Estimating flooding extent at high return period for ungauged braided systems using remote sensing: a case study of Cuvelai Basin, Angola

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.

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

Hydrology and Earth System Sciences Discussions ◽

10.5194/hessd-7-5413-2010 ◽

2010 ◽

Vol 7 (4) ◽

pp. 5413-5440 ◽

Cited By ~ 1

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.

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Statistical Estimates of PMP Values

Hydrology Research ◽

10.2166/nh.1994.0010 ◽

1994 ◽

Vol 25 (4) ◽

pp. 301-312 ◽

Cited By ~ 10

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.

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