scholarly journals Statistical Estimates of PMP Values

1994 ◽  
Vol 25 (4) ◽  
pp. 301-312 ◽  
Author(s):  
Jónas Elíasson
Keyword(s):  
Statistical Methods ◽  
Return Period ◽  
The Other ◽  
Statistical Distributions ◽  
Return Periods ◽  
Statistical Estimates ◽  
High Return ◽  
Bounded Data ◽  
Limiting Value

The article discusses two statistical methods to estimate PMP values, the Hershfield and the NERC methods. Neither method offers any explanation why the PMP values can be calculated by the use of unbounded statistical distributions, but both methods include the use of envelope curves that are not independent of the region. Bounded data that fits an unbounded distribution must deviate from the distribution for high return periods and tend to a limiting value, and then there exists, a limiting reduced variate that can be used to find the PMP value. When the distribution is EV1, the limiting reduced variate can be defined by a mapping transformation, or by cutting off the distribution. It is shown that when Hershfield or NERC methods are used, the limiting reduced variate is included in the PMP values and can be separated from regional parameters. It is suggested that the limiting reduced variate, that depends solely on return period, may more easily be transferred between regions than the other parameters. This may be a great help in finding PMP values in regions where observations are not extensive enough to define limiting return periods with necessary certainty. A case study with data from Iceland demonstrates, that using the limiting reduced variate, similarities emerge in the Icelandic data and the NERC PMP that justify the acceptance of the NERC method.

scholarly journals Global flood hazard map and exposed GDP comparison: a China case study

2020 ◽  
Author(s):  
Jerom P. M. Aerts ◽  
Steffi Uhlemann-Elmer ◽  
Dirk Eilander ◽  
Philip J. Ward
Keyword(s):  
Return Period ◽  
Flood Hazard ◽  
Regional Scale ◽  
Flood Protection ◽  
Economic Losses ◽  
Return Periods ◽  
Hazard Maps ◽  
High Exposure ◽  
Pluvial Flooding

Abstract. Floods are among the most frequent and damaging natural hazard events in the world. In 2016, economic losses from flooding amounted to $56 bn globally, of which $20 bn occurred in China (Munich Re, 2017). National or regional scale mapping of flood hazard is at present providing an inconsistent and incomplete picture of floods. Over the past decade global flood hazard models have been developed and continuously improved. There is now a significant demand for testing of the global hazard maps generated by these models in order to understand their applicability for international risk reduction strategies and for reinsurance portfolio risk assessments using catastrophe models. We expand on existing methods for comparing global hazard maps and analyse 8 global flood models (GFMs) that represent the current state of the global flood modelling community. We apply our comparison to China as a case study and, for the first time, we include industry models, pluvial flooding, and flood protection standards in the analysis. We find substantial variability between the flood hazard maps in modelled inundated area and exposed GDP across multiple return periods (ranging from 5 to 1500 years) and in expected annual exposed GDP. For example, for the 100 year return period undefended (assuming no flood protection) hazard maps the percentage of total affected GDP of China ranges between 4.4 % and 10.5 % for fluvial floods. For the majority of the GFMs we see only a small increase in inundated area or exposed GDP for high return period undefended hazard maps compared to low return periods, highlighting major limitations in the models’ resolution and their output. The inclusion of industry models which currently model flooding at higher spatial resolution, and which additionally include pluvial flooding, strongly improves the comparison and provides important new benchmarks. Pluvial flooding can increase the expected annual exposed GDP by as much as 1.3 % points. Our study strongly highlights the importance of flood defenses for a realistic risk assessment in countries like China that are characterized by high concentrations of exposure. Even an incomplete (1.74 % of area of China) but locally detailed layer of structural defenses in high exposure areas reduces the expected annual exposed GDP to fluvial and pluvial flooding from 4.1 % to 2.8 %.

scholarly journals Modelling of rainfall intensity in a watershed: A case study in Amprong watershed, Kedungkandang, Malang, East Java of Indonesia

2018 ◽  
Vol 38 (1) ◽  
pp. 75-84
Author(s):  
Lily Montarcih Limantara ◽  
Donny H. Harisuseno ◽  
Vita A.K. Dewi
Keyword(s):  
Return Period ◽  
Rainfall Intensity ◽  
Negative Impact ◽  
Mean Absolute Error ◽  
Absolute Error ◽  
Equation Model ◽  
The Other ◽  
Average Value ◽  
Rainfall Occurrence

AbstractAnalysis of rainfall intensity with specific probability is very important to control the negative impact of rainfall occurrence. Rainfall intensity (I), probability (p) and return period (T) are very important variables for the discharge analysis. There are several methods to estimate rainfall intensity, such as Talbot, Sherman, and Ishiguro. The aim of this research is to develop equation model which can predict rainfall intensity with specific duration and probability. The equation model is compared with the other methods. The result of rainfall intensity model with the value of correlation >0.94 and Nash–Sutcliffe coefficient >99 is quite good enough if compared with the observation result. For specific return period, the modelling result is less accurate which is most likely caused by election of duration. Advanced research in other location indicates that short duration gives the better result for rainfall intensity modelling, which is shown by the decreasing average value of mean absolute error (MAE) from 12.963 to 8.26.

Assessment of techniques to include historical information in flood frequency distributions for hydrological dam safety assessment

2021 ◽  
Author(s):  
Enrique Soriano Martín ◽  
Antonio Jiménez ◽  
Luis Mediero
Keyword(s):  
Return Period ◽  
Uncertainty Reduction ◽  
Flood Frequency ◽  
Dam Safety ◽  
Return Periods ◽  
Historical Information ◽  
Probability Weighted Moments ◽  
High Return ◽  
Partial Probability ◽  
Quantile Estimates

<p>Flood peak quantiles for return periods up to 10 000 years are required for dam design and safety assessment, though flood series usually have a record length of around 20-40 years that leads to a high uncertainty. The utility of historical data of flooding is generally recognised for estimating the magnitude of extreme events with return periods in excess of 100 years. Therefore, historical information can be incorporated in flood frequency analyses to reduce uncertainties in high return period flood quantile estimates that are used in hydrological dam safety analyses.</p><p>This study assesses a set of existing techniques to incorporate historical information of flooding in extreme frequency analyses, focusing on their reliability and uncertainty reduction for high return periods that are used for dam safety analysis. Monte Carlo simulations are used to assess both the reliability and uncertainty in high return period quantile estimates. Varying lengths in the historical (Nh = 100 and 200 years) and systematic (Ns = 20, 40 and 60 years) periods are considered. In addition, a varying number of known flood magnitudes that exceed a given perception threshold in the historical period are also considered (k = 1-2). The values of Nh, Ns and k used in the study are the most usual in practice.</p><p>The reliability and uncertainty reduction in flood quantile estimates for each technique depend on the statistical properties of flood series. Therefore, a set of feasible combinations of L-coefficient of variation (L-CV) and skewness (L-CS) values should be considered. The analysis aims to understand how each technique behaves in terms of flood quantile reliability and uncertainty reduction depending on the L-moment statistics of flood series. In this study, L-CV and L-CS regional values in the 29 homogeneous regions identified in Spain for developing the national map of flood quantiles by the Centre for Hydrographic Studies of CEDEX are considered.</p><p>The results show that the maximum likelihood estimator (MLE) and weighted moments (WM) techniques show the best results in the regions with small L-CS values. However, the biased partial probability weighted moments (BPPWM) technique shows the best results in the regions with high L-CS values. While the expected moments algorithm (EMA) tends to underestimate flood quantiles for high return periods, the unbiased partial probability weighted moments (UPPWM) technique tends to overestimate them. In addition, including historical information of flooding in flood frequency analyses improves flood quantile estimates in most cases regardless the technique that is used. Uncertainty reduction in high return period flood quantile estimates are higher for short systematic time series, regions with high L-CS values and long historical periods.</p><p><strong>Acknowledgments:</strong> This research has been supported by the project SAFERDAMS (PID2019-107027RB-I00) funded by the Spanish Ministry of Science and Innovation.</p>

Impact of river confluences on return periods of large floods

2020 ◽  
Author(s):  
Björn Guse ◽  
Luzie Wietzke ◽  
Sophie Ullrich ◽  
Bruno Merz ◽  
Sergiy Vorogushyn
Keyword(s):  
River Basin ◽  
Triple Point ◽  
Return Period ◽  
Return Periods ◽  
Flood Wave ◽  
Main River ◽  
High Return ◽  
Flood Magnitude ◽  
River Confluences ◽  
The Impact

<p>The severity of floods is not only affected by the physiogeographic characteristics and the meteorological conditions of the catchment, but also by the river network. If a flood occurs at the same time in tributary and main river, the tributary flood wave can amplify the flood wave in the main river. To investigate the impact of flood wave superposition, the 6-10 largest floods in the four main German river basins (Danube, Elbe, Rhine, Weser) are analyzed. The flood waves are tracked along the river course. Flood magnitude and flood timing are analyzed at each triple point. A triple point consists of the hydrological stations in the tributary and in the main river (upstream and downstream of the confluence). The return periods are calculated separately at each triple point for all three hydrological stations. In addition, changes in the return periods along a river course are analyzed for each flood event. The flood magnitudes and their return periods are compared with the spatiotemporal precipitation distributions and other influencing factors. The results show that the contribution of the different confluences to the flood severity at the main river is event-specific. Partly, the return period is only high at the lower parts of the river basin, partly a high return period in the upper parts of the river basin does not lead to a high return period downstream.</p>

scholarly journals Estimation of high return period flood quantiles using additional non-systematic information with upper bounded statistical models

2010 ◽  
Vol 14 (12) ◽  
pp. 2617-2628 ◽  
Author(s):  
B. A. Botero ◽  
F. Francés
Keyword(s):  
Return Period ◽  
Robustness Analysis ◽  
Distribution Functions ◽  
Systematic Information ◽  
Estimation Uncertainty ◽  
Upper Limit ◽  
High Return ◽  
Probable Maximum Flood ◽  
Quantile Estimates

Abstract. This paper proposes the estimation of high return period quantiles using upper bounded distribution functions with Systematic and additional Non-Systematic information. The aim of the developed methodology is to reduce the estimation uncertainty of these quantiles, assuming the upper bound parameter of these distribution functions as a statistical estimator of the Probable Maximum Flood (PMF). Three upper bounded distribution functions, firstly used in Hydrology in the 90's (referred to in this work as TDF, LN4 and EV4), were applied at the Jucar River in Spain. Different methods to estimate the upper limit of these distribution functions have been merged with the Maximum Likelihood (ML) method. Results show that it is possible to obtain a statistical estimate of the PMF value and to establish its associated uncertainty. The behaviour for high return period quantiles is different for the three evaluated distributions and, for the case study, the EV4 gave better descriptive results. With enough information, the associated estimation uncertainty for very high return period quantiles is considered acceptable, even for the PMF estimate. From the robustness analysis, the EV4 distribution function appears to be more robust than the GEV and TCEV unbounded distribution functions in a typical Mediterranean river and Non-Systematic information availability scenario. In this scenario and if there is an upper limit, the GEV quantile estimates are clearly unacceptable.

scholarly journals Estimation of high return period flood quantiles using additional non-systematic information with upper bounded statistical models

2010 ◽  
Vol 7 (4) ◽  
pp. 5413-5440 ◽  
Author(s):  
B. A. Botero ◽  
F. Francés
Keyword(s):  
Return Period ◽  
Robustness Analysis ◽  
Distribution Functions ◽  
Statistical Estimator ◽  
Systematic Information ◽  
Estimation Uncertainty ◽  
High Return ◽  
Probable Maximum Flood ◽  
Flood Quantiles

Abstract. This paper proposes the estimation of high return period quantiles using upper bounded distribution functions with Systematic and additional Non-Systematic information. The aim of the developed methodology is to reduce the estimation uncertainty of these quantiles, assuming the upper bound parameter of these distribution functions as a statistical estimator of the Probable Maximum Flood (PMF). Three upper bounded distribution functions, firstly used in Hydrology in the 90's (referred to in this work as TDF, LN4 and EV4), were applied at the Jucar River in Spain. Different methods to estimate the upper limit of these distribution functions have been merged with the Maximum Likelihood (ML) method. Results show that it is possible to obtain a statistical estimate of the PMF value and to establish its associated uncertainty. The behaviour for high return period quantiles is different for the three evaluated distributions and, for the case study, the EV4 gave better descriptive results. With enough information, the associated estimation uncertainty is considered acceptable, even for the PMF estimate. From the robustness analysis, EV4 distribution function appears to be more robust than the GEV and TCEV unbounded distribution functions in a typical Mediterranean river and Non-Systematic information availability scenario.

scholarly journals Assessment and comparison of extreme sea levels and waves during the 2013/2014 storm season in two UK coastal regions

2015 ◽  
Vol 3 (4) ◽  
pp. 2665-2708 ◽  
Author(s):  
M. P. Wadey ◽  
J. M. Brown ◽  
I. D. Haigh ◽  
T. Dolphin ◽  
P. Wisse
Keyword(s):  
Sea Level ◽  
Return Period ◽  
Data Sets ◽  
Return Periods ◽  
National Scale ◽  
Sea Levels ◽  
Extreme Sea Levels ◽  
Study Sites

Abstract. The extreme sea levels and waves experienced around the UK's coast during the 2013/2014 winter caused extensive coastal flooding and damage. In such circumstances, coastal managers seek to place such extremes in relation to the anticipated standards of flood protection, and the long-term recovery of the natural system. In this context, return periods are often used as a form of guidance. We therefore provide these levels for the winter storms, as well as discussing their application to the given data sets and case studies (two UK case study sites: Sefton, northwest England; and Suffolk, east England). We use tide gauge records and wave buoy data to compare the 2013/2014 storms with return periods from a national dataset, and also generate joint probabilities of sea level and waves, incorporating the recent events. The UK was hit at a national scale by the 2013/2014 storms, although the return periods differ with location. We also note that the 2013/2014 high water and waves were extreme due to the number of events, as well as the extremity of the 5 December 2013 "Xaver" storm, which had a very high return period at both case study sites. Our return period analysis shows that the national scale impact of this event is due to its coincidence with spring high tide at multiple locations as the tide and storm propagated across the continental shelf. Given that this event is such an outlier in the joint probability analyses of these observed data sets, and that the season saw several events in close succession, coastal defences appear to have provided a good level of protection. This type of assessment should be recorded alongside details of defence performance and upgrade, with other variables (e.g. river levels at estuarine locations) included and appropriate offsetting for linear trends (e.g. mean sea level rise) so that the storm-driven component of coastal flood events can be determined. Local offsetting of the mean trends in sea level allows long-term comparison of storm severity and also enables an assessment of how sea level rise is influencing return levels over time, which is important when considering long-term coastal resilience in strategic management plans.

scholarly journals Multivariate return periods of sea storms for coastal erosion risk assessment

2012 ◽  
Vol 12 (8) ◽  
pp. 2699-2708 ◽  
Author(s):  
S. Corbella ◽  
D. D. Stretch
Keyword(s):  
Return Period ◽  
Coastal Erosion ◽  
Design Method ◽  
Return Periods ◽  
Current Form ◽  
Erosion Risk ◽  
Storm Characteristics ◽  
Relationship Of ◽  
The Relationship

Abstract. The erosion of a beach depends on various storm characteristics. Ideally, the risk associated with a storm would be described by a single multivariate return period that is also representative of the erosion risk, i.e. a 100 yr multivariate storm return period would cause a 100 yr erosion return period. Unfortunately, a specific probability level may be associated with numerous combinations of storm characteristics. These combinations, despite having the same multivariate probability, may cause very different erosion outcomes. This paper explores this ambiguity problem in the context of copula based multivariate return periods and using a case study at Durban on the east coast of South Africa. Simulations were used to correlate multivariate return periods of historical events to return periods of estimated storm induced erosion volumes. In addition, the relationship of the most-likely design event (Salvadori et al., 2011) to coastal erosion was investigated. It was found that the multivariate return periods for wave height and duration had the highest correlation to erosion return periods. The most-likely design event was found to be an inadequate design method in its current form. We explore the inclusion of conditions based on the physical realizability of wave events and the use of multivariate linear regression to relate storm parameters to erosion computed from a process based model. Establishing a link between storm statistics and erosion consequences can resolve the ambiguity between multivariate storm return periods and associated erosion return periods.

scholarly journals A systematic comparison of statistical and hydrological methods for design flood estimation

2019 ◽  
Vol 50 (6) ◽  
pp. 1665-1678 ◽  
Author(s):  
Kenechukwu Okoli ◽  
Maurizio Mazzoleni ◽  
Korbinian Breinl ◽  
Giuliano Di Baldassarre
Keyword(s):  
Model Selection ◽  
Statistical Methods ◽  
Model Averaging ◽  
Return Periods ◽  
Rainfall Runoff ◽  
Design Flood ◽  
High Return ◽  
Flood Estimation ◽  
Rainfall Runoff Model ◽  
Runoff Model

Abstract We compare statistical and hydrological methods to estimate design floods by proposing a framework that is based on assuming a synthetic scenario considered as ‘truth’ and use it as a benchmark for analysing results. To illustrate the framework, we used probability model selection and model averaging as statistical methods, while continuous simulations made with a simple and relatively complex rainfall–runoff model are used as hydrological methods. The results of our numerical exercise show that design floods estimated by using a simple rainfall–runoff model have small parameter uncertainty and limited errors, even for high return periods. Statistical methods perform better than the linear reservoir model in terms of median errors for high return periods, but their uncertainty (i.e., variance of the error) is larger. Moreover, selecting the best fitting probability distribution is associated with numerous outliers. On the contrary, using multiple probability distributions, regardless of their capability in fitting the data, leads to significantly fewer outliers, while keeping a similar accuracy. Thus, we find that, among the statistical methods, model averaging is a better option than model selection. Our results also show the relevance of the precautionary principle in design flood estimation, and thus help develop general recommendations for practitioners and experts involved in flood risk reduction.

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