An Adaptive Metropolis-Hastings Optimization Algorithm of Bayesian Estimation in Non-Stationary Flood Frequency Analysis

Xu, Wentao; Jiang, Cong; Yan, Lei; Li, Lingqi; Liu, Shuonan

doi:10.1007/s11269-017-1873-5

Cited by 28 publications

(16 citation statements)

References 41 publications

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“…A well-known approach in uncertainty analysis of model parameters is the behavioral approach [10,11]. Examples of this approach are as follows: Generalized Likelihood Uncertainty Estimation (GLUE) method [12][13][14]; Bayesian method using Metropolis-Hasting algorithm and Adaptive Metropolis (AM) algorithm [1,15,16]; and Markov chain Monte Carlo [17][18][19]. In this approach, the input and output errors are ignored and the threshold of objective functions for selecting parameter values were determined.Using the threshold to select parameter values was developed in the GLUE method, firstly introduced by Beven and Binley [12].…”

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confidence: 99%

Uncertainty Estimation Using the Glue and Bayesian Approaches in Flood Estimation: A case Study—Ba River, Vietnam

Thi

Ball

Dao

2018

Water

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In the last few decades tremendous progress has been made in the use of catchment models for the analysis and understanding of hydrologic systems. A common application involves the use of these models to predict flows at catchment outputs. However, the outputs predicted by these models are often deterministic because they focused only on the most probable forecast without an explicit estimate of the associated uncertainty. This paper uses Bayesian and Generalized Likelihood Uncertainty Estimation (GLUE) approaches to estimate uncertainty in catchment modelling parameter values and uncertainty in design flow estimates. Testing of join probability of both these estimates has been conducted for a monsoon catchment in Vietnam. The paper focuses on computational efficiency and the differences in results, regardless of the philosophies and mathematical rigor of both methods. It was found that the application of GLUE and Bayesian techniques resulted in parameter values that were statistically different. The design flood quantiles estimated by the GLUE method were less scattered than those resulting from the Bayesian approach when using a closer threshold value (1 standard deviation departed from the mean). More studies are required to evaluate the impact of threshold in GLUE on design flood estimation.2 of 15 applied the Bayesian inference to estimate rainfall uncertainty characterized by two parameters k and rMult for Abercrombie River's daily flow. Rainfall flood events were simulated as random processes (e.g., [1,[4][5][6][7][8][9]). The model parameter error and output error, in this case, were combined into a single random process.Model error: The model error is estimated mainly by analysis of model parameter uncertainty. A well-known approach in uncertainty analysis of model parameters is the behavioral approach [10,11]. Examples of this approach are as follows: Generalized Likelihood Uncertainty Estimation (GLUE) method [12][13][14]; Bayesian method using Metropolis-Hasting algorithm and Adaptive Metropolis (AM) algorithm [1,15,16]; and Markov chain Monte Carlo [17][18][19]. In this approach, the input and output errors are ignored and the threshold of objective functions for selecting parameter values were determined.Using the threshold to select parameter values was developed in the GLUE method, firstly introduced by Beven and Binley [12]. This procedure recognizes the equifinality of different sets of parameters in the generation of acceptable catchment response. The parameters producing acceptable responses are assigned "behavioural" and will be accepted [12]. Identifying the threshold in the GLUE method is based on an acceptable range of performance measures such as Nash-Sutcliffe Efficiency (E), Root Mean Square Errors, percent bias, and correlation coefficient (e.g., [20,21]. For example, in the hydrograph measure of fit using Nash-Sutcliffe Efficiency (E), the range of E was established. Cameron [21] and Zhao [20] selected threshold of 0.7, Shen [22] accepted the threshold of 0.5. In design flood quantile...

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Uncertainty Estimation Using the Glue and Bayesian Approaches in Flood Estimation: A case Study—Ba River, Vietnam

Thi

Ball

Dao

2018

Water

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“…Flood events can be described in terms of the multivariate characteristic variables of peak discharge, water stage and suspended sediment load, which are all relevant to risk analyses. Univariate frequency analysis for these hydrological variables mentioned above can be found in many literatures [2][3][4][5]. Unlike the common frequency distribution, theoretically derived distributions of flood peak are constructed based on dominant runoff generation mechanisms [6].…”

Section: Introductionmentioning

confidence: 99%

Nonstationary Analysis for Bivariate Distribution of Flood Variables in the Ganjiang River Using Time-Varying Copula

Wen

Jiang

2019

Water

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Nonstationarity of univariate flood series has been widely studied, while nonstationarity of some multivariate flood series, such as discharge, water stage, and suspended sediment concentrations, has been studied rarely. This paper presents a procedure for using the time-varying copula model to describe the nonstationary dependence structures of two correlated flood variables from the same flood event. In this study, we focus on multivariate flood event consisting of peak discharge (Q), peak water stage (Z) and suspended sediment load (S) during the period of 1964–2013 observed at the Waizhou station in the Ganjiang River, China. The time-varying copula model is employed to analyze bivariate distributions of two flood pairs of (Z-Q) and (Z-S). The main channel elevation (MCE) and the forest coverage rate (FCR) of the basin are introduced as the candidate explanatory variables for modelling the nonstationarities of both marginal distributions and dependence structure of copula. It is found that the marginal distributions for both Z and S are nonstationary, whereas the marginal distribution for Q is stationary. In particular, the mean of Z is related to MCE, and the mean and variance of S are related to FCR. Then, time-varying Frank copula with MCE as the covariate has the best performance in fitting the dependence structures of both Z-Q and Z-S. It is indicated that the dependence relationships are strengthen over time associated with the riverbed down-cutting. Finally, the joint and conditional probabilities of both Z-Q and Z-S obtained from the best fitted bivariate copula indicate that there are obvious nonstationarity of their bivariate distributions. This work is helpful to understand how human activities affect the bivariate flood distribution, and therefore provides supporting information for hydraulic structure designs under the changing environments.

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“…However, the stationary assumption is being increasingly challenged by climate change (Milly et al, 2008;Li et al, 2017;Rolim et al, 2017;Yan et al, 2017a;Xu et al, 2018;Zhang et al, 2018). design rainfall) derived from the probability distribution of extreme rainfall, which is based on historical rainfall records and assumed to be stationary.…”

Section: Introductionmentioning

confidence: 99%

“…design rainfall) derived from the probability distribution of extreme rainfall, which is based on historical rainfall records and assumed to be stationary. However, the stationary assumption is being increasingly challenged by climate change (Milly et al, 2008;Li et al, 2017;Rolim et al, 2017;Yan et al, 2017a;Xu et al, 2018;Zhang et al, 2018). It is anticipated that the frequency and magnitude of extreme rainfall will increase due to global climate change (Intergovernmental Panel on Climate Change (IPCC), 2013).…”

Section: Introductionmentioning

confidence: 99%

Impacts of Climate Change on Urban Extreme Rainfall and Drainage Infrastructure Performance: A Case Study in Wuhan City, China

Xiong

Yan

et al. 2018

Irrigation and Drainage

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The design of stormwater drainage infrastructure in urban areas in China is based on the statistical stationary assumption of probability distribution of extreme rainfall, which is being increasingly challenged by climate change. However, quantitative assessment of the performance of urban drainage systems in response to climate change with the latest emission scenarios of the Coupled Model Intercomparison Project Phase 5 in China is quite limited. This study aims to investigate potential changes of extreme rainfall and their influence on drainage infrastructure in a representative urban area in Wuhan city, China. The Storm Water Management Model is established to investigate the response of drainage infrastructure to future design rainfall. It is found that the probability distribution of extreme rainfall for two historical sub‐periods (1961–1985 and 1986–2005) has changed, especially in the head and tail of the frequency curves. Furthermore, the design rainfall with return periods of 2, 3, 4 and 5 years increases more significantly than those of 10 and 20 years. Consequently, the incapability of the current drainage infrastructure in the study area is aggravated. Moreover, the results of SWMM modelling provide detailed information about the performance of current drainage infrastructure, which can provide technical support for future modifications of the current drainage infrastructure of the study area. © 2018 John Wiley & Sons, Ltd.

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An Adaptive Metropolis-Hastings Optimization Algorithm of Bayesian Estimation in Non-Stationary Flood Frequency Analysis

Cited by 28 publications

References 41 publications

Uncertainty Estimation Using the Glue and Bayesian Approaches in Flood Estimation: A case Study—Ba River, Vietnam

Uncertainty Estimation Using the Glue and Bayesian Approaches in Flood Estimation: A case Study—Ba River, Vietnam

Nonstationary Analysis for Bivariate Distribution of Flood Variables in the Ganjiang River Using Time-Varying Copula

Impacts of Climate Change on Urban Extreme Rainfall and Drainage Infrastructure Performance: A Case Study in Wuhan City, China

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