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Application of Index Flood Approach in Regional Flood Estimation Using L-Moments in Both Fixed Region and Region of Influence Framework
Published in Saeid Eslamian, Faezeh Eslamian, Flood Handbook, 2022
Ayesha S. Rahman, Zaved K. Khan, Fazlul Karim, Saeid Eslamian
The performance of IFM is expected to be dependent on the degree of homogeneity of the proposed region. Numerous researchers have adopted homogeneity tests in RFFE [2,13,14,19–29]. For example, the method proposed in [2] is based on the sampling distribution of the standardized 10% AEP flood (Q10), assuming an Extreme Value 1 (EV1) distribution; whereas [27,30] presented a test based on the sampling distribution of Cv of the AM flood data. However, the problem with these distribution-specific tests is that, when the hypothesis of homogeneity is rejected, the group of sites can still be homogeneous with a different parent distribution [14]. A problem can also arise due to the adoption of conventional moments to estimate the parameters of the hypothesized distribution as these moments are subject to higher sampling variability due to the squaring and cubing of the flood observations. Also, in the case of the maximum likelihood method, a smaller size sample may under- or overestimate the parameters. Application of L-moments-based homogeneity analysis can be more effective in these cases as L-moments are analogous to conventional moments with measures of location (mean), scale (standard deviation), and shape (skewness and kurtosis) and do not involve squaring or cubing the observations. L-moments are linearly transformed probability-weighted moments (PWM) that can estimate the parameters of a distribution; this feature of the L-moments makes them more robust and less sensitive to outliers.
Groundwater Hydrology
Published in Mohammad Karamouz, Azadeh Ahmadi, Masih Akhbari, Groundwater Hydrology, 2020
Mohammad Karamouz, Azadeh Ahmadi, Masih Akhbari
L-moments are a sequence of statistics used to summarize theoretical probability distributions and observed samples. They are linear combinations of order statistics (L-statistics) analogous to ordinary moments, which are able to calculate quantities of standard deviation, skewness, and kurtosis. L-moment computes these quantities from the linear combinations of ordered values in the terms of L-scale, L-skewness, and L-kurtosis, respectively. The advantages of the L-moment method are as follows (Central Water Commission, 2010): Wider range of probability distributions could be characterized.Less sensitive to outlier data points.Less sensitive to sample sizes and populations.Better approximation of asymptotic normal distribution.
Peak period statistics associated with significant wave heights by conditional mean functions of the distributions
Published in C. Guedes Soares, T.A. Santos, Progress in Maritime Technology and Engineering, 2018
G. Muraleedharan, C. Lucas, C. Guedes Soares
L‐moments or linear combination of probability weighted moments (PWMs) form the basis of an elegant mathematical theory and it facilitates the estimation process. L‐moment methods are superior to MLE, and method of moments. L‐moment ratios measure the shape of a distribution independent of its scale of measurement. L‐moments are more robust to the presence of outliers in the data and are less subjected to bias in the estimation (Hosking and Wallis, 1997). Incorrect data values, outliers, trends and shifts in the mean of a sample can all be reflected in the L‐moments of the sample. The mean (Tp¯) $ (\overline{{T_{p} }} ) $ and average of the one‐third the highest peak periods (Tp(1/3)¯) $ (\overline{{T_{p(1/3)} }} ) $ are deduced from the Conditional Mean Functions of the distributions. Most probable maximum peak periods (Tp(mpm)) and mean maximum peak periods (Tp(max)¯) $ (\overline{{T_{{p( {\text{max }})}} }} ) $ are also estimated from the parametric relatLons derived from three‐parameter Weibull and generalized Pareto distributions.
Spatiotemporal analysis of monthly rainfall over Saudi Arabia and global teleconnections
Published in Geomatics, Natural Hazards and Risk, 2022
Amro Elfeki, Jarbou Bahrawi, Muhammad Latif, Abdelwaheb Hannachi
Figure 9a shows the L-moment diagram for L-skewness (L-Skew) and L-kurtosis (L-Kurt) ratios. Image (a) in the figure shows the dry season for all stations. The points are scattered and show different distributions (Person type III, generalized Pareto, and Log-normal) however the majority of the points are out of the regions of the distributions between the Pearson type III and the overall lower bound. However, for the wet season in image (b), the data in the overall stations seems to follow generalized extreme value as an upper boundary, Person type III, Log-normal, generalized logistic, and generalized Pareto. Image (c) shows the average over the 12 months for the 28 stations. Most of the data lie between the Patriot distribution and the overall lower bound. There is no obvious probability distribution since the data is averaged over the 12 months. However, for image (d), where the average is performed over all stations for each month, there is an obvious probability distribution for the wet season (January, February, March, April, May, November, and December) which is Person type III while there is no obvious probability distribution for the dry months (June, July, August, September, and October). This might be due to data scarcity in these months.
Evaluation of an urban drainage system using functional and structural resilience approach
Published in Urban Water Journal, 2022
Mitthan Lal Kansal, Deepak Singh Bisht
Extreme events, viz., severe storms, and floods frequently affect the hydraulic network. Probability distribution techniques can be used to estimate the frequency of occurrence of extreme events. In the present study, frequency analysis of extreme events, defined by annual maximum rainfall values, to estimate design storm is carried out using EV1, GEV and LP3 distributions. The GEV and LP3 are three parameter distributions (i.e. scale, location and shape), whereas EV1 only has two parameters (i.e. scale and location). The L-moments method (Hosking 1990; Hosking and Wallis 1997), which has been widely used in various hydrological studies (Kumar and Chatterjee 2011; Jena et al. 2014; Samantaray et al. 2015; Bisht et al. 2016, 2019, 2020; Jacob et al. 2020), is applied for the parameter estimation of GEV, LP3 and EV1 distributions. The L-moments method is a modification of probability-weighted moments (PWMs) and is nearly unbiased. This method is less sensitive to outliers, easy to work with, and provides a greater degree of accuracy for a small sample size as compared to other methods. More details on this method can be obtained in (Millington, Das, and Simonovic 2011) and Hosking (1990). Mathematical expression for the cumulative distribution function (CDF) of EV1 distribution is (Hosking and Wallis 1997),
Rainfall flood hazard at nuclear power plants in India
Published in Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, 2018
In this study, a regional frequency analysis approach based on L-moments (Hosking and Wallis 1997) has been used to produce rainfall growth curve with an extreme value distribution. L-Moments are used for solving distribution parameters for the selected probability distribution. They are a dramatic improvement over conventional product moment statistics for characterising the shape of a probability distribution and estimating the distribution parameters, particularly for environmental data where sample sizes are commonly small. Unlike product moments, the sampling properties for L-moments statistics are nearly unbiased – even in small samples – and follow a normal distribution. These properties make them well suited for characterising environmental data that commonly exhibit moderate to high skewness (L-Moments Statistics 2011). The three L-moment ratios L-CV, L-Skewness and L-Kurtosis have been determined for the annual maximum rainfall for each site (first moment is mean value). The L-moment ratios are direct measures of the extreme value distribution and as such provide a better illustration of change than fitted Extreme Value parameters themselves (Fowler and Kilsby 2003). Figure 4 shows the variation of L-CV against L-Skewness for various sites. In simple terms, this represents a change in extreme rainfall properties, with increased variability (rising L-CV) and increased intensity (rising L-Skewness) in the region.