Evaluating the Performance of a Max-Stable Process for Estimating Intensity-Duration-Frequency Curves
Abstract
:1. Introduction
2. Methods and Data
2.1. Estimation of IDF Curves
2.1.1. Using the Duration-Dependent GEV
2.1.2. Using a Max-Stable Process
2.2. Verification and Model Comparison
2.3. Data
2.3.1. Synthetic Data
2.3.2. Observations
3. Results
3.1. Case Study
3.1.1. Structure of the Extremal Dependence
3.1.2. Estimation of IDF Curves
3.1.3. Performance Averaged over All Durations
3.1.4. Performance for Individual Durations
3.2. Simulation Study
4. Discussion
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
IDF | Intensity-Duration-Frequency (curve) |
GEV | Generalized Extreme Value distribution |
d-GEV | Duration-dependent GEV |
rd-GEV | Reduced d-GEV-based approach for modeling IDF curves |
MS-GEV | Max-stable-based approach for modeling IDF curves |
QS | Quantile Score |
QSS | Quantile Skill Score |
QSI | Quantile Skill Index |
Appendix A. Inference from the Brown-Resnick Max-Stable Process
Appendix B. Comparison of 100-year Return Level between Euclidean and Log-Distance for MS-GEV Approach
Appendix C. QQ-Plots for Selected Stations and Durations
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Station | c | |||||
---|---|---|---|---|---|---|
Bever | 1.42 | 2.09 | 13.32 | 2.84 | 0.03 | −0.58 |
Buchenhofen | 1.39 | 2.22 | 13.38 | 3.03 | 0.02 | −0.63 |
Leverkusen | 1.32 | 2.19 | 10.74 | 2.34 | 0.05 | −0.64 |
Lindscheid | 1.54 | 2.44 | 13.69 | 3.23 | 0.06 | −0.64 |
Neumuehle | 1.54 | 1.84 | 13.52 | 2.74 | 0.04 | −0.60 |
Schwelm | 1.53 | 1.74 | 13.07 | 2.77 | 0.05 | −0.62 |
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Jurado, O.E.; Ulrich, J.; Scheibel, M.; Rust, H.W. Evaluating the Performance of a Max-Stable Process for Estimating Intensity-Duration-Frequency Curves. Water 2020, 12, 3314. https://doi.org/10.3390/w12123314
Jurado OE, Ulrich J, Scheibel M, Rust HW. Evaluating the Performance of a Max-Stable Process for Estimating Intensity-Duration-Frequency Curves. Water. 2020; 12(12):3314. https://doi.org/10.3390/w12123314
Chicago/Turabian StyleJurado, Oscar E., Jana Ulrich, Marc Scheibel, and Henning W. Rust. 2020. "Evaluating the Performance of a Max-Stable Process for Estimating Intensity-Duration-Frequency Curves" Water 12, no. 12: 3314. https://doi.org/10.3390/w12123314