Simulation of remotely sensed rainfall fields using copulas [Elektronische Ressource] / von Amir AghaKouchak

Amir Aghakouchak

Informations

• Publié par: universitat_stuttgart
• Publié le: 01 janvier 2010
• Nombre de lectures: 32
• Langue: English
• Poids de l'ouvrage: 8 Mo

Extrait

Heft 188 Amir AghaKouchak

Simulation of Remotely Sensed
Rainfall Fields Using Copulas



Simulation of Remotely Sensed Rainfall Fields Using
Copulas







Von der Fakultät Bau- und Umweltingenieurwissenschaften der
Universität Stuttgart zur Erlangung der Würde eines
Doktor-Ingenieurs (Dr.-Ing.) genehmigte Abhandlung



Vorgelegt von
Amir AghaKouchak
aus Iran




Hauptberichter: Prof. András Bárdossy
Mitberichter: Prof. Uwe Haberlandt




Tag der mündlichen Prüfung: 8. Februar 2010







Institut für Wasserbau der Universität Stuttgart
2010





Heft 188 Simulation of Remotely
Sensed Rainfall Fields Using
Copulas




von
Dr.-Ing.
Amir AghaKouchak













Eigenverlag des Instituts für Wasserbau der Universität Stuttgart D93 Simulation of Remotely Sensed Rainfall Fields Using Copulas
























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AghaKouchak, Amir:
Simulation of Remotely Sensed Rainfall Fields Using Copulas /
von Amir AghaKouchak. Institut für Wasserbau,
Universität Stuttgart. - Stuttgart: Inst. für Wasserbau, 2010

(Mitteilungen / Institut für Wasserbau, Universität Stuttgart: H. 188)
Zugl.: Stuttgart, Univ., Diss., 2010
ISBN 978-3-933761-92-7
NE: Institut für Wasserbau <Stuttgart>: Mitteilungen


Gegen Vervielfältigung und Übersetzung bestehen keine Einwände, es wird lediglich
um Quellenangabe gebeten.




Herausgegeben 2010 vom Eigenverlag des Instituts für Wasserbau
Druck: Document Center S. Kästl, Ostfildern
Acknowledgments
Completing this dissertation has definitely been a challenge and could not have been ac-
complished without the assistance and support of many individuals and institutions. My
deepest gratitude goes to Prof. Andras´ Bar´ dossy for his detailed criticism and unyield-
ing support. His profound knowledge and expertise in this area of research has always
led me throughout my work. I am also thankful for the knowledge I gained while at-
tending his doctoral classes and conducting research with him. I would like to thank my
dissertation chairman, Prof. Markus Friedrich, and the rest of my committee members
Prof. Uwe Haberlandt, Prof. Rainer Helmig and Dr. Gabriele Hartmann for their time
and efforts. Prof. Haberlandt and Prof. Helmig provided excellent feedback that helped
me broaden my research perspectives, particularly for future applications of this study.
I am appreciative to Dr. Hartmann for her continuous support throughout my doctoral
program.
I am pleased to acknowledge that a major portion of the funding for this study
was provided by a fellowship from the Department of Civil Engineering, University
of Louisiana at Lafayette, USA, through a Research Development grant for uncertainty
analysis of radar rainfall estimates. Without this financial assistance this study could not
have been undertaken. I would like to express my gratitude to Dr. Habib, Department
of Civil Engineering, University of Louisiana at Lafayette, who challenged my ideas and
my writing with his sharp comments. His knowledge of weather radar systems has been
invaluable, and I greatly appreciate his assistance and guidance. Without his encourage-
ment, effort and advice, this work would not have been realized. I also want to praise Dr.
Jing Li for her extraordinary advice and willingness to share her knowledge and expe-
rience. Appreciation is expressed to Dr. Gabriele Villarini, Princeton University, for his
thoughtful comments upon an early draft of a manuscript prepared based on Chapter
6 of this dissertation. I am deeply indebted to Prof Soroosh Sorooshian, Director of the
Center for Hydrometeorology and Remote Sensing, University of California Irvine for
his support at the last stages of my work. I would like to take this opportunity to thank
the National Oceanic and Atmospheric Administration (NOAA) Educational Partnership
Program award that allowed me to meet many students and researchers. The program
played a significant role in sparking my interest in remote sensing research.
I am very grateful to Jeff Tuhtan, William Roth and Amy Henschke who have given so
generously of their time reviewing this document and offering editorial suggestions forimprovement. I offer special thanks to Manuel Lorenz for all the time he spent on writing
the German version of the summary of my dissertation. I would like to thank my friends
and colleagues who have provided support in a variety of ways. These individuals in-
clude Mahyar Mehdizadeh, Jeff Tuhtan, Krista Uhrmann, Min Zhang, Nasrin Nasrollahi,
Thomas Pfaff, Dr. Jochen Seidel, Claudia Hojak, Dr. Matthias Schneider, Dr. Marx, Aaron
LaFramboise, Dr. Riegger, Diane Hohnbaum, Dr. McManis, Prof. Kobus, Dr. Ciach, Dr.
Thapa, Amin Darbandi, Marieh Zargar, Ehsan Rabiei, Henning Lebrenz and Dr. Scharf.
Furthermore, thanks to all the faculty members and colleagues at the Institute for Hy-
draulic Engineering, University of Stuttgart and the Department of Civil Engineering,
University of Louisiana at Lafayette for the overall good working atmosphere. Your con-
tribution is appreciated.
Finally, I am extremely grateful to my beloved family, my parents and my wife Nas-
rin, for their unconditional love and support over the last few years. To Nasrin, whose
extraordinary faith in my abilities, ceaseless encouragement and emotional support
inspired me to complete my studies and this research. She has made many sacrifices
to assist me with my work on this project. Her love and support of my endeavors can
never be repaid. Thank you for so graciously volunteering all the extra effort and for
never complaining about the weekends I had to work.
AMIR AGHAKOUCHAK
November2009
”Mywordsareunabletoexpressthemysteryoflove,
beyondthelimitofnarration,istheexplanationoflonging.”
Hafez 1315-1390 A.D.Contents
List of symbols xvi
List of Abbreviations xviii
Zusammenfassung 3
1 Introduction 17
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.3 Structure of the Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2 Copulas 23
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2.1 Gaussian Copula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2.2 t-Copula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2.3 V-Transformed Copula . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3 Copula-Based Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3 Study Areas and Data Resources 35
3.1 The Little Washita Watershed . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 The Goodwin Creek W . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3 Data Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.4 Rainfall Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4 Simulation Using Elliptical Copulas 42
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.2 Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.3 Parameter Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.4 Rainfall Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.5 Spatial and Temporal Dependencies . . . . . . . . . . . . . . . . . . . . . . 58
4.6 Extreme Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.7 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66