L-moments

Any hydropower project requires an ample availability of stream flow data. Unfortunately, most of the hydropower projects especially small hydropower projects are conducted on ungauged river and consequently hydrologists have for a longtime used stream flow estimation methods using the mean annual flows to gauge rivers. Unfortunately flow estimation methods which include the runoff data method, area ratio method and the correlation flow methods employ a lot of assumptions which affect their uncertainty. This study was conducted on Bua River in Malawi to unveil the uncertainties of these flow estimation methods. The study was done on a well gauged catchment in order to highlight the variations between the observed, true stream flows and the estimated stream flows for uncertainty analysis. After regionalizing the homogenous sites, catchments using L-moments, an uncertainty analysis was done which showed that the area method is better followed by the correlating flow method and lastly the runoff data method in terms of bias, accuracy and uncertainty.

For evaluating the severity of drought in a certain month, two indexes of cumulative precipitation deficit (CPD) and maximum precipitation deficit (MPD) are used such that a regional frequency analysis has been carried out by L-moments. These measures of drought are strongly related to moisture deficits for the vegetation during the growing season. In this paper, 11 synoptic stations in Isfahan province, Iran, with a semiarid environment are used. The stations have a minimum of 10 years of data. The two drought indexes are calculated for all of them in whole months. The WeatherMan tool is used for completing missing data. The Food and Agriculture Organization of the United Nations Penman-Monteith (FAO-PM) method is used for calculating reference evapotranspiration [ET ðFAO-PMÞ ]. According to previous studies , this method is suitable for this region. The Hosking homogeneity test is applied for identifying a homogeneous region. The Hosking goodness-of-fit test is performed to select the best regional distribution. The results show that the region is homogeneous in months 5 to 10, and in the rest of the months, the region becomes homogeneous after using clustering techniques and dividing the region into two smaller regions. Also, the best regional distribution is distinguished generalized logistic in the most months. Therefore, the severity of drought is estimated with various return periods by CPD and MPD. The maximum intensity of drought in the all stations happens in months 6 to 8, which are in late spring to midsummer. The severity of drought in Ardestan, Khoorbiabanak, and Naeen stations is greater than the remaining stations. Using the outcome of this study, the amount of required water can be estimated for agriculture each month, and the amount of water available is effectively managed in this province.

Developing methods that can give a suitable prediction of hydrologic events is always interesting for both hydrologists and statisticians, because of its importance in designing hydraulic structures and water resource management. Because of the computer revolution in statistical computation and lack of robustness in at-site frequency analysis, since early 1990 the application of regional frequency analysis based on L-moments has been considered more for flood analysis. In this study, the above-mentioned method has been used for the selection of parent distributions to fit maximum monthly rainfall data of 18 sites in the Zayandehrood basin, Iran, and as a consequence the generalized extreme-value and Pearson type-III distributions have been selected and model parameters have been estimated. The obtained extreme rainfall values can be used for meteorological drought management in the arid zone.

In this study we analysed that how much L-moments application is valuable in flood frequency analysis. These give the simple and proper estimation of distribution parameters and characteristics of the data which are used in hydrologic application. Generally, engineers or a hydrologists and researchers face problem for calculating the reliable floods where there is no record available of river flow as well as rainfall for both small to medium size catchments. L-moments are useful to find out the statistical properties of hydrological data for particular region. I. INTRODUCTION Floods cause a number of severe causes as economic loss, loss of human life etc. Hence for controlling this problem it is necessary to estimates the flood, design and economic appraisal of a variety of engineering works, including hydraulic structures, economic evaluation of flood protection projects etc. Deterministic approach and Statistical approach are the two methods used for flood estimation. Uncertainties involved is more in case of Deterministic approach and less in statistical approach for the analysis of data, hence statistical approaches generally used. Frequency analysis is the method of estimation which specified us how an event will occur. For a many year in hydrology regional frequency analysis method is established, flood procedure by Dalrymple (1960) is an example of this. Chaudhary et al (1991) suggested using General extreme distribution (GEV) of index-based approach for estimation of food frequency model. In India flood frequency analysis using probability weighted moments (PWM) has been carried out (1992, NIH, Kumar et al.) for which GEV method found out to be the best. According to Karim and Chaudhary (1995) the three-parameter distribution i.e. GEV method is the best method for flood frequency analysis in case of Bangladesh (India) flood using both the analysis L-moment ratio diagram and best-of-fit analysis. L-Moments were found out first time by the Hosking (1990), defined L-moments as are the linear combination of Probability Weighted Moments. These give the simple and proper estimation of distribution parameters and characteristics of the data which are used in hydrologic application. The significance of L-moments in flood analysis:

Normality tests are used in the statistical analysis to determine whether a normal distribution is acceptable as a model for the data analysed. A wide range of available tests employs different properties of normal distribution to compare empirical and theoretical distributions. In the present paper, we perform the Monte Carlo simulation to analyse test power. We compare commonly known and applied tests (standard and robust versions of the Jarque-Bera test, Lilliefors test, chi-square goodness-of-fit t est, S hapiro-Francia test, Cramer-von Mises goodness-of-fit test, Shapiro-Wilk test, D'Agostino test, and Anderson-Darling test) to the test based on robust L-moments. In the text, in Jarque-Bera type test the moment characteristics of skewness and kurtosis are replaced with their robust versions-L-skewness and L-kurtosis. The distributions with heavy tails (lognormal, Weibull, loglogistic and Student) are used to draw random samples to show the performance of tests when applied on data with outliers. Small sample properties (from 10 observations) are analysed up to large samples of 200 observations. Our results concerning the properties of the classical tests are in line with the conclusion of other recent articles. We concentrate on properties of the test based on L-moments. This normality test is comparable to well-performing and reliable tests; however, it is outperformed by the most powerful Shapiro-Wilks and Shapiro-Francia tests. It works well for Student (symmetric) distribution, comparably with the most frequently used Jarque-Berra tests. As expected, the test is robust to the presence of outliers in comparison with sensitive tests based on product moments or correlations. The test turns out to be very universally reliable.

This study presents the estimation of regional quantiles of Annual Total Rainfall (ATR) for 30 meteorological stations using index flood procedure based on L-moments. Discordancy measure based on L-moments was used to screen the ATR. As a matter of the fact, highly elevated areas of Pakistan receive more rainfall, the study area was divided into four different regions. Further to justify the homogeneity of these regions, L-moment based heterogeneity measure (H) was calculated for each region using four parameter Kappa distribution. For each region, best distribution was found among Pearson type III (PE3), Generalized Normal (GNO), Generalized Extreme Value (GEV), Generalized Logistic (GLO) and Generalized Pareto (GPA) distribution using Z-statistic and L-moment ratio diagram. Regional quantiles on the basis of best-fit distribution for each region were determined and further for robustness, the accuracy measures for the estimated regional quantiles were calculated using Monte Carlo simulations. It was found that PE3 was most suitable choice for large return period for first three regions while for small return period GNO and GEV. Similarly, for region IV GEV was declared as the best fit for lower return period's up to 20 years while for a period of 50, 100, 500 and 1000 years GNO was the best one.

Estimation of peak flood discharge (PFD) for a desired return period is of utmost importance for planning, design and management of hydraulic structures. This can be determined by fitting of probability distributions to the series of annual peak discharge (APD) data. Method of L-moments is used for determination of parameters of the distributions. Goodness-of-Fit (GoF) tests such as Chisquare and Kolmogorov-Smirnov are applied for checking the adequacy of fitting of five probability distributions to the recorded APD. A diagnostic test of D-index is employed for the selection of a suitable probability distribution for estimation of PFD. Based on the GoF and diagnostic tests results, the paper presents the Gumbel (EV1) is better suited amongst five distributions used in estimation of PFD for Malakkara and Neeleswaram.

A reliable gait features are required to extract the gait sequences from an images. In this paper suggested a simple method for gait identification which is based on moments. Moment values are extracted on different number of frames of Gray Scale and Silhouette images of CASIA database. These moment values are considered as feature values. Fuzzy logic and Nearest Neighbor Classifier are used for classification. Both achieved higher recognition.