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Determining the Daily Rainfall Characteristics from the Monthly Rainfall Totals in Central and Northeastern Thailand

Permanent Link: http://ufdc.ufl.edu/UFE0025162/00001

Material Information

Title: Determining the Daily Rainfall Characteristics from the Monthly Rainfall Totals in Central and Northeastern Thailand
Physical Description: 1 online resource (98 p.)
Language: english
Creator: Szyniszewska, Anna
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: climate, gamma, markov, precipitation, rainfall, thailand
Geography -- Dissertations, Academic -- UF
Genre: Geography thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Daily rainfall attributes are crucial in the risk assessment of climate conditions that may have damaging effect on agriculture. Although daily rainfall totals data accessibility is frequently limited, monthly rainfall data are most abundant in space and time in Thailand. The daily rainfall totals in four provinces of central and north-east Thailand (Lopburi, Chachengsao, Buriram and Sisaket) were analyzed in order to establish their relationship to rainfall monthly totals. The study area is characterized by a high diversity of crops, thus there is no single criterion that can be set for what may constitute an agro-meteorological shock. Daily rainfall is often modeled as a Markov process involving transitions from wet and dry days and the representation of daily rainfall totals, all of which are expected to vary seasonally and spatially. The transition probabilities for consecutive days with rain or no rain were calculated for each month. The magnitudes of daily rainfalls are represented by the gamma distribution, which parameters can be simply estimated from the mean and variance. The relationship between the observed monthly rainfall and the transition probabilities, mean and standard deviation of daily rainfall is examined using deterministic approach finding the most likely values of parameters of interest according to 6 different intervals of monthly rainfall totals. These probability expressions provide useful information on climatic shock occurrence likelihood on the basis of widely available, monthly rainfall data in Thailand.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Anna Szyniszewska.
Thesis: Thesis (M.S.)--University of Florida, 2009.
Local: Adviser: Waylen, Peter R.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2011-12-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0025162:00001

Permanent Link: http://ufdc.ufl.edu/UFE0025162/00001

Material Information

Title: Determining the Daily Rainfall Characteristics from the Monthly Rainfall Totals in Central and Northeastern Thailand
Physical Description: 1 online resource (98 p.)
Language: english
Creator: Szyniszewska, Anna
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: climate, gamma, markov, precipitation, rainfall, thailand
Geography -- Dissertations, Academic -- UF
Genre: Geography thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Daily rainfall attributes are crucial in the risk assessment of climate conditions that may have damaging effect on agriculture. Although daily rainfall totals data accessibility is frequently limited, monthly rainfall data are most abundant in space and time in Thailand. The daily rainfall totals in four provinces of central and north-east Thailand (Lopburi, Chachengsao, Buriram and Sisaket) were analyzed in order to establish their relationship to rainfall monthly totals. The study area is characterized by a high diversity of crops, thus there is no single criterion that can be set for what may constitute an agro-meteorological shock. Daily rainfall is often modeled as a Markov process involving transitions from wet and dry days and the representation of daily rainfall totals, all of which are expected to vary seasonally and spatially. The transition probabilities for consecutive days with rain or no rain were calculated for each month. The magnitudes of daily rainfalls are represented by the gamma distribution, which parameters can be simply estimated from the mean and variance. The relationship between the observed monthly rainfall and the transition probabilities, mean and standard deviation of daily rainfall is examined using deterministic approach finding the most likely values of parameters of interest according to 6 different intervals of monthly rainfall totals. These probability expressions provide useful information on climatic shock occurrence likelihood on the basis of widely available, monthly rainfall data in Thailand.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Anna Szyniszewska.
Thesis: Thesis (M.S.)--University of Florida, 2009.
Local: Adviser: Waylen, Peter R.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2011-12-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0025162:00001


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DETERMINING THE DAILY RAINFALL CHARACTERISTICS FROM THE MONTHLY RAINFALL TOTALS IN CENTRA L AND NORTHEASTERN THAILAND By ANNA MARIA SZYNISZEWSKA A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2009 1

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2009 Anna Maria Szyniszewska 2

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To my beloved husband, Stefan 3

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ACKNOWLEDGMENTS I am very indebted to Dr. Peter Waylen, Dr. Michael Binford and Dr. Corene Matyas, members of my advisory committee, for th eir academic support and encouragement on the completion of this research. I would like to expre ss my special gratitude to my advisor Dr. Peter Waylen, who proved to be not onl y an outstanding research mentor and the committee chair, but also a great teacher, cheerf ul spirit and an excellent manager of our department. I am thankful to all members of the Geogr aphy Department, both faculty and students for creating a cozy and very supportiv e atmosphere that makes every day of work so enjoyable. People make places, and theref ore I would like to thank all my wonderful friends at the department for making me feel like at home in Gainesville. My special thanks to Andrea Wolf for her friendship and help with proofreading this document. I am also extremely appreciative to Risa Patarasuk and her family for their Thai hospitality in Bangkok and invaluable help in obtaining data for this research. I would like to thank the Townsend Thai project and Dr. Michael Binf ord for the financial support during the first year of my study. I am appreciative to John Felkner at the University of Chicago for helping me in obtaining initial rainfall data. In Thailand, I tha nk the staff of the Thai Family Research Centre at Lopburi and Chachoengsao province for their help in reaching the survey sites. There are no words that could describe my gratitude to my husband Stefan who was my teacher in programming that saved me many months of work on this analysis. But mostly I thank him for his immense love, unconditional support in any of my endeavors and his contagious belief that the only thing that is limiting us is our imagination. If it wasnt him to teach me that every dream can come true, I wouldnt be pursuin g a graduate degree at an American university. 4

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Finally, I would like to express my special gr atitude to my family in Poland my loving brothers and their families, wonderful in-laws, as well as my always patient and devoted parents Maria and Stefan for all their sa crifices and support, that I feel very strong even thousand miles away from home. 5

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TABLE OF CONTENTS page ACKNOWLEDGMENTS ............................................................................................................... 4LIST OF TABLES ...........................................................................................................................7LIST OF FIGURES .........................................................................................................................8ABSTRACT ...................................................................................................................... .............13CHAPTER 1 INTRODUCTION ................................................................................................................ ..15Problem Statement ............................................................................................................. .....15Importance .................................................................................................................... ..........15Research Objectives ........................................................................................................... .....162 DETERMINING THE DAILY RAINFA LL CHARACTERISTICS FROM THE MONTHLY RAINFALL TOTALS IN CENTRAL AND NORTHEASTERN THAILAND ............................................................................................................................17Introduction .................................................................................................................. ...........17Literature Review ...................................................................................................................18Rainfall Variability in Southeast Asia .............................................................................18Rainfall and the Agriculture ............................................................................................19Spells of Dry and Wet Days ............................................................................................20Daily Precipitation Magnitudes .......................................................................................20Study Area and Data ...............................................................................................................21Methodology ................................................................................................................... ........22Results .....................................................................................................................................26Intra-Provincial Variability .............................................................................................26Seasonal Changes in Tran sition Probabilities .................................................................27Gamma Distribution ........................................................................................................28Rainfall Magnitudes Parameter Values ...........................................................................28Parameter Changes According to Monthly Totals ..........................................................30Discussion .................................................................................................................... ...........31Conclusions .............................................................................................................................333 CONCLUSIONS ................................................................................................................. ...92LIST OF REFERENCES ...............................................................................................................95BIOGRAPHICAL SKETCH .........................................................................................................98 6

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LIST OF TABLES Table page 2-1 Kolmogorov-Smirnov two sample test for statistical difference between daily rainfall parameters in Lopburi province. ...........................................................................352-2 Kolmogorov-Smirnov two sample test for statistical difference between daily rainfall parameters in Chachoengsao province. .................................................................362-3 Kolmogorov-Smirnov two sample test for statistical difference between daily rainfall parameters in Buriram province. ...........................................................................372-4 Kolmogorov-Smirnov two sample test for statistical difference between daily rainfall parameters in Sisaket province.. ............................................................................382-5 Average daily rainfall parame ter values in Lopburi province. .........................................392-6 Average daily rainfall parameter values in Chachoengsao province. ...............................402-7 Average daily rainfall paramete r values in Buriram province. .........................................412-8 Average daily rainfall parameter values in Sisaket province. ...........................................422-9 Chi-square Goodness-of-Fit test betw een theoretical gamma distribution and empirical Weibull distribu tion, Lopburi province. ............................................................432-10 Chi-square Goodness-of-Fit test betw een theoretical gamma distribution and empirical Weibull distributi on, Chachoengsao province. ..................................................442-11 Chi-square Goodness-of-Fit test betw een theoretical gamma distribution and empirical Weibull distribu tion, Buriram province.. ...........................................................452-12 Chi-square Goodness-of-Fit test betw een theoretical gamma distribution and empirical Weibull distribu tion, Sisaket province. ..............................................................46 7

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LIST OF FIGURES Figure page 2-1 Administrative map of Thailand with highlighted provinces of interest and chosen for the study synoptic stations............................................................................................472-2 Synoptic stations used in this study within the closest distance to the survey villages. ....482-3 Monthly precipitati on in Buachum, 1970-2006. ................................................................482-4 Monthly precipitati on in Lopburi, 1951-2006. ..................................................................492-5 Monthly precipitati on in Suphanburi, 1951-2006. .............................................................492-6 Monthly precipitati on in Wichianburi, 1970-2006. ...........................................................492-7 Monthly precipitation in Bangkok Metropolis, 1951-2006. ..............................................502-8 Monthly precipitat ion in Chonburi, 1951-2006. ................................................................502-9 Monthly precipitat ion in Donmuang, 1951-2006. .............................................................502-10 Monthly precipitati on in Kabinburi, 1970-2006. ...............................................................512-11 Monthly precipitati on in Prachinburi, 1951-2006. ............................................................512-12 Monthly precipitation in Aranyaprathet, 1970-2006. ........................................................512-13 Monthly precipitati on in Chokchai, 1970-2006. ................................................................522-14 Monthly precipitation in Nakhon Ratchasima, 1951-2006. ...............................................522-15 Monthly precipitat ion in Nangrong, 1970-2006. ...............................................................522-16 Monthly precipitation in RoiEt, 1951-2006. ......................................................................532-17 Monthly precipitati on in ThaTum, 1970-2006. .................................................................532-18 Monthly precipitation in Ubon Ratchathani, 1951-2006. ..................................................532-19 Sample cumulative gamma distribution f unction for constant shape parameter value alpha (a= .5) and three different beta parameter values compared to exponential distribution (a=1). ........................................................................................................... ...542-20 Sample cumulative gamma distribution f unction for constant scale parameter value beta (b=20) and three diffe rent alpha parameter values compared to exponential distribution (a=1). ........................................................................................................... ...54 8

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2-21 Gamma CDF with constant mean and changing standard deviation value. ......................552-22 Gamma CDF with constant standard deviation and changing mean value. ......................552-23 Contour map showing the relationship betw een various standard deviation and mean values and the alpha parameter value, Suphan Buri station. ..............................................562-24 Contour map showing the relationship betw een various standard deviation and mean values and the beta parameter value, Suphan Buri station. ................................................562.25 The average number of signi ficantly different parameter values per month according to K-S test between all stations per each province. ...........................................................572-26 Number of rejected K-S tests between stations, Lopburi province. ..................................572-27 Number of rejected K-S tests betw een stations, Chachoengsao province. ........................582-28 Number of rejected K-S tests between stations, Buriram province. ..................................582-29 Number of rejected K-S tests between stations, Sisaket province. ....................................592-30 Average p00 transition probabilities va lues per month in Lopburi province. ...................602-31 Average p00 transition probabilities valu es per month in Chachoengsao province. .........602-32 Average p00 transition probabilities va lues per month in Buriram province. ...................612-33 Average p00 transition probabilities va lues per month in Sisaket province. .....................612-34 Average p11 transition probabilities va lues per month in Lopburi province. ...................622-35 Average p11 transition probabilities valu es per month in Chachoengsao province. .........622-36 Average p11 transition probabilities va lues per month in Buriram province. ...................632-37 Average p11 transition probabilities va lues per month in Sisaket province. .....................632-38 Average monthly daily rainfall magnitudes means in Lopburi province. .........................642-39 Average monthly daily rainfall magnitudes means in Chachoengsao province. ...............642-40 Average monthly daily rainfall magnitudes means in Buriram province. .........................652-41 Average monthly daily rainfall magn itudes means in Sisaket province. ...........................652-42 Average standard deviations of daily rainfall magnitudes per month in Lopburi province..............................................................................................................................66 9

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2-43 Average standard deviations of daily rainfall magnitudes per month in Chachoengsao province. ....................................................................................................662-44 Average standard deviations of daily rainfall magnitudes per month in Buriram province..............................................................................................................................672-45 Average standard deviations of daily rainfall magnitudes per month in Sisaket province..............................................................................................................................672-46 Gamma CDF for Buachum station, 1970-2006. ...............................................................682-47 Gamma CDF for Lopburi station 1951-2006....................................................................682-48 Gamma CDF for Suphanburi station 1951-2006. .............................................................692-49 Gamma CDF for Wichianburi station 1970-2006. ...........................................................692-50 Gamma CDF for Bangkok Metropolis station 1951-2006 ...............................................702-51 Gamma CDF for Chonburi station 1951-2006 .................................................................702-52 Gamma CDF for Donmuang station 1951-2006 ...............................................................712-53 Gamma CDF for Kabinburi station 1970-2006. ...............................................................712-54 Gamma CDF for Prachinburi station 1951-2006. ............................................................722-55 Gamma CDF for Aranyaprathet station 1951-2006. .........................................................722-56 Gamma CDF for Chokchai station 1970-2006. ................................................................732-57 Gamma CDF for Nakhon Ra tchasima station 1951-2006. ...............................................732-58 Gamma CDF for NangRong station 1970-2006. ..............................................................742-59 Gamma CDF for Surin station 1951-2006. .......................................................................742-60 Gamma CDF for RoiEt station 1951-2006. ......................................................................752-61 Gamma CDF for ThaTum station 1970-2006. ..................................................................752-62 Gamma CDF for Ubon Ratchathani station 1951-2006 ...................................................762-63 Empirical (Weibull) vs. theoretical cu mulative gamma distribution function April, Lopburi. ...................................................................................................................... ........762-64 Empirical (Weibull) vs. theoretical cumulative gamma distribution function May, Lopburi. ...................................................................................................................... ........77 10

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2-65 Empirical (Weibull) vs. theoretical cu mulative gamma distribution function June, Lopburi. ...................................................................................................................... ........772-66 Empirical (Weibull) vs. theoretical cu mulative gamma distribution function July, Lopburi. ...................................................................................................................... ........782-67 Empirical (Weibull) vs. theoretical cumulative gamma distribution function August, Lopburi. ................................................................................................................782-68 Empirical (Weibull) vs. theoretical cumulative gamma distribution function September, Lopburi. ...........................................................................................................792-69 Empirical (Weibull) vs. theoretical cumulative gamma distribution function October, Lopburi. ...............................................................................................................792-70 Average mean daily precipitation magnit udes according to different monthly rainfall totals intervals in Lopburi province. ..................................................................................802-71 Average mean daily precipitation magnit udes according to different monthly rainfall totals intervals in Chachoengsao province. ........................................................................802-72 Average mean daily precipitation magnit udes according to different monthly rainfall totals intervals in Buriram province. ..................................................................................812-73 Average mean daily precipitation magnit udes according to different monthly rainfall totals intervals in Sisaket province.. ..................................................................................822-74 Average standard deviation of daily precipitation magnitudes according to different monthly rainfall totals intervals in Lopburi province. .......................................................832-75 Average standard deviation of daily precipitation magnitudes according to different monthly rainfall totals interval s in Chachoengsao province.. ............................................832-76 Average standard deviation of daily precipitation magnitudes according to different monthly rainfall totals intervals in Buriram province. .......................................................842-77 Average standard deviation of daily precipitation magnitudes according to different monthly rainfall totals intervals in Sisaket province..........................................................852-78 Average p00 transition probabilities accord ing to different monthly rainfall totals intervals in Lopburi province. ............................................................................................862-79 Average p00 transition probabilities accord ing to different monthly rainfall totals intervals in Chachoengsao province. .................................................................................862-80 Average p00 transition probabilities accord ing to different monthly rainfall totals intervals in Buriram province. ...........................................................................................87 11

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2-81 Average p00 transition probabilities accord ing to different monthly rainfall totals intervals in Sisaket province. .............................................................................................882-82 Average p11 transition probabilities accord ing to different monthly rainfall totals intervals in Lopburi province. ............................................................................................892-83 Average p11 transition probabilities accord ing to different monthly rainfall totals intervals in Chachoengsao province. .................................................................................892-84 Average p11 transition probabilities accord ing to different monthly rainfall totals intervals in Buriram province. ...........................................................................................902-85 Average p11 transition probabilities accord ing to different monthly rainfall totals intervals in Sisaket province. .............................................................................................91 12

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Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science DETERMINING THE DAILY RAINFALL CHARACTERISTICS FROM THE MONTHLY RAINFALL TOTALS IN CENTRA L AND NORTHEASTERN THAILAND By Anna Maria Szyniszewska December 2009 Chair: Peter R. Waylen Major: Geography Daily rainfall attributes are crucial in the risk assessment of climate conditions that may have damaging effect on agriculture Although daily rainfall totals data accessibility is frequently limited, monthly rainfall data are most abundant in space and time in Thailand. The daily rainfall totals in four provinces of central and north -east Thailand (Lopburi, Chachengsao, Buriram and Sisaket) were analyzed in order to establish their relationship to rainfall monthly totals. The study area is characterized by a hi gh diversity of crops, thus there is no single criterion that can be set for what may constitute an agro-meteorologi cal shock. Daily rainfall is often modeled as a Markov process involving transitions from wet and dry days and the representation of daily rainfall totals, all of which are expected to vary seasonally and sp atially. The transition probabilities for consecutive days with rain or no rain were calculated for each month. The magnitudes of daily rainfalls are represented by the gamma distribution, which parameters can be simply estimated from the mean and variance. The relationship between the observed monthly rainfall and the transition probabilities, mean and standard deviation of daily rainfall is examined using deterministic approach finding the most likely values of parameters of interest according to 6 different intervals of monthly rainfall totals These probability expr essions provide useful 13

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14 information on climatic shock occurrence likelih ood on the basis of widely available, monthly rainfall data in Thailand.

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CHAPTER 1 INTRODUCTION Problem Statement The distribution of rain s and climatic shocks play a cr itical role in the Thai economy, therefore the ability to assess pr obability of climatic shock is very important for agriculture and the food supply. The country has a climate de termined by its position in tropical latitudes between two ocean masses and its exposure to the monsoon winds. High temperatures and heavy rains with a high level of regi onal variability are common to this region (Lau and Yang 1997; Khedari 2000). The investigation of the abundanc e and magnitude of rain on a daily basis can give a signal whether a climatic shock has o ccurred or not. The nature of the relationship between monthly rainfall totals a nd daily rainfall characteristics in this region is investigated in this study. Importance The distribution of rain s is an important factor in count ries water resources and plays an important role in agricultural planning and ma nagement. Thailand has the largest proportion of agricultural land of all countries in Southeast As ia: from 20 to 25 million hectares, or 40 to 50% of the countrys total area (Kermel-Torres 2004). Given that 42.6% of the Thai labor force is employed in the agriculture sector, climatic va riability has a direct and indirect impact on household incomes. The significance of this sector is also on the international level, as Thailand is a leading exporter of food in Asia and has a rich variety of crops cultivated on its area due to the policy of crops diversificat ion (Kono and Saha 1995). Despite th e countrys effort to develop sustainable irrigation starting in the 1950s, Thai agricu lture still remains highly vulnerable to seasonal fluctuations in precipitation with 23% of cultivable land classified as irrigated in 1996 (Kermel-Torres 2004). Many rice cultivation areas require additional irrigation even during the 15

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16 monsoon season. As the countrys economy is highly dependent on revenue from the agricultural sector, it is vital to understand th e nature of the short-time clim ate variability in this region. Research Objectives The goal of this study was to find the probability of climate shock occurrences in four Thai provinces: Chachoengsao, Buriram, Sisaket and Lopbur i. These particular pr ovinces were chosen because each contained one county that had been sampled every year by the comprehensive Thai Socio-Economic Survey, thus providing comparativ e information of climatic variables. A major task of the large interdisci plinary project that this study is part of is to qu antify the risk of climate variation and change and then link that to actual versus potential insuran ce, economic, and social decisions. The variability of the precipitation causing damage to the agriculture and was estimated in this research. The events of interest are extremes of high or low rainfall that exceed thresholds that have agricultural or other significance, e.g., a series of rainfall events that causes floods, or a series of dry days that cause droughts. For the events when rain occurred, the probability of extremely low and extremely high rainfall magnitudes was estimated for certain thresholds of monthly rainfall totals.

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CHAPTER 2 DETERMINING THE DAILY RAINFALL CHARACTERISTICS FROM THE MONTHLY RAINFALL TOTALS IN CENTRA L AND NORTHEASTERN THAILAND Introduction The distribution of rain s and climatic shocks resulting from deviations to the anticipated spatial and temporal patterns play important roles in the Thai economy (Paxson 1992). According to the CIA World Factbook estimates from 2005, over 42% of the countrys labor force is employed in the agricu ltural sector which directly re lies on summer monsoon to bring moisture to support the crop growth. When th e climate deviates from its normal pattern, agricultural activ ities are disrupted and household income s are directly affected (Gadgil and Kumar 2006). Thailand, with its tropical posit ion is subjected to large inte rannual and seasonal variability in precipitation and thus often e xperiences excess or dearth of ra in that cause severe floods or droughts respectively which affect agriculture (B oochabun et al. 2004). More over, the country is characterized by a high diversity of crops and irrigation methods, thus no single criterion can be set for what constitutes an agro-meteorological shock. This study, which is part of a larger interdisciplinary project, investigates the empiri cal relationship between monthly rainfall totals which are more abundant in both space and time, a nd chosen daily rainfall characteristics that describe the probabilities of conditions that might be considered agricultural shocks. A major task is to quantify the risk of climate variati on and then link that to actual versus potential insurance, economic and social decisions. Two main properties of the daily totals are investigated on a mont hly basis: 1) Is it raining on given day? 2) If yes, how much rain falls ? Daily rainfall occurrences are modeled as a Markov process involving transiti ons between wet and dry days, and daily rainfall totals by an appropriate probability distribution. These propert ies are calculated at 17 synoptic stations over 17

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periods of 1951-2006 or 1970-2006 depending on locati on. Four provinces are selected for this study, two in the central Thailand and two in th e northeast Thailand. For each province, daily rainfall data from the four closest synoptic stations were examined. Ideally, the properties of wet-day rainfall totals can be represented by a probability distribution, sufficiently flexible to be used in all locations through the rainy season. The parameters should be estimated easily and be physically in terpretable, in order that they may be linked deterministically to observe d monthly totals. High probabiliti es of long sequences of rainy days, combined with high probabilities of large ma gnitudes of daily rain create a setting in which excess of rains and floods are likely. Conversel y, high probabilities of se quences of dry days accompanied by low magnitudes of precipitation create a setting favorable for drought. Derived empirical estimates provide useful information on the most likely combination of daily rainfall characteristics for a particular magnitude of monthly rainfall, which are more ubiquitous in Thailand. Literature Review Rainfall Variability in Southeast Asia Thailand is situated between the two large o cean water bodies of the Pacific and Indian Oceans. Its climate is dominated by two air streams: a dry northeast monsoon that commences in November and lasts until February, and the wet southwestern Asian monsoon that commences in mid-May and lasts until mid-October (Lu et al. 2006). The monsoons are controlled by the Intertropical Convergence Zone (ITCZ), which migrates over Thailand no rthwards in May and southwards during September (Lau and Yang 1997; Kermel-Torres 2004; Khedari 2000). The country is subjected to strong intraand interannual variabil ity in precipitation, potentially conditioned upon the El Nio-Sout hern Oscillation (ENSO) phenomenon. The relationship between ENSO, one of the most important modes of global climate variab ility, and the Indian 18

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summer monsoon has been widely studied for India, but there are far fewe r studies investigating links to summer rainfall in Thailand (Kripala ni and Kulkarni 1997). While the relationship between the Indian monsoon and ENSO has weakened in past decades (Kumar 1999), the negative association between warm phases of ENSO and summer rainfall over Thailand may have strengthened since 1980 (Singharattna et al. 2005). Rainfall and the Agriculture Agriculture is one of the most climate dependent human endeavors (Mendelsohn 2007; Murdiyarso 2000). More than half of worlds population relies on the Asian monsoon to sustain agriculture, the dominant source of income in Southeast Asia. Rice is the main food staple in this region it accounts for about 90% of the agricultural area and 92% of global rice production, with Thailand being the worl ds largest rice exporter. Rain is the most limiting factor for rice produ ction in South and Southeast Asia therefore when the summer monsoon deviates from its nor mal pattern, the agricultural operations are disrupted accordingly. Too much or too little rain causes the crop to suffer moisture stress that can have disastrous effects on the people and eco nomy. In general, the impacts of drought are known to be more harmful than those of ex cess rainfall (Gadgil and Kumar 2006). While rice predominates in the study area, Thailand has rece ntly undergone a process of crop diversification particularly in the center of the country mainly the Chao Praya river basin, which is the heart of national agricultural and economic activities. Other major crop s include sugar cane, cassava, rubber, maize, mung bean and soybean. Thus, there is no single cr iterion that would be responsible for agricultura l shock in this area as various crop s are resistant to different levels of moisture stress. However, Gadgil and Kumar (2006) indicate d that there are three most important characteristics of rain that can have affect on the agricu lture: rainfall magnitude, spells of dry and wet days, and the monsoon onset. 19

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Spells of Dry and Wet Days A Markov chain is a stochastic process widely used in clim atology to represent the time series of discrete states, in th is case the sequence day, or states, with rain or no rain. It provides information about the risk s of dry or wet spells, both of which are poten tial agricultural shocks. An important characteri stic of this model is the degree of dependence of each observation upon the state observed previously, c ontrolled by the order of the model (Haan 1977, Wilks 1998, 1999, 2006). Most commonly a simple 1st order is generally assumed, although higher orders have also been us ed (Katz 1981). A two-state first-order Markov model consists of four parameters: p00 (the probabili ty of a dry day following a dry da y), p01 (the probability of a wet day following a dry day), p10 (the probability of a dry day following a wet day) and p11 (the probability of a wet day following a wet day). As the values p00 with p01, and p11 with p10, always sum to 1 only one of each pair is require d to fully characterize the process. Numerous studies have shown the applicabil ity of the first order Markov ch ain to rainfall modeling (Caskey 1963; Katz 1977, 1981; Coe and Stern 1981; Harrison and Waylen 2000). Daily Precipitation Magnitudes The magnitude of daily, non-zero precipitation to tals can be represented by one of many exponential-types of continuous probability distri butions such as the gamma, Generalized Pareto, Pearson or generalized extreme value (Katz 1977; Coe and Stern 1982; Stern and Coe 1984; Rosbjerg et al. 1992; Madsen et al. 1997; Stephenson et al. 1 999), which have a lower bound of zero as there is no negative pr ecipitation. Distributions such as the Generalized Pareto and gamma are sensitive to the important values in the tail of the distribution. Both are described by two parameters that are derived from the samp le mean and variance via the method of moments (Barger and Thom 1949, Thom 1958, Ison et al 1971, Shenton and Bowman 1973, Rosbjerg et al. 1992; Madsen et al. 1997; Stephenson et al 1999). Among many distributions that were 20

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attempted to be fit to the empi rical data the gamma distribution was found to have the best fit across the study area and was thus chosen to represent daily rainfall total magnitudes. Study Area and Data Four Thai provinces (changwats): Chachoengs ao and Lopburi located in central Thailand and Buriram and Sisaket in the Northeast are c hosen as each contains one county (amphoe) that had been sampled every year by the comprehens ive Thai Socio-Economic Survey, providing a benchmark for comparative studies between environmental and socio-economic variables. The Central and northeast areas range fr om relatively wealthy to relativ ely poor, not only in terms of income measures, but also in moisture availability, soil fertility, land cover, and other environmental characteristics. The center of the country stretches over a vast alluvial plain drained by the Chao Phraya River, while the nor theast of Thailand occupies the Khorat plateau. The central area has a relatively hi gh diversity of crops and is fa irly well irrigated, whereas the northeast is less diversified and the percent of irrigated arable land is relatively low (Gleick 1993). In the former, the percent of households deriving income from agriculture is estimated to be between 38 and 53% and in the latter betw een 65 and 81% (Kernel-Torres 2004). Daily precipitation data are obtained from the Thailand Meteorological Department for seventeen synoptic stations in central and northeast Thailand region for the period of 1951-2006 or 1970-2006 depending on the location (Fig. 2-1 and 2-2). The stations used in the study are selected according to the distance from the so cio-economic survey villages and the duration of full daily rainfall record. Stations with at least 30 years of daily rainfall record and within a distance no larger than 100 km are sought in orde r to provide a reasonable estimation of daily rainfall characteristics in the survey villages. The monthly precipitation regimes of the stations are repres ented in Figures 2-3 through 218. Those of the center of the country exhibit a vi sible reduction in precip itation in the middle of 21

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the rainy season, which corresponds to the ITCZ s most northerly position before moving southward in the end of the season. The regime of the northeast evinces a less pronounced bimodal distribution of rainfall. Precipitation ge nerally peaks during September and the central provinces show a secondary maximum in May. The research focuses on the seven wettest months starting with April until the October, that include the summer monsoon season, which accounts for over 80% of annual precipitation. Methodology A wet day in this study is defined to be one on which there is at least 0.1mm of precipitation on record. This threshold could possi bly be modified according to the application needs. The transition probabilities for consecutive days with rain or no rain are calculated for each month. Markov chain models are created by conditioning the probability of the occurrence of rainfall on one day upon whether measurable rainfall was observed on the previous days. These are characterized by transit ion probabilities (Equation 2-1). mt tttt ttttXXXXXXXXXX ,...,,Pr,...,,Pr21 1 121 1 (2-1) The most common Markov chain used in research is first order two-st ate model (Gates and Tong 1976; Katz 1977; Guzman and Torrez 1985; Hosking and Wallis 1987; Harrison and Waylen 2000). This yields four parameters, two of which are employed in this study: the probabilities of no rain being followed by no rain (p00), and that of rain followed by rain (p11). Higher probabilities of p00 indica te higher likelihood of long dry sp ells and drought in terms of monthly totals. On the other hand, higher probabi lities of p11 indicate a greater lik elihood of long sequences of wet days and therefore supe rsaturated soils that may lead to floods. Rainfall totals are modeled by the expone ntial-like gamma distribution (Haan 1977; Rosbjerg et al. 1992; Madsen et al. 1997; Wilks 2006). (Figur e 2-19 and 2-20). Equation 2-2 22

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defines the gamma cumulative di stribution function (CDF) and 2-3 the density function. The two parameters alpha ( ) and beta ( ) can be easily estimated from sample mean and variance using method of moments (Equ ation 2-3 and 2-4). 0,, / / )( )/exp()/( )( )( )/exp()( )(2 22 1 1 x xs sx x x xf x x xf (2-2) (2-3) (2-4) (2-5) Parameters are estimated from precipitation magnitudes observed during a specific month, across all years of record. Alpha controls the shape of the distribution. For < 1 the distribution is strongly skewed to the right as illustrated on Figure 2-20. The values of alpha increase as the sample mean increases but decrease as the standard deviation increases. The larger alpha the more skewed is the distribution and, as a result the lower probability of receiving small rainfall values. The special case of = 1 arises for an exponential distribution and it has been illustrated on the same figure. In that case the distribution is flatter and less sensitive to the daily rainfall properties in the tail. Beta, the scale parameter, controls the spread of the distribution (F igure 2-20), stretching or squeezing the distribution to the right or left depending on the magnitudes of the observed data. The value of this paramete r exponentially increases as the sa mple standard deviation value increases and decreases as the sample mean increases. Figures 2-21 and 2-22 illustrate how the shap e of the distribution changes with a changing sample standard deviation function (with cons tant mean) and with a changing mean (with 23

PAGE 24

constant standard deviation). The mean has st ronger influence on the shape of the distribution while standard deviation regulates its extent. The empirical distribution of the rainfall magnitudes to which fitted distributions are compared, is calculated using the Weibull plotting position where Pemp is the exceedance probability of the ith ranked observation (lowest rainfall magnitude to the highest) with the highest rank, N, being the number of tota l observations in the sample (Cunnane 1978). Pemp = i/(N+1) (2-6) The estimated gamma distributions, with parameters varying according to month and locations, are then compared with the empirical cumulative distribution of rainfall magnitudes and tested for agreement using Chi-Square goodness-of-fit (GOF) test. Chi-square GOF is one of the most commonly used formal tests to evaluate agreement between chosen hypothesized cumulative distribution functions with the catego rized hydrologic data (Huang et al. 2008). In this test an atypical hypothesis test setting is applied, where evidence in favor of the null hypothesis is sought that the data were drawn fr om the hypothesized distri bution. It compares a data histogram with the probability distribution function. The test involves the counts of data values falling into each class in relation to the computed theoretical probabilities. kExpected Expected Observed # )# (#2 2 (2-7) The number of bins k into which the histogram is divided is calculated as shown in the Equation 2-8. It is recommended that no bin cont ain less than 3 observed frequencies, therefore the last bin extends into infinity. 24

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4.0 k (2-8) The number of degrees of freedom (DOF) is cal culated using the number of bins minus the number of the parameters of fit minus 1 (Equation 2-9). DOF = (# of bins # of parameters of fit 1) (2-9) Four properties of daily rainfall, which summa rize the risks of agricultural shock, are therefore examined: the first order transition probab ility from state of no rain to no rain (p00), the first order transition probability from state of rain to rain (p11), as well as mean and standard deviation of the daily rainfall magnitudes on days wh en rain occurred. Parameters of interest are calculated at every station for i ndividual months. The primary research problem is to associate the most likely combinations of these statistics (and thus parameters) with the respective monthly rainfall totals, in order to provide a means of downscaling from the monthly rainfall totals, which are more abundant both in space and time across Thailand, to the likely, and unknown, daily rainfall characteristics in the past Monthly rainfall totals are then grouped into six different arbitraril y chosen intervals (0100mm, 100-200mm, 200-300mm, 300-400mm, 400-500mm and 500-900mm) and relative frequency distributions of the values each of the four parameters of interest corresponding to these intervals, by month, are c onstructed, the mean parametric value in each interval is calculated and plotted in a summarizing graph that illustrates empirically the most likely parameter value for a given interval of monthly tota l for each month. In order to test for any heterogeneity of th ese characteristics with in a province, a twosample Kolmogorov-Smirnov (K-S) test is em ployed. The test compares the observed distributions of the four calcula ted monthly parameters mean, standard deviation, p00 and p11 between the stations in each province searching for evidence that these parameters vary 25

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significantly between stations, in a given month. The K-S test uses the test statistic D indicating the largest absolute distance between th e two empirical functions (Equation 2-9): Dn = max |Fn(x)-F(x)|, (2-9) where Fn(x) is one empirical cumulative probabi lity and F(x) is the other. The null hypothesis is that the observed data were drawn from the sa me distribution (Wackerly 2002). Results Intra-Provincial Variability The K-S goodness-of-fit test indi cates very few significant diffe rences in the distributions of similar parameters within any province (tab les 2-1 to 2-4). Figure 2-25 depicts the average number of occasions that the rejected null hypothesis is rejected in each province. The maximum possible value would be 42 (6 ways of cross-comparing four st ations times 7 months of comparison), or 70 in the Buriram and Ch achoengsao provinces for which there are 5 recording stations. Figures 2-26 through 2-29 are constellation diagrams illustrating the number of significantly different monthly parameter values between e ach pair of stations, their interstation distances and geographic di sposition. By far the largest intra-provincial heterogeneity is observed in Chachoengsao (figure 2-27) with a ma rked difference between the group of stations located close to the Gulf of Thailand (Bangkok, Donmuang and Chonburi) compared to group of two stations located in the nor th of the province Prachinburi and Kabinburi. While there is greater overall homogeneity the Lop buri province (Figure 2-26), in ter-station distance appears to exert the greatest control. In Buriram (Figure 228), the highest differences are again generally observed between the most distant stations like Surin, Nakhonratchasima and Aranyaprathet, while Sisaket preserves the st rongest intra-provincial homoge neity among all four provinces (Figure 2-29). It seems reasonable therefore to treat the parameters derived from statistically alike stations in each province, as if they were all records or r ealizations drawn from the same 26

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provincial population, and combine them to obtain a greater sample size. Further evidence for this assumption is pursued through an investigation of the seasonal changes in the mean values of the rainfall model parameters. Seasonal Changes in Transition Probabilities Various spatial and temporal trends are apparent in magn itudes of p00 and p11 parameters. Figures 2.30 through 2.37 represent averaged tr ansition probabilities for each month, within a province. April as the month of the onset of the monsoon has been shown to possess high interannual variability and is by far the driest month chosen for this study. It is therefore expected, that in April we observe the highest values of p00 in the season. In Chachoengsao and Lopburi province p00 value is above .80, whereas in the Si saket and Buriram this value is about .70. This tendency is different from the anticipated spa tial variability as it would be expected that geographically the monsoon season commences first in the ce ntral provinces. As the monsoon season progresses, the values of p00 decrease at sli ghtly different rates depending on location, although there appears to be no major difference between provinces or central and northeastern regions. Values in Lopburi show a leveling between May and June and gently decrease afterwards, while Sisaket displays the most constant values of p00 at about .50 starting in May through September. Buriram e xperiences the greatest fluctuations both temporally and spatially although the same overall trend is apparent. Values in Chachoengsao are gently decreasing from .70-.85 in April up to 35-.45 in September indicating lower probability of dry-dry transitions every month. This decreasing trend comes to an abrupt end in October at all stations and provinces as the monsoon retreats, thus increasing the probability of two consecutive dry days. 27

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As might be expected, the values of p11 tend to mirror those of p00. Values in April in all of the provinces are approximately .30-.40 with Lopburi province having the highest internal variability in the range of .25-.35 in the southwest and .35-.45 in the northeast. As the monsoon season commences fully in May values are the highest in Chachoengsao province (.60-.70) and slightly less (.50-.60) in the other provinces, increasing gradually until September in Sisaket, Buriram and the easternmost stations of Chachoengsao while the rise is delayed until in June in the more westerly Lopburi and western portions of Chachoengsao. September represents the highest p11 parameter values at all locations at the range of .60-.80 and are very homogeneous at the intra-provincial level. The end of the monsoon season is marked by a decline, although not as sharp as the increase observed in p00. The p11 values are in th e range of May and June values and decrease to the range of .45-.70 with th e highest values and the lowest intra-provincial variability in westernmost Chachoengsao and the largest intraprovincial variability together with lowest values in easternmost Sisaket. Gamma Distribution The Chi-squared results as detailed in (tab les 2-9 through 2-12) and example plots the distributions of daily total are presented in Figures 2-63 through 2-69 for the seven months at Lopburi station. In only 10% of the cases (13 of 126) was the null hypothe sis of no significant differences rejected. Eight of these cases were m onths in Buriram province, in which the fitted gamma failed to approximate the observed records at Nangrong. No month appeared particularly more susceptible than other, although 6 of the poor fits did occu r in April and May. Rainfall Magnitudes Parameter Values Figures 2-23 and 2-24 graph the relationshi p between increasing standard deviation (s) and mean (x) daily rainfall values a nd the values of alpha () and beta () respectively. Most records 28

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produced combinations of mean and standard deviation that plot between al pha values of 0.4 and 0.6 roughly on the 45 degrees slope. The al pha values for at Suphanburi indicate higher variances in proportion to mean s early in the monsoon season ( <0.5) and lower variances at the end of the season ( >0.5). Figure 2-24 displays the same re lationship for the beta parameter. The higher density of contour lin es on y axis indicates the greater sensitivity of to the value of the standard deviation. June, July a nd August have the lowest values of standard deviation and also the lowest parameter, therefore the distribution w ill be least dispersed. May and September have the same value, although in May we observe lower x and lower s. April has the highest scale parameter values and therefore the distribution is mo re stretched compared to May, which indicates more likely high rainfall values (Figure 2-48). The average expected mean and standard deviat ion values for each station averaged for all years and represented by month are shown in Figures 2-38 through 2-45. Worth mentioning is the fact that the standard deviation is always larger than th e mean and as a consequence values fall always below 1.0 and more specificall y in the range of .40 .60. At the same time, values of x and s are highly correlated. Most of the tr ends indicate the b imodal peaks of both mean and standard deviation values in Ma y and September. The highest mean rainfall magnitudes accompanied with the highest s values are expected at the end of the monsoon season peaking in September. Conversely, the lowest x and s values are in the middle of the monsoon season starting in June until August. Stations located in the vicinity of Chachoengsao province have the highest peak mean daily rainfall between 14-17 mm for that month and a standard deviation of 18.3-22.2 mm. The lowest mean daily totals are observed in the middle of the monsoon season from June through August, with the exception of Kabinburi and Prachinburi stations in Chachoengsao, where the 29

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monthly means increase steadily and gradually from April to Septembe r, and decrease slightly in August. Variability between different expected mean daily rainfall magnitudes in the middle of the monsoon season in this province represents the most prominent source of intra-provincial variability. The same is the case for the standard deviation scores in thes e two stations. Similar trend of changes in x and s is observed in the Lopburi province with higher x and s values at the end and the beginning of the monsoon season, and considerably lower in the middle (Figures 238 and 2-42). Parameter Changes According to Monthly Totals The final results of this study identify the mo st likely four rainfall parameter values associated with the observed monthly rainfall totals. Figures 2-70 through 2-73 show considerable homogeneity in the relationship between the monthly rainfall totals and the daily mean rainfall magnitudes (x) across all four provinces. With each 100mm increment of monthly rainfall totals, the expected daily rainfall value is increasing by about 5 mm. Among the various months, April has the highest slope of increase, indicating less frequent but more intensive daily precipitatio n. This characteristic is common to each of the four provinces. The standard deviations (Figur es 2-74 2-77) follow a similar trend, although as might be expected given that they are sec ond order moments they tend to be a little noisier. Only in April and October, when daily rainfall occurs least frequently, does the variability increase markedly compared to other months as the monthly totals increase. As it could be expected, p00 tends to decline with increasing monthly rainfall totals, and p11 increases (Figures 2-78 2-85). However consid erable spatial and temporal variability about this pattern can be identified, particularly during July, August and September. In Lopburi in August, p00 tends to increase with monthly rainfa ll totals, and although p11 values do rise they 30

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tend to do so at a lower rate than in other m onths. Similar behavior is observed in Buriram during September. The southern province of Chachoe ngsao a large spatial variability in trends of changes in p00 values for these three months accor ding to various monthly rainfall totals values. This could result from the lower sample size in certain monthly rainfall totals intervals. Discussion The rainfall magnitudes are well described us ing the gamma distributions. In the majority of months the mean and standard deviation of daily rainfall magnitudes increase steadily with increasing monthly rainfall totals, although there is some individual variability. April is by far the most unusual month, generally showing a far higher rate of change (but low totals). The absolute levels of mean daily rainfall magnitude s increase with higher monthly rainfall totals throughout the summer monsoon season. However, va rious months are characterized by slightly different absolute (as opposed to slope) levels of the mean, especially on the interprovincial level, indicative of the generally wetter conditions in the westerly provinces of Chachoengsao and Lopburi. Seasonal patterns are dominated by the advance and retreat of the monsoon as well as migration of ITCZ zone. For instance, at Lopburi station, April ha s average value of 10 mm of daily precipitation when the monthly total is between 0 and 100 mm, in May it is 8 mm, and in August it is less than 5 mm. With increasing monthly rainfall to tal, April, May and October, display constantly higher mean daily rainfall ma gnitudes than other, wett er months. Because of the limited number of days with rain in these mo nths, the longest dry spells of dry days can be expected, and increased monthly rain fall totals can be expected as a result of higher totals (mean) falling in the few days of rain. P00 usually stays at similar high levels in these months regardless of monthly rainfall totals (low slopes to lines). The likelihood of consecuti ve rainy days is the lowest in April; however it rises sharply as the mo nthly total increases. Rain is less frequent than in other months, but on average more intense. Gr eater variability is observed in changes of the 31

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transition probabilities on the intra-annual scale, than in means and standard deviations, implying that the frequency with which the rainfall gene rating process is changing through the season. The least intense but most persistent rains occur in September as implied by the stable values of p00 and p11. In October the rain is less persistent and the averag e expected rainfall magnitudes are relatively high. These analyses in combinati on with the previous anal ysis of intra-provincial homogeneity, suggest that a single provincial relationship between monthly rainfall total and each of the four parameters can reasonably be de rived by taking an average of the relationships for each station. Figures 2-70 through 2-85 show the most likel y parameters of the daily rainfall models associated with a given interval of monthly rainfa ll totals at a specific tim e and location. The risk of some specific shock to occur in the future (e.g. unusual sequence of dry days, or unusually large daily rainfall totals) can be simply derived as shown in the examples below. For instance, for a crop that cannot sustain mois ture stress that woul d exceed 10 consecutive days without rain, the risk of this stress to occur can be estimat ed multiplying the p00 transition probability at the closest synoptic station accordi ng to the monthly rainfall total interval. For the monthly rainfall total of 167mm in the southwest part of Lopburi pr ovince, in May this risk would be estimated 0.66 to the power of 10 which returns 1.58% chan ce. For the same monthly rainfall total in the wetter months of July and September this ch ance would be even lower: 0.28% and 0.08% respectively. The chance of the same conditions in the same months but for higher monthly rainfall totals decreases. For the interval of 300-400mm it is 0.06% in May, 0.04% in July and 0.01% in September. Conversely, the risk of hi gh moisture conditions can be calculated with the application of p11 and a gamma distribution. If the risk of 2 consecutive days of rain each exceeding 25 mm is to be calculated for the same three months and location, the p11 need to be 32

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risen to the power of 2, and multiplied by the probability of 25mm exceedance derived from the gamma distribution raised to the power of 2. The gamma distribution needs to be described by the most likely mean and standard deviation values. The results return an extremely low chance of this event to happen for the monthly rainfa ll total interval of 100-200mm: 0.01% in May, 0.00% in July and 0.02% in September. For the monthly rainfall total interval of 300-400mm these chances increase: 0.17% in May, 0. 09% in July and 0.31% in September. The risk of various sets of conditions can be calculated for the future using the same approach and selecting the average parameter values at a specific location. This is an easy and straightforward way to assess the risk of a certain agro-meteorological condition to occur as well as track the most likely conditi ons that occurred in the past. Conclusions Excess or dearth of rain can have a negative effect on local agriculture, which is the source of majority household incomes in Thailand. The main research goal of the larger interdisciplinary project was to link the climatologic variables with the socio-economic surveys conducted in four provinces of Thailand: two in the center and two in the northeast of the country. The climatological modeling problem was to assess the risk of occurrence of certain agro-meteorological conditions, or shocks that could create a moisture stress setting for a variety of crops in the region. The results of this study provide a straightforward and easy for a non-statistician method of predicting the risk of these conditions to happen and it could be adopted by various end-users, fo r instance local farmers or insu rance companies that can apply these findings according to their needs. In additi on, given the paucity and lack of reliability of the daily rainfall records in the villages themselv es, this research establishes means by which the parameters that defined the risks of various shoc ks can be estimated based solely upon the more widely available records of monthly rainfall totals. 33

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The strength of this method is that four daily rainfall characteristics can be simply estimated using the transition probabilities, means and standard deviations of daily rainfall totals. This direct approach makes it at tractive to various users includ ing non-statisticians. The derived probability expressions furnish useful informati on on risks of variously defined daily rainfall climatic shocks in the future, with the appli cation of average conditions expected at seven wettest months in a year during the last decad es. Likewise, for the purpose of hindcasting the daily rainfall conditions in the past, these pr obabilities can be assesse d according to various monthly rainfall totals and respective most likely four parameter values. The results from this study have show that the rainfall generating pr ocess in time and space are reasonably homogenous within (and to a lesser degree, between) those four regions, and that a single provincial relationship between monthly ra infall totals and the four parameters are all that is needed. Two parameters describing da ily rainfall magnitudes: mean and standard deviation are shown to be highly correlated not on ly one with another, bu t also with increasing monthly rainfall totals. The biggest cause of the in tra-annual variabil ity is not so much variability in the daily rainfall tota ls, as in the frequency and persis tence of rainy days, described by p11 and p00. As expected, p00 and p11 values tend to decrease and increase respectively with increasing monthly rainfall totals, however relatively large variabil ity in the behavior of these parameters is observed at various locations. The periods of consecutive days with or without rain, is highly variable both throughout the s eason and also according to various magnitudes of monthly rainfall totals. 34

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Table 2-1. Kolmogorov-Smirnov two sample test fo r statistical difference between daily rainfall parameters in Lopburi province. Stations ar e identified as: 1) Buachum, 2) Lopburi, 3) Suphanburi and 4) Wichianburi. For p<0.05 = 1. Month Parameters 1-2 1-3 1-4 2-3 2-4 3-4 April Mean 0 0 0 0 0 0 St.dev. 0 0 0 0 0 0 p00 0 1 0 0 1 1 p11 0 1 0 0 0 1 May Mean 1 0 1 0 0 0 St.dev. 1 0 1 0 0 0 p00 0 1 0 0 1 1 p11 0 0 0 0 0 0 June Mean 0 0 0 0 0 0 St.dev. 0 0 0 0 0 0 p00 0 0 0 0 0 0 p11 0 0 0 0 0 0 July Mean 0 0 0 0 0 0 St.dev. 0 0 0 0 0 0 p00 0 0 0 0 0 0 p11 1 1 0 0 0 0 August Mean 0 0 0 0 1 1 St.dev. 0 0 0 0 1 1 p00 0 0 0 0 0 0 p11 1 1 0 0 1 1 September Mean 0 0 0 0 0 0 St.dev. 0 0 0 0 0 0 p00 0 0 0 0 0 0 p11 0 0 0 0 0 0 October Mean 0 0 0 1 0 1 St.dev. 0 1 0 1 0 1 p00 0 0 0 0 0 1 p11 0 0 0 0 0 0 Total of rejected cases: 4 6 2 2 5 9 35

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Table 2-2. Kolmogorov-Smirnov two sample test fo r statistical difference between daily rainfall parameters in Chachoengsao province. Stations are identif ied as: 1) Bangkok Metropolis, 2) Donmuang, 3) Chonburi, 4) Prachinburi and 5) Kabinburi. For p<0.05 = 1. Month Parameters 1-2 1-3 1-4 1-5 2-3 2-4 2-5 3-4 3-5 4-5 April Mean 0 0 1 0 0 1 0 0 0 1 St.dev. 0 0 0 0 0 0 0 0 0 0 p00 0 0 1 1 0 1 0 1 1 0 p11 0 0 0 0 0 0 0 0 0 0 May Mean 0 0 0 0 0 0 0 0 0 0 St.dev. 0 0 0 0 0 0 0 0 0 0 p00 0 0 1 1 0 0 0 1 0 0 p11 0 0 0 1 0 0 1 0 0 0 June Mean 0 0 1 1 0 1 1 1 1 0 St.dev. 0 0 1 0 0 1 1 1 0 0 p00 0 1 1 0 0 1 0 0 0 0 p11 0 0 1 1 0 1 1 1 1 1 July Mean 0 0 1 1 0 1 1 1 1 0 St.dev. 0 0 1 1 0 1 1 1 1 0 p00 0 0 1 1 0 1 1 1 0 0 p11 0 0 1 1 0 1 1 1 1 0 August Mean 0 0 1 1 0 1 1 1 1 0 St.dev. 0 0 1 1 0 1 1 1 1 1 p00 0 0 1 0 0 1 1 0 0 0 p11 0 0 1 1 0 1 1 1 1 0 September Mean 0 0 0 0 0 1 0 0 0 0 St.dev. 0 0 0 0 0 0 0 0 1 0 p00 0 0 0 0 0 0 0 0 0 0 p11 0 0 0 0 0 0 0 0 0 0 October Mean 0 0 1 1 0 0 0 0 1 0 St.dev. 1 0 1 1 0 0 0 0 1 0 p00 1 1 0 1 0 0 0 0 0 0 p11 0 0 0 0 0 0 0 0 0 0 Total rejected: 2 2 17 15 0 15 12 12 12 3 36

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Table 2-3. Kolmogorov-Smirnov two sample test fo r statistical difference between daily rainfall parameters in Buriram province. Stations are identified as: 1) Aranyaprathet, 2) Chokchai, 3) Nangrong, 4) Surin and 5) Nakhon Ratchasima. For p<0.05 = 1. Month Parameters 1-2 1-3 1-4 1-5 2-3 2-4 2-5 3-4 3-5 4-5 April Mean 0 0 0 0 0 0 0 0 0 0 St.dev. 0 0 0 1 0 0 0 0 0 0 p00 0 0 0 0 0 0 0 0 0 0 p11 0 0 0 0 0 0 0 0 0 0 May Mean 0 0 0 0 0 0 0 0 0 0 St.dev. 0 0 0 0 0 0 0 0 0 0 p00 0 0 0 0 0 0 0 0 0 0 p11 0 0 1 0 0 0 0 0 0 0 June Mean 0 0 0 1 0 1 0 1 0 1 St.dev. 0 0 0 0 0 0 0 0 0 1 p00 1 0 0 0 1 1 1 0 0 0 p11 0 0 1 1 0 0 1 0 0 0 July Mean 0 0 0 1 0 1 0 0 0 1 St.dev. 0 0 1 0 0 0 0 0 0 1 p00 0 0 0 0 1 0 0 0 1 0 p11 1 1 1 1 0 1 0 0 0 1 August Mean 0 0 0 1 0 1 0 0 1 1 St.dev. 0 0 0 0 0 0 0 0 0 0 p00 0 0 0 0 0 0 0 0 0 1 p11 1 0 1 1 1 0 0 1 1 0 September Mean 1 0 0 0 0 0 0 0 0 0 St.dev. 0 0 0 0 0 0 0 0 0 0 p00 0 0 0 0 0 0 0 0 0 0 p11 0 0 0 0 0 0 0 0 0 0 October Mean 0 0 0 0 0 0 0 0 0 0 St.dev. 0 0 0 0 0 0 0 0 0 0 p00 0 0 1 1 0 0 1 0 0 0 p11 0 0 1 0 0 0 0 0 0 0 Total rejected: 4 1 7 8 3 5 3 2 3 7 37

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Table 2-4. Kolmogorov-Smirnov two sample test fo r statistical difference between daily rainfall parameters in Sisaket province. Stations are identified as: 1) RoiEt, 2) Sisaket, 3) Thatum and 4) Ubon Ratchathani. For p<0.05 = 1. Month Parameters 1-2 1-3 1-4 2-3 2-4 3-4 April Mean 0 0 0 0 0 0 St.dev. 0 0 0 0 0 0 p00 0 0 0 0 0 0 p11 0 0 0 0 0 0 May Mean 0 0 0 0 0 0 St.dev. 0 0 0 0 0 0 p00 0 0 0 0 0 0 p11 0 0 0 0 0 0 June Mean 1 0 0 0 1 0 St.dev. 0 0 0 0 0 0 p00 0 0 0 0 0 0 p11 0 0 1 0 0 0 July Mean 0 0 0 0 1 0 St.dev. 0 0 0 0 0 0 p00 1 1 1 0 0 0 p11 0 1 1 1 1 0 August Mean 1 0 0 0 1 0 St.dev. 0 0 0 0 0 0 p00 1 0 1 0 0 0 p11 0 0 1 0 1 0 September Mean 0 0 0 0 0 0 St.dev. 0 0 0 0 0 0 p00 0 0 0 0 0 0 p11 0 0 0 0 0 0 October Mean 0 0 0 0 0 0 St.dev. 0 0 0 0 0 1 p00 1 0 0 0 0 0 p11 1 1 0 0 0 1 Total rejected: 6 3 5 1 5 2 38

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Table 2-5. Average daily rainfall pa rameter values in Lopburi province. Station Month Mean St.Dev. alpha () beta () p00 p11 Buachum April 11.4 16.3 0.49 23.42 0.76 0.43 May 9.7 13.3 0.53 18.33 0.55 0.60 June 9.5 14.3 0.44 21.69 0.56 0.59 July 8.8 12.7 0.48 18.33 0.56 0.65 August 10.3 15.1 0.47 21.99 0.44 0.73 September 14.8 20.1 0.54 27.30 0.46 0.75 October 11.4 16.1 0.50 22.63 0.74 0.55 Lopburi April 12.8 17.9 0.51 24.95 0.83 0.34 May 12.2 15.4 0.63 19.40 0.65 0.53 June 9.7 13.2 0.54 17.87 0.59 0.53 July 9.6 13.9 0.47 20.29 0.54 0.55 August 9.8 13.0 0.57 17.23 0.48 0.60 September 14.6 18.8 0.61 24.19 0.46 0.70 October 12.3 17.6 0.49 25.27 0.72 0.58 Suphanburi April 12.5 19.5 0.41 30.57 0.86 0.27 May 11.7 17.3 0.45 25.73 0.67 0.52 June 8.3 11.7 0.50 16.56 0.58 0.51 July 7.9 11.2 0.49 15.91 0.58 0.57 August 8.7 12.5 0.49 17.96 0.53 0.62 September 14.3 19.0 0.56 25.36 0.45 0.73 October 15.1 20.5 0.54 27.97 0.70 0.60 Wichianburi April 11.8 16.8 0.49 23.89 0.77 0.38 May 11.5 17.1 0.45 25.59 0.56 0.61 June 10.5 14.4 0.52 19.97 0.56 0.60 July 10.5 14.3 0.54 19.45 0.51 0.65 August 11.4 15.0 0.58 19.65 0.44 0.71 September 13.1 17.5 0.56 23.53 0.45 0.70 October 10.8 14.0 0.59 18.28 0.75 0.53 39

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Table 2-6. Average daily rainfall para meter values in Chachoengsao province. Station Month Mean St.Dev. alpha () beta () p00 p11 Bangkok April 11.6 17.6 0.44 26.52 0.83 0.39 Metropolis May 13.3 20.2 0.43 30.59 0.65 0.63 June 9.5 14.3 0.44 21.51 0.59 0.60 July 9.5 14.2 0.45 21.13 0.53 0.65 August 10.4 14.5 0.51 20.23 0.47 0.70 September 16.0 21.3 0.56 28.36 0.44 0.78 October 15.0 20.7 0.52 28.71 0.72 0.68 Chonburi April 9.8 14.2 0.48 20.54 0.78 0.36 May 11.6 15.5 0.57 20.53 0.62 0.60 June 9.0 14.8 0.37 24.20 0.54 0.56 July 9.4 14.2 0.44 21.34 0.55 0.60 August 9.1 13.6 0.45 20.34 0.48 0.66 September 14.3 19.6 0.53 27.04 0.46 0.75 October 12.9 17.5 0.54 23.92 0.62 0.67 Donmuang April 11.4 17.4 0.43 26.48 0.82 0.38 May 12.9 19.2 0.46 28.42 0.58 0.62 June 10.1 15.6 0.42 24.22 0.51 0.62 July 10.0 15.0 0.45 22.42 0.49 0.64 August 9.8 14.2 0.48 20.48 0.44 0.70 September 15.6 20.4 0.58 26.78 0.36 0.77 October 13.8 19.8 0.48 28.60 0.64 0.65 Kabinburi April 10.6 14.9 0.50 21.11 0.74 0.38 May 11.8 14.5 0.67 17.70 0.58 0.69 June 12.3 15.1 0.66 18.50 0.49 0.75 July 12.9 16.2 0.64 20.15 0.42 0.76 August 14.0 17.1 0.67 20.90 0.39 0.79 September 15.3 19.0 0.65 23.57 0.41 0.77 October 11.5 16.5 0.48 23.78 0.66 0.62 Prachinburi April 13.1 19.0 0.47 27.60 0.72 0.38 May 12.8 16.4 0.61 20.99 0.55 0.64 June 13.7 18.5 0.55 24.84 0.45 0.69 July 14.1 18.1 0.61 23.21 0.40 0.74 August 16.0 20.6 0.61 26.44 0.34 0.78 September 17.2 20.7 0.69 24.82 0.40 0.76 October 12.0 17.4 0.48 25.12 0.68 0.60 40

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Table 2-7. Average daily rainfall pa rameter values in Buriram province. Station Month Mean St.Dev. alpha () beta () p00 p11 Aranyaprathet April 10.0 14.6 0.47 21.32 0.72 0.37 May 10.3 13.3 0.60 17.21 0.52 0.63 June 9.9 13.1 0.57 17.44 0.44 0.71 July 10.0 12.2 0.67 14.97 0.53 0.74 August 10.5 13.8 0.57 18.24 0.50 0.77 September 13.3 17.0 0.61 21.69 0.39 0.73 October 11.3 15.5 0.53 21.17 0.64 0.64 Chokchai April 9.6 13.9 0.48 20.16 0.73 0.36 May 10.3 16.1 0.41 25.18 0.56 0.60 June 8.8 13.7 0.41 21.43 0.63 0.63 July 8.6 13.8 0.39 22.16 0.56 0.58 August 9.2 13.9 0.44 20.90 0.45 0.64 September 11.5 15.5 0.55 20.87 0.41 0.74 October 11.1 17.7 0.40 28.11 0.68 0.61 Nakhon April 8.6 12.9 0.45 19.21 0.75 0.38 Ratchasima May 10.3 15.1 0.46 22.33 0.57 0.58 June 8.1 12.6 0.42 19.45 0.57 0.55 July 8.5 12.5 0.46 18.29 0.56 0.58 August 8.5 13.5 0.40 21.48 0.52 0.66 September 13.0 18.8 0.48 27.10 0.45 0.72 October 12.6 17.1 0.54 23.36 0.75 0.60 Nangrong April 9.2 12.7 0.53 17.49 0.73 0.32 May 10.8 14.8 0.53 20.40 0.52 0.58 June 9.7 14.4 0.45 21.35 0.51 0.64 July 9.5 13.7 0.48 19.72 0.46 0.63 August 10.4 15.2 0.46 22.38 0.46 0.75 September 12.8 17.6 0.53 24.17 0.40 0.72 October 11.0 17.8 0.38 28.83 0.70 0.55 Surin April 11.3 16.3 0.48 23.42 0.77 0.38 May 11.8 16.8 0.49 23.95 0.55 0.56 June 11.1 16.2 0.47 23.65 0.48 0.65 July 11.6 16.2 0.51 22.75 0.48 0.66 August 11.6 16.3 0.51 22.77 0.44 0.69 September 13.7 17.7 0.59 23.04 0.47 0.73 October 11.2 16.7 0.44 25.12 0.74 0.55 41

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Table 2-8. Average daily rainfall pa rameter values in Sisaket province. Station Month Mean St.Dev. alpha () beta () p00 p11 RoiEt April 11.5 15.7 0.54 21.34 0.78 0.33 May 13.0 17.9 0.52 24.75 0.60 0.58 June 13.5 19.6 0.48 28.49 0.58 0.63 July 12.8 18.4 0.48 26.62 0.58 0.64 August 13.9 19.1 0.53 26.21 0.52 0.69 September 15.3 21.3 0.52 29.63 0.53 0.71 October 10.7 16.3 0.43 24.75 0.79 0.47 Surin April 11.3 16.3 0.48 23.42 0.77 0.38 May 11.8 16.8 0.49 23.95 0.55 0.56 June 11.1 16.2 0.47 23.65 0.48 0.65 July 11.6 16.2 0.51 22.75 0.48 0.66 August 11.6 16.3 0.51 22.77 0.44 0.69 September 13.7 17.7 0.59 23.04 0.47 0.73 October 11.2 16.7 0.44 25.12 0.74 0.55 Thatum April 12.1 19.0 0.40 29.99 0.78 0.38 May 12.2 16.1 0.57 21.32 0.56 0.58 June 12.8 18.9 0.45 28.13 0.49 0.68 July 12.4 17.7 0.49 25.13 0.50 0.73 August 12.9 17.4 0.55 23.38 0.47 0.75 September 14.8 21.3 0.48 30.61 0.50 0.73 October 12.3 19.5 0.40 30.94 0.78 0.60 UbonRatchathani April 11.3 15.3 0.54 20.93 0.78 0.35 May 13.6 19.9 0.47 29.08 0.59 0.61 June 14.0 19.6 0.51 27.59 0.48 0.70 July 13.7 19.1 0.51 26.72 0.45 0.72 August 14.2 19.7 0.52 27.32 0.39 0.76 September 14.4 19.5 0.55 26.26 0.45 0.74 October 9.9 15.6 0.41 24.41 0.76 0.51 42

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Table 2-9. Chi-square Goodness-of-Fit test between theoretical ga mma distribution and empirical Weibull distribution, L opburi province. Ho=0, alpha=0.10. Station Month DOF Chi2 Ho/Ha BuaChum April 6 2.650 0 May 7 7.091 0 June 6 7.569 0 July 7 8.038 0 August 8 4.709 0 September 9 3.841 0 October 5 8.081 0 LopBuri April 7 6.497 0 May 8 18.324 1 June 9 11.430 0 July 10 14.376 0 August 10 4.262 0 September 11 9.364 0 October 8 5.011 0 SuphanBuri April 7 3.759 0 May 7 6.452 0 June 10 14.557 0 July 9 10.167 0 August 11 21.069 1 September 9 6.035 0 October 8 8.234 0 WichianBuri April 6 10.625 0 May 7 9.092 0 June 9 3.268 0 July 8 2.859 0 August 9 3.086 0 September 10 6.311 0 October 6 9.718 0 43

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Table 2-10. Chi-square Goodness-of-Fit test between theoretical gamma distribution and empirical Weibull distribution, Chach oengsao province. Ho=0, alpha=0.10. Station Month DOF Chi2 Ho/Ha Bangkok April 5 5.414 0 Metropolis May 9 10.436 0 June 10 15.571 0 July 9 5.695 0 August 11 14.376 0 September 11 8.597 0 October 11 11.503 0 ChonBuri April 7 10.746 0 May 9 4.444 0 June 9 10.364 0 July 8 9.396 0 August 8 3.875 0 September 10 6.131 0 October 10 6.527 0 Donmuang April 5 11.538 1 May 9 9.016 0 June 9 11.730 0 July 9 6.867 0 August 8 6.746 0 September 11 2.509 0 October 9 4.411 0 KabinBuri April 6 8.009 0 May 8 9.242 0 June 9 6.997 0 July 11 10.224 0 August 8 11.528 0 September 9 7.367 0 October 8 4.828 0 PrachinBuri April 7 4.570 0 May 9 5.098 0 June 10 6.974 0 July 10 15.394 0 August 11 17.099 0 September 11 14.580 0 October 10 4.987 0 44

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Table 2-11. Chi-square Goodness-of-Fit test between theoretical gamma distribution and empirical Weibull distribution, Bu riram province. Ho=0, alpha=0.10. Station Month DOF Chi2 Ho/Ha Aranyaprathet April 9 25.446 1 May 9 15.689 1 June 9 4.702 0 July 9 5.012 0 August 9 8.531 0 September 9 3.964 0 October 7 6.106 0 ChokChai April 7 5.057 0 May 7 9.040 0 June 6 10.336 0 July 8 5.098 0 August 7 6.194 0 September 8 22.177 1 October 7 9.012 0 Nakhon April 7 11.194 0 Ratchasima May 11 7.727 0 June 9 11.142 0 July 9 12.523 0 August 8 7.678 0 September 12 20.280 1 October 10 18.861 1 NangRong April 6 12.482 1 May 8 29.264 1 June 8 4.960 0 July 7 19.887 1 August 9 9.491 0 September 8 7.497 0 October 6 3.034 0 Surin April 8 8.232 0 May 10 2.090 0 June 10 7.216 0 July 11 12.113 0 August 9 13.157 0 September 9 4.600 0 October 7 5.206 0 45

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Table 2-12. Chi-square Goodness-of-Fit test between theoretical gamma distribution and empirical Weibull distribution, Si saket province. Ho=0, alpha=0.10. Station Month DOF Chi2 Ho/Ha RoiEt April 6 2.967 0 May 11 6.736 0 June 9 10.746 0 July 9 9.592 0 August 10 14.210 0 September 9 9.283 0 October 7 4.926 0 ThaTum April 5 3.821 0 May 8 7.651 0 June 9 8.852 0 July 8 17.690 1 August 7 3.429 0 September 8 8.665 0 October 6 2.895 0 Ubon April 8 8.929 0 Ratchathani May 10 10.394 0 June 9 26.858 1 July 11 9.341 0 August 9 9.678 0 September 9 7.892 0 October 8 7.228 0 Surin April 8 8.232 0 May 10 2.090 0 June 10 7.216 0 July 11 12.113 0 August 9 13.157 0 September 9 4.600 0 October 7 5.206 0 46

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Figure 2-1. Administrative map of Thailand with highlighted provin ces of interest and chosen for the study synoptic stations. 47

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Figure 2-2. Synoptic stations used in this study within the closest di stance to the survey villages. Stations with consecutive record of daily rainfall from 1951 to 2006 are highlighted in yellow and stations with record for 1970-2006 are marked with green. 0 200 400 600 800 100 300 500 700 Monthly P r ecipitation [mm] Ja n FebMarAprMayJu n Ju l Au g SepOctNovDec Figure 2-3. Monthly precipit ation in Buachum, 1970-2006. 48

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0 200 400 600 800 100 300 500 700 Monthly P r ecipitation [mm] Ja n FebMa r Ap r MayJu n Ju l Au g SepOctNo v De c Figure 2-4. Monthly precipit ation in Lopburi, 1951-2006. 0 200 400 600 800 100 300 500 700 Monthly P r ecipitation [mm] Ja n FebMa r Ap r MayJu n Ju l Au g SepOctNo v De c Figure 2-5. Monthly precipit ation in Suphanburi, 1951-2006. 0 200 400 600 800 100 300 500 700 Monthly P r ecipitation [mm] Ja n FebMa r Ap r MayJu n Ju l Au g SepOc t No v De c Figure 2-6. Monthly precipit ation in Wichianburi, 1970-2006. 49

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0 200 400 600 800 100 300 500 700 Monthly P r ecipitation [mm] JanFebMa r Ap r MayJunJu l Au g SepOctNo v De c Figure 2-7. Monthly precipitat ion in Bangkok Metropolis, 1951-2006. 0 200 400 600 800 100 300 500 700 Monthly P r ecipitation [mm] JanFebMa r Ap r MayJunJu l Au g Se p OctNo v Dec Figure 2-8. Monthly precipitation in Chonburi, 1951-2006. 0 200 400 600 800 100 300 500 700 Monthly P r ecipitation [mm] Ja n FebMa r Ap r MayJu n Ju l Au g SepOctNo v De c Figure 2-9. Monthly precipit ation in Donmuang, 1951-2006. 50

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0 200 400 600 800 100 300 500 700 Monthly P r ecipitation [mm] Ja n FebMa r Ap r MayJu n Ju l Au g SepOctNo v Dec Figure 2-10. Monthly precipi tation in Kabinburi, 1970-2006. 0 200 400 600 800 100 300 500 700 Monthly P r ecipitation [mm] Ja n FebMa r Ap r MayJu n Ju l Au g SepOctNo v De c Figure 2-11. Monthly precipita tion in Prachinburi, 1951-2006. 0 200 400 600 800 100 300 500 700 Monthly P r ecipitation [mm] Ja n FebMa r Ap r MayJu n Ju l Au g SepOctNo v De c Figure 2-12. Monthly precipitati on in Aranyaprathet, 1970-2006. 51

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0 200 400 600 800 100 300 500 700 Monthly P r ecipitation [mm] Ja n FebMa r Ap r MayJu n Ju l Au g SepOctNo v De c Figure 2-13. Monthly precipi tation in Chokchai, 1970-2006. 0 200 400 600 800 100 300 500 700 Monthly P r ecipitation [mm] Ja n FebMa r Ap r MayJu n Ju l Au g SepOctNo v De c Figure 2-14. Monthly precipitati on in Nakhon Ratchasima, 1951-2006. 0 200 400 600 800 100 300 500 700 Monthly P r ecipitation [mm] Ja n FebMa r Ap r MayJu n Ju l Au g SepOctNo v Dec g g Figure 2-15. Monthly precipitation in Nangrong, 1970-2006. 52

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0 200 400 600 800 100 300 500 700 Monthly P r ecipitation [mm] Ja n FebMa r Ap r MayJu n Ju l Au g SepOctNo v De c Figure 2-16. Monthly precipitation in RoiEt, 1951-2006. 0 200 400 600 800 100 300 500 700 Monthly P r ecipitation [mm] Ja n FebMa r Ap r MayJu n Ju l Au g SepOctNo v Dec Figure 2-17. Monthly precipi tation in ThaTum, 1970-2006. 0 200 400 600 800 100 300 500 700 Monthly P r ecipitation [mm] Ja n FebMa r Ap r MayJu n Ju l Au g SepOctNo v Dec Figure 2-18. Monthly precipitation in Ubon Ratchathani, 1951-2006. 53

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0 10 20 30 40 50 60 70 80 90 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Rain [mm]CDF a=.5, b=15 Gamma a=.5, b=20 Gamma a=.5, b=25 Gamma a= 1, b=20 Exponential Figure 2-19. Sample cumulative gamma distributi on function for constant shape parameter value alpha (a= .5) and three different beta pa rameter values compared to exponential distribution (a=1). 0 10 20 30 40 50 60 70 80 90 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Rain [mm]CDF a=.4, b=20 Gamma a=.5, b=20 Gamma a=.6, b=20 Gamma a= 1, b=20 Exponential Figure 2-20. Sample cumulative gamma distributi on function for constant scale parameter value beta (b=20) and three diffe rent alpha parameter values compared to exponential distribution (a=1). 54

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0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0102030405060708090100Cumulative Distribution Function (CDF)Rainfall [ mm ] x=12.9, s=16.2, a=.64, b=20.15 x=12.9, s=17.5, a=.54, b=23.92 x=12.9, s=19.2, a=.46, b=28.42 Figure 2-21. Gamma CDF with constant mean and changing standard deviation value. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0102030405060708090100Cumulative Distribution Function (CDF)Rainfall [ mm ] x=12.1, s=19.0, a=.40, b=29.99 x=13.1, s=19.0, a=.47, b=27.60 x=14.3, s=19.0, a=.56, b=25.36 x=15.3, s=19.0, a=.65, b=23.57 Figure 2-22. Gamma CDF with constant sta ndard deviation and changing mean value. 55

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0 2 0 20 3 0 3 0 30 4 0 4 0 40 5 0 5 0.5 0 50 6 0 6 0 6 0 60 7 0 7 0 7 0 70 8 0 8 0 80 9 0 9 0 91 1 11 .1 1 1 1 11 2 1 2 1 .21 3 1 31 4 1 41 5 1 51 6 1 61 7 1 7 1 8 1 81 92 2 12 2 2 32 4 2 52 6meanstdAprMayJunJulAugSepOct 7 8 9 10 11 12 13 14 15 16 17 10 11 12 13 14 15 16 17 18 19 20 21 Figure 2-23. Contour map showing the relations hip between various standard deviation and mean values and the alpha parameter value, Suphan Buri station. 1 01 01 01 5151 51 52 02 02 02 02 52 52 52 53 03 03 03 53 54 04 04 5 5 05 56 0 meanstdAprMayJunJulAugSepOct 7 8 9 10 11 12 13 14 15 16 17 10 11 12 13 14 15 16 17 18 19 20 21 Figure 2-24. Contour map showing the relations hip between various standard deviation and mean values and the beta parame ter value, Suphan Buri station. 56

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0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 LopburiChachoengsaoBuriramSisaket Means St.Dev. p00 p11 Figure 2-25. The average number of significan tly different parameter values per month according to K-S test between all stations per each province. Figure 2-26. Number of rejected K-S te sts between stations, Lopburi province. 57

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Figure 2-27. Number of rejected K-S test s between stations, Chachoengsao province. Figure 2-28. Number of rejected K-S te sts between stations, Buriram province. 58

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Figure 2-29. Number of rejected K-S te sts between stations, Sisaket province. 59

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0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 A pr Ma y JunJu l Au g Se p Octp00 Buachum Lopburi Suphanburi Wichianburi Figure 2-30. Average p00 transition probabilit ies values per month in Lopburi province. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 A pr Ma y JunJu l Au g Se p Octp00 Bangkok M. Chonburi Donmuang Prachinburi KabinBuri Figure 2-31. Average p00 transi tion probabilities values per month in Chachoengsao province. 60

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0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 A pr Ma y JunJu l Au g Se p Octp00 Aranyaprathet ChokChai NangRong Surin NakhonRatchasima Figure 2-32. Average p00 transi tion probabilities values per month in Buriram province. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 A pr Ma y JunJu l Au g Se p Octp00 RoiEt Surin ThaTum UbonRatchathani Figure 2-33. Average p00 transi tion probabilities values per month in Sisaket province. 61

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0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 A pr Ma y JunJu l Au g Se p Octp11 Buachum Lopburi Suphanburi Wichianburi Figure 2-34. Average p11 transition probabilit ies values per month in Lopburi province. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 A pr Ma y JunJu l Au g Se p Octp11 Bangkok M. Chonburi Donmuang Prachinburi KabinBuri Figure 2-35. Average p11 transi tion probabilities values per month in Chachoengsao province. 62

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0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 A pr Ma y JunJu l Au g Se p Octp11 Aranyaprathet ChokChai NangRong Surin NakhonRatchasima Figure 2-36. Average p11 transi tion probabilities values per month in Buriram province. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 A pr Ma y JunJu l Au g Se p Octp11 RoiEt Surin ThaTum UbonRatchathani Figure 2-37. Average p11 transi tion probabilities values per month in Sisaket province. 63

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0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 AprMayJunJulAugSepOctMean [mm] Buachum Lopburi Suphanburi Wichianburi Figure 2-38. Average monthly daily rainfa ll magnitudes means in Lopburi province. 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 AprMayJunJulAugSepOctMean [mm] Bangkok M. Chonburi Donmuang Prachinburi KabinBuri Figure 2-39. Average monthly daily rainfall magnitudes means in Chachoengsao province. 64

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0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 AprMayJunJulAugSepOctMean [mm] Aranyaprathet ChokChai NangRong Surin NakhonRatchasima Figure 2-40. Average monthly daily rainfall magnitudes means in Buriram province. 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 AprMayJunJulAugSepOctMean [mm] RoiEt Surin ThaTum UbonRatchathani Figure 2-41. Average monthly daily rainfall magnitudes means in Sisaket province. 65

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0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 AprMayJunJulAugSepOctStandard Deviation [mm] Buachum Lopburi Suphanburi Wichianburi Figure 2-42. Average standard de viations of daily rainfall magnitudes per month in Lopburi province. 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 AprMayJunJulAugSepOctStandard deviation [mm] Bangkok M. Chonburi Donmuang Prachinburi KabinBuri Figure 2-43. Average standard deviations of daily rainfall magnitudes per month in Chachoengsao province. 66

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0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 AprMayJunJulAugSepOctStandard deviation [mm] Aranyaprathet ChokChai NangRong Surin NakhonRatchasima Figure 2-44. Average standard de viations of daily rainfall ma gnitudes per month in Buriram province. 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 AprMayJunJulAugSepOctStandard devaition [mm] RoiEt Surin ThaTum UbonRatchathani Figure 2-45. Average standard de viations of daily rainfall ma gnitudes per month in Sisaket province. 67

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0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0255075100125150175200225250Cumulative Distribution Function (CDF)Rainfall [mm] April May Jun Jul Aug Sep Oct 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 101520253035 Figure 2-46. Gamma CDF for Buachum station, 1970-2006. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0255075100125150175200225250Cumulative Distribution Function (CDF)Rainfall [mm] April May Jun Jul Aug Sep Oct 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 101520253035 Figure 2-47. Gamma CDF for Lopburi station 1951-2006. 68

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0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0255075100125150175200225250Culumative Distribution Function (CDF)Rainfall [mm] April May Jun Jul Aug Sep Oct 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 101520253035 Figure 2-48. Gamma CDF for Suphanburi station 1951-2006. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0255075100125150175200225250Cumulative Distribution Function (CDF)Rainfall [mm] April May Jun Jul Aug Sep Oct 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 101520253035 Figure 2-49. Gamma CDF for Wichianburi station 1970-2006. 69

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0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0255075100125150175200225250Cumulative Distribution Function (CDF)Rainfall [mm] April May Jun Jul Aug Sep Oct 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 101520253035 Figure 2-50. Gamma CDF for Ba ngkok Metropolis station 1951-2006 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0255075100125150175200225250Cumulative Distribution Function (CDF)Rainfall [mm] April May Jun Jul Aug Sep Oct 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 101520253035 Figure 2-51. Gamma CDF for Chonburi station 1951-2006 70

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0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0255075100125150175200225250Cumulative Distribution Function (CDF)Rainfall [mm] April May Jun Jul Aug Sep Oct 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 101520253035 Figure 2-52. Gamma CDF for Donmuang station 1951-2006 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0255075100125150175200225250Cumulative Distribution Function (CDF)Rainfall [mm] April May Jun Jul Aug Sep Oct 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 101520253035 Figure 2-53. Gamma CDF fo r Kabinburi station 1970-2006. 71

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0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0255075100125150175200225250Cumulative Distribution Function (CDF)Rainfall [mm] April May Jun Jul Aug Sep Oct 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 101520253035 Figure 2-54. Gamma CDF for Prachinburi station 1951-2006. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0255075100125150175200225250Cumulative Distribution Function (CDF)Rainfall [mm] April May Jun Jul Aug Sep Oct 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 101520253035 Figure 2-55. Gamma CDF for Ar anyaprathet station 1951-2006. 72

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0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0255075100125150175200225250Cumulative Distribution Function (CDF)Rainfall [mm] April May Jun Jul Aug Sep Oct 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 101520253035 Figure 2-56. Gamma CDF for Chokchai station 1970-2006. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0255075100125150175200225250Cumulative Distribution Function (CDF)Rainfall [mm] April May Jun Jul Aug Sep Oct 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 101520253035 Figure 2-57. Gamma CDF for Nakho n Ratchasima station 1951-2006. 73

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0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0255075100125150175200225250Cumulative Distribution Function (CDF)Rainfall [mm] April May Jun Jul Aug Sep Oct 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 101520253035 Figure 2-58. Gamma CDF fo r NangRong station 1970-2006. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0255075100125150175200225250Cumulative Distribution Function (CDF)Rainfall [mm] April May Jun Jul Aug Sep Oct 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 101520253035 Figure 2-59. Gamma CDF for Surin station 1951-2006. 74

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0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0255075100125150175200225250Cumulative Distribution Function (CDF)Rainfall [mm] April May Jun Jul Aug Sep Oct 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 101520253035 Figure 2-60. Gamma CDF for RoiEt station 1951-2006. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0255075100125150175200225250Cumulative Distribution Function (CDF)Rainfall [mm] April May Jun Jul Aug Sep Oct 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 101520253035 Figure 2-61. Gamma CDF for ThaTum station 1970-2006. 75

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0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0255075100125150175200225250Cumulative Distribution Function (CDF)Rainfall [mm] April May Jun Jul Aug Sep Oct 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 101520253035 Figure 2-62. Gamma CDF for U bon Ratchathani station 1951-2006 0 20 40 60 80 100 120 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Rain [mm]CDF Empirical Fitted Gamma Figure 2-63. Empirical (Weibull) vs. theoretical cumulative gamma distribution function April, Lopburi. 76

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0 20 40 60 80 100 120 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Rain [mm]CDF Empirical Fitted Gamma Figure 2-64. Empirical (Weibull) vs. theoretical cumulative gamma distribution function May, Lopburi. 0 20 40 60 80 100 120 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Rain [mm]CDF Empirical Fitted Gamma Figure 2-65. Empirical (Weibull) vs. theoretical cumulative gamma distribution function June, Lopburi. 77

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0 20 40 60 80 100 120 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Rain [mm]CDF Empirical Fitted Gamma Figure 2-66. Empirical (Weibull) vs. theoretical cumulative gamma distribution function July, Lopburi. 0 10 20 30 40 50 60 70 80 90 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Rain [mm]CDF Empirical Fitted Gamma Figure 2-67. Empirical (Weibull) vs. theoretic al cumulative gamma distribution function August, Lopburi. 78

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0 50 100 150 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Rain [mm]CDF Empirical Fitted Gamma Figure 2-68. Empirical (Weibull) vs. theoretic al cumulative gamma distribution function September, Lopburi. 0 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Rain [mm]CDF Empirical Fitted Gamma Figure 2-69. Empirical (Weibull) vs. theoretic al cumulative gamma distribution function October, Lopburi. 79

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0 100 200 300 400 500 900 0 10 20 30 40 50 60 [mm][mm] April May June July August September October 0 100 200 300 400 500 900 0 10 20 30 40 50 60 [mm][mm] April May June July August September October A B Figure 2-70. Average mean daily precipitati on magnitudes according to different monthly rainfall totals intervals in Lopburi pr ovince: A Buachum and Wichianburi; B Lopburi and Suphanburi. 0 100 200 300 400 500 900 0 10 20 30 40 50 60 [mm][mm] April May June July August September October 0 100 200 300 400 500 90 0 0 10 20 30 40 50 60 [mm][mm] April May June July August September October A B Figure 2-71. Average mean daily precipitati on magnitudes according to different monthly rainfall totals intervals in Chachoe ngsao province: A Bangkok Metropolis, Chonburi and Donmuang; B Kabinburi and Prachinburi. 80

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0 100 200 300 400 500 900 0 10 20 30 40 50 60 [ mm] [mm] April May June July August September October 0 100 200 300 400 500 900 0 10 20 30 40 50 60 [mm][mm] April May June July August September October 0 100 200 300 400 500 900 0 10 20 30 40 50 60 [mm][mm] April May June July August September October 0 100 200 300 400 500 900 0 10 20 30 40 50 60 [mm][mm] April May June July August September October A B C D Figure 2-72. Average mean daily precipitati on magnitudes according to different monthly rainfall totals intervals in Buriram provi nce: A Aranyaprathe t and Nangrong; B Chokchai; C Nakhonratchasima; D Surin. 81

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0 100 200 300 400 500 90 0 0 10 20 30 40 50 60 [ mm ] [mm] April May June July August September October A 0 100 200 300 400 500 900 0 10 20 30 40 50 60 [mm][mm] April May June July August September October 0 100 200 300 400 500 90 0 0 10 20 30 40 50 60 [m m ] [mm] April May June July August September October B C Figure 2-73. Average mean daily precipitati on magnitudes according to different monthly rainfall totals intervals in Sisaket province: A Surin and Thatum; B Roiet; C Ubonratchathani. 82

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0 100 200 300 400 500 900 0 10 20 30 40 50 60 [mm][mm] April May June July August September October 0 100 200 300 400 500 900 0 10 20 30 40 50 60 [mm][mm] April May June July August September October A B Figure 2-74. Average standard deviation of daily precipitation magnitudes according to different monthly rainfall totals intervals in L opburi province: A Buachum and Wichianburi; B Lopburi and Suphanburi. 0 100 200 300 400 500 900 0 10 20 30 40 50 60 [mm][mm] April May June July August September October 0 100 200 300 400 500 900 0 10 20 30 40 50 60 [mm][mm] April May June July August September October A B Figure 2-75. Average standard deviation of daily precipitation magnitudes according to different monthly rainfall totals intervals in Chac hoengsao province: A Bangkok Metropolis, Chonburi and Donmuang; B Kabinburi and Prachinburi. 83

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0 100 200 300 400 500 900 0 10 20 30 40 50 60 [mm][mm] April May June July August September October 0 100 200 300 400 500 900 0 10 20 30 40 50 60 [mm][mm] April May June July August September October A B 0 100 200 300 400 500 900 0 10 20 30 40 50 60 [ mm ] [mm] April May June July August September October 0 100 200 300 400 500 900 0 10 20 30 40 50 60 [mm][mm] April May June July August September October C D Figure 2-76. Average standard deviation of daily precipitation magnitudes according to different monthly rainfall totals intervals in Bu riram province: A Aranyaprathet and Nangrong; B Chokchai; C Nakh onratchasima; D Surin. 84

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0 100 200 300 400 500 900 0 10 20 30 40 50 60 [mm][mm] April May June July August September October A 0 100 200 300 400 500 900 0 10 20 30 40 50 60 [mm][mm] April May June July August September October B 0 100 200 300 400 500 900 0 10 20 30 40 50 60 [mm][mm] April May June July August September October C Figure 2-77. Average standard deviation of daily precipitation magnitudes according to different monthly rainfall totals intervals in Sisa ket province: A Surin and Thatum; B Roiet; C Ubonratchathani. 85

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0 100 200 300 400 500 900 0 0.2 0.4 0.6 0.8 1 [mm]P00 April May June July August September October 0 100 200 300 400 500 900 0 0.2 0.4 0.6 0.8 1 yp [ ] [mm]P00 April May June July August September October Figure 2-78. Average p00 transition probabilities according to different monthly rainfall totals intervals in Lopburi province: A Bu achum and Wichianburi; B Lopburi and Suphanburi. 0 100 200 300 400 500 900 0 0.2 0.4 0.6 0.8 1 yp [ ] [mm]P00 April May June July August September October 0 100 200 300 400 500 900 0 0.2 0.4 0.6 0.8 1 [mm]P00 April May June July August September October A B Figure 2-79. Average p00 transition probabilities according to different monthly rainfall totals intervals in Chachoengsao province: A Bangkok Metropolis, Chonburi and Donmuang; B Kabinburi and Prachinburi. 86

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0 100 200 300 400 500 900 0 0.2 0.4 0.6 0.8 1 [ mm ] P00 April May June July August September October 0 100 200 300 400 500 900 0 0.2 0.4 0.6 0.8 1 [ mm ] P00 April May June July August September October A B 0 100 200 300 400 500 90 0 0 0.2 0.4 0.6 0.8 1 [mm]P00 April May June July August September October 0 100 200 300 400 500 9 0 0 0.2 0.4 0.6 0.8 1 [mm]P00 April May June July August September October C D Figure 2-80. Average p00 transition probabilities according to different monthly rainfall totals intervals in Buriram province: A Ara nyaprathet and Nangrong; B Chokchai; C Nakhonratchasima; D Surin. 87

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0 100 200 300 400 500 900 0 0.2 0.4 0.6 0.8 1 [mm]P00 April May June July August September October A 0 100 200 300 400 500 900 0 0.2 0.4 0.6 0.8 1 [mm]P00 April May June July August September October B 0 100 200 300 400 500 900 0 0.2 0.4 0.6 0.8 1 [mm]P00 April May June July August September October C Figure 2-81. Average p00 transition probabilities according to different monthly rainfall totals intervals in Sisaket provin ce: A Surin and Thatum; B Roiet; C Ubonratchathani. 88

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0 100 200 300 400 500 900 0 0.2 0.4 0.6 0.8 1 [mm]P11 April May June July August September October 0 100 200 300 400 500 900 0 0.2 0.4 0.6 0.8 1 [mm]P11 April May June July August September October A B Figure 2-82. Average p11 transition probabilities according to different monthly rainfall totals intervals in Lopburi province: A Bu achum and Wichianburi; B Lopburi and Suphanburi. 0 100 200 300 400 500 900 0 0.2 0.4 0.6 0.8 1 [mm]P11 April May June July August September October 0 100 200 300 400 500 90 0 0 0.2 0.4 0.6 0.8 1 [mm]P11 April May June July August September October A B Figure 2-83. Average p11 transition probabilities according to different monthly rainfall totals intervals in Chachoengsao province: A Bangkok Metropolis, Chonburi and Donmuang; B Kabinburi and Prachinburi. 89

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0 100 200 300 400 500 900 0 0.2 0.4 0.6 0.8 1 [m m ] P11 April May June July August September October 0 100 200 300 400 500 900 0 0.2 0.4 0.6 0.8 1 [mm]P11 April May June July August September October A B 0 100 200 300 400 500 900 0 0.2 0.4 0.6 0.8 1 [mm]P11 April May June July August September October 0 100 200 300 400 500 900 0 0.2 0.4 0.6 0.8 1 [mm]P11 April May June July August September October C D Figure 2-84. Average p11 transition probabilities according to different monthly rainfall totals intervals in Buriram province: A Ara nyaprathet and Nangrong; B Chokchai; C Nakhonratchasima; D Surin. 90

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0 100 200 300 400 500 900 0 0.2 0.4 0.6 0.8 1 [mm]P11 April May June July August September October A 0 100 200 300 400 500 900 0 0.2 0.4 0.6 0.8 1 [mm]P11 April May June July August September October 0 100 200 300 400 500 900 0 0.2 0.4 0.6 0.8 1 [mm]P11 April May June July August September October B C Figure 2-85. Average p11 transition probabilities according to different monthly rainfall totals intervals in Sisaket provin ce: A Surin and Thatum; B Roiet; C Ubonratchathani. 91

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CHAPTER 3 CONCLUSIONS In many areas of Thailand, climate shocks have profound effects on livelihoods and the economy on a local and national scale. As in mo st countries whose reve nue structure is highly dependent on agriculture, the consequences of climatic extremes can have damaging effect on the crop yields and therefore on both nationa l and household incomes (Boochabun et al. 2004). This effect is even more profound in less deve loped regions with monocultural agriculture and less developed irrigation systems (Kono and Sa ha 1995; Yao 1997). This study focused on two regions of Thailand central a nd northeast with the center being relatively wealthy, diversified and irrigated, and the latter relatively poor, less diversified and in larg e percent consisting of rain-fed arable land. Consequently, the ability to assess the pr obability of excess or dearth of rainfall occurrences is an essential aspect for planni ng both for the national economy and insurance companies investing the Thai region. For the de cision making process it is crucial that farmers have an appealing and straightforward way to as sess the risk of unfavorable agro-meteorological conditions that occur in their region. This method showed to be flexible enough that it could be applied for a variety of crops. At the same time, the insurance companies are interested in knowing the risk of potential agro-climatic shock occurrences in order to set premiums that would not bring losses to their enterprises. This study looks at a series of daily rainfall properties that could potentially constitute the climatic shock at the socio-economic survey lo cations. These surveys provide an important link between environmental variables and information about local farmers and their income. It was important to assess how past weat her conditions can be determined from monthly rainfall totals, so that this information can be linked to the fi nancial well-being of the local people. Neighboring 92

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national network stations provide invaluable insight into longer climate variability and fluctuations, and allow assessment of the probability of the climate shocks that occurred in the past and could occur in the future. Located with in a close distance to the survey locations, the data collected at these stations can represent with high likelihood conditi ons that occurred in locations where no daily data is available. Th e chosen rainfall parameters are crucial in determining extreme conditions like flood or drou ght. These parameters include the transition probability of a day with no rain to be followed by a day with no rain and for the rainy day to be followed by a consecutive rainy day. The second important characterist ics are the rainfall magnitudes and the likelihood of extremely low or high daily rainfall totals. One unique example of this site is that the daily rainfall precipi tation has been shown to follow gamma distribution properties and is highly sensitive to changes in the rainfall transition probabilities throughout the season and at various locations. This result can be attributed to the convective precipitation pattern in the season and highly variable number and sequence of daily rainfall. The outcome of this study provides insight in to statistical examination of precipitation properties which is less studied in tropical areas compared to temperate regions, where long time daily rainfall records are more abundant. On the macro-regional sc ale, there is considerably less research done in the area of Southeast Asia compared to South Asia with the focus on India and East Asia with the focus on China (Stephens on et al. 1999; Krishnamurthy and Goswami 2000; Ding and Chan 2005; Ding 2007; Yancheva et al 2007). This refers both to the research regarding the monsoon properties an d likewise the ENSO impact on th e interannual va riability of rainfall. This is however an equally important is sue in the entire region of South, Southeast and East Asia, where agriculture is one of the esse ntial parts of the economy and household incomes. 93

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While this research is focused exclusively on the rainfall characteristics of four provinces in Thailand, the results provide important means of understanding similar problems on the larger national scale and possibly in many other areas of the globe, especially in the monsoonal areas of the Southeast Asia and possibly in other tropical countries. This method can be applied for any problems looking at the probability of extreme events to happen not only in climatology, but also in a many sections of geography and possibl y in many other scien tific disciplines. 94

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LIST OF REFERENCES Barger, G. L., and H.C.S. Thom, 1949: Evaluation of drought hazard. Agronomy Journal, 41, 519. Boochabun, K., W. Tych, N. A. Chappell, P. A. Carling, K. Lorsirirat, and S. Pa-Obsaeng, 2004: Statistical modeling of rainfall and river flow in Thailand. Journal Geological Society of India, 64, 503-516. Caskey, J. E., 1963: A Markov chain model for the probability of precipitation occurrence in intervals of various length. Monthly Weather Review, 91, 298-301. Coe, R., and R.D.Stern, 1982: Fittin g models to daily rainfall data. Journal of Applied Meteorology, 21, 1024-1031. Cunnane, C., 1978: Unbiased plotting positions A review. Journal of Hydrology, 37, 205-222. Ding, Y., 2007: The variability of the Asian summer monsoon. Journal of the Meteorological Society of Japan, 85B, 21-54. Ding, Y., and J. C. L. Chan, 2005: The East Asian summer monsoon: an overview. Meteorology and Atmospheric Physics, 89, 117-142. Gadgil, S., and K. R Kumar, 2006: The Asian monsoon agriculture and economy. The Asian Monsoon, B. Wang, Ed., Springer, 844 pp. Gates, P., and H. Tong, 1976: On Mar kov chain modeling to some weather data. Journal of Applied Meteorology, 15, 1145-1151. Gleick, P. H. 1993: Water in Crisis: A Guide to the Worlds Fresh Water Resources. Oxford University Press, 473 pp. Guzman, A. G., and W. C. Torrez, 1985: Daily rainfall probabilities: Conditional upon prior occurrence and amount of rain. Journal of Climate and Applied Meteorology, 24, 10091014. Harrison, M., and P. R. Waylen, 2000: A note concerning the proper choice for Markov model order for daily precipitation in the hu mid tropics: A Case Study in Costa Rica. International Journal of Climatology, 20, 1861-1872. Hosking, J. R. M., and J. R. Wallis, 1987: Para meter and quantile estimation for the generalized Pareto distribution. Technometrics, 29, 339-349. Huang, Y., C. Lee, and C. Ting, 2008: Improved estimation of hydrologic data using the Chisquare goodness-of-fit test. Journal of the Chinese Institute of Engineers, 31, 515-521. Ison, N.T., A.M. Feyerherm, and L.D. Bark 1971: Wet period precipitation and the gamma distribution. Journal of Applied Meteorology, 10, 658. 95

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Katz, R. W., 1977: Precipitation as chain-dependent process. Journal of Applied Meteorology, 16, 671-676. Katz, R. W., 1981: On some criteria for estimating the order of a Markov chain. Technometrics, 23, 243-249. Kermel-Torrs, D., 2004: Atlas of Thailand: Spatial Structures and Development. Silkworm Books, 209 pp. Khedari, J., A. Sanprajak, and J. Hir unlabh, 2002: Thailand climatic zones. Renewable Energy, 25, 267-280. Kono, Y., and P.K. Saha, 1995: Land and water re sources management for crop diversification in the Chao Phraya Delta, Thailand: A case study of citrus cultivation in the North Rangsit Irrigation Project. Southeast Asian Studies, 33, 169-186. Kripalani, R. H., and A. Kulkarni, 1997: Rainfall variability over South-East Asia Connections with Indian monsoon and ENSO extremes: New perspectives. International Journal of Climatology, 17, 1155-1168. Krishna Kumar, K., B. Rajagopalan, and M. A. Cane, 1999: On the weakening relationship between the Indian monsoon and ENSO. Science, 284, 2156-2159. Krishnamurthy, V., and B. N. Goswami, 2000: Indian monsoon ENSO relationship on interdecadal timescale. Journal of Climate, 13, 579. Lau, K. M., and S. Yang, 1997: Climatology and interannual variability of the Southeast Asian summer monsoon. Advances in Atmospheric Sciences, 14, 141-16. L, J., Q. Zhang, S. Tao, and J. Ju, 2006: Th e onset and advance of the Asian summer monsoon. Chinese Science Bulletin, 51, 80-88. Madsen, H., P. F. Rasmussen, and D. Rosbje rg, 1997: Comparison of annual maximum series and partial duration series methods for modeling extreme hydrologic events. 1. At-site modeling. Water Resources Research, 33, 747-757. Mendelsohn, R., 2007: What causes crop failure?. Climatic Change, 81, 61-70. Mendelsohn, R., A. Basist, A. Dinar, P. Kurukul asuriya, and C. Williams, 2007: What explains agricultural performance: climat e normals or climate variance?. Climatic Change, 81, 8599. Murdiyarso, D., 2000: Adaptation to climatic va riability and change: Asian perspectives on agriculture and food security. Environmental Monitoring and Assessment, 61, 123-131. Paxson, C. H., 1992: Using weather variability to estimate the res ponse of savings to transitory income in Thailand. The American Economic Review, March, 15-32. 96

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Rosbjerg, D., H. Madsen, and P. F. Rasmussen, 1992: Prediction in partia l duration series with generalized Pareto-distributed exceedances. Water Resources Research, 28, 3001-3010. Shenton, L. R., and K. O. Bowman, 1973: Note on the sample size to achieve normality for estimators for the gamma distribution. Monthly Weather Review, 101, 891. Singhrattna, N., B. Rajagopalan, K. Krishna Kumar, and M. Clark, 2005: Interannual and interdecadal variability of Thailand summer monsoon season. Journal of Climate, 18, 1697-1708. Stephenson, D. B., K. Ru pa Kumar, F. J. Doblas-Reyes, J. F. Royer, and F. Chauvin, 1999: Extreme daily rainfall events and their imp act on ensemble forecasts of the Indian monsoon. Monthly Weather Review, 127, 1954-1966. Stern, R.D. and R. Coe, 1984: A model f itting analysis of daily rainfall data. Journal of Royal Statistical Society, 147, 1-34. Thom, H.C.S., 1958: A note on the gamma distribution. Monthly Weather Review, 86, 117. Wackerly, D. D., W. Mendenhall II I, and R. L. Scheaffer, 2002: Mathematical Statistics with Applications. Duxbury, 853 pp. Wilks, D. S., 1998: Multisite generalization of a daily stochastic precipitation generation model. Journal of Hydrology, 210, 178-191. Wilks, D. S., and R. L. Wilby, 1999: The weather generation game: a review of stochastic weather models. Progress in Physical Geography, 23, 329-357. Wilks, D. S., 2006: Statistical Methods in the Atmospheric Sciences. Academic Press, 627 pp. Yancheva, G., N. R. Nowaczyk, J. Mingram, P. Dulski G. Schettler, J. F. W. Negendank, J. Liu, D. M. Sigman, L. C. Peterson, and G. Haug, 2007: Influence of the intertropical convergence zone on the East Asian monsoon. Nature, 445, 74-77. Yao, S., 1997: Comparative advant ages and crop diversification: A policy analysis matrix for Thai agriculture. Journal of Agricultural Economics, 48, 211-222. 97

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98 BIOGRAPHICAL SKETCH Anna Szyniszewska was born in Poznan, Poland. She received Bachelor of Arts degree in Tourism and Leisure from the Adam Mickiewicz University, Department of Geographical and Geological Sciences in Poznan, Poland in 2003. Sh e spent 1.5 years in Japan where she attended the Kanazawa University as a part-time student and research assistant on the Hovsgol Drilling Project research on long-term c limate changes in Central Asia. Her interest in climatology brought her to the Un iversity of Florida to pursue her masters degree. She plans to continue her education at the University of Florida to the doctorate level.