................................................................... 39
Figure 2. 3 Rate of rainfall scatters plot between JWD(y-axis) and rain gauge
from CWB (x-axis). ...................................................................................... 40
Figure 2. 4 Reflectivity probability scatter plot between JWD (x-axis) and
QPESUMS (y-axis). Regression line (black dashed line) and two standard
deviations (red dashed line) are also shown. Color indicates the percentage of
occurrence. ................................................................................................... 40
Figure 2. 5 Classification of precipitation into stratiform and convective type on
the basis of radar reflectivity (Steiner, 1995) ............................................... 41
Figure 3. 1 Overview of (a) rate of rainfall (mm/hr) and (b) radar reflectivity (dBZ)
calculated from JWD in different seasons over a period of ten years. Color
bar represents the occurrence frequency in log scale. .................................. 42
Figure 3. 2 Raindrop concentration [log10N(D), mm-1m-3] vs. raindrop diameter
(D, mm) for the six seasons over a period of ten years. The number in the
legend represents data sample. ..................................................................... 42
Figure 3. 3 Statistical value of Gamma parameters over period of ten years. ... 43
Figure 3.4 (a) Distribution of log10Nw (mm-1 m-3) and Dm (mm) over period
viii
of ten years (all seasons). Inclined black dashed line defined by Bringi et
al.,(2003) separates the precipitation into stratiform and convective. Green
and red rectangular boxes represent maritime like convection and continental
like convection respectively. (b) Radar reflectivity of CFADs over period of
ten years (all seasons) with mean reflectivity profile in white star dotted line.
Horizontal white dotted line represents the height of the melting layer
obtained from radiosonde. ............................................................................ 43
Figure 3. 5 Statistical values of (a) Dm in blue and Nw in red (b) μ (c) λ in six
seasons .......................................................................................................... 44
Figure 3. 6 Variations in raindrop concentration [log10N(D), mm-1m-3] with
drop diameter (D, mm) in six seasons after applying Gamma parameter to
N(D). ............................................................................................................. 45
Figure 3. 7 Microphysical conceptual model proposed by Thompson et al. (2015).
...................................................................................................................... 45
Figure 3. 8 (a) Mean values of Dm and Nw scatter in different seasons. (b)
Deviations in mass weighted mean diameter (Dm,, blue bars) and liquid water
content (LWC, in red bars) between each season and all seasons. .............. 46
Figure 3. 9 CFAD of radar reflectivity obtained from QPESUMS of CWB for six
seasons (a) Mei-Yu, (b) summer, (c) typhoon, (d) autumn, (e) spring and (f)
winter. A number of data points in each season are represented in brackets.
Star dotted line in white and red color refer to mean reflectivity of six seasons
and individual seasons respectively.............................................................. 49
Figure 3. 10 Statistical value (a) Dm in blue and Nw in red bar (b) μ (c) λ of
stratiform precipitation, defined by Steiner et al. (1995) in different seasons.
...................................................................................................................... 50
Figure 3. 11 Gamma distribution using the mean value in Fig3.10 of stratiform
ix
DSD in different seasons. The mean rate of rainfall is also shown in the legend.
...................................................................................................................... 51
Figure 3. 12 (a) Mean value of Dm and Nw scatter in stratiform precipitation in
different seasons. (b) Total mean CFADs of stratiform with -40 and 0 °C
(horizontal dotted line) and mean vertical dBZ(stars). ................................ 51
Figure 3. 13 Radar reflectivity of CFADs of stratiform precipitation for (a) Mei-
Yu (b) Summer (c) typhoon (d) autumn (e) spring and (f) winter. The number
of data points in each season are represented in brackets. Star dotted lines in
white and red indicate the mean reflectivity of six seasons and individual
season respectively. Horizontal red dotted lines represent altitude of 0oC and
-40oC. Melting layer height obtained from radiosonde is denoted in
horizontal white dotted line for six seasons. ................................................ 54
Figure 3. 14 Statistical value (a) Dm in blue and Nw in red bar (b) μ (c)λ of
convective precipitation which defined by Steiner et al. (1995) in different
seasons. ......................................................................................................... 55
Figure 3. 15 Gamma distribution which uses the mean value in Fig3.14 of
convective DSD in different seasons. Mean rate of rainfall also shown in the
legend. .......................................................................................................... 56
Figure 3. 16 (a) Mean value of Dm and Nw scatter in different seasons of
convective precipitation.(b) Total mean CFADs of convection with -40 and 0
°C (horizontal dotted line) and mean vertical dBZ(stars). ........................... 56
Figure 3. 17 Radar reflectivity CFADs of convective precipitation for (a) Mei-Yu
(b) Summer ................................................................................................... 59
Figure 3. 18 HVS ((a)Mei-yu, (b)Summer, (c)Typhoon) of Dm and log10Nw are
displayed in terms of probability distribution. Stratiform and convection are
marked by shaded and contoured areas, respectively. Mean values of Dm and
x
Nw in stratiform and convection are also shown in red triangle and star,
respectively. The inclined black dashed line defined by Bringi et al. (2003)
separates the precipitation into stratiform and convective. Green and red
rectangular boxes represent maritime like convection and continental-like
convection respectively. ............................................................................... 61
Figure 3. 19 LVS ((a)autumn, (b)spring, (c)winter) of Dm and log10Nw are
displayed in terms of probability distribution . Stratiform and convection are
marked by shaded and contoured areas, respectively. Mean values of Dm and
Nw in stratiform and convection are also shown in red triangle and star
respectively. The inclined black dashed line defined by Bringi et al. (2003)
separates the precipitation into stratiform and convective. Green and red
rectangular boxes represent maritime like convection and continental-like
convection respectively. ............................................................................... 63
Figure 3. 20 Z-R relation between various seasons: (a) ten years, (b)stratiform,
and (c) convection. The formula is shown in the legend. ............................ 64
Figure 4. 1 Mean value of Dm and Nw scatter of stratiform and convection in
different seasons. “ * ” indicate the convection and “ + ” indicate the
stratiform system. ......................................................................................... 65
1
Chapter 1 Introduction
1.1 Geographical environment in Taiwan
Taiwan is located in a subtropical monsoon area in the western Pacific Ocean, located
off continental East Asia. The climate is strongly influenced by the East Asian monsoon.
The terrain is dominated by the central mountain range, the north-south orientation of
which causes large spatial variations in the island climate.
1.2 Seasons in Taiwan
Chen and Chen (2003) reported that the monsoon greatly influences precipitation in
Taiwan. In the winter, the cloud water content is not high and water vapor is distributed in
stratified layers, resulting in lower rainfall over the north and northeast coast of Taiwan.
Spring is a transition period when southwestern flow gradually increases, bringing warm
air from the South China Sea above 850 hpa, which often meets a cold front from the
leeward side of the Tibetan plateau. This causes a transition from steady rainfall in the
winter to convective-type rainfall in the spring. The Mei-Yu front and orographic rain are
the main sources of rainfall during the Mei-Yu season, both of which are affected by the
southwest monsoon and sub-synoptic scale of the disturbance from the Tibetan plateau,
causing considerable rainfall on the windward side of the western parts of the central
mountain range in southern Taiwan. Typhoons and convective systems combine with the
southwesterly monsoon bringing considerable rainfall in the summer. Autumn is not the
rainiest season in Taiwan; however, typhoons and frontal systems during this period bring
considerable rainfall. Following the onset of the northeast monsoon, precipitation
increases greatly on the windward side (over north and north-east Taiwan), and decreases
2
greatly on the leeward side. During this period, rainfall patterns change from convective
to stratiform.
1.3 Precipitation processes
Precipitation is a weather phenomenon that refers to the condensation of water vapor
and its movement (in various states) down to the surface of the planet. Most of the moisture
in the atmosphere is concentrated in the troposphere, and the amount of moisture held is
proportional to the temperature. When the air is filled with 100% water vapor, it is said to
be saturated; however, this condition is insufficient for condensation to take place. The
supersaturation of air through adiabatic cooling induced by an uplift of the air parcel leads
raises the possibility of water vapor condensing into droplets. Through the process of
hygroscopic condensation nucleation, water vapor condenses into clouds. Cloud droplets
comprising ice crystals are too small to overcome the resistance of updrafts. Thus, the
cloud droplets continue growing under the effects of cooling or a continued supply of water
vapor from the environment until the drops are large enough that the upward motion of air
is unable to keep them aloft. At this point, rain, snow, or hail begin falling; i.e.,
precipitation occurs. The formation of a rain drop dictates whether it is classified as warm
rain or cold rain.
3
1.3.1 Rain types: warm rain and cold rain
Warm rain is defined as cloud formation without processes involving the ice phase.
The formation of raindrops can be divided into several microphysical steps: (1) activation
of droplets around a cloud condensation nuclei (CCN), (2) condensation growth (limited
by vapor diffusion), and (3) coalescence growth (accelerated by an increase in falling
speed and collision efficiency) (Beard and Ochs, 1993). The coalescence of water droplets
within the cloud is the primary effect of falling at different terminal velocities. This tends
to occur more readily in marine clouds; however, this requires sufficient liquid water and
updraft to sustain collision-coalescence. Thus, warm rain is not restricted to low-to-middle
level clouds; i.e., it may also occur in deep convective clouds (Glickman, 2000; Lau and
Wu, 2003; Schumacher and Houze, 2003).
Conversely, ice crystals may form in clouds extending to altitudes at which the
temperature is below 0°C, resulting in cold rain. Two-phase transition can lead to the
formation of ice: the freezing of liquid droplets or the direct sublimation from vapor to the
solid phase. Relative to liquid, water vapor in a cloud is saturated; therefore, relative to ice,
water vapor is supersaturated.
In the following, we present a short summary of the microphysical processes involved
in these two types of rain. Collision and coalescence drives the growth of droplets in warm
clouds, whereas riming and aggregation are more important in the formation of cold rain.
These differences can be observed in DSD using a disdrometer and radar.
4
1.3.2 Microphysical process
The size distribution of raindrops is the fundamental property of precipitation from
the perspective of microphysical investigation and remote sensing using radar. In 1948,
Marshall and Palmer (M-P) proposed the rain drop size distribution (DSD), which can be
written in exponential form as follows:
N(D) = 𝑁0𝑒(−ΛD) (1)
where N(D) (m-3 mm-1), the concentration of rain drops is number of rain drops per unit
volume per unit drop size, D (mm) is the drop size, N0 is a constant (8000 mm-3 m-1), and
Λ is the function of rate of rainfall (Λ = 4.1R-0.21 (mm/hr)). Ulbrich (1983) claimed that
most observations do not fit the M-P method well, particularly when dealing with rain
drops of small size. Ulbrich and Atlas (1984) subsequently proposed the use of Gamma
distribution, as follows:
N(D) = 𝑁0𝐷𝜇𝑒(−ΛD) (2)
which includes parameter μ to deal with changes in the concentration of smaller rain drops.
The unit N0 represents the intercept as mm-1-μm-3, μ represents the shape, and Λ represents
the slope of drop size distribution. Kozu and Nakamura (1991) reported that Gamma
distribution is more accurate than the M-P method in describing the characteristics of DSD.
In the analysis of tropical rainfall events, Tokay and Short (1996) advanced the N0-R
relationship to the classification of precipitation as convective and stratiform systems and
also determined that most of the reflectivity in convective systems exceeds 40 dBZ.
However, they noticed that the effects of coalescence and evaporation are higher in
convection systems than in stratiform systems, such that the Gamma parameter (N0)
becomes smaller. In their analysis of data from a Joss-Waldvogel disdrometer (JWD) and
radar in Switzerland, Huggel et al. (1996) discovered that precipitation with a bright band
is strongly correlated with large droplets and small N0 and Λ.
5
Gamma parameters can be used to describe drop size distribution; however, the value
of N0 (mm-1-μ m-3,) is influenced by the value of μ. Testud et al. (2001) proposed the
normalization of N0, resulting in a redefinition of intercept parameter Nw (mm-1 m-3).
Bringi et al. (2003) used the method proposed by Testud et al. (2001) in the analysis of
observation data (2DVD, JWD, and DSD) from radar in various climatic regions. They
demonstrated that Dm and Nw are strongly negatively correlated in stratiform systems. This
may be due to the two characteristics of microphysical processes in stratiform systems.
The first is an obvious bright band indicating the melting of large low density snowflakes
into rain, resulting in a large value for Nw and small value for Dm. The second is the lack
of a bright band indicating the melting of small solid graupel and rimed snow particles into
rain, causing a small value for Nw and large value for Dm. This was actually called “N0
jump” in Waldvogel (1974). They, Bringi et al. (2003), also identified two types of
convection system: a “continental-like” system with a large value for Nw and a small value
for Dm, and an “ocean-like” system with a small value for Nw and large value for Dm.
Tokay et al. (2001) claimed that JWD underestimated the rain rate which compare with
the rain gauge. JWD does not perform particularly well with heavy rainfall, due to the so-
called dead time effect. This led Sauvageot and Lacaux (1995) to develop a method in
which the count of large droplets multiplied each diameter as a weighting to revise the
number of medium and small droplets, in a process called “dead time correction”. Tokay
et al. (2008) used reflectivity (dBZ) to classify the Gamma parameter based on
observations of tropical cyclones over the Atlantic and Pacific Oceans. The μ, λ, and Dm
are similar in these two areas and Dm was shown to increase with dBZ.
Most previous research in Taiwan has focused on particular cases over short periods.
Chang (2002) employed first-generation two-dimensional video disdrometers (2DVD) to
6
investigate Typhoon Nari. The increasing rate of rainfall caused DSD to broaden and the
concentration of small drops to increase. Furthermore, the Z-R relationship (Z=300R1.4)
underestimated the rate of rainfall during Typhoon Nari. When examining the differences
between disdrometer instruments (JWD and 2DVD), Hsu (2005) found that when the rate
of rainfall exceeded 20 mm/hr, JWD counted fewer drops than 2DVD did. Nonetheless,
these differences were shown to not affect the estimation of rainfall considerably. Chien
(2006) used JWD data to analyze various types of precipitation in various seasons in
Northern Taiwan over the period 2001-2006. They found more small drops and lower rain
fall in winter. The drops in spring and Mei-Yu were larger, but those in the summer were
the largest. When investigating the convection and stratiform of heavy rainfall in 2005-
2006, Mao (2007) observed a higher proportion of small drops in stratiform precipitation,
whereas the Gamma parameters of stratiform precipitation were lower than those of
convection. Chang et al. (2009) observed a relationship between Dm and height in typhoons
observed by 2DVD and radar during 2001-2005. Chaing (2010) analyzed the physical
aspects of precipitation observed in the South-west Monsoon Experiment in 2009
(SoWMEX2009). She noticed differences in DSD between Northern and Southern Taiwan
as well as regional characteristics. Lu (2012) found that Dm increased with the rate of
rainfall during Typhoon Fanapi; however, this trend levelled off after a certain period.
These results indicate that the growth of rain drops is limited by the balance among
breakup, coalescences and collision. Chen (2013) analyzed the Mei-Yu front with
southwesterly flow, which is responsible for flooding in Northern Taiwan.
7
1.4 Main objective of the study
As mentioned previously, this thesis focuses on the value of Gamma parameters in
various regions; however, we also compare long-term data from JWD and radar in order
to take into account the actual microphysical processes that determine DSD.
Our findings provide an understanding of seasonal variations in DSD and rain type
and elucidate the factors affecting DSD observed on the ground.
8
Chapter 2 Data and Methods
In this chapter, we outline the instruments (disdrometer, radar, and sounding data)
and methods used in the present study. We also describe efforts to reduce noise and thereby
bolster the reliability of the results.
2.1 Disdrometer
2.1.1 Data collection
We used a Joss-Waldvogel disdrometer (JWD, RD-69, Fig 2.1) located at the National
Central University (NCU; 24o58’18’’N,121o11’3’’E) campus in Taoyuan City, Taiwan, as
shown in Figure 2.2. Measurements were obtained over a period of ten years (January
2005 to December 2014).
2.1.2 Instrument
The outdoor RD-69 disdrometer is connected to an indoor analog-to-digital converter
(ADA-90), which converts drop pulses into digital signal and sends them to a personal
computer. The disdrometer has a cross-sectional area of F= 0.005 m2. The range of drop
sizes is divided into 20 categories covering a range of 0.359-5.373 mm (listed in Table
2.1). Classification was based on the Empirical Table of Terminal Velocity by Gunn and
Kinzer (1949). The vertical drop speed cannot be observed using JWD; therefore, we
adopted the empirical formula proposed by Gunn and Kinzer (1949) to calculate the
precipitation parameters. The JWD is unable to measure drops outside the given range
(0.359 mm-5.373 mm).
9
2.1.3 Data quality control
To obtain reliable data, it was stipulated that any one-minute sample containing fewer
than 10 drops or any one-minute sample with a rate of rainfall of less than 1 mm/hr would
be regarded as noise and excluded.
Limitations inherent in JWD observation leaves the system susceptible to
underestimating the number of small drops or omitting them altogether in cases of heavy
precipitation. This situation is referred to as “dead time effect’’. We adopted the equation
proposed by Sauvageot and Lacux (1995) to overcome this problem, as follows:
𝑁𝑖∗ = 𝑁𝑖 exp {0.035
𝑇 ∑ 𝑁𝑘 ∗ log [ 𝐷𝑘
(0.85𝐷𝑖−0.25)]𝐷20
𝐷𝑘=0.85𝐷𝑖} (3)
where 𝑁𝑖∗ is the number of rain drops after correction, i is the catalog of the drop size,
Ni is the original number of observed raindrops (the same as (3) ni), Dk is the diameter of
the rain drop, k is the catalog of the drop size that is selected by 0.85Di , and T is the
sampling interval time. Figure 2.3 shows the degree of correlation between the
regression for the rate of rainfall between JWD and the automatic rain gauge at a weather
station of the Central Weather Bureau (CWB). This positive correlation means that most
of the rain event can be captured by JWD.
2.1.4 Calculation of drop size distribution
Once a minute, the JWD records the number of drops in each category in order to
obtain the drop size distribution N(Di), as follows:
N(Di) = 𝑛𝑖(F∗T∗V(Di)∗ΔDi)
(4)
where N(Di) is the number of drops per cubic meter per millimeter (mm-1m-3), F is the
10
cross sectional area (0.005 m2), T is the integral time (60 seconds), V(Di) is the terminal
velocity (m/s) of catalog i ,ΔDi is the range of drop size in catalog i , and ni is the number
of drops in catalog i.
2.1.5 Gamma distribution
Formula (1) can be used to convert the number of the rain drops into drop size
distribution N(Di) by fitting the observation data to the Gamma distribution (Kozu and
Nakamura, 1991) using Eq. (2): N0, μ, Λ. The formula is derived by substituting Eq. (2) into
Eq. (5):
Mx=∫ 𝐷𝑥 ∗ 𝑁(𝐷)𝑑𝐷∞0 (5)
According to the traits of Gamma function (6), Eq. (5) can be simplified to Eq. (7),
where Mx is the integral precipitation parameter:
Г(𝑣)Λ𝑣 = ∫ 𝑥𝑣−1𝑒−𝑥𝑑𝑥∞
0 (6)
𝑀𝑥 = Г(x+μ+1)Λ𝑥+μ+1 (7)
The result from Eq. (3) is then substituted into Eq. (5), and x=3,4,6 is selected to
obtain M3, M4, M6. Parameter G can then be derived using Eq. (8):
G= 𝑀43
𝑀32𝑀6
1 (8)
Equation (7) is substituted into (8) to obtain Eqs. (9), (10), and (11) as the three
parameters of Gamma distribution (No, μ, Λ). DSD can be reconstructed using the three
parameters, as follows:
μ = 11𝐺−8+√𝐺(𝐺+8)2(1−𝐺)
(9)
11
Λ = (μ+4)𝑀3𝑀4
= (μ+4)𝐷𝑚
(10)
𝑁0 = Λμ+4𝑀3Г(μ+4)
(11)
where Dm (mm, Mass weighted average diameter) can be calculated using DSD.
Given parameter D0 (the median volume diameter), the sum of minimum drop size to
median volume diameter is equal to half of the liquid water content, as follows:
∫ 𝐷3𝑁(𝐷)𝑑𝐷 = 12 ∫ 𝐷3𝑁(𝐷)𝑑𝐷𝐷𝑚𝑎𝑥
𝐷𝑚𝑖𝑛
𝐷0𝐷𝑚𝑖𝑛
(12)
This means that when the rate of rainfall or amount of liquid water remains the same,
a larger D0 value indicates a larger drop size. According to Ulbrich (1983), when Dmax
approaches infinity, D0 can be approximated using the following:
𝐷0 = 3.67+μΛ
(13)
Similar to Eq. (10), we can also show D0 as (14):
𝐷0 = 𝐷𝑚3.67+𝜇
4+𝜇 (14)
2.1.6 Normalization of Gamma distribution
The three parameters in the Gamma distribution can be used to provide an objective
description of DSD; however, N0 (mm-1-μ m-3) cannot be used in the same manner because
it changes with parameter μ. Testud et al. (2001) resolved this problem by first calculating
the liquid water content W (gm-3) as follows:
W = 10−3 𝜋6
𝜌𝑤𝑁0Г(𝜇+4)(3.67+𝜇)𝜇+4 𝐷0
𝜇+4 (15)
where 𝜌𝑤 is the density of water (𝜌𝑤 =1gcm-3) and D0 (mm) is the median volume
diameter.
12
Equation (2) can then be rewritten as follows:
N(D) = 𝑁0 𝐷𝜇 exp [−(3.67 + 𝜇) 𝐷𝐷0
] (16)
Using Eqs. (15) and (16), the normalized N(D) can be represented as follows:
𝑁𝑛𝑜𝑟𝑚𝑎𝑙(𝐷) = 𝜌𝑤 𝐷04
103 𝑊 𝑁(𝐷) (17)
Given the new parameter Nw (mm-1m-3) in the form of Eq. (18) and a non-dimensional
unit parameter f(μ) in the form of Eq. (19), when μ equals zero, f(μ) equals 1. Thus, we
derive Eq. (20) and the relationship between N0 and Nw is given as Eq. (21).
𝑁𝑤 = (3.67)4
𝜋 𝜌𝑤 (103 𝑊
𝐷04 ) (18)
f(μ) = 6(3.67)4 (3.67+μ)μ+4
Г(μ+4) (19)
N(D) = 𝑁𝑤 𝑓(μ) ( 𝐷𝐷0
)μ exp [−(3.67 + μ) 𝐷𝐷0
] (20)
𝑁0 = 𝑁𝑤 𝑓(μ) 𝐷0−μ (21)
Both Nw and N0 describe the number concentration of rain drops; however, they differ
in that N0 (mm-1-μ m-3) is influenced by parameter μ, whereas Nw (mm-1 m-3) is not. The
benefit is that Nw is the same as N(D); therefore, Nw is better than N0 for describing DSD.
Ulbrich (1983) proposed a formula to calculate the rainfall integral parameter (22).
Assume that N(D) is a Gamma distribution, we substitute Eq. (2) into Eq. (23), as follows:
P = 𝑎𝑝 ∫ 𝐷𝑝𝑁(𝐷)𝑑𝐷∞0 (22)
P = 𝑎𝑝𝑁0 ∫ 𝐷𝑝+𝜇𝑒𝑥𝑝(−Λ𝐷)𝑑𝐷∞0 . (23)
The integral part can use Gamma Function (6) to rewrite (24) and substitute (13) into
13
(25), as follows:
P = 𝑎𝑝𝑁0[ 1Λ𝑝+𝜇+1]Γ(𝑝 + 𝜇 + 1) (24)
P = 𝑎𝑝Γ(𝑝+𝜇+1)
(3.67+𝜇)𝑝+𝜇+1 𝑁0𝐷0𝑝+𝜇+1 (25)
The coefficient of P, p, and 𝑎𝑝 can be obtained by referring to Table 2.2.
2.2 Z-R relation
According to previous studies, there is a power law relation between radar reflectivity
(dBZ) and the rate of rainfall (mm/hr), referred to as the Z-R relation, as follows:
Z = aRb . (26)
Z-R relation can be calculated using Eq. (22), as described by Ulbrich (1983), and Z
(dBZ) and R (mm/hr) can be modified as Eqs. (27) and (28):
Z = 106 Γ(6+μ+1)(3.67+𝜇)3.67+𝜇+1 𝑁0𝐷0
6+𝜇+1 , (27)
R = 33.31 Γ(3.67+μ+1)(3.67+𝜇)3.67+𝜇+1 𝑁0𝐷0
3.67+𝜇+1 . (28)
Using Eq. (26), coefficients a and b can be written as follows:
a = 106Γ(6+μ+1)𝑁01−𝑏
[33.31Γ(3.67+μ+1)]𝑏 , (29)
b = 6+μ+13.67+μ+1
. (30)
Coefficients a and b are related to the parameter of Gamma distribution (𝜇).
2.3 Radar data
Radar data from QPESUMS (from six operational Doppler radar units) can be used to
differentiate the various types of rain:
(1) Wu-Fan San (RCWF) is an S-band Doppler radar belonging to CWB, which is located
at 121.77o E/ 25.07o N at 766 m above sea level. The Nyquist velocity is 26.6 m/s,
14
22.5 m/s and 31.0 m/s at low, medium, and high elevations, respectively. This radar
system can be used to obtain the reflectivity (dBZ), radial wind (Vr) and spectrum
width (SW).
(2) Hua-Lien (RCHL) is an S-band Doppler radar belonging to CWB, which is located at
121.619o E/ 23.989o N at 53 m above sea level. The scanning interval is seven and
half minutes and the Nyquist velocity is 21.6 m/s. This radar unit can be used to obtain
the reflectivity (dBZ), radial wind (Vr) and spectrum width (SW).
(3) Chi-Gu (RCCG) is an S-band Doppler radar belonging to CWB, which is located at
120.086o E/ 23.1467o N at 53 m above sea level. The scanning time interval is seven
and half minutes and the Nyquist velocity is 21.6 m/s. This radar can be used to obtain
the reflectivity (dBZ), radial wind (Vr) and spectrum width (SW).
(4) Ken-Ting (RCKT) is an S-band Doppler radar belonging to CWB, which is located at
120.849o E/ 21.899o N at 40 m above sea level. The scanning time interval is seven
and half minutes and the Nyquist velocity is 49.5 m/s. This radar can be used to obtain
the reflectivity (dBZ), radial wind (Vr) and spectrum width (SW).
(5) Ma-Kung (RCMK) is a C-band dual polarimetric radar belonging to the Air Force,
which is located at 119.634o E/ 23.563o N at 48 m above sea level. The scanning time
interval is seven and half minutes and the Nyquist velocity is 37.18 m/s. This radar
can be used to obtain the reflectivity (dBZ), radial wind (Vr) and spectrum width (SW)
and also the polarization parameters: differential reflectivity (Zdr), differential phase
(Φdp), correlation coefficient (ρhv) and specific difference phase (Kdp).
15
(6) Ching-Chuan-Kang (RCCK) is a C-band dual polarimetric radar belonging to the Air
Force, which is located at 120.63o E/ 24.25o N at 48 m above sea level. The maximum
observation range is 150 km and the Nyquist velocity is 37.5 m/s. This radar can be
used to obtain the reflectivity (dBZ), radial wind (Vr) and spectrum width (SW) as
well as the polarization parameters: differential reflectivity (Zdr), differential phase
(Φdp), correlation coefficient (ρhv) and specific difference phase (Kdp).
The distribution of observation stations in Taiwan is presented in Figure 2.2.
Observations of reflectivity from the individual radars were combined to generate 3D
reflectivity mosaic grids (Zhang et al. 2005). The mosaic grids have a spatial resolution
of 0.0125 degrees on the latitude–longitude coordinate system and a 10-min update
cycle. The degree of reflectivity calculated from JWD is positively correlated to the data
obtained from QPESUMS (Fig 2.4). Clearly, the radar data is underestimated when
compared with that of JWD; however, most of the data falls within two standard
deviations. This data is used as the vertical structure of reflectivity, which can be
provided by CFADs. The location of NCU is the center of the domain (5 x 5 grid points)
used to calculate CFADs.
16
2.4 Classification of stratiform and convective precipitation
Various methods were used to classify stratiform and convective precipitation.
Waldvogel (1974) found that N0 undergoes dramatic changes when the precipitation
system changes. This phenomenon is referred to as N0 jump. Gamache and Houze (1982)
used a threshold of 38 dBZ in reflectivity to differentiate the type of precipitation. Tokay
and Short (1996) found that the N0-R distribution may change with the precipitation
system, using 40 dBZ to differentiate between the various types of precipitation. Tokay et
al. (1999) designated a rainfall rate exceeding 10 mm/hr as convective precipitation. Bringi
et al. (2003) applied a standard deviation smaller than 1.5 mm/hr to stratiform precipitation
and a standard deviation greater than 1.5 mm/hr to convective precipitation. Chang et al.
(2009) reported that a threshold rainfall rate of 10 mm/hr can be used to differentiate
among the various types of precipitation.
We adopted the method developed by Steiner et al. (1995) for the differentiation of
stratiform and convective systems. This precipitation classification technique can be
applied to measurements of ground radar reflectivity. The algorithm is based on the
following three steps (Fig 2.5):
(a) Intensity: Areas where the reflectivity of grid points at an elevation of 3 km
exceeds 40dBZ could never be stratiform, and are therefore regarded
as convective centers.
(b) Peakedness: Grid points that are not defined as a convective center in (a), but
exceeds the average intensity over the surrounding background (11 km)
are also identified as convective centers. The background intensity is
calculated by the linear mean values of non-zero echo reflectivity.
(c) Surrounding area: All grid points surrounding those identified as convective
centers in accordance with either of the above two criteria can be
17
extended by the mean value of background reflectivity, and are
therefore designated as a convective area.
2.5 Radiosonde data:
Sounding data plays an important role in defining the melting level and altitude where
the temperature drops to -40o C, to enable a clear distinction between the various
microphysical processes. In this study, we adopted radio sound data released twice daily (00
UTC and 12 UTC) by the Banqiao and Hualien meteorological observation stations over
the period of 2005-2014.
(1) Banqiao meteorological observation station (No.46692) is located at 121.441o E/
24.997o N , 10 m above sea level.
(2) Hua-Lien meteorological observation station (No.46699) is located at 121.619o
E/ 23.989o N , 16.1 m above sea level.
These two stations obtain ground observations (temperature (oC), dew temperature
(oC), humidity (%), pressure (hpa), rate of rainfall (mm), wind speed (m/s), and wind
direction (o)) as well as sounding data (temperature (oC), humidity (%), wind speed (m/s),
wind direction (o) and pressure (hpa)).
Figure 2.2 presents the distributions of observation meteorological stations in Taiwan.
The temperature profile is the parameter used to calculate the mean elevations at which
the temperature dropped to 0oC and -40oC over a period of ten years.
18
Chapter 3 Results and discussion
This chapter outlines the long-term DSD characteristics in subtropical Northern
Taiwan, followed by the statistical properties of the normalized parameters used in the
Gamma model. Chen and Chen (2003) classified the seasons of Taiwan into 6 groups:
winter, spring, Mei-Yu, summer, autumn, and typhoons (hereafter referred to as six
seasons). The DSD characteristics in the six seasons in Northern Taiwan were recorded
using the JWD disdrometer. Variations in DSD and the Gamma parameter of the six
seasons can be attributed to the use of contour frequency altitude diagrams (CFADs) of
radar reflectivity obtained from Doppler weather radar.
Numerous studies have been conducted on Gamma parameters (Maki, 2001; Kozu,
2006; Ulbrich, 2007; Islam, 2012; Tenório, 2012; Chen, 2013; Marzuki, 2013; Jayalakshmi
and reddy, 2014; Krishna et al., 2016). However, most studies in Taiwan have been limited
to case studies or short-term observational data sets (Chang 2002; Hsu 2005; Chien 2006;
Wu 2006; Mao 2007; Chang 2009; Chiang 2010). In this thesis, we present a long-term
(10-year) perspective of Gamma parameters through the six rainfall seasons in Northern
Taiwan. To elucidate the impact of DSD by season and precipitation type, we first examine
the long-term mean DSD and Gamma parameters, and then conduct a comparison with the
mean Gamma parameters in other locations. The DSD characteristics and vertical
structures associated with the various types of rainfall in each season are discussed in a
later chapter.
19
3.1 Overview of DSD
To understand rainfall patterns in the six seasons in Northern Taiwan, we obtained
the rate of rainfall and radar reflectivity from JWD, as shown in Fig. 3.1. The frequency
of rainfall occurrence and radar reflectivity are represented using a logarithmic scale in
Figs. 3.1(a) and 3.1(b), respectively. As shown in Fig. 3.1(a), the rate of rainfall is
generally less than 20 mm/hr. The most extensive rainfall rate distribution was observed
during the typhoon and Mei-Yu seasons, whereas the narrowest rainfall rate distribution
was observed during the winter. The results pertaining to reflectivity (Fig. 3.1.b) are
consistent with the rainfall rate distribution; i.e., the rainfall during the typhoon and
Mei-Yu seasons tended to be heavier. Figure 3.2 presents the DSD distribution in the six
seasons. After applying quality control to DSD of six seasons, we obtained a nearly
equal number of samples for each season except summer, as described in the legend of
Fig. 3.2. A larger number of large drops and fewer small drops were observed during
the typhoon, Mei-Yu, and summer seasons. The distribution in winter is closer to
exponential, which means that there were a larger number of smaller drops during that
period. In every season, we observed raindrops with a diameter ranging from 0.3 mm to
the limit of the instrument at 5.4 mm.
Figure 3.3 and Table 3.2 present the occurrence percentage of Gamma parameters
(Dm, Nw, μ, λ) in JWD observations over a period of ten years (combining all seasons).
The formula for skewness is as follows:
Sk = E(x−μ)3
𝜎3 (31)
where μ is the mean value of x, 𝜎 is the standard deviation, and E is the
expectations of (x-μ).
20
The occurrence percentage of Gamma parameters quantitatively defines the DSD
in the rainfall in Northern Taiwan using the following: Dm (1.23 mm), μ (5.54 (-)), λ
(7.33 mm-1), and Nw (4.08 mm-1 m-3). Precipitation in Northern Taiwan presented higher
numbers of small and medium-size drops than what was observed in tropical Malaysia
(Hong et al., 2014), as shown in Table 3.1
Figures 3.4(a) and 3.4(b) respectively present the normalized intercept parameter
(Nw), mass weighted mean diameter (Dm) (from JWD), and CFADs of reflectivity (from
radar) from observations over a period of ten years. Current Dm-Nw distributions are
compared with the classifications of precipitation (stratiform, convective, maritime,
continental) proposed by Bringi et al. (2003), which are represented in Fig. 3.4(a) as
follows: maritime (red box), continent (blue box), separation between stratiform and
convective rainfall (black dotted line). Most of the rain appeared to be stratiform, which
is consistent with Fig. 3.1. Moreover, the convective systems are close to those seen in
“maritime-like” systems. The CFADs (Figs. 3.4b) display the vertical structure of
reflectivity in combination with the melting level, as calculated using sounding data.
These results show that the mean melting level is at approximately 4.2 km, and that
reflectivity decreases with an increase in elevation, thereby indicating that the particles
are smaller and icing process is more pronounced at higher elevations. These results are
used as a reference in a discussion of seasonal variations in Section 3.2.
21
3.2 Seasonal variation
Gamma parameters can be used to quantitatively define the DSD. Figure 3.5 and
Table 3.3 display the mean, standard deviation, and skewness of each parameter in each
season. The use of these Gamma parameters (Fig 3.5) makes it possible to reconstruct
the DSD in Gamma distribution form (Fig. 3.6), which is similar to that in Fig. 3.2 but
slightly smoother. In a comparison of Figs. 3.5a and 3.6, we can see that the highest
mean value of Dm was observed in summer, whereas the highest mean value of Nw was
observed in winter. This means that more large drops are observed in summer, whereas
more small drops are observed in winter.
Thompson et al. (2015) proposed a conceptual model (Fig 3.7) to describe the
microphysical processes using a scatter plot or D0 and Nw. Increasing LWC by
increasing the size of drops in both stratiform and convection was shown to enhance the
process of icing. Conversely, weak convection with small drops was dominated by
condensation and coalescence. Figure 3.8(a) provides a scatter plot of Dm and Nw for
the six seasons; Fig. 3.8(b) depicts the difference between mean LWC and mass-
weighted mean diameter (Dm) in each season, as well as the mean LWC and Dm in the
six seasons. The mean Dm and Nw values in all of the seasons are above the convective
and stratiform classification line (black dotted line in Fig 3.8a). From the figure, it is
clear that stratiform-type precipitation is prominent in all seasons, which is consistent
with Figs. 3.1 and 3.4a. Deviations in LWC and Dm can be seen in Fig. 3.8(b), indicating
that the ice processes differ according to season. To more fully elucidate the cloud
formation and rain processes in each season, we constructed CFADs for the six seasons,
as shown in Fig. 3.9. On the basis of radar reflectivity of CFADs, the six seasons were
then classified as high vertical structures (HVS) and low vertical structures (LVS).
22
Based on the CFAD of reflectivity, Mei-Yu, summer, and typhoon seasons (Fig.3.9 a-c)
are associated with HVS, whereas spring, autumn, and winter (Figs. 3.9 d-f) are
associated with LVS. The mean melting elevation associated with strong icing
conditions is approximately 5 km (Figs. 3.9a, b, c), whereas mean melting elevation
associated with weak icing conditions is 4 km (Figs. 3.9 d, e, f).
The melting layer is considered the transition zone for ice and rain processes, above
which super-cooled water and ice particles can be found. HVS seasons are associated
with a warmer environment and stronger vertical motion, which means that a greater
volume of water vapor can be carried up to higher elevations, thereby increasing the
size of drops. Due to the Bergeron process, the diffusion growth of ice crystals is more
efficient than the diffusion growth of droplets. When the vertical velocity is insufficient
to hold aloft the weight of the ice crystals, they begin falling. The ice crystals pass
through the melting layer, whereupon aggregation and accretion changes to collision
and coalescence, such that HVS produces drops that are larger than those produced by
LVS.
The mean reflectivity profile (red line) in each HVS season (Fig. 3.9a-c) is greater
than the annual mean reflectivity profile (white line). In contrast, the mean reflectivity
profile in each LVS season (Figs. 3.9d-f) is lower than the annual mean reflectivity
profile. The accumulation of ice crystals at higher elevations causes a decrease in
reflectivity with height. Thus, the degree of tilting can be regarded as the intensity of
vertical motion of hydrometeors associated with various microphysical processes. To
sum up, vertical development is the dominant factor in DSD. In a later section, we use
CFADs to examine various types of rain.
23
3.3 Comparison of stratiform and convective systems
The fact that DSD is strongly influenced by the type of rain means that DSD must
be taken into account when investigating the stratiform and convective forms of
precipitation. Most of the rain in Northern Taiwan is stratiform-like (Fig. 3.1a, and 3.4a),
rainfall in each season can be classified as stratiform or convective using the reflectivity
classification technique developed by Steiner et al. (1995). Figure 3.10 and Table 3.4
show the mean Gamma parameter values in a stratiform system in each season. The Dm
and μ values in HVS seasons exceed those in LVS season; however, the Nw and λ are
lower. Furthermore, Dm is the largest in summer and Nw is the largest in winter. Because
of the quantitative Gamma parameter, we may reconstruct the DSD in Gamma form
(Fig3.11). In every season, the drop diameter was shown to range between 0.3 mm and
4.2 mm, whereas raindrop concentration was from 100 – 1000 m-3mm-1 , and the rate of
rainfall was from 3.2 mm/hr (winter) to 6.21 mm/hr (typhoon season). Moreover, we
observed the widest DSD in summer, which means that summer is associated with a
greater proportion of large drops than small drops.
Figure 3.12 presents a scatter plot for Nw and Dm associated with stratiform
precipitation in the six seasons. From the figure, it is clear that winter and summer
produce different microphysical processes. However, the Dm-Nw values in every season
run parallel to the stratiform line defined by Bringi et al. (2003). Figure 3.13 presents
the CFADs in stratiform type of different seasons. A comparison of CFADs in summer
(Fig. 3.13b) and winter (Fig. 3.13d) reveals a clear difference in the vertical structure of
reflectivity. As reported by Chen and Chen.(2003), the water content in clouds is not
high and tends to be concentrated within a stratified layer, which results in less rainfall
comprising small drops in winter. In contrast, a large amount of water vapor from the
24
south-west monsoon and incoming solar radiation produce strong vertical motion in
summer. This tends to exacerbate the icing process resulting in larger drops in summer.
However, the vertical structure is nearly the same during spring (Fig. 3.13e), autumn
(Fig. 3.13d), the typhoon season (Fig. 3.13c), and the Mei-Yu season (Fig. 3.13a), such
that stratiform systems tend to produce the same DSD.
Figure 3.14 and Table 3.5 list the Gamma parameters associated with convective
precipitation in the six seasons as well as the reconstructed DSD in these seasons. The
legend of Fig. 3.15 lists the maximum diameter ranging from 4.5 mm to the limitation
of the instrument (5.3 mm), N(D) ranging from 10 m-3mm-1 to 103 m-3mm-1, and the
mean rate of rainfall ranging from 5.47 mm/hr to 16.36 mm/hr. A larger number of large
drops are observed in summer than in winter (Fig. 3.15), which is in general agreement
with the results in Figure 3.11 and Figure 3.6. Figure 3.16(a) presents a scatter plot of
Nw and Dm for the six seasons in the convective regime. Figure 3.16(b) presents the
CFADs of convective precipitation in every season. Vertical development is clearly
greater in summer than in winter; however, the highest Nw value (Fig3.14) was observed
in the Mei-Yu season. The mean Nw value in winter and Mei-Yu differ by only a small
value of log10(0.03). Figure 3.17 presents the CFADs of the six seasons in the convective
regime. A heat cell developing into a thunderstorm is typical in summer, whereas the
Mei-Yu season is more strongly associated with frontal systems with little convection,
a wide stratiform area, and widespread rainfall. Thus, a higher number of small and
medium-size drops tend to be produced during the Mei-Yu season, leading to a large
value for Nw. Furthermore, the vertical structures observed in spring and autumn are
similar, resulting in similar DSD in the two seasons.
Figures 3.18 and 3.19 respectively present the probability distribution of log10Nw
25
and Dm for HVS (Mei-Yu, summer, and typhoon season) and LVS (autumn, spring, and
winter). As shown in these two figures, the convective distribution in HVS (Figs. 3.18a,
b, c) approach to the green box defined as maritime-like convection by Bringi (2003).
This indicates that coalescence growth is more efficient in HVS than in LVS (Figs. 3
19a, b, c). Higher coalescence growth in HVS is due to enhanced collision efficiency
[E(R,r)] involving raindrops of different sizes. However, the environment coupled with
the southwestern wind with an amount of water vapor drives higher raindrop growth
than LVS in convective and stratiform precipitations.
In the six seasons, the convective systems presented larger drops and lower
concentration than that observed in stratiform sytems. Greater vertical motion in
convective systems tends to carry water vapor to higher altitudes, such that the growth
of ice crystals is more rapid than that of water droplets above the melting layer, due to
the effects of the Bergeron process. Strong collision efficiency below the melting layer
is also responsible for the formation of larger raindrops in convective systems,
compared to stratiform systems.
3.4 Rainfall integral parameter Z-R
One approach to the estimation of rainfall is Z=aRb, as shown in Eq. (26) and Table
2.2. Table 3.6 presents the coefficients “a” and “b” and Fig. 3.20 presents the curve
associated with different seasons and types of precipitation. Because of the variation od
DSD, the same reflectivity corresponds to the different rate of rainfall. Coefficient “a”
is higher in HVS seasons (Mei-yu, summer, and typhoon season) than in LVS seasons.
This may be due to differences in Gamma parameter N0, as shown in Eq. 3.9. An
increase in N0 (more droplets per cubic unit) leads to a decrease in coefficient “a”. In
26
contrast, the value of number concentration is largest in the winter, which means that a
greater number of small droplets influence coefficient “a”. Coefficient “b” is also
affected by Gamma parameter μ, which is used to adjust the concentration of small
drops.
27
Chapter 4 Conclusions and future work
Taiwan is a subtropical island dominated by mountain range reaching from north to
south over 4000 m. Significant land and sea distribution with complex terrain greatly
hinder efforts to forecast the weather. This study sought to overcome some of these
difficulties by elucidating seasonal characteristics manifesting in the type of rain. We
employed a disdrometer (JWD in NCU) and radar reflectivity (QPESUMS from CWB) to
observe the rain events in each season. We also calculated integral rainfall and Gamma
parameters to identify the factors and microphysical processes that determine DSD.
4.1 Conclusions
We determined that DSD in Northern Taiwan is determined by the season and type of
precipitation. Furthermore, strong vertical motion associated with surface water vapor
from the southwest is responsible for the formation of larger raindrops.
Figure 4.1 presents a summary of seasonal variations in the type of rainfall. Most
convective precipitation presents a large Dm value and small Nw value. Vertical motion and
vertical structures (as indicated by CFAD) play an important role in DSD. Droplets in the
summer tend to be larger due to strong vertical motion in conjunction with large amounts
of water vapor brought from the ocean by winds to the south-west of the island. The
smaller droplets and narrower DSD in winter are due to high winds from Siberia in
conjunction with a lack of water vapor and weak vertical motion. Stronger icing processes,
such as aggregation and accretion, tend to accelerate the rate of droplet growth.
Mei-Yu has been classified as HVS; however, the height of vertical development is
28
lower than that observed in summer. As a result, the Dm during Mei-Yu is approximately
1.5 mm. The mean value of Nw is nearly the same in the convective systems in the winter
and Mei-Yu seasons, resulting in the larger number of small and medium-size droplets
observed by JWD. Through the CFADs, the vertical structure in Mei-Yu is greater than the
winter; however, spreading below the melting layer is similar, which indicates that the
Mei-Yu front combines mesoscale convective systems (MCS) with wide-spread stratiform
precipitation. By the wind effect, JWD might detect the rain drops not only from MCS but
also from stratiform.
The classification of convection in Typhoon mix a lot of small rate of rainfall which
defined as convection by radar, decreasing the value of Dm and Nw. Furthermore, the DSD
is similar in spring and autumn (the transition seasons in Taiwan) that is because the similar
vertical structure.
4.2 Future work
The separation of stratiform and convective systems according to the rate of rainfall
(10 mm/hr) or reflectivity (40 dBZ) is far more pronounced than that using reflectivity
values from radar. This is evidenced by the fact that the rate of rainfall does not correspond
precisely to reflectivity. This may be due to the fact that this method is not well-suited to
the complex weather systems found in Taiwan. Furthermore, the use of reflectivity from
Doppler radar is suitable only for inferring a rough approximation of particle size. In future
research, we are planning to use the parameters obtained from dual polarimetric radar, such
as reflectivity (Zhh), differential reflectivity (Zdr), specific differential phase (Kdp), and
zero lag cross-correlation of horizontal and vertical waves (Rhv) for the classification of
hydrometeor particles, based on fuzzy logic analysis.
29
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33
Table
Table 2. 1 Drop size classes of JWD
Drop size
classification Average diameter of drops in class i ,
Di mm
Fall velocity of a drop with diameter
Di V(Di) m/s
Diameter interval of drop size class i,
Delta Di mm
1 0.359 1.435 0.092 2 0.455 1.862 0.1 3 0.551 2.267 0.091 4 0.656 2.692 0.119 5 0.771 3.154 0.112 6 0.913 3.717 0.172 7 1.116 4.383 0.233 8 1.331 4.986 0.197 9 1.506 5.423 0.153 10 1.665 5.793 0.166 11 1.912 6.315 0.329 12 2.259 7.009 0.364 13 2.584 7.546 0.286 14 2.869 7.903 0.284 15 3.198 8.258 0.374 16 3.544 8.556 0.319 17 3.916 8.784 0.423 18 4.35 8.965 0.446 19 4.859 9.076 0.572 20 5.373 9.137 0.455
34
Table 2. 2 Coefficient of precipitation integral parameters of Gamma distribution
Precipitation integral parameter P
Index p
Coefficient ap
Z (mm6m-3) 6 106 mm6cm-6
W (gm-3) 3 0.524 g cm-3
R (mmh-1) 3.67 33.31 mmh-1 m3cm-3.67
Table 3. 1 Statistics of DSD parameters derived from disdrometer data (Jan 1992- Dec 1994,1
min rain data, total number of data=61384.) in Malaysia. (Hong et al.2014)
Parameter Mean SD Skewness
Normalized Gamma
logNw 3.52 0.50 -0.76 Dm 1.74 0.59 1.33 μ 6.14 4.53 1.67 λ 7.34 4.89 2.28
Table 3. 2 Statistics of DSD parameters derived from disdrometer data (Jan 2005- Dec
2014,10 min rain data) in Northern Taiwan.
Parameter Mean SD Skewness
Normalized Gamma
logNw 4.08 0.47 -0.17 Dm 1.23 0.39 0.25 μ 5.54 2.91 1.17 λ 7.33 2.77 0.53
35
Table 3. 3 Statistics of overall DSD parameters derived from disdrometer data (Jan 2005- Dec
2014,10 min rain data) in different seasons in Northern Taiwan.
Parameter Mean SD Skewness
Typhoon logNw 3.92 0.41 -0.32
Dm 1.3 0.41 -0.27 μ 5.59 3.3 1.22 λ 7.34 2.74 0.32
Parameter Mean SD Skewness
Mei-yu logNw 4.01 0.44 -0.35
Dm 1.33 0.4 0.01 μ 5.98 2.64 0.95 λ 7.17 2.65 0.55
Parameter Mean SD Skewness
Summer logNw 3.78 0.49 -0.74
Dm 1.45 0.46 0.2 μ 6.24 3.31 1.44 λ 6.6 2.77 0.75
Parameter Mean SD Skewness
Winter logNw 4.24 0.47 -0.18
Dm 1.09 0.31 0.65 μ 4.66 2.68 0.69 λ 7.65 2.86 0.53
Parameter Mean SD Skewness
Spring logNw 4.08 0.47 -0.09
Dm 1.23 0.36 0.36 μ 5.22 2.81 1.69 λ 7.21 2.73 0.62
Parameter Mean SD Skewness
Autumn logNw 4.12 0.48 -0.04
Dm 1.18 0.38 0.15 μ 5.28 2.54 0.83 λ 7.47 2.84 0.55
36
Table 3. 4 Statistics of stratiform DSD parameters derived from disdrometer data (Jan 2005-
Dec 2014,10 min rain data) in different seasons in Northern Taiwan.
Parameter Mean SD Skewness
Typhoon logNw 3.95 0.42 -0.19
Dm 1.24 0.38 -0.51 μ 6.71 3.26 0.94 λ 7.65 2.78 0.24
Parameter Mean SD Skewness
Mei-yu logNw 4.05 0.47 0.03
Dm 1.2 0.34 -0.08 μ 5.75 2.58 0.86 λ 7.52 2.77 0.43
Parameter Mean SD Skewness
Summer logNw 3.78 0.5 -0.49
Dm 1.3 0.37 0.39 μ 6.15 3.17 1.22 λ 7.1 2.96 0.47
Parameter Mean SD Skewness
Winter logNw 4.31 0.49 -0.2
Dm 1.03 0.28 0.44 μ 4.67 2.69 0.64 λ 8 2.96 0.41
Parameter Mean SD Skewness
Spring logNw 4.15 0.5 -0.07
Dm 1.13 0.33 0.35 μ 5.19 2.75 0.84 λ 7.55 2.87 0.45
Parameter Mean SD Skewness
Autumn logNw 4.17 0.5 0.02
Dm 1.11 0.36 0.15 μ 5.33 2.54 0.68 λ 7.75 2.92 0.42
37
Table 3. 5 Statistics of convection DSD parameters derived from disdrometer data (Jan 2005-
Dec 2014,10 min rain data) in different seasons in Northern Taiwan.
Parameter Mean SD Skewness
Typhoon logNw 3.88 0.39 -1.18
Dm 1.42 0.45 -0.12 μ 6.62 3.54 1.72 λ 6.75 2.57 0.3
Parameter Mean SD Skewness
Mei-yu logNw 3.96 0.36 -1.1
Dm 1.5 0.39 -0.26 μ 6.33 2.71 1 λ 6.77 2.42 0.64
Parameter Mean SD Skewness
Summer logNw 3.78 0.5 -0.97
Dm 1.58 0.47 -0.09 μ 6.42 3.48 1.51 λ 6.28 2.69 0.97
Parameter Mean SD Skewness
Winter logNw 3.93 0.37 -0.84
Dm 1.28 0.32 0.8 μ 4.99 2.75 0.74 λ 6.76 2.41 0.73
Parameter Mean SD Skewness
Spring logNw 3.85 0.36 -0.74
Dm 1.42 0.35 0.25 μ 5.38 2.81 2.9 λ 6.54 2.31 0.86
Parameter Mean SD Skewness
Autumn logNw 3.86 0.39 -0.51
Dm 1.43 0.36 -0.31 μ 5.42 2.64 1.16 λ 6.42 2.3 0.96
38
Table 3. 6 Coefficient of Z=aRb in different season and different precipitation type.
a b
Typhoon Total 233.09 1.22
Stratiform 217.40 1.22 Convection 262.41 1.22
Winter
Total 151.94 1.27 Stratiform 135.44 1.27 Convection 199.16 1.26
Mei-yu
Total 255.65 1.23 Stratiform 201.80 1.23 Convection 256.40 1.22
Spring
Total 198.78 1.25 Stratiform 176.07 1.25 Convection 247.57 1.24
Summer
Total 293.05 1.23 Stratiform 259.46 1.23 Convection 322.88 1.22
Autumn
Total 193.34 1.24 Stratiform 176.33 1.24 Convection 259.59 1.24
39
Figure
Figure 2. 1 Appearance of JWD and receiver.
Figure 2. 2 Distribution of radar and JWD. Location of radar sites are marked with black “ X ”
(Wu-Fan San (RCWF), Hua-Lien (RCHL), Chi-Gu (RCCG), Ken-Ting (RCKT),
Ma-Kung (RCMK) and Ching-Chuan-Kang (RCCK)、JWD and automatic weather
station of CWB (C0C520) are marked with red “ * ”, and meteorological
observation stations are marked with blue “o” .
40
Figure 2. 3 Rate of rainfall scatters plot between JWD(y-axis) and rain gauge from CWB (x-axis).
Figure 2. 4 Reflectivity probability scatter plot between JWD (x-axis) and QPESUMS (y-axis).
Regression line (black dashed line) and two standard deviations (red dashed line)
are also shown. Color indicates the percentage of occurrence.
41
Figure 2. 5 Classification of precipitation into stratiform and convective type on the basis of
radar reflectivity (Steiner, 1995)
b)
c)
42
Figure 3. 1 Overview of (a) rate of rainfall (mm/hr) and (b) radar reflectivity (dBZ) calculated
from JWD in different seasons over a period of ten years. Color bar represents the
occurrence frequency in log scale.
Figure 3. 2 Raindrop concentration [log10N(D), mm-1m-3] vs. raindrop diameter (D, mm) for
the six seasons over a period of ten years. The number in the legend represents data
sample.
(a) (b)
43
Figure 3. 3 Statistical value of Gamma parameters over period of ten years.
Figure 3.4 (a) Distribution of log10Nw (mm-1 m-3) and Dm (mm) over period of ten years (all
seasons). Inclined black dashed line defined by Bringi et al.,(2003) separates the precipitation
into stratiform and convective. Green and red rectangular boxes represent maritime like
convection and continental like convection respectively. (b) Radar reflectivity of CFADs over
period of ten years (all seasons) with mean reflectivity profile in white star dotted line.
Horizontal white dotted line represents the height of the melting layer obtained from radiosonde.
(a) (b)
44
Figure 3. 5 Statistical values of (a) Dm in blue and Nw in red (b) μ (c) λ in six seasons
(a)
(b)
(c)
45
Figure 3. 6 Variations in raindrop concentration [log10N(D), mm-1m-3] with drop diameter (D,
mm) in six seasons after applying Gamma parameter to N(D).
Figure 3. 7 Microphysical conceptual model proposed by Thompson et al. (2015).
Log 1
0N(D
)
D(mm)
46
Figure 3. 8 (a) Mean values of Dm and Nw scatter in different seasons. (b) Deviations in mass
weighted mean diameter (Dm,, blue bars) and liquid water content (LWC, in red
bars) between each season and all seasons.
(b)
(a)
47
(a)
(b)
48
(c)
(d)
49
Figure 3. 9 CFAD of radar reflectivity obtained from QPESUMS of CWB for six seasons (a)
Mei-Yu, (b) summer, (c) typhoon, (d) autumn, (e) spring and (f) winter. A number
of data points in each season are represented in brackets. Star dotted line in white
and red color refer to mean reflectivity of six seasons and individual seasons
respectively.
(e)
(f)
50
Figure 3. 10 Statistical value (a) Dm in blue and Nw in red bar (b) μ (c) λ of stratiform
precipitation, defined by Steiner et al. (1995) in different seasons.
51
Figure 3. 11 Gamma distribution using the mean value in Fig3.10 of stratiform DSD in different
seasons. The mean rate of rainfall is also shown in the legend.
Figure 3. 12 (a) Mean value of Dm and Nw scatter in stratiform precipitation in different seasons.
(b) Total mean CFADs of stratiform with -40 and 0 °C (horizontal dotted line) and
mean vertical dBZ(stars).
(a) (b
52
Stratiform
(a)
(b)
53
(c)
(d)
54
Figure 3. 13 Radar reflectivity of CFADs of stratiform precipitation for (a) Mei-Yu (b) Summer (c) typhoon (d) autumn (e) spring and (f) winter. The number of data points in each season are represented in brackets. Star dotted lines in white and red indicate the mean reflectivity of six seasons and individual season respectively. Horizontal red dotted lines represent altitude of 0oC and -40oC. Melting layer height obtained from radiosonde is denoted in horizontal white dotted line for six seasons.
(e)
(f)
55
Figure 3. 14 Statistical value (a) Dm in blue and Nw in red bar (b) μ (c)λ of convective
precipitation which defined by Steiner et al. (1995) in different seasons.
56
Figure 3. 15 Gamma distribution which uses the mean value in Fig3.14 of convective DSD in
different seasons. Mean rate of rainfall also shown in the legend.
Figure 3. 16 (a) Mean value of Dm and Nw scatter in different seasons of convective
precipitation.(b) Total mean CFADs of convection with -40 and 0 °C (horizontal
dotted line) and mean vertical dBZ(stars).
(a) (b)
57
Convection
58
59
Figure 3. 17 Radar reflectivity CFADs of convective precipitation for (a) Mei-Yu (b) Summer (c) Typhoon (d) Autumn (e) Spring and (f) Winter. A Number of data points in each season are represented in brackets. Star dotted line in white and red color are mean reflectivity of six seasons and individual season respectively. Horizontal red dotted lines represent altitude of 0oC and -40oC. Melting layer height obtained from radiosonde is denoted in horizontal white dotted line for six seasons.
60
61
Figure 3. 18 HVS ((a)Mei-yu, (b)Summer, (c)Typhoon) of Dm and log10Nw are displayed in
terms of probability distribution. Stratiform and convection are marked by
shaded and contoured areas, respectively. Mean values of Dm and Nw in
stratiform and convection are also shown in red triangle and star, respectively.
The inclined black dashed line defined by Bringi et al. (2003) separates the
precipitation into stratiform and convective. Green and red rectangular boxes
represent maritime like convection and continental-like convection respectively.
62
63
Figure 3. 19 LVS ((a)autumn, (b)spring, (c)winter) of Dm and log10Nw are displayed in terms
of probability distribution . Stratiform and convection are marked by shaded and
contoured areas, respectively. Mean values of Dm and Nw in stratiform and
convection are also shown in red triangle and star respectively. The inclined
black dashed line defined by Bringi et al. (2003) separates the precipitation into
stratiform and convective. Green and red rectangular boxes represent maritime
like convection and continental-like convection respectively.
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Figure 3. 20 Z-R relation between various seasons: (a) ten years, (b)stratiform, and (c)
convection. The formula is shown in the legend.
(a)Total
(b)Stratiform
(c)Convection
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Figure 4. 1 Mean value of Dm and Nw scatter of stratiform and convection in different seasons.
“ * ” indicate the convection and “ + ” indicate the stratiform system.
Str
Con
