Intensity–Duration–Frequency Curves for Dependent Datasets
Abstract
:1. Introduction
2. Classical Models and Vine Copula Approach
- Rainfall intensity sample definition;
- Determination and estimation of the marginal distributions and, for the sampled series, estimation of the copula parameters and construction of the joint distribution;
- Estimation of the quantiles corresponding to specified return periods;
- Adjustment of an IDF relationship to the estimated quantiles;
2.1. GEV-Distribution-Based Rainfall Quantiles
2.2. Vine-Copula-Based Rainfall Quantiles
- 1.
- .
- 2.
- is a tree of nodes and a set of edges denoted by .
- 3.
- For , is a tree of nodes and a set of edges denoted by .
2.3. IDF Curve Formulation
3. Study Area and Dataset
4. Results and Discussion
4.1. Quantile Estimation and Comparison
4.2. IDF Curve Estimation and Comparison
5. IDF Projections for Global Climate Models (GCMs)
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
References
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Station | ID | Lat. | Long. | Alt (m) | Years | Start | End |
---|---|---|---|---|---|---|---|
Moncton Int A | NB- 103201 | 46 7 N | 64 41 W | 70 | 67 | 1946 | 2016 |
Tree | Edge | ||||
---|---|---|---|---|---|
1 | 2,1 | Sur BB8 (6, 0.57) | N (0.7) | N (0.76) | N (0.88) |
3,2 | Gumbel (2.57) | Gumbel (2.57) | Gumbel (2.57) | Gumbel (2.57) | |
4,3 | N (0.76) | N (0.76) | N (0.76) | N (0.76) | |
5,4 | N (0.90) | N (0.90) | N (0.90) | N (0.90) | |
6,5 | N (0.92) | N (0.92) | N (0.92) | N (0.92) | |
2 | 3,1;2 | I (0) | I (0) | I (0) | I (0) |
4,2;3 | r270 BB7 () | r270 BB7 () | r270 BB7 () | r270 BB7 () | |
5,3;4 | r90 Joe () | r90 Joe () | r90 Joe () | r90 Joe () | |
6,4;5 | Frank () | Frank () | Frank () | Frank () | |
3 | 4,1;3,2 | I (0) | I (0) | I (0) | I (0) |
5,2;4,3 | Frank (1.5) | Frank (1.5) | Frank (1.5) | Frank (1.5) | |
6,3;5,4 | I (0) | I (0) | I (0) | I (0) | |
4 | 5,1;4,3,2 | I (0) | I (0) | I (0) | I (0) |
6,2;5,4,3 | I (0) | I (0) | I (0) | I (0) | |
5 | 6,1;5,4,3,2 | Frank () | r90 Clayton () | r90 Clayton () | Frank () |
Intensities over the Different Durations | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
T (Years) | min | min | min | min | ||||||||
2 | 74.6 | 76.6 | 2.7 | 52.5 | 51.8 | 40.7 | 40.2 | 27.1 | 27.2 | 0.3 | ||
5 | 106.2 | 115.9 | 8.4 | 74.5 | 82.6 | 9.8 | 57.3 | 63.8 | 10.2 | 37.2 | 40.7 | 8.7 |
10 | 128.5 | 140.2 | 8.3 | 90.1 | 106.8 | 15.7 | 69.3 | 82.9 | 16.5 | 44.4 | 51.7 | 14.1 |
25 | 158.4 | 168.2 | 5.8 | 110.8 | 141.6 | 21.7 | 85.7 | 111.6 | 23.2 | 54.2 | 68.2 | 20.6 |
50 | 181.7 | 191.4 | 5.0 | 127.1 | 172.1 | 26.1 | 98.9 | 137.4 | 28.0 | 61.9 | 82.5 | 25.0 |
100 | 206.0 | 215.2 | 4.3 | 144.1 | 203.6 | 29.2 | 112.9 | 165.0 | 31.6 | 70.1 | 98.5 | 28.9 |
Intensities over the Different Durations | |||||
---|---|---|---|---|---|
T (Years) | h | h | h | h | h |
2 | 18.0 | 12.2 | 6.6 | 4.1 | 2.4 |
5 | 24.4 | 16.2 | 8.6 | 5.4 | 3.3 |
10 | 29.6 | 19.5 | 9.9 | 6.4 | 3.9 |
25 | 37.6 | 24.5 | 11.6 | 7.6 | 4.7 |
50 | 44.7 | 29.1 | 12.8 | 8.5 | 5.3 |
100 | 52.9 | 34.4 | 14.0 | 9.4 | 5.9 |
Duration | RCP2.6 | RCP4.5 | RCP8.5 | Observations | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
2 Years | 10 Years | 100 Years | 2 Years | 10 Years | 100 Years | 2 Years | 10 Years | 100 Years | 2 Years | 10 Years | 100 Years | |
5 min | 119 | 178.8 | 260 | 129.4 | 198.7 | 293.2 | 126.4 | 188.6 | 273.1 | 71.3 | 113.1 | 155.3 |
10 min | 72.2 | 108.6 | 157.8 | 78.6 | 120.6 | 178 | 76.7 | 114.5 | 165.8 | 50.2 | 79.2 | 108.4 |
15 min | 53.9 | 81.1 | 117.9 | 58.7 | 90.1 | 132.9 | 57.3 | 85.5 | 123.8 | 40.5 | 62.7 | 85.1 |
30 min | 32.8 | 49.2 | 71.6 | 35.6 | 54.7 | 80.7 | 34.8 | 51.9 | 75.2 | 27 | 40.7 | 54.5 |
1 h | 19.9 | 29.9 | 43.4 | 21.6 | 33.2 | 49 | 21.1 | 31.5 | 45.6 | 17.9 | 25.5 | 33.2 |
2 h | 12.1 | 18.1 | 26.4 | 13.1 | 20.2 | 29.7 | 12.8 | 19.1 | 27.7 | 12.1 | 16.8 | 21.5 |
6 h | 5.5 | 8.2 | 12 | 6 | 9.1 | 13.5 | 5.8 | 8.7 | 12.6 | 6.5 | 9.6 | 12.7 |
12 h | 3.3 | 5 | 7.3 | 3.6 | 5.5 | 8.2 | 3.5 | 5.3 | 7.6 | 4.1 | 6 | 8 |
24 h | 2 | 3 | 4.4 | 2.2 | 3.4 | 5 | 2.1 | 3.2 | 4.6 | 2.4 | 3.6 | 4.8 |
Duration | RCP2.6 | RCP4.5 | RCP8.5 | ||||||
---|---|---|---|---|---|---|---|---|---|
2 Years | 10 Years | 100 Years | 2 Years | 10 Years | 100 Years | 2 Years | 10 Years | 100 Years | |
5 min | 67 | 58 | 67 | 82 | 76 | 89 | 77 | 67 | 76 |
10 min | 44 | 37 | 46 | 56 | 52 | 64 | 53 | 45 | 53 |
15 min | 33 | 29 | 39 | 45 | 44 | 56 | 41 | 36 | 46 |
30 min | 21 | 21 | 31 | 32 | 34 | 48 | 29 | 28 | 38 |
1 h | 11 | 17 | 31 | 21 | 30 | 48 | 18 | 24 | 38 |
2 h | 0 | 8 | 23 | 8 | 20 | 38 | 6 | 14 | 29 |
6 h | −16 | −14 | −6 | −9 | −5 | 6 | −11 | −10 | −1 |
12 h | −18 | −17 | −10 | −11 | −8 | 2 | −13 | −13 | −5 |
24 h | −16 | −16 | −9 | −9 | −7 | 3 | −11 | −11 | −4 |
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El Hannoun, W.; Boukili Makhoukhi, A.; Zoglat, A.; El Adlouni, S.-E. Intensity–Duration–Frequency Curves for Dependent Datasets. Water 2023, 15, 2641. https://doi.org/10.3390/w15142641
El Hannoun W, Boukili Makhoukhi A, Zoglat A, El Adlouni S-E. Intensity–Duration–Frequency Curves for Dependent Datasets. Water. 2023; 15(14):2641. https://doi.org/10.3390/w15142641
Chicago/Turabian StyleEl Hannoun, Wafaa, Anas Boukili Makhoukhi, Abdelhak Zoglat, and Salah-Eddine El Adlouni. 2023. "Intensity–Duration–Frequency Curves for Dependent Datasets" Water 15, no. 14: 2641. https://doi.org/10.3390/w15142641