Analysis of Flood Risk of Urban Agglomeration Polders Using Multivariate Copula
Abstract
:1. Introduction
2. Materials and Methods
2.1. Study Area and Data
2.2. Methodology
2.2.1. Archimedean Copula
2.2.2. Dependence and Ranks
- Chi-plot
- K-plot
2.2.3. Goodness of Fit
3. Results
3.1. Dependence of Flood Characteristics
3.2. Marginal Distribution
3.3. Joint Distribution
4. Discussion
4.1. Impacts on Flood Risks of Polders
4.2. Impacts on Flood Risks of Polder Area
- (a)
- Jurong City Circle only;
- (b)
- Jurong, Qianhancun City Circle combined;
- (c)
- Jurong, Qianhancun, Dongshan City Circle combined; and
- (d)
- Jurong, Qianshancun, Dongshan, Lishui City Circle combined.
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A
Variable | With UAP | Without UAP | ||
---|---|---|---|---|
Spearman | Kendall | Spearman | Kendall | |
V&P | 0.921(4.5 × 10−6) | 0.762(5.8 × 10−8) | 0.877(9.5 × 10−7) | 0.686(2.4 × 10−6) |
V&Z | 0.893(5.1 × 10−8) | 0.73(4.4 × 10−6) | 0.821(3.4 × 10−6) | 0.619(3.2 × 10−5) |
P&Z | 0.974(1.2 × 10−13) | 0.921(6.6 × 10−9) | 0.926(4.7 × 10−6) | 0.8(6.0 × 10−9) |
Statistics | Without UAP | With UAP | ||||
---|---|---|---|---|---|---|
V | P | Z | V | P | Z | |
Mean | 126.03 | 591.21 | 6.99 | 143.99 | 729.01 | 7.84 |
Std. | 112.81 | 350.50 | 1.45 | 118.17 | 419.10 | 1.41 |
Skewness | 1.90 | 0.59 | 0.30 | 1.73 | 0.74 | 0.18 |
Kurtosis | 6.20 | 2.32 | 2.20 | 5.64 | 2.72 | 2.32 |
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Copula | Trivariate Coupla Function |
---|---|
GH | |
Clayton | |
Frank |
Without UAPs (Urban Agglomeration Polders) | With UAPs (Urban Agglomeration Polders) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Location | Scale | Shape | KS | P | Location | Scale | Shape | KS | P | ||
V | P-Ш | 28.38 | 0.004 | 0.44 | 0.23 | 0.20 | 14.40 | 0.006 | 0.83 | 0.20 | 0.34 |
GEV | 72.60 | 53.86 | 0.31 | 0.12 | 0.88 | 87.17 | 61.07 | 0.28 | 0.12 | 0.86 | |
LN | 4.51 | 0.87 | - | 0.14 | 0.79 | 4.68 | 0.80 | - | 0.14 | 0.79 | |
P | P-Ш | −247.93 | 0.006 | 4.63 | 0.15 | 0.71 | 32.16 | 0.003 | 2.16 | 0.16 | 0.56 |
GEV | 424.66 | 263.84 | 0.05 | 0.16 | 0.61 | 526.58 | 301.26 | 0.09 | 0.19 | 0.39 | |
LN | 6.18 | 0.70 | - | 0.14 | 0.73 | 6.42 | 0.63 | - | 0.15 | 0.66 | |
Z | P-Ш | 0.56 | 2.49 | 16.00 | 0.14 | 0.79 | −0.21 | 3.63 | 29.22 | 0.16 | 0.63 |
GEV | 6.42 | 1.29 | −0.17 | 0.16 | 0.63 | 7.33 | 1.33 | −0.24 | 0.17 | 0.49 | |
LN | 1.92 | 0.21 | - | 0.16 | 0.63 | 2.04 | 0.18 | - | 0.17 | 0.54 |
Copula | Without UAPs | With UAPs | ||||
---|---|---|---|---|---|---|
Theta | RMSE | AIC | Theta | RMSE | AIC | |
GH | 3.680 | 0.015 | −111.45 | 3.149 | 0.015 | −111.42 |
Clayton | 2.773 | 0.022 | −94.58 | 2.463 | 0.018 | −102.31 |
Frank | 15.905 | 0.013 | −117.43 | 14.040 | 0.014 | −113.36 |
JRP (/a) | Without UAPs | With UAPs | ||||
---|---|---|---|---|---|---|
V (m3) | P (m3/s) | Z (m) | V (m3) | P (m3/s) | Z (m) | |
10 | 331.03 | 1514.57 | 9.80 | 370.81 | 1738.81 | 10.40 |
20 | 473.94 | 2010.97 | 10.63 | 514.92 | 2232.61 | 11.13 |
50 | 702.69 | 2683.57 | 11.51 | 738.23 | 2884.44 | 11.89 |
100 | 914.87 | 3216.57 | 12.05 | 940.25 | 3392.11 | 12.35 |
200 | 1172.74 | 3783.76 | 12.55 | 1180.64 | 3925.00 | 12.74 |
Flood Volume Return Period | ‘OR’ Exceedance Probability | ‘AND’ Exceedance Probability | ||||
---|---|---|---|---|---|---|
No UAPs | UAPs | Δ (%) | No UAPs | UAPs | Δ (%) | |
10 | 0.0224 | 0.0425 | 89.91 | 0.0113 | 0.0234 | 28.67 |
20 | 0.0401 | 0.0667 | 66.27 | 0.0107 | 0.0222 | 17.31 |
50 | 0.0545 | 0.0842 | 54.36 | 0.0103 | 0.0215 | 13.29 |
100 | 0.0600 | 0.0904 | 50.83 | 0.0102 | 0.0213 | 12.25 |
200 | 0.0628 | 0.0936 | 49.14 | 0.0102 | 0.0212 | 11.77 |
Average | - | - | 62.10 | - | - | 16.66 |
Flood No. | Scenario (a) | Scenario (b) | ||||||
Flood Volume (m3) | Peak Flow (m3/s) | Water Level (m) | Integrated Risk | Flood Volume (m3) | Peak Flow (m3/s) | Water Level (m) | Integrated Risk | |
1989 | 0.6636 | 0.8256 | 0.8077 | 0.6510 | 0.6796 | 0.8492 | 0.8140 | 0.6682 |
1987 | 0.8582 | 0.8372 | 0.8405 | 0.7934 | 0.8642 | 0.8449 | 0.8664 | 0.8102 |
1991 | 0.9603 | 0.9773 | 0.9731 | 0.9565 | 0.9644 | 0.9807 | 0.9828 | 0.9626 |
Flood No. | Scenario (c) | Scenario (d) | ||||||
Flood Volume (m3) | Peak Flow (m3/s) | Water Level (m) | Integrated Risk | Flood Volume (m3) | Peak Flow (m3/s) | Water Level (m) | Integrated Risk | |
1989 | 06990 | 0.8662 | 0.8652 | 0.6933 | 0.7140 | 0.8910 | 0.9515 | 0.7123 |
1987 | 0.8715 | 0.8579 | 0.8937 | 0.8290 | 0.8773 | 0.8743 | 0.9081 | 0.8446 |
1991 | 0.9632 | 0.9847 | 0.9838 | 0.9622 | 0.9645 | 0.9877 | 0.9937 | 0.9642 |
Scenario | (1) Ratio of Area Protected by Polders | (2) Integrated Risk | (1) × (2) | ||||
---|---|---|---|---|---|---|---|
1989 | 1987 | 1991 | 1989 | 1987 | 1991 | ||
a | 0.13 | 0.651 | 0.7934 | 0.9565 | 0.56 | 0.69 | 0.83 |
b | 0.23 | 0.6682 | 0.8102 | 0.9626 | 0.52 | 0.63 | 0.74 |
c | 0.34 | 0.6933 | 0.829 | 0.9622 | 0.46 | 0.55 | 0.64 |
d | 0.45 | 0.7123 | 0.8446 | 0.9642 | 0.39 | 0.47 | 0.53 |
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Gao, Y.; Wang, D.; Zhang, Z.; Ma, Z.; Guo, Z.; Ye, L. Analysis of Flood Risk of Urban Agglomeration Polders Using Multivariate Copula. Water 2018, 10, 1470. https://doi.org/10.3390/w10101470
Gao Y, Wang D, Zhang Z, Ma Z, Guo Z, Ye L. Analysis of Flood Risk of Urban Agglomeration Polders Using Multivariate Copula. Water. 2018; 10(10):1470. https://doi.org/10.3390/w10101470
Chicago/Turabian StyleGao, Yuqin, Dongdong Wang, Zhenxing Zhang, Zhenzhen Ma, Zichen Guo, and Liu Ye. 2018. "Analysis of Flood Risk of Urban Agglomeration Polders Using Multivariate Copula" Water 10, no. 10: 1470. https://doi.org/10.3390/w10101470