Heft 194 Jan Bliefernicht

Probability Forecasts of Daily Areal
Precipitation for Small River Basins



Probability Forecasts of Daily Areal Precipitation
for Small River Basins







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



Vorgelegt von
Jan Bliefernicht
aus Wesenstedt




Hauptberichter: Prof. András Bárdossy
Mitberichter: Prof. Charles Obled


Tag der mündlichen Prüfung: 22. Juni 2010









Institut für Wasserbau der Universität Stuttgart
2010







Heft 194 Probability Forecasts of
Daily Areal Precipitation for
Small River Basins


von
Dr.-Ing.
Jan Bliefernicht













Eigenverlag des Instituts für Wasserbau der Universität Stuttgart D93 Probability Forecasts of Daily Areal Precipitation for Small River Basins























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Bliefernicht, Jan:
Probability Forecasts of Daily Areal Precipitation for Small River Basins
von Jan Bliefernicht. Institut für Wasserbau, Universität Stuttgart.
Stuttgart: Inst. für Wasserbau, 2010

(Mitteilungen / Institut für Wasserbau, Universität Stuttgart: Heft 194)
Zugl.: Stuttgart, Univ., Diss., 2010
ISBN 978-3-933761-98-9
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, OstfildernAcknowledgements
First of all, I want to thank Prof. Ba´rdossy who has given me the chance to work in
hisgroup,forhiscontinuoussupportandforhispatiencewithme. Healsosupported
me with many ideas so that I have still a plenty of work to do in the future. Many
thanks also to Prof. Obled for being my external reviewer, his detailed revision, for
his help and for the fruitful discussions during his stay in Stuttgart.
The work was counter-checked by my colleagues, Ferdinand, Christian, Mahboob,
Thomas P., Thomas J., Dirk, Shailesh and Claus. They gave me many valuable
comments that improved the work a lot. The English spelling and grammar was
proof-read by Leo Redcliffe in a very professional way.
Many further research colleagues and friends helped me directly or indirectly
during the preparation of my work. Here, I would like to give a special mention to
the following persons: My colleague Christian - we had more than five years a very
good time in the same office; my current and former colleagues for the excellent
working atmosphere in our group and the enjoyable coffee breaks; Norbert Demuth
from the State Agency Rhineland-Palatinate for his patience during the project
work so that I had enough time to complete my dissertation; my project colleagues
in HORIX and in PREVIEW for the very good collaboration and for providing me
with all necessary information; my roommates, Alice, Dagmar, Ralf and Nowo, for
the perfect refuge when I had a bad working day.
Lastbutnotleast, Iwouldliketothankmyparents, MargretandKarl-Heinz, and
the most important person in my life, my partner Rebekka. Due to the continuous
support and the tolerance of my parents I was in the lucky position to study envi-
ronmental science (geoecology) and to receive a PhD in hydrology. The help, the
understanding and the ease of mind of Rebekka were extremely important during
hard times. I am looking forward to our common future.
iAcknowledgements





iiContents
Acknowledgements i
List of Figures vii
List of Tables viii
List of Abbreviations xi
List of Symbols xiii
Zusammenfassung xv
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Objective and Research Questions . . . . . . . . . . . . . . . . . . . . 5
1.3 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Basic Theory 9
2.1 Weather Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.1 Global Numerical Weather Prediction . . . . . . . . . . . . . . 10
2.1.2 Downscaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.3 Dynamical Downscaling and Deterministic Forecasting . . . . 13
2.1.4 Dynamical Downscaling and Ensemble Forecasting . . . . . . 15
2.1.5 Statistical Downscaling and Forecasting. . . . . . . . . . . . . 19
2.2 Forecast Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.1 What is a Good Forecast? . . . . . . . . . . . . . . . . . . . . 23
2.2.2 Skill Scores . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.3 Probability Forecast . . . . . . . . . . . . . . . . . . . . . . . 26
2.2.4 Binary Forecast . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.5 Cost-Loss Situation and Forecast Value . . . . . . . . . . . . . 31
3 Data and Study Areas 35
3.1 Description of Study Regions . . . . . . . . . . . . . . . . . . . . . . 37
3.2 Description of Predictor Information . . . . . . . . . . . . . . . . . . 44
4 Analog Method 49
4.1 Principle of the Analog Method . . . . . . . . . . . . . . . . . . . . . 49
4.2 Pattern Closeness and Pattern Similarity . . . . . . . . . . . . . . . . 52
4.3 Maximizing the Forecast Value . . . . . . . . . . . . . . . . . . . . . 55
4.4 Probabilistic Precipitation Forecast . . . . . . . . . . . . . . . . . . . 58
4.5 Strategy of the Model Development . . . . . . . . . . . . . . . . . . . 60
iiiContents
4.6 Influence of User-Defined Criteria . . . . . . . . . . . . . . . . . . . . 62
4.6.1 Predictor Selection and Predictor Configuration . . . . . . . . 62
4.6.2 Predictor Domain . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.6.3 Distance Parameters and Predictor Weights . . . . . . . . . . 67
4.6.4 Number of Analogs and Probability Functions . . . . . . . . . 72
4.6.5 Selection Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.7 Forecast Skill and Value . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.7.1 Optimal Use of a Probability Forecast . . . . . . . . . . . . . 74
4.7.2 Intra-annual Variability . . . . . . . . . . . . . . . . . . . . . 79
4.8 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 80
5 Classification 83
5.1 Subjective and Objective Classification . . . . . . . . . . . . . . . . . 83
5.2 Why Objective Classification in Weather Forecasting? . . . . . . . . . 84
5.3 Fuzzy Rule-Based Classification . . . . . . . . . . . . . . . . . . . . . 86
5.3.1 Basic Methodology . . . . . . . . . . . . . . . . . . . . . . . . 86
5.3.2 Objective Functions . . . . . . . . . . . . . . . . . . . . . . . 87
5.3.3 Validation Procedure . . . . . . . . . . . . . . . . . . . . . . . 91
5.4 Wetness Index and Anomaly Maps . . . . . . . . . . . . . . . . . . . 92
5.5 Forecast Skill and Value . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.5.1 Pure Classification . . . . . . . . . . . . . . . . . . . . . . . . 96
5.5.2 Classification vs. Analog Forecasting . . . . . . . . . . . . . . 97
5.5.3 Conditional Forecast Value . . . . . . . . . . . . . . . . . . . . 100
5.6 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 101
6 Metric Optimization 103
6.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.1.1 Weighted Euclidean Distance . . . . . . . . . . . . . . . . . . 104
6.1.2 Simulated Annealing . . . . . . . . . . . . . . . . . . . . . . . 105
6.1.3 Objective Function . . . . . . . . . . . . . . . . . . . . . . . . 106
6.2 Model Development and Validation Strategy . . . . . . . . . . . . . . 108
6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.3.1 Air Flow Indices and Data Resolution. . . . . . . . . . . . . . 109
6.3.2 Optimization Performance and Metric Weights . . . . . . . . . 111
6.3.3 Forecast Accuracy and Value . . . . . . . . . . . . . . . . . . 114
6.3.4 Selection Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.4 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 120
7 Data Depth 123
7.1 How Can We Measure the Centrality of a Weather State? . . . . . . . 125
7.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7.3 Precipitation Probability and Risk Index . . . . . . . . . . . . . . . . 128
7.4 Forecast Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.5 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 134
8 Operational Application 137
8.1 Model History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
8.2 Global Forecast System . . . . . . . . . . . . . . . . . . . . . . . . . . 138
iv