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 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.

Modelling uncertainty of flood quantile estimations at ungauged sites by Bayesian networks

2013 ◽  
Vol 16 (4) ◽  
pp. 822-838 ◽  
Author(s):  
D. Santillán ◽  
L. Mediero ◽  
L. Garrote
Keyword(s):  
Bayesian Networks ◽  
Explanatory Variables ◽  
Modelling Uncertainty ◽  
Ungauged Sites ◽  
Estimation Uncertainty ◽  
Linear Relationships ◽  
Flood Quantiles ◽  
Quantile Estimations ◽  
Probabilistic Nature

Prediction at ungauged sites is essential for water resources planning and management. Ungauged sites have no observations about the magnitude of floods, but some site and basin characteristics are known. Regression models relate physiographic and climatic basin characteristics to flood quantiles, which can be estimated from observed data at gauged sites. However, some of these models assume linear relationships between variables and prediction intervals are estimated by the variance of the residuals in the estimated model. Furthermore, the effect of the uncertainties in the explanatory variables on the dependent variable cannot be assessed. This paper presents a methodology to propagate the uncertainties that arise in the process of predicting flood quantiles at ungauged basins by a regression model. In addition, Bayesian networks (BNs) were explored as a feasible tool for predicting flood quantiles at ungauged sites. Bayesian networks benefit from taking into account uncertainties thanks to their probabilistic nature. They are able to capture non-linear relationships between variables and they give a probability distribution of discharge as a result. The proposed BN model can be applied to supply the estimation uncertainty in national flood discharge mappings. The methodology was applied to a case study in the Tagus basin in Spain.

scholarly journals A contribution to improved flood magnitude estimation in base of palaeoflood record and climatic implications – Guadiana River (Iberian Peninsula)

2009 ◽  
Vol 9 (1) ◽  
pp. 229-239 ◽  
Author(s):  
J. A. Ortega ◽  
G. Garzón
Keyword(s):  
Return Period ◽  
Distribution Functions ◽  
Rating Curve ◽  
Systematic Information ◽  
High Magnitude ◽  
Data Record ◽  
Flood Magnitude ◽  
The Moment ◽  
Hydrologic Conditions ◽  
Frequency Curves

Abstract. The Guadiana River has a significant record of historical floods, but the systematic data record is only 59 years. From layers left by ancient floods we know about we can add new data to the record, and we can estimate maximum discharges of other floods only known by the moment of occurrence and by the damages caused. A hydraulic model has been performed in the area of Pulo de Lobo and calibrated by means of the rating curve of Pulo do Lobo Station. The palaeofloods have been dated by means of 14C y 137Cs. As non-systematic information has been used in order to calculate distribution functions, the quantiles have changed with respect to the same function when using systematic information. The results show a variation in the curves that can be blamed on the human transformations responsible for changing the hydrologic conditions as well as on the latest climate changes. High magnitude floods are related to cold periods, especially at transitional moments of change from cold to warm periods. This tendency has changed from the last medium-high magnitude flood, which took place in a systematic period. Both reasons seem to justify a change in the frequency curves indicating a recent decrease in the return period of big floods over 8000 m3 s−1. The palaeofloods indicate a bigger return period for the same water level discharge thus showing the river basin reference values in its natural condition previous to the transformation of the basin caused by anthropic action.

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.

Robustness analysis: a case study

2003 ◽  
Author(s):  
J. Ackermann ◽  
H.Z. Hu ◽  
D. Kaesbauer
Keyword(s):  
Robustness Analysis

scholarly journals ESTIMATION OF WORST-CLASS TROPICAL CYCLONE AND STORM SURGE, AND ITS RETURN PERIOD -CASE STUDY FOR ISE BAY-

2015 ◽  
Vol 71 (2) ◽  
pp. I_1513-I_1518 ◽  
Author(s):  
Yoko SHIBUTANI ◽  
Sota NAKAJO ◽  
Nobuhito MORI ◽  
Sooyoul KIM ◽  
Hajime MASE
Keyword(s):  
Tropical Cyclone ◽  
Storm Surge ◽  
Return Period ◽  
Ise Bay

Reliability-based covariate analysis for complex systems in heterogeneous environment: Case study of mining equipment

2018 ◽  
Vol 233 (4) ◽  
pp. 593-604
Author(s):  
Amin Moniri-Morad ◽  
Mohammad Pourgol-Mohammad ◽  
Hamid Aghababaei ◽  
Javad Sattarvand
Keyword(s):  
Complex Systems ◽  
Cox Regression ◽  
Reliability Evaluation ◽  
Distribution Functions ◽  
Heterogeneous Environment ◽  
Mining Equipment ◽  
Data Set ◽  
Explanatory Variables ◽  
The Impact

Operational heterogeneity and harsh environment lead to major variations in production system performance and safety. Traditional probabilistic model is dealt with time-to-event data analysis, which does not have the capability of quantifying and simulation of these types of complexities. This research proposes an integrated methodology for analyzing the impact of dominant explanatory variables on the complex system reliability. A flexible parametric proportional hazards model is developed by focusing on standard parametric Cox regression model for reliability evaluation in complex systems. To achieve this, natural cubic splines are utilized to create a smooth and flexible baseline hazards function where the standard parametric distribution functions do not fit into the failure data set. A real case study is considered to evaluate the reliability for multi-component mechanical systems such as mining equipment. Different operational and environmental explanatory variables are chosen for the analysis process. Research findings revealed that precise estimation of the baseline hazards function is a major part of the reliability evaluation in heterogeneous environment. It is concluded that an appropriate maintenance strategy potentially mitigate the equipment failure intensity.

scholarly journals On the asymptotic behavior of flood peak distributions

2006 ◽  
Vol 10 (2) ◽  
pp. 233-243 ◽  
Author(s):  
E. Gaume
Keyword(s):  
Frequency Distribution ◽  
Return Period ◽  
Asymptotic Properties ◽  
Flood Frequency ◽  
Point Of View ◽  
Rainfall Runoff ◽  
New Approach ◽  
Flood Peak ◽  
Flood Quantiles ◽  
The Impact

Abstract. This paper presents some analytical results and numerical illustrations on the asymptotic properties of flood peak distributions obtained through derived flood frequency approaches. It confirms and extends the results of previous works: i.e. the shape of the flood peak distributions are asymptotically controlled by the rainfall statistical properties, given limited and reasonable assumptions concerning the rainfall-runoff process. This result is partial so far: the impact of the rainfall spatial heterogeneity has not been studied for instance. From a practical point of view, it provides a general framework for analysis of the outcomes of previous works based on derived flood frequency approaches and leads to some proposals for the estimation of very large return-period flood quantiles. This paper, focussed on asymptotic distribution properties, does not propose any new approach for the extrapolation of flood frequency distribution to estimate intermediate return period flood quantiles. Nevertheless, the large distance between frequent flood peak values and the asymptotic values as well as the simulations conducted in this paper help quantifying the ill condition of the problem of flood frequency distribution extrapolation: it illustrates how large the range of possibilities for the shapes of flood peak distributions is.

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