Incorporating uncertainty of distribution parameters due to sampling errors in flood‐damage‐reduction project evaluation

Su, Hsin Ting; Tung, Yeou‐Koung

doi:10.1002/wrcr.20116

Cited by 16 publications

(30 citation statements)

References 30 publications

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“…(1). Examples of cost-benefit analysis in the hydrologic/hydraulic context can be found in the literature (Bao et al, 1987;Ganoulis, 2003;Jonkman et al, 2004;Tung, 2005), with only a few of them accounting for uncertainty (Al-Futaisi and Stedinger, 1999;Su and Tung, 2013). Botto et al (2014) further demonstrated that the optimal design flood obtained from the cost-benefit analysis with linear cost and damage functions is equivalent to the design flood Q T obtained from the standard frequency analysis, provided that uncertainty is not accounted for and the ratio between d and c equals the return period T .…”

Section: Introductionmentioning

confidence: 99%

Technical note: Design flood under hydrological uncertainty

Botto

Ganora

Claps

et al. 2017

Hydrol. Earth Syst. Sci.

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Abstract. Planning and verification of hydraulic infrastructures require a design estimate of hydrologic variables, usually provided by frequency analysis, and neglecting hydrologic uncertainty. However, when hydrologic uncertainty is accounted for, the design flood value for a specific return period is no longer a unique value, but is represented by a distribution of values. As a consequence, the design flood is no longer univocally defined, making the design process undetermined. The Uncertainty Compliant Design Flood Estimation (UNCODE) procedure is a novel approach that, starting from a range of possible design flood estimates obtained in uncertain conditions, converges to a single design value. This is obtained through a cost–benefit criterion with additional constraints that is numerically solved in a simulation framework. This paper contributes to promoting a practical use of the UNCODE procedure without resorting to numerical computation. A modified procedure is proposed by using a correction coefficient that modifies the standard (i.e., uncertainty-free) design value on the basis of sample length and return period only. The procedure is robust and parsimonious, as it does not require additional parameters with respect to the traditional uncertainty-free analysis. Simple equations to compute the correction term are provided for a number of probability distributions commonly used to represent the flood frequency curve. The UNCODE procedure, when coupled with this simple correction factor, provides a robust way to manage the hydrologic uncertainty and to go beyond the use of traditional safety factors. With all the other parameters being equal, an increase in the sample length reduces the correction factor, and thus the construction costs, while still keeping the same safety level.

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Section: Introductionmentioning

confidence: 99%

Technical note: Design flood under hydrological uncertainty

Botto

Ganora

Claps

et al. 2017

Hydrol. Earth Syst. Sci.

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“…The expected (mean) value of the annual net inundation reduction benefit ( B IR ) for each design alternative due to reduced flood damage, E [ B IR ], is used to represent the average economic return from implementing such an alternative of an FDR system. The value of E [ B IR ] for design alternative‐ A i can be computed by (Su and Tung, )

\begin{matrix} E [B_{I R, A_{i}} | n] = E_{Q} [E_{Q_{T}} [D_{w / o - w / A_{i}} (Q_{T}) | n], Q_{T} = Q] \\ = \int_{Q} [true {false\int}_{Q_{T}} ([], D_{w false/ o - w false/ A_{i}} ((), q_{T})) h_{Q_{T}} ((), q_{T} false| n) \cdot d q_{T}] f_{Q} (q) d q \end{matrix}

where

D_{w false/ o - w false/, A_{i}} ((), q_{T}) = D_{w false/ o, A_{i}} ((), q_{T}) - D_{w false/, A_{i}} ((), q_{T})

, with

D_{w false/ o, A_{i}} ((), q_{T})

and

D_{w false/, A_{i}} ((), q_{T})

, respectively, being the damage functions under the conditions of ‘ without ’ and ‘ with project alternative‐ A i ’; and

h_{Q_{T}} ((), q_{T} false| n)

is the sampling distribution of T ‐year flood quantile estimator,

…”

Section: Proposed Methods For Evaluating Decision Making Under Uncertamentioning

confidence: 99%

Effects of statistical sampling errors on flood‐damage‐reduction project evaluation

Tung

2016

J Flood Risk Management

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Risk‐based decision making of flood‐damage‐reduction (FDR) projects evaluates different design alternatives that have uncertain inundation–reduction benefits and costs. Uncertainties in FDR projects arise from, but are not limited to, the natural randomness of hydrological events, knowledge deficiency in hydrologic models, and the parameters, among others. This study investigates how the flood damage estimation is affected by the epistemic uncertainty resulting from using finite flood data in defining the flood‐frequency relationship and its effects on risk‐based decision making. A Monte Carlo simulation is applied in the study to simulate the epistemic uncertainty associated with the sampling error of the flood magnitude. The model parameter uncertainty is explicitly considered in the estimation of statistical features of flood damage. A recently developed decision rule on the basis of expected opportunity loss (EOL) is applied to the risk‐based evaluation of the relative merits of several competing flood mitigation projects. EOL‐based decision rule has the advantages of considering a decision maker's risk‐aversion attitude and incorporating more complete statistical features of project outcomes, including their correlations. The influence of the model parameter uncertainty on the project evaluation results is examined through an example FDR project with five design alternatives in which flood magnitude follows a Gumbel distribution.

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“…Steps (a)–(d) can be repeated to reduce the uncertainty of total cost when new data or distribution models are included. Compared to previous methods [e.g., Su and Tung , , ; Botto et al ., ], this new IPDF approach provides the upper and lower bounds of minimum total cost for a specific T year design flood, as a result of considering different types of epistemic uncertainties. Details of each component are presented in the following subsections.…”

Section: Imprecise Probabilistic Framework For Design Flood Estimationmentioning

confidence: 96%

“…Conventionally, flood frequency analysis (FFA) is used to estimate design floods, i.e., fitting probability distribution functions (PDFs) to observed flood data and deriving a design flood discharge through the extrapolation of the upper distribution tail to specified low exceedance probabilities [ Merz and Blöschl , ]. Recently, cost‐benefit analysis has been incorporated into FFA to compare different design floods and obtain a cost‐effective design value [ Tung and Mays , ; Bao et al ., ; Ganoulis , ; Jonkman et al ., ; Abrishamchi et al ., ; Rossi et al ., ; Su and Tung , , ; Botto et al ., ]. It has been proven that the design flood value calculated using cost‐benefit analysis with the assumption of liner damage and cost functions is equivalent to the flood value from the conventional FFA method [ Botto et al ., ].…”

Section: Introductionmentioning

confidence: 99%

“…The inherent variability of flood events which is of aleatory uncertainty in nature is represented using a PDF. Significant uncertainties exist regarding the PDF derivation, such as the use of insufficient historical data, selection of PDFs, and estimation of PDF parameters; most of these uncertainties are epistemic in nature and related to imprecise and incomplete knowledge about flood systems [ Merz and Thieken , ; Fu et al ., ; Su and Tung , ].…”

Section: Introductionmentioning

confidence: 99%

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Imprecise probabilistic estimation of design floods with epistemic uncertainties

Zhang

et al. 2016

Water Resources Research

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An imprecise probabilistic framework for design flood estimation is proposed on the basis of the Dempster-Shafer theory to handle different epistemic uncertainties from data, probability distribution functions, and probability distribution parameters. These uncertainties are incorporated in cost-benefit analysis to generate the lower and upper bounds of the total cost for flood control, thus presenting improved information for decision making on design floods. Within the total cost bounds, a new robustness criterion is proposed to select a design flood that can tolerate higher levels of uncertainty. A variance decomposition approach is used to quantify individual and interactive impacts of the uncertainty sources on total cost. Results from three case studies, with 127, 104, and 54 year flood data sets, respectively, show that the imprecise probabilistic approach effectively combines aleatory and epistemic uncertainties from the various sources and provides upper and lower bounds of the total cost. Between the total cost and the robustness of design floods, a clear trade-off which is beyond the information that can be provided by the conventional minimum cost criterion is identified. The interactions among data, distributions, and parameters have a much higher contribution than parameters to the estimate of the total cost. It is found that the contributions of the various uncertainty sources and their interactions vary with different flood magnitude, but remain roughly the same with different return periods. This study demonstrates that the proposed methodology can effectively incorporate epistemic uncertainties in cost-benefit analysis of design floods.

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Incorporating uncertainty of distribution parameters due to sampling errors in flood‐damage‐reduction project evaluation

Cited by 16 publications

References 30 publications

Technical note: Design flood under hydrological uncertainty

Technical note: Design flood under hydrological uncertainty

Effects of statistical sampling errors on flood‐damage‐reduction project evaluation

Imprecise probabilistic estimation of design floods with epistemic uncertainties

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