Estimating IDF Curves Consistently over Durations with Spatial Covariates
Abstract
:1. Introduction
- Under which conditions is the spatial d-GEV approach an improvement compared to the separate application of the GEV for each duration and station?
- Does the spatial d-GEV approach provide reliable estimates at ungauged sites?
2. Methods
2.1. Data
2.2. d-GEV as a Model for Annual Maxima for Different Durations
2.2.1. Station-Wise Model for a Range of Durations (d-GEV)
2.2.2. Adding Spatial Covariates
2.3. Model Selection
2.4. Verification
2.5. Confidence Intervals
3. Results
3.1. Model Performance
3.1.1. Overall Performance
3.1.2. Dependence on Time Series Length
3.1.3. Ungauged Sites
3.2. Quantile Estimation and Uncertainty
4. Discussion
5. Summary
Supplementary Materials
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
BHM | Bayesian Hierarchical Model |
DWD | German Weather Service (Deutscher Wetterdienst) |
EVT | Extreme Value Theory |
GEV | Generalized Extreme Value distribution |
d-GEV | duration-dependent GEV |
IDF | Intensity-Duration-Frequency (curve) |
QS | Quantile Score |
QSS | Quantile Skill Score |
QSI | Quantile Skill Index |
VGLM | Vector generalized linear model |
VGAM | Vector generalized additive model |
Appendix A. Overview of Verification Variations
- the overall performance
- the dependence of the model performance on the length of the time series used for training the model
- the model performance at ungauged sites.
Overall Performance | Dependence on Time Series Length | Ungauged Sites | |||||
---|---|---|---|---|---|---|---|
Training | Validation | Training | Validation | Training | Validation | ||
spatial d-GEV | station | () years | 3 years | years | 3 years | - | 3 years |
remaining stations | all data | - | all data | - | all data | - | |
GEV | station | () years | 3 years | years | 3 years | years | 3 years |
remaining stations | - | - | - | - | - | - |
Appendix B. Coverage of Confidence Intervals
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Provider | Number of Stations | Measuring Interval | Device | Length of Time Series |
---|---|---|---|---|
DWD | 69 | 1 day | Hellmann | 9–121 years |
DWD | 17 | 1 min | Pluvio | 5–14 years |
WV | 6 | 1 hour | Pluvio | 38 years |
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Ulrich, J.; Jurado, O.E.; Peter, M.; Scheibel, M.; Rust, H.W. Estimating IDF Curves Consistently over Durations with Spatial Covariates. Water 2020, 12, 3119. https://doi.org/10.3390/w12113119
Ulrich J, Jurado OE, Peter M, Scheibel M, Rust HW. Estimating IDF Curves Consistently over Durations with Spatial Covariates. Water. 2020; 12(11):3119. https://doi.org/10.3390/w12113119
Chicago/Turabian StyleUlrich, Jana, Oscar E. Jurado, Madlen Peter, Marc Scheibel, and Henning W. Rust. 2020. "Estimating IDF Curves Consistently over Durations with Spatial Covariates" Water 12, no. 11: 3119. https://doi.org/10.3390/w12113119