洪水灾害的频率分析
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DOI: 10.1061/͑ASCE͒1084-0699͑2005͒10:2͑100͒
CE Database subject headings: Frequency analysis; Flood damage; Risk analysis; Probability.
Introduction
Flooding is one of the leading causes of loss of life and property. Half of all losses caused by natural phenomena are usually attributed to flooding. In recent years, flood damage has been on the rise, largely because of changes in land use and other human activities, and possibly because of climate change. In a recent 10-year period ͑1991 to 2000͒, the losses casued by flooding in the world have mounted to more than $250 billion ͑Kron 2000͒. According to FEMA ͑2001͒, during the same period, the total flood damagபைடு நூலகம் in Alabama, Louisiana, Mississippi, and Texas has been approximately $477, $3,403, $394, and $6,492 million ͑in terms of 1995 dollars͒, respectively. The damage caused by flooding is affected by a multitude of factors: • Severe rainfall • Modification of flood plains • Inadequate criteria for design of hydraulic works • Residential dwellings in flood-prone zones • Endurance for the damage.
Frequency analysis of flood damage is fundamental to the development of a comprehensive risk methodology and to the design of flood mitigation measures. A flood-damage time series may contain zero values, which indicate that either no flood damage or very small flood damage that might be ignored, has occurred. Thus, its frequency analysis consists of two parts: frequency analysis of the zero-damage part and frequency analysis of nonzero damage, i.e., damage caused by flood events exceed-
ing a threshold. For deriving a probability distribution of flood damage, one needs to consider the probability distribution of flood events below a certain threshold that contribute to the zerodamage part and the probability distribution of flood events above the threshold that contribute to the flood damage.
Frequency Analysis of Flood Damage
L. Zhang1 and Vijay P. Singh, F.ASCE2
Abstract: Determination of flood damage frequencies constitutes a fundamental component of any comprehensive flood-risk methodology. A time series of flood damage may contain zero values. Therefore, the probability distribution of damage should be derived taking into consideration these zero values. This distribution was derived using the total probability theorem ͑in conjunction with gamma, log-normal and Weibull distributions͒, order statistics, kinematic diffusion ͑KD͒ model, and the Box-Cox transformation. Flood damage frequencies determined using these methods were compared with those determined empirically for Alabama, Louisiana, Mississippi, and Texas in the United States. For the four southern states studied, it is found that of all three different analysis methods, the method based on the total probability theorem gave the best results for the flood damage analysis containing zero-damage, and the KD model method is not suitable for the flood damage analysis.
Literature Review
Analogous to a flood-damage time series, a multitude of hydrologic and environmental time series contain zero values. Thus, the methods of frequency analysis applicable to these time series may also be applicable to the damage time series. Haan ͑1977͒ discussed three methods for dealing with zero values in a data set. One method was to add a small amount to all the values in the data set and then fit a certain probability distribution to the data. Very little improvement in the accuracy of damage analysis was achieved by this method ͑Jennings and Benson 1969͒. The second method ignored the zero values that should not be ignored in the data and analyzed only nonzero values, but the actual statistical characteristics contributed by the zero values would be lost by this method. The third method was developed, based on the total probability theory. Jennings and Benson ͑1969͒ found that this method best fitted the data containing zero values.
Bao et al. ͑1987͒ considered the uncertainty of a flood magnitude estimated for a specified return period in evaluating annual expected flood damage by a damage function. They concluded that the effect of uncertainty in a flood magnitude estimate on the annual expected damage was quite significant and was sensitive to the sample size and the probability distribution used. Haimes and Lambert ͑1992͒ used the partitioned multiobjective risk method ͑PMRM͒ for flood risk analysis. They partitioned the probability axis into a set of ranges and generated conditional expectations of damage, given that the damage fell within a par-
1Research Assistant, Dept. of Civil and Environmental Engineering, Louisiana State Univ., Baton Rouge, LA 70803-6405.
2A. K. Barton Professor, Dept. of Civil and Environmental Engineering, Louisiana State Univ. Baton Rouge, LA 70803-6405. E-mail: cesing@lsu.edu
Note. Discussion open until August 1, 2005. Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this paper was submitted for review and possible publication on October 13, 2003; approved on July 5, 2004. This paper is part of the Journal of Hydrologic Engineering, Vol. 10, No. 2, March 1, 2005. ©ASCE, ISSN 1084-0699/2005/2-100–109/$25.00.
The objectives of this study are to demonstrate a frequency analysis of flood damage using order statistics, total probability, Box-Cox transformation, and the kinematic diffusion model; evaluate these methods using the flood-damage data of Alabama, Louisiana, Mississippi and Texas; and therefore recommend a method that might be suitable for damage analysis.
CE Database subject headings: Frequency analysis; Flood damage; Risk analysis; Probability.
Introduction
Flooding is one of the leading causes of loss of life and property. Half of all losses caused by natural phenomena are usually attributed to flooding. In recent years, flood damage has been on the rise, largely because of changes in land use and other human activities, and possibly because of climate change. In a recent 10-year period ͑1991 to 2000͒, the losses casued by flooding in the world have mounted to more than $250 billion ͑Kron 2000͒. According to FEMA ͑2001͒, during the same period, the total flood damagபைடு நூலகம் in Alabama, Louisiana, Mississippi, and Texas has been approximately $477, $3,403, $394, and $6,492 million ͑in terms of 1995 dollars͒, respectively. The damage caused by flooding is affected by a multitude of factors: • Severe rainfall • Modification of flood plains • Inadequate criteria for design of hydraulic works • Residential dwellings in flood-prone zones • Endurance for the damage.
Frequency analysis of flood damage is fundamental to the development of a comprehensive risk methodology and to the design of flood mitigation measures. A flood-damage time series may contain zero values, which indicate that either no flood damage or very small flood damage that might be ignored, has occurred. Thus, its frequency analysis consists of two parts: frequency analysis of the zero-damage part and frequency analysis of nonzero damage, i.e., damage caused by flood events exceed-
ing a threshold. For deriving a probability distribution of flood damage, one needs to consider the probability distribution of flood events below a certain threshold that contribute to the zerodamage part and the probability distribution of flood events above the threshold that contribute to the flood damage.
Frequency Analysis of Flood Damage
L. Zhang1 and Vijay P. Singh, F.ASCE2
Abstract: Determination of flood damage frequencies constitutes a fundamental component of any comprehensive flood-risk methodology. A time series of flood damage may contain zero values. Therefore, the probability distribution of damage should be derived taking into consideration these zero values. This distribution was derived using the total probability theorem ͑in conjunction with gamma, log-normal and Weibull distributions͒, order statistics, kinematic diffusion ͑KD͒ model, and the Box-Cox transformation. Flood damage frequencies determined using these methods were compared with those determined empirically for Alabama, Louisiana, Mississippi, and Texas in the United States. For the four southern states studied, it is found that of all three different analysis methods, the method based on the total probability theorem gave the best results for the flood damage analysis containing zero-damage, and the KD model method is not suitable for the flood damage analysis.
Literature Review
Analogous to a flood-damage time series, a multitude of hydrologic and environmental time series contain zero values. Thus, the methods of frequency analysis applicable to these time series may also be applicable to the damage time series. Haan ͑1977͒ discussed three methods for dealing with zero values in a data set. One method was to add a small amount to all the values in the data set and then fit a certain probability distribution to the data. Very little improvement in the accuracy of damage analysis was achieved by this method ͑Jennings and Benson 1969͒. The second method ignored the zero values that should not be ignored in the data and analyzed only nonzero values, but the actual statistical characteristics contributed by the zero values would be lost by this method. The third method was developed, based on the total probability theory. Jennings and Benson ͑1969͒ found that this method best fitted the data containing zero values.
Bao et al. ͑1987͒ considered the uncertainty of a flood magnitude estimated for a specified return period in evaluating annual expected flood damage by a damage function. They concluded that the effect of uncertainty in a flood magnitude estimate on the annual expected damage was quite significant and was sensitive to the sample size and the probability distribution used. Haimes and Lambert ͑1992͒ used the partitioned multiobjective risk method ͑PMRM͒ for flood risk analysis. They partitioned the probability axis into a set of ranges and generated conditional expectations of damage, given that the damage fell within a par-
1Research Assistant, Dept. of Civil and Environmental Engineering, Louisiana State Univ., Baton Rouge, LA 70803-6405.
2A. K. Barton Professor, Dept. of Civil and Environmental Engineering, Louisiana State Univ. Baton Rouge, LA 70803-6405. E-mail: cesing@lsu.edu
Note. Discussion open until August 1, 2005. Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this paper was submitted for review and possible publication on October 13, 2003; approved on July 5, 2004. This paper is part of the Journal of Hydrologic Engineering, Vol. 10, No. 2, March 1, 2005. ©ASCE, ISSN 1084-0699/2005/2-100–109/$25.00.
The objectives of this study are to demonstrate a frequency analysis of flood damage using order statistics, total probability, Box-Cox transformation, and the kinematic diffusion model; evaluate these methods using the flood-damage data of Alabama, Louisiana, Mississippi and Texas; and therefore recommend a method that might be suitable for damage analysis.