Peaks<scp>O</scp>ver<scp>T</scp>hreshold (<scp>POT</scp>): A methodology for automatic threshold estimation using goodness of fit<i>p</i>‐value

Solari, Sebastián; Egüen, Marta; Polo, María José; Losada, Miguel Á.

doi:10.1002/2016wr019426

Cited by 74 publications

(50 citation statements)

References 30 publications

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“…In general, a P value can be seen as a continuous measure of the compatibility of the data with the entire model (Greenland et al, ), but as far as we know, no theoretical argument has been provided to show that MAXPV will lead to better estimates, and its empirical behaviour has been studied in a limited number of situations (Solari et al, ). Because the P values p i are computed from nested samples (except perhaps some differences due to declustering), they are likely autocorrelated.…”

Section: Methodsologymentioning

confidence: 99%

“…Examples of such application were presented by Choulakian and Stephens (2001) on Canadian rivers and by Li, Cai, and Campbell (2005) on extreme precipitation in South-West Australia. However, according to Solari, Egüen, Polo, and Losada (2017), the range of valid thresholds derived from this strategy can be larger than what is practically acceptable, which motivated them to investigate the selection of thresholds associated with the highest P value. Their study showed that, in some situations, their approach led to higher and more relevant thresholds.…”

Section: Introductionmentioning

confidence: 99%

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Comparison of automatic procedures for selecting flood peaks over threshold based on goodness‐of‐fit tests

Durocher

Zadeh

Burn

et al. 2018

Hydrological Processes

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In comparison with the traditional analysis of annual maximums, the peaks over threshold method provides many advantages when performing flood frequency analysis and trend analysis. However, the choice of the threshold remains an important question without definite answers and common visual diagnostic tools are difficult to reproduce on a large scale. This study investigates the behaviour of some automatic methods for threshold selection based on the generalized Pareto model for flood peak exceedances of the threshold and the Anderson–Darling test for fitting this model. In particular, the choice of a critical significance level to define an interval of acceptable values is addressed. First, automatic methods are investigated using a simulation study to assess fitting and prediction performance in a controlled environment. It is shown that P values approximated by an existing table of critical values can speed up computation without affecting the quality of the outcomes. Second, a case study compares automatically and manually selected thresholds for 285 sites across Canada by flood regime and super regions based on site characteristics. Correspondences are examined in terms of prediction of flood quantiles and trend analysis. Results show that trend detection is sensitive to the threshold selection method when studying the evolution of the number of peaks per year. Finally, a hybrid method is developed to combine automatic methods and is calibrated on the basis of super regions. The outcomes of the hybrid method are shown to more closely reproduce the estimates of the manually selected thresholds while reducing the model uncertainty.

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Section: Methodsologymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Comparison of automatic procedures for selecting flood peaks over threshold based on goodness‐of‐fit tests

Durocher

Zadeh

Burn

et al. 2018

Hydrological Processes

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“…First, the interpretation of these plots is unclear in practice [17], and it is clearly difficult to determine which portion of the curve is completely linear. Second, graphical techniques cannot be automated and the uncertainty associated with threshold selection cannot be estimated [55]. Figure 2 shows a range of potential optimum threshold values, making the use of a single value from the range in the analysis subjective.…”

Section: Threshold Selection Methodsmentioning

confidence: 99%

Assessment of the Combined Effects of Threshold Selection and Parameter Estimation of Generalized Pareto Distribution with Applications to Flood Frequency Analysis

Gharib

Davies

Goss

et al. 2017

Water

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Abstract:Floods are costly natural disasters that are projected to increase in severity and frequency into the future. Exceedances over a high threshold and analysis of their distributions, as determined through the Peak Over Threshold (POT) method and approximated by a Generalized Pareto Distribution (GPD), respectively, are widely used for flood frequency analysis. This study investigates the combined effects of threshold selection and GPD parameter estimation on the accuracy of flood quantile estimates, and develops a new, widely-applicable framework that significantly improves the accuracy of flood quantile estimations. First, the performance of several parameter estimators (i.e., Maximum Likelihood; Probability Weighted Moments; Maximum Goodness of Fit; Likelihood Moment; Modified Likelihood Moment; and Nonlinear Weighted Least Square Error) for the GPD was compared through Monte Carlo simulation. Then, a calibrated Soil and Water Assessment Tool (SWAT) model for the province of Alberta, Canada, was used to reproduce daily streamflow series for 47 watersheds distributed across the province, and the POT was applied to each. The Goodness of Fit for the resulting flood frequency models was measured by the upper tail Anderson-Darling (AD) test and the root-mean-square error (RMSE) and demonstrated improvements for more than one-third of stations by averages of 65% (AD) and 47% (RMSE), respectively.

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“…An indicator for determining if a threshold was correctly selected is to use a goodness-of-fit test to verify that GPA is a proper 120 distribution (Davison and Smith, 1990). The p-value of such tests were used recently to develop automatic selection procedures based on the identification of the maximum p-value and the first threshold respecting a given significance level (Durocher et al, 2018b;Solari et al, 2017).…”

Section: Regions 105mentioning

confidence: 99%

Comparison of estimation methods for a nonstationary index-flood model in flood frequency analysis using peaks over threshold

Durocher¹,

Burn²,

Ashkar³

2019

Preprint

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Accurate estimation of flood frequency is crucial for designing safe infrastructures. To reduce model uncertainty, threshold modeling techniques are often useful in bringing more valuable flood information into the analysis than traditional models based on annual maximum 15 discharges. Due to climatic or anthropogenic causes, changes in flood magnitudes in many parts of the world have been observed and are expected to continue in the future. To characterize such changes, nonstationary models have focussed on the modeling of stations with long records, but in practice such models may be needed to improve the evaluation of flood risk for stations having shorter records. In this study, a nonstationary index-flood model for peaks over threshold 20is investigated to reduce model uncertainty. The assumption of an index-flood model is used to define a probability structure that is stable in time. This allows to extend existing (stationary) procedures to automatically calibrate the proposed model in an at-site and regional context. As part of this procedure, four estimators are investigated in a simulation study to determine which 3 perform best in different situations. Two methods are based on the combination of regression 25 techniques and L-moments, while the other two methods employ likelihood-based techniques. A case study of 425 stations in Canada is considered to verify if a nonstationary index-flood model using pooling groups that combine stationary and nonstationary stations can reduce the uncertainty of design levels associated with a finite reference period.

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PeaksOverThreshold (POT): A methodology for automatic threshold estimation using goodness of fitp‐value

Cited by 74 publications

References 30 publications

Comparison of automatic procedures for selecting flood peaks over threshold based on goodness‐of‐fit tests

Comparison of automatic procedures for selecting flood peaks over threshold based on goodness‐of‐fit tests

Assessment of the Combined Effects of Threshold Selection and Parameter Estimation of Generalized Pareto Distribution with Applications to Flood Frequency Analysis

Comparison of estimation methods for a nonstationary index-flood model in flood frequency analysis using peaks over threshold

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