Deriving Design Flood Hydrograph Based on Conditional Distribution: A Case Study of Danjiangkou Reservoir in Hanjiang Basin
Design flood hydrograph (DFH) for a dam is the flood of suitable probability and magnitude adopted to ensure safety of the dam in accordance with appropriate design standards. Estimated quantiles of peak discharge and flood volumes are necessary for deriving the DFH, which are mutually correlated an...
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2016-01-01
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Series: | Mathematical Problems in Engineering |
Online Access: | http://dx.doi.org/10.1155/2016/4319646 |
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doaj-44573827727d41d79429eb7c0b9192912020-11-25T01:57:55ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472016-01-01201610.1155/2016/43196464319646Deriving Design Flood Hydrograph Based on Conditional Distribution: A Case Study of Danjiangkou Reservoir in Hanjiang BasinChangjiang Xu0Jiabo Yin1Shenglian Guo2Zhangjun Liu3Xingjun Hong4State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, ChinaState Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, ChinaState Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, ChinaState Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, ChinaState Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, ChinaDesign flood hydrograph (DFH) for a dam is the flood of suitable probability and magnitude adopted to ensure safety of the dam in accordance with appropriate design standards. Estimated quantiles of peak discharge and flood volumes are necessary for deriving the DFH, which are mutually correlated and need to be described by multivariate analysis methods. The joint probability distributions of peak discharge and flood volumes were established using copula functions. Then the general formulae of conditional most likely composition (CMLC) and conditional expectation composition (CEC) methods that consider the inherent relationship between flood peak and volumes were derived for estimating DFH. The Danjiangkou reservoir in Hanjiang basin was selected as a case study. The design values of flood volumes and 90% confidence intervals with different peak discharges were estimated by the proposed methods. The performance of CMLC and CEC methods was also compared with conventional flood frequency analysis, and the results show that CMLC method performs best for both bivariate and trivariate distributions which has the smallest relative error and root mean square error. The proposed CMLC method has strong statistical basis with unique design flood composition scheme and provides an alternative way for deriving DFH.http://dx.doi.org/10.1155/2016/4319646 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Changjiang Xu Jiabo Yin Shenglian Guo Zhangjun Liu Xingjun Hong |
spellingShingle |
Changjiang Xu Jiabo Yin Shenglian Guo Zhangjun Liu Xingjun Hong Deriving Design Flood Hydrograph Based on Conditional Distribution: A Case Study of Danjiangkou Reservoir in Hanjiang Basin Mathematical Problems in Engineering |
author_facet |
Changjiang Xu Jiabo Yin Shenglian Guo Zhangjun Liu Xingjun Hong |
author_sort |
Changjiang Xu |
title |
Deriving Design Flood Hydrograph Based on Conditional Distribution: A Case Study of Danjiangkou Reservoir in Hanjiang Basin |
title_short |
Deriving Design Flood Hydrograph Based on Conditional Distribution: A Case Study of Danjiangkou Reservoir in Hanjiang Basin |
title_full |
Deriving Design Flood Hydrograph Based on Conditional Distribution: A Case Study of Danjiangkou Reservoir in Hanjiang Basin |
title_fullStr |
Deriving Design Flood Hydrograph Based on Conditional Distribution: A Case Study of Danjiangkou Reservoir in Hanjiang Basin |
title_full_unstemmed |
Deriving Design Flood Hydrograph Based on Conditional Distribution: A Case Study of Danjiangkou Reservoir in Hanjiang Basin |
title_sort |
deriving design flood hydrograph based on conditional distribution: a case study of danjiangkou reservoir in hanjiang basin |
publisher |
Hindawi Limited |
series |
Mathematical Problems in Engineering |
issn |
1024-123X 1563-5147 |
publishDate |
2016-01-01 |
description |
Design flood hydrograph (DFH) for a dam is the flood of suitable probability and magnitude adopted to ensure safety of the dam in accordance with appropriate design standards. Estimated quantiles of peak discharge and flood volumes are necessary for deriving the DFH, which are mutually correlated and need to be described by multivariate analysis methods. The joint probability distributions of peak discharge and flood volumes were established using copula functions. Then the general formulae of conditional most likely composition (CMLC) and conditional expectation composition (CEC) methods that consider the inherent relationship between flood peak and volumes were derived for estimating DFH. The Danjiangkou reservoir in Hanjiang basin was selected as a case study. The design values of flood volumes and 90% confidence intervals with different peak discharges were estimated by the proposed methods. The performance of CMLC and CEC methods was also compared with conventional flood frequency analysis, and the results show that CMLC method performs best for both bivariate and trivariate distributions which has the smallest relative error and root mean square error. The proposed CMLC method has strong statistical basis with unique design flood composition scheme and provides an alternative way for deriving DFH. |
url |
http://dx.doi.org/10.1155/2016/4319646 |
work_keys_str_mv |
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