Multivariate Flood Risk Analysis at a Watershed Scale Considering Climatic Factors
Abstract
:1. Introduction
2. Materials and Methods
2.1. Study Area and Data
2.2. Methodology
2.2.1. Definition of flood risk
2.2.2. Archimedean Copula
2.2.3. Parameter Estimation and Goodness-of-fit Test
2.2.4. Scenario Hypothesis
2.2.5. Climate Scenarios
3. Results
3.1. Flood Response Analysis Under Different Climate Scenarios
3.2. Hydrological Response of Different Climate Scenarios
3.2.1. Analysis of the Impact of Temperature Changes on Floods
3.2.2. Analysis of the Impact of Rainfall Changes on Floods
3.2.3. Analysis of the Combined Effects of Temperature and Rainfall
3.3. Copula Function Fitting
4. Discussion
4.1. Multivariate Flood Risk Analysis
4.1.1. Flood Risk Analysis Under Current Situation
4.1.2. Flood Risk Analysis Considering Climate Change Impact
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
Appendix A
Flood | Relative Flood Change (%) | ||||||
---|---|---|---|---|---|---|---|
Rank | Number | T-2P0 | T2P0 | T5P0 | |||
Q (m3/s) | V (108 m3) | Q (m3/s) | V (108 m3) | Q (m3/s) | V (108 m3) | ||
light | 20040618 | 15.43 | 16.75 | −17.15 | −19.11 | −20.69 | −24.06 |
medium | 19870701 | 2.40 | 5.65 | −0.16 | −2.48 | −1.91 | −7.45 |
heavy | 19910630 | 0.25 | 1.41 | −0.89 | −1.55 | −1.59 | −2.98 |
average | 6.03 | 7.94 | −6.07 | −7.71 | −8.06 | −11.50 |
Floods | Relative Flood Change (%) | ||||||||
---|---|---|---|---|---|---|---|---|---|
Rank | Number | T0P2 | T0P4 | T0P8 | T0P14 | ||||
Q (m3/s) | V (108 m3) | Q (m3/s) | V (108 m3) | Q (m3/s) | V (108 m3) | Q (m3/s) | V (108 m3) | ||
light | 20040618 | 4.33 | 4.62 | 8.89 | 9.41 | 18.43 | 19.47 | 33.11 | 35.16 |
medium | 19870701 | 4.23 | 3.82 | 8.66 | 7.64 | 17.50 | 15.27 | 30.02 | 26.80 |
heavy | 19910630 | 2.74 | 2.72 | 5.41 | 5.48 | 11.01 | 11.20 | 19.34 | 24.62 |
average | 3.76 | 3.72 | 7.65 | 7.51 | 15.64 | 15.31 | 27.49 | 28.86 |
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Distribution | Probability Density Function | Denotes |
---|---|---|
P-III | where, | , , are shape scale and location parameter respectively. |
GEV | k, a and u are shape scale and location parameter respectively. | |
LN | and are the expectation and variance of the logarithm of the original sample |
Copula | Expression | |
---|---|---|
GH | = | [0, 1] |
Clayton | = | [−1, 1]\{0} |
Frank | = | [−1, 1]\{0} |
ΔT (°C) | ΔP (%) | ||||
---|---|---|---|---|---|
0 | 2% | 4% | 8% | 14% | |
−2 | T-2P0 | T-2P2 | T-2P4 | T-2P8 | T-2P14 |
0 | T0P0 | T0P2 | T0P4 | T0P8 | T0P14 |
2 | T2P0 | T2P2 | T2P4 | T2P8 | T2P14 |
5 | T5P0 | T5P2 | T5P4 | T5P8 | T5P14 |
Scenario | Heavy (19910630) | Median (19870701) | Light (20040618) | |||
---|---|---|---|---|---|---|
Q (m3/s) | V (108 m3) | Q (m3/s) | V (108 m3) | Q (m3/s) | V (108 m3) | |
T-2P0 | 1240.3 | 12.21 | 831.5 | 6.00 | 843.1 | 2.80 |
T-2P2 | 1274.2 | 12.55 | 866.0 | 6.22 | 871.7 | 2.91 |
T-2P4 | 1308.8 | 12.90 | 901.6 | 6.44 | 900.4 | 3.02 |
T-2P8 | 1377.3 | 13.69 | 974.3 | 6.88 | 958.5 | 3.24 |
T-2P14 | 1578.7 | 16.23 | 1081.2 | 7.56 | 1079.0 | 3.64 |
T0P0 | 1237.2 | 12.04 | 812.0 | 5.68 | 730.4 | 2.40 |
T0P2 | 1271.0 | 12.37 | 846.3 | 5.90 | 762.0 | 2.51 |
T0P4 | 1304.1 | 12.70 | 882.3 | 6.11 | 795.3 | 2.63 |
T0P8 | 1373.3 | 13.39 | 954.1 | 6.55 | 865.0 | 2.87 |
T0P14 | 1476.4 | 15.00 | 1055.7 | 7.20 | 972.2 | 3.24 |
T2P0 | 1226.1 | 11.85 | 810.7 | 5.54 | 605.1 | 1.94 |
T2P2 | 1260.0 | 12.18 | 843.2 | 5.75 | 630.2 | 2.03 |
T2P4 | 1293.0 | 12.50 | 876.0 | 5.96 | 655.4 | 2.13 |
T2P8 | 1360.7 | 13.16 | 942.0 | 6.40 | 711.7 | 2.34 |
T2P14 | 1463.8 | 14.22 | 1041.4 | 7.06 | 795.3 | 2.65 |
T5P0 | 1217.5 | 11.68 | 796.5 | 5.26 | 579.3 | 1.82 |
T5P2 | 1250.5 | 12.01 | 828.0 | 5.46 | 602.9 | 1.90 |
T5P4 | 1284.4 | 12.36 | 860.2 | 5.68 | 626.6 | 1.98 |
T5P8 | 1352.1 | 13.03 | 925.1 | 6.14 | 677.4 | 2.15 |
T5P14 | 1453.6 | 14.01 | 1023.1 | 6.81 | 757.1 | 2.44 |
Scenario | Relative Peak Flow Change (%) | Average | Relative Flood Volume Change (%) | Average | ||||
---|---|---|---|---|---|---|---|---|
Light 20040618 | Medium 19870701 | Heavy 19910630 | Light 20040618 | Medium 19870701 | Heavy 19910630 | |||
T2P2 | −13.7 | 3.8 | 1.80 | −2.70 | −15.30 | 1.20 | 1.20 | −4.30 |
T2P4 | −10.3 | 7.9 | 4.50 | 0.70 | −11.20 | 5.00 | 3.80 | −0.80 |
T2P8 | −2.6 | 16 | 10.00 | 7.80 | −2.60 | 12.70 | 9.30 | 6.47 |
T2P14 | 8.9 | 28.3 | 18.30 | 18.50 | 10.40 | 24.40 | 18.10 | 17.63 |
T5P2 | −17.5 | 2 | 1.10 | −4.80 | −20.80 | −3.80 | −0.20 | −8.27 |
T5P4 | −14.2 | 5.9 | 3.80 | −1.50 | −17.50 | 0.00 | 2.60 | −4.97 |
T5P8 | −7.3 | 13.9 | 9.30 | 5.30 | −10.40 | 8.20 | 8.20 | 2.00 |
T5P14 | 3.7 | 26 | 17.50 | 15.73 | 1.70 | 19.80 | 16.40 | 12.63 |
Copula | θ | RMSE | AIC |
---|---|---|---|
G-H | 4.9273 | 0.009 | −134.272 |
Clayton | 3.1097 | 0.011 | −123.354 |
Frank | 17.7637 | 0.009 | −132.292 |
Return Period | Univariate Design Value | Bivariate Design Value | Joint Return Period | Co-occurrence Return Period | ||
---|---|---|---|---|---|---|
Q (m3/s) | V (108 m3) | Q (m3/s) | V (108 m3) | |||
5 | 825 | 3.93 | 868 | 4.38 | 4.41 | 5.76 |
10 | 1049 | 6.95 | 1089 | 7.72 | 8.76 | 11.66 |
20 | 1253 | 11.87 | 1292 | 13.17 | 17.44 | 23.44 |
30 | 1367 | 16.11 | 1404 | 17.83 | 26.13 | 35.22 |
50 | 1504 | 23.54 | 1541 | 26.09 | 43.50 | 58.78 |
100 | 1683 | 39.20 | 1718 | 43.41 | 86.94 | 117.67 |
Scenario | Flood Risk | ||||||||
---|---|---|---|---|---|---|---|---|---|
Light (20040618) | Medium (19870701) | Heavy (19910630) | |||||||
Q (m3/s) | V (108 m3) | Joint | Q (m3/s) | V (108 m3) | Joint | Q (m3/s) | V (108 m3) | Joint | |
T-2P0 | 0.8251 | 0.6740 | 0.6725 | 0.6342 | 0.8891 | 0.6341 | 0.9649 | 0.9665 | 0.9606 |
T-2P2 | 0.8356 | 0.6873 | 0.6859 | 0.6499 | 0.8943 | 0.6498 | 0.9681 | 0.9679 | 0.9633 |
T-2P4 | 0.8456 | 0.6997 | 0.6985 | 0.6654 | 0.8992 | 0.6654 | 0.9711 | 0.9693 | 0.9657 |
T-2P8 | 0.8639 | 0.7233 | 0.7224 | 0.6951 | 0.9081 | 0.6950 | 0.9761 | 0.9720 | 0.9698 |
T-2P14 | 0.8954 | 0.7584 | 0.7579 | 0.7342 | 0.9194 | 0.7342 | 0.9865 | 0.9788 | 0.9783 |
T0P0 | 0.7769 | 0.6170 | 0.6146 | 0.6250 | 0.8782 | 0.6249 | 0.9646 | 0.9657 | 0.9600 |
T0P2 | 0.7916 | 0.6340 | 0.6319 | 0.6410 | 0.8843 | 0.6409 | 0.9678 | 0.9671 | 0.9627 |
T0P4 | 0.8061 | 0.6507 | 0.6489 | 0.6571 | 0.8900 | 0.6570 | 0.9707 | 0.9685 | 0.9650 |
T0P8 | 0.8332 | 0.6819 | 0.6806 | 0.6871 | 0.9002 | 0.6870 | 0.9759 | 0.9711 | 0.9690 |
T0P14 | 0.8679 | 0.7232 | 0.7224 | 0.7254 | 0.9129 | 0.7253 | 0.9819 | 0.9758 | 0.9748 |
T2P0 | 0.7080 | 0.5349 | 0.5313 | 0.6243 | 0.8703 | 0.6242 | 0.9635 | 0.9648 | 0.9588 |
T2P2 | 0.7233 | 0.5528 | 0.5495 | 0.6395 | 0.8771 | 0.6394 | 0.9668 | 0.9663 | 0.9616 |
T2P4 | 0.7379 | 0.5710 | 0.5679 | 0.6543 | 0.8833 | 0.6542 | 0.9698 | 0.9677 | 0.9640 |
T2P8 | 0.7677 | 0.6069 | 0.6042 | 0.6822 | 0.8946 | 0.6821 | 0.9750 | 0.9703 | 0.9681 |
T2P14 | 0.8061 | 0.6534 | 0.6515 | 0.7203 | 0.9089 | 0.7202 | 0.9813 | 0.9737 | 0.9728 |
T5P0 | 0.6915 | 0.5108 | 0.5073 | 0.6175 | 0.8593 | 0.6173 | 0.9626 | 0.9640 | 0.9578 |
T5P2 | 0.7067 | 0.5270 | 0.5238 | 0.6325 | 0.8674 | 0.6323 | 0.9659 | 0.9656 | 0.9607 |
T5P4 | 0.7212 | 0.5433 | 0.5402 | 0.6473 | 0.8749 | 0.6471 | 0.9690 | 0.9671 | 0.9632 |
T5P8 | 0.7499 | 0.5758 | 0.5732 | 0.6753 | 0.8882 | 0.6752 | 0.9744 | 0.9697 | 0.9675 |
T5P14 | 0.7894 | 0.6239 | 0.6219 | 0.7136 | 0.9038 | 0.7135 | 0.9807 | 0.9731 | 0.9722 |
Scenario | Flood Characteristics | Light (20040618) | Medium (19870701) | Heavy (19910630) | |||
---|---|---|---|---|---|---|---|
Risk | Relative Change (%) | Risk | Relative Change (%) | Risk | Relative Change (%) | ||
T0P0 | Q (m3/s) | 0.7769 | - | 0.6250 | - | 0.9646 | - |
V (108 m3) | 0.6170 | - | 0.8782 | - | 0.9657 | - | |
Joint | 0.6146 | - | 0.6249 | - | 0.9600 | - | |
T-2P0 | Q (m3/s) | 0.8251 | 6.21 | 0.6342 | 1.47 | 0.9649 | 0.03 |
V (108 m3) | 0.6740 | 9.24 | 0.8891 | 1.24 | 0.9665 | 0.08 | |
Joint | 0.6725 | 9.42 | 0.6341 | 1.47 | 0.9606 | 0.06 | |
T0P14 | Q (m3/s) | 0.8679 | 11.71 | 0.7254 | 16.06 | 0.9819 | 1.80 |
V (108 m3) | 0.7232 | 17.21 | 0.9129 | 3.95 | 0.9758 | 1.05 | |
Joint | 0.7224 | 17.55 | 0.7253 | 16.07 | 0.9748 | 1.54 | |
T-2P14 | Q (m3/s) | 0.8954 | 15.25 | 0.7342 | 17.48 | 0.9865 | 2.27 |
V (108 m3) | 0.7584 | 22.91 | 0.9194 | 4.70 | 0.9788 | 1.35 | |
Joint | 0.7579 | 23.32 | 0.7342 | 17.49 | 0.9783 | 1.91 |
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Gao, Y.; Guo, Z.; Wang, D.; Zhang, Z.; Liu, Y. Multivariate Flood Risk Analysis at a Watershed Scale Considering Climatic Factors. Water 2018, 10, 1821. https://doi.org/10.3390/w10121821
Gao Y, Guo Z, Wang D, Zhang Z, Liu Y. Multivariate Flood Risk Analysis at a Watershed Scale Considering Climatic Factors. Water. 2018; 10(12):1821. https://doi.org/10.3390/w10121821
Chicago/Turabian StyleGao, Yuqin, Zichen Guo, Dongdong Wang, Zhenxing Zhang, and Yunping Liu. 2018. "Multivariate Flood Risk Analysis at a Watershed Scale Considering Climatic Factors" Water 10, no. 12: 1821. https://doi.org/10.3390/w10121821
APA StyleGao, Y., Guo, Z., Wang, D., Zhang, Z., & Liu, Y. (2018). Multivariate Flood Risk Analysis at a Watershed Scale Considering Climatic Factors. Water, 10(12), 1821. https://doi.org/10.3390/w10121821