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Climate change and human activity has increased the degree of nonstationarity in the annual runoff series of the Weihe River Basin, making it difficult to conduct a traditional hydrological frequency analysis in this study area. Most of the existing nonstationary frequency analysis methods are still controversial and cannot be applied in practice. Furthermore, the nonstationarity of the annual runoff series is caused by nonstationary changes in some specific influencing factors. In this study, we remove the nonstationarity from the annual runoff series by quantifying the relationship between the annual runoff and its driving factors. This denonstationarity process removes the nonstationary influence of the driving factors and is not limited to some specific types of nonstationarity, such as trend and abrupt change. For the annual runoff series of the Weihe River, the annual average temperature (Tave) , irrigation area (IA) , and reservoir index (RI) are used as the reconstruction factors, respectively. And the decreasing trends in the first and second moments, and an abrupt change in 1993 are removed simultaneously by this denonstationarity method. The stationarity of the denonstationarity series reconstructed by Tave is the best, followed by the denonstationarity series reconstructed by the IA and the RI. Climate change has a more significant impact than human activity on the nonstationary change of the annual runoff. Once the reconstructed series are stationary, the traditional hydrological frequency analysis method is adopted. Reconstructed series with a higher degree of stationarity result in lower uncertainties in the design quantile of the annual runoff, whereas the significant nonstationarity in the original series results in large design value uncertainties. [ABSTRACT FROM AUTHOR]

Knowledge of how the frequency and intensity of extreme events are affected by climate variability will contribute to answering questions related to drought and water availability that are important in water resources management. A tool titled the "International Center for Integrated Water Resources Management-Regional Analysis of Frequency Tool" (ICI-RAFT), which includes a database of several climate indices, was developed to accomplish this using rainfall observations on the ground. The method used was applied to rainfall obtained from 20 rain gauges in western central Argentina and hurricanes in the Atlantic Ocean during the respective active seasons. The global climate index that was found to have the greatest impact in both cases was the Madden-Julian Oscillation (MJO), which is the focus of the current study. Specifically, MJO activity over central Africa (MJO9) using a lag of 4 months and the western Indian Ocean (MJO10) using zero lag had the greatest influences, respectively. It was found that knowledge of the value of the MJO at these locations allows the prediction of below- or above-average rainfall or hurricane conditions for the current season and even allows a more precise quantitative estimate of this activity to be made. [ABSTRACT FROM AUTHOR]

Hydrologists widely use regional flood frequency analysis to predict flood quantiles for ungauged and sparsely gauged target locations. The analysis involves: (1) use of a regionalization approach to identify a group of watersheds (region) resembling the watershed of target location by searching in watershed-related attribute space, and (2) use of information pooled from the region to perform regional frequency analysis (RFA) for flood quantile estimation. Conventional regionalization approaches prove ineffective for identification of regions in situations where there are outliers in the attribute space. This paper proposes an entropy-based clustering approach (EBCA) to identify regions by accounting for outliers and recommends applying a recently proposed RFA approach on the regions for quantile estimation. The EBCAyielded seven new homogeneous regions in four major river basins (Mahanadi, Godavari, Krishna, and Cauvery) of India. The regions are shown to be effective compared to six existing regions (used by an Indian government organization) and those delineated using global K-means clustering and region-of-influence approaches, in terms of regional homogeneity and utility in arriving at reliable flood quantile estimates for ungauged sites. [ABSTRACT FROM AUTHOR]

This study investigated the possible problems of using the concept of critical rainfall duration (CRD) for estimating the design flood. The investigation focused on the evaluation of the difference between the annual maximum independent rainfall event series (IRES) and the annual maximum short-duration rainfall series in Seoul, Korea. Annual maximum IRES was determined by applying Freund's bivariate exponential distribution, which were also used for frequency analysis by applying the Gumbel's bivariate logistic model. Both the annual maximum IRES and the frequency analysis results were then compared with those of the conventional annual maximum fixed-duration rainfall series (FDRS). The results are summarized as follows. First, the mean rainfall intensity of the annual maximum IRES was found to be little changed regardless of their durations. Thus, most of the annual maximum short-duration rainfall series would be selected in the annual maximum IRES. Second, results of the bivariate frequency analysis of the annual maximum IRES were found to be similar to those of the annual maximum long-duration rainfall series. It means that the annual maximum long-duration rainfall series could represent the annual maximum IRES. In conclusion, the short-duration rainfall series is rather artificial and the possibility of their occurrence in reality is rare. Considering the typical shape of rainfall temporal distribution, the peak of a short-duration design rainfall could be much smaller than that of a long-duration one. The use of the concept of CRD finally could result in smaller design floods especially in small basins. [ABSTRACT FROM AUTHOR]

The three-parameter Burr XII distribution has been seldom used in hydrological applications, although it is particularly appealing because its range covers positive values only, which is convenient when modeling streamflows or rainfall data. Moreover, it has two shape parameters, allowing it to be quite adaptable to different samples because it covers a wide range of skewness and kurtosis values. Parameter estimation methods currently available in the literature require the numerical solution of two joint nonlinear equations to estimate the shape parameters of the distribution. This work proposes a simplified, although accurate, method to analytically compute the two shape parameters starting from the dimensionless L-moments ratios representing the distribution's variability (L-CV) and skewness (L-skewness). The obtained parameters can be directly used in practical applications or otherwise may be useful to properly initialize the algorithms to obtain a numerical solution for the shape parameters. A detailed analysis of the accuracy of the approximated solution is performed, showing that the errors in the estimation of the distribution quantiles are negligible compared with the sample variability typically affecting hydrological samples. An extensive data set of empirical flow duration curves from stations located in northwestern Italy is considered to demonstrate the suitability of the extended Burr XII distribution to represent flow duration curves in a wide range of situations. [ABSTRACT FROM AUTHOR]

The use of partial duration series (PDS) in hydrological application includes the difficulty in determining the exceedance threshold or the number of average peaks per year () used to define extreme events from observation. The difficulty is exacerbated when the PDS is used in the context of regional frequency analysis; however, there are only limited studies to address this difficulty. This study aims to investigate the determination of an optimum regional value of for the North Island of New Zealand by examining the performance of the PDS when used in a regional frequency analysis (RFA). The suitability of a number of frequency distributions to be used in the regional frequency is examined. The results confirmed that the generalized Pareto (GP) best described the PDS in the study area. The results also show that the best PDS/GP performance is obtained when the value of is equal to 5. [ABSTRACT FROM AUTHOR]

Flood hazard and arising risks due to associated vulnerabilities still appear to be among the common problems in today's hydrology in spite of highly motivated assessments and increasing knowledge and awareness as well as targeted measures for mitigation, preparedness, and emergency management. Beside the role of overall inaction, deficiencies in precautionary actions and presence of natural barriers and inaccurate or incomplete approaches in flood studies towards estimating flood magnitudes and frequencies are also assumed to have considerable impacts on limited control against the flood phenomenon. Prevalent claims about the invalidity of the stationarity assumption in hydrologic studies indicate any ignorance of nonstationarity as potential sources of ineffective flood assessments and the associated improper actions. The presented study investigates potential impacts and relative significance of observed trends on the magnitude and frequency of floods through comparisons performed over stationary and nonstationary flood frequency analyses. Results indicate slightly significant discrepancies between the estimates from both the stationary and nonstationary analyses by potentially pointing out to the arising needs for considering the nonstationarity in flood studies. [ABSTRACT FROM AUTHOR]

The return period of a rainfall event is estimated by the frequency analysis for a given rainfall duration. Thus, it is possible to derive different return periods with different rainfall durations for a given rainfall event. The longest derived return period is generally cited to represent the rainfall event. However, it is not clear if the longest derived return period is a representative measure of the given rainfall event. In this study, as a solution for this problem, a bivariate frequency analysis was introduced. As a first step, annual maximum rainfall events were selected by applying a bivariate exponential distribution. As an application, a total of 1,534 rainfall events observed in Seoul, Korea, over the last 46 years were analyzed. The annual maximum rainfall event series were then analyzed by applying a bivariate logistic model. The results were also compared with those from a conventional univariate frequency analysis. The findings of this study are summarized as follows: (1) the bivariate exponential distribution satisfactorily represented the duration and total rainfall depth data of all independent rainfall events, and the annually estimated parameters of the bivariate exponential distribution were more reasonable with respect to annual changes in the climatic conditions than those for the entire data period; (2) by using the bivariate logistic model, the return period was able to be assigned to each annual maximum rainfall event; and (3) rainfall quartiles of the univariate frequency analysis were bigger than those from the bivariate frequency analysis for rather short return periods of less than 30 years, but smaller for rather long return periods exceeding 100 years, primarily attributable to the smaller variance of the univariate annual maximum series. [ABSTRACT FROM AUTHOR]

Regional frequency analysis of extreme precipitation after a drought event based on the L-moment method has provided promising insights into drought risk management. The drought index of continuous noneffective rainy days was applied to analyze the droughts with the characteristics of increasing frequency, severity, and duration in the Heihe River Basin. Based on the typical drought records, the precipitation intensity after drought was shown to be greater than the long-term average values. Regional pooling of the precipitation after drought and under normal conditions for 1960-2010 from 14 sites across the Heihe River Basin was applied in a regional frequency analysis based on L-moments to estimate the quantiles for given return-period precipitation events in each of the three homogeneous regions for both the drought and normal series. From the study results, the following observations were made: (1) the Heihe River Basin (14 sites) can be classified into three homogeneous regions by the analysis of discordancy measure and heterogeneity measure. The results of goodness-of-fit measures showed that the Pearson type III (PE3) and generalized extreme value (GEV) distributions were suitable for the basin, but their respective performances for the drought and normal series were clearly different; and (2) the estimated quantiles at a given return period (, 2, 5, 10, 20, and 50 years) for the drought and normal series revealed that the high-intensity precipitation after drought was more than that under normal conditions in all three of the regions. In addition, the spatial variation of extreme precipitation in the drought and normal series was noticeable. [ABSTRACT FROM AUTHOR]

At any location, flood magnitudes can result from multiple causes (e.g., riverine flooding, tidal surges, snowmelt runoff, pluvial flooding, etc.) that occur simultaneously or independently. Analyzing flood data that resulted from simultaneous occurrences but treating the individual magnitudes as independent factors can lead to inaccurate estimates of flood depths, probability, and risk. While the assumption of independence is computationally convenient, it can be hydrologically incorrect. A method of joint flood frequency analysis that is based on copulas is proposed to address cases where the assumption of independence does not apply. For example, flooding at a coastal site can be the result of high riverine flows that simultaneously happen with high storm surges. The individual flood records would not adequately describe flood depths where both flood types occurred. The proposed method can be applied with two or more causes of flooding. The method is demonstrated using data from a site in coastal Florida, with the results showing that differences in flood estimates can be significant when independence is assumed for cases when a dependency exists. [ABSTRACT FROM AUTHOR]

This paper studies the frequency analysis of droughts using a copula with the application of regionalization in the context of a bivariate homogeneity analysis. Drought events indicated by severity and duration were extracted from monthly flow averages. A K-means clustering algorithm was used to form initial regions. A fuzzy C-means algorithm was used to form the final groups of sites that meet the criteria of bivariate discordancy, bivariate homogeneity, and size. The application of the Gumbel, Clayton, and Frank copulas for bivariate drought frequency analysis was studied. Results show the importance of a clear definition of drought in every scenario since, in our example, the longest drought does not necessarily correspond to the most severe one. Another important observation of this study was that, given the average annual rainfall of a catchment, droughts seem to occur in almost all regions, humid or arid. However, areas with higher annual rainfall can experience shorter but more severe drought. The procedures of this study are applicable for flood frequency analysis as well. Furthermore, ungauged sites can be integrated in the procedure of regionalization. [ABSTRACT FROM AUTHOR]

Flood risk assessment in many locations, especially in low-income countries, is severely hindered by a lack of hydrologic data. This study illustrates the application of regional rainfall frequency analysis, combined with ungauged basin analysis, to estimate flood discharges in the Gonaives basin in Haiti. Using limited daily rainfall data from seven gauges within and near the watershed, a regional extreme value distribution is selected and design storms are developed. These design storms are then input to a rainfall-runoff model, the parameters of which are estimated from spatial analysis of physical watershed characteristics. As a case study, the flood discharge and associated return period are estimated for the 2004 event that claimed 1,650 lives, and model outputs for other synthetic design storms are compared with large observed floods in other Caribbean basins similar in size to the Gonaives basin. Results of the comparative analysis indicate that the simulated peak flood flows of the Gonaives watershed are within the range of the maximum floods observed in other Caribbean basins with similar drainage areas, topography, and vegetation cover. [ABSTRACT FROM AUTHOR]

The Rational method is widely used in the design of hydraulic structures, such as storm sewers and culverts. Many engineers consider the Rational equation a rule-of-thumb method and dismiss it in favor of regional flood-frequency equations. This paper presents a regional flood-frequency analysis of 72 gaged watersheds in Kansas, ranging in size from . The analysis results in regression equations for the 2-year to 100-year peak discharges that are statistically indistinguishable from the Rational equation. The resulting Rational equations explain more of the variance in flood quantiles than the standard form of the USGS regional flood-frequency equations that are used in Kansas. [ABSTRACT FROM AUTHOR]

A collection of archived hydrographs for 28 ephemeral streams provided a unique opportunity to quantify hydrograph characteristics for channels of the arid/semiarid Southwestern United States. Recurrence of flow and volume calculated using annual maxima converge with those of the complete series by 7 years, suggesting that records of annual maxima are sufficient for estimates of extreme event recurrence. The relationship between peak discharge and volume for a flow event cannot be tightly constrained without consideration of event duration. As a result, volumes , for recurrence intervals , cannot be estimated from corresponding peaks . Instead, volume recurrence should be estimated based on the joint distribution of peak discharge and duration. Although the density governing event duration in these semiarid study regions decays as a power law with time, the authors could not identify a probability density that provides a good fit to volume magnitude. Deterministic relationships exist between peak discharge and volume for an event of a given magnitude for the Las Vegas, Nevada; Phoenix, Arizona; and Albuquerque, New Mexico regions. [ABSTRACT FROM AUTHOR]

Flood events consist of flood peaks and flood volumes that are mutually correlated and need to be described by multivariate analysis methods, of which the copula functions are most desirable. Until now, the multivariate flood frequency analysis methods based on copulas does not consider the historical floods or paleological information. This may underestimate or overestimate the flood quantiles or conditional probabilities corresponding to high return periods, especially when the length of gauged record data series is relatively short. In this paper, a modified inference functions for margins (MIFM) method is proposed and used to estimate the parameters of both marginal distribution and joint distribution with incorporation of historical information. The conditional probabilities of flood volumes given that the peak discharge exceeding various values were derived. The Three Gorges reservoir (TGR) in China was selected as a case study. The bivariate flood quantiles were obtained based on bivariate return period and compared with current univariate design values. It is shown that the proposed method provides an alternative way for multivariate frequency analysis with historical information. [ABSTRACT FROM AUTHOR]

Bangladesh is a flood prone country where huge damages take place every year. Therefore, to minimize flood extremes, it is important to control the flood peaks at the upstream area through suitable watershed management practices. The flood control management at the watershed scale requires good quality flood data. However, in developing countries like Bangladesh, such hydrological information is rarely available at the watershed level. Under such circumstances, it is important to use a hydrological model representing the rainfall-runoff process to arrive at the extreme flows in the rivers, which require extreme rainfall data as a major inflow to the hydrologic system. Furthermore, the density of rain gauges in Bangladesh is low and the quality of available flood data is poor. Considering this, it is important to develop regional extreme rainfall maps for the reliable estimation of flood flows in the river by using a suitable modeling approach. Therefore, in the present paper, an attempt has been made to derive the regional best fit extreme rainfall pattern for Bangladesh for the estimation of extreme rainfall quantiles. This study uses the annual maximum daily rainfall of 68 rain gauge stations. An autocorrelation test is applied to test the independency of the data. Later, considering the heterogeneity in the hydroclimatic and topographic details, entire rain gauge stations have been clustered into six hydroclimatically homogeneous regions; namely, northeast (NE), northwest (NW), southeast (SE), southwest (SW), coastal, and central regions, by using the -mean clustering technique. The stations that did not pass the discordant and heterogeneity test were discarded from the regional frequency analysis. For regional frequency analysis, the L-moment method was applied. Based on the goodness of fit test and the L-moment ratio diagram, the generalized extreme values distribution was identified as the best fit for the SE, NW, and coastal regions. However, for NE, central, SW regions, the best fit distributions were generalized logistic and generalized Pareto, respectively. Using the derived distributions, regional extreme rainfall quantiles were estimated, followed by geo-mapping in ArcGIS 9.2. [ABSTRACT FROM AUTHOR]

Federal guidelines specify the log-Pearson Type III (LP3) distribution as the basis for the estimation of the 100-year peak discharge that serves as the regulatory flood for floodplain management in the United States. The LP3 distribution has been shown to provide a reasonable and flexible model of flood risk. Use of the LP3 distribution involves a number of explicit assumptions about the annual maximum series that are often implicitly assumed but not shown directly to be satisfied in flood frequency analysis studies of individual stations. In this case study, the validity of these assumptions for the Red River of the North at Grand Forks gaging station is examined. None of the four examined assumptions are satisfied completely. The stationarity assumption is not met because the regional climate samples two separate climatic modes, the peak discharge time series is not a random and independent set of events, the precipitation-runoff relationships are not uniform over time, and the flood peaks result from two flood-causing mechanisms. It is recommended that the validity of the explicit assumptions of the LP3 distribution be demonstrated directly as a standard step in flood frequency analyses, both as a means of advancing estimation of the regulatory flood and as a way to better inform decisions by floodplain managers and decision makers. [ABSTRACT FROM AUTHOR]

Flood events consist of flood peaks and flood volumes that are mutually correlated and need to be described by multivariate analysis methods, of which the copula functions are most desirable. Until now, the multivariate flood frequency analysis methods based on copulas does not consider the historical floods or paleological information. This may underestimate or overestimate the flood quantiles or conditional probabilities corresponding to high return periods, especially when the length of gauged record data series is relatively short. In this paper, a modified inference functions for margins (MIFM) method is proposed and used to estimate the parameters of both marginal distribution and joint distribution with incorporation of historical information. The conditional probabilities of flood volumes given that the peak discharge exceeding various values were derived. The Three Gorges reservoir (TGR) in China was selected as a case study. The bivariate flood quantiles were obtained based on bivariate return period and compared with current univariate design values. It is shown that the proposed method provides an alternative way for multivariate frequency analysis with historical information. [ABSTRACT FROM AUTHOR]

A case study was conducted in the Teesta subcatchment in Bangladesh for determining design flood flows and corresponding flood stages for different return periods using frequency analysis and MIKE 11 model. Different distribution functions of frequency analysis were tested for their goodness of fit. The observed discharge data at Kaunia on the river Teesta were used for estimation of design flood. The Pearson type-III distribution was found best fitted by the Kolmogorov-Smirnov, D-index, and L-moment diagram ratio tests, and accordingly 25-, 50-, and 100-year return period design floods were computed. The river network of Teesta River was extracted from SRTM 90-m digital elevation model. The river network of Teesta subcatchment was then simulated by MIKE 11 rainfall-runoff Nedbor-Afstromnings-Model (NAM) and HD model. The resultant time series of river stage was then compared with corresponding observed values. From the model, a stage-discharge relationship (Q-h) curve and respective equation were developed for Kaunia station on the river Teesta. The developed equation determines the corresponding flood stage of estimated flood flow of 25-, 50-, and 100-year return periods. The resulting flows and stages will be useful to design hydraulic structures, prepare flood extent maps, assess vulnerability of flood damage for different return periods, and provide flood forecasting for early warnings of floods. The approach presented would be applicable to similar river basin systems where data are limited and scarce. [ABSTRACT FROM AUTHOR]

Statistical criteria used to evaluate the best distribution fit give large weights to the center of distributions. This is, however, not consistent with the objective of frequency analysis which is to estimate the quantiles with large return periods. In this study, the usefulness of a recently proposed decision support system (DSS), which defines the class of distributions prior to a model selection practice with respect to tail behavior of sample data, was investigated using three large hydroclimatic databases [Reference Hydrometric Basin Network (RHBN), precipitation, and UNESCO]. According to the DSS, although a considerable majority of RHBN flood sample data belonged to Class C (regularly varying distributions), a slight and great majority of UNESCO discharge as well as annual precipitation sample data, respectively, belonged to Class D (subexponential distributions). This difference in classification is attributed to the nature of studied variables: RHBN sample data represent extreme events with heavy tails (Class C), whereas UNESCO and especially precipitation sample data come from relatively lighter tailed processes and therefore belong mostly to Class D distributions. The impact of classification on model selection was the largest for the RHBN and the smallest for precipitation sample data. This confirms that discriminating between classes of competing models prior to model selection is critical when the sample data come from extreme events. Observed inconsistency in model selection for the RHBN database resulted in an underestimation of quantiles in more than 2/3 of the cases regardless of class of distributions. For the UNESCO and precipitation data, however, inappropriate model selection resulted equally in over- and under-estimation in Class C, whereas it resulted in underestimation of quantiles in Class D in the majority of observed inconsistencies. It can be concluded that an inappropriate model selection due to choosing a wrong class of distributions leads, in the majority of cases, to an underestimation of the quantity of the variable under study which is associated with a higher socioeconomy risk compared to that corresponding to an overestimation of a specific quantile. It was also observed that model selection using Bayesian Information Criterion (compared to Akaike Information Criterion) is more consistent with tail behavior of the natural processes. [ABSTRACT FROM AUTHOR]

The natural variability of floods cannot be represented appropriately by single design floods. Different hydrological scenarios are needed for sustainable design of flood protection structures such as flood control reservoirs and polders. In this paper a method to estimate the probability of generated hydrological scenarios for the risk analysis of a flood control system is presented. Bivariate probability analyses of different flood variables using copulas are applied to overcome the problem that univariate probability analysis may lead to an over- or underestimation of the hydrological risk. The mesoscale Unstrut river basin in Germany, which consists of two reservoirs located downstream of the main tributaries and flood polders, serves as test case. The spatial distribution of flood events within the river basin is analyzed by the joint probability of the inflow peaks at the two reservoirs. Furthermore, in a second application copulas are used for risk analysis of the individual flood detention structures. This study corroborated that consideration of the flood volume in addition to the flood peak is important for risk-based planning and design. [ABSTRACT FROM AUTHOR]

One of the first steps in removing a dam is the construction of a cofferdam so that demolition activities can proceed safely. The time necessary for removing a small low-head dam is often on the order of a few months. To minimize the cofferdam construction cost, these dams are generally removed during the low flow months of the year. Therefore, design of cofferdams should be based on river flow series during the dam removal period, rather than the entire year. In this study, available hourly and daily average records at the recently removed Marmot Dam on the Sandy River, Oregon are analyzed for four dam removal periods, varying from 1 to 4 months (July through October). L-moment ratio diagrams and probability plot correlation coefficients are used to select log-Pearson Type 3 and two- and three-parameter lognormal probability distribution functions for representing at-site maximum flow series. From a hydrologic engineering consideration, the analysis suggests an optimal dam removal period of 3 months (July through September). An estimate of flow on the basis of annual maximum series is an order of magnitude higher, which would result in an uneconomical design of the cofferdam. [ABSTRACT FROM AUTHOR]

Two models are herein presented to derive at-site hourly based rainfall depth-duration-frequency (DDF) relationships by incorporating daily rainfall information. The model development is motivated by the desire to utilize daily rainfall data that are in existence prior to the conversion from a manned gauge to an automatic one for improving the establishment of hourly based rainfall DDF relation at the site. The performance of the proposed models is assessed by comparing the rainfall DDF relationships derived from the conventional method using solely annual maximum rainfalls of various durations. Hourly rainfall data at Hong Kong Observatory over the period of 1884–1990 are used to demonstrate the application of the two proposed models and to examine their performance. Results from the numerical experiments show that the two proposed models, which incorporate daily rainfall data, are capable of producing more accurate and reliable rainfall DDF relationships than the conventional method solely on the basis of annual maximum hourly rainfalls. [ABSTRACT FROM AUTHOR]

The accuracy of flood quantile estimates is constrained by the data available at a site. To improve the accuracy of quantile estimators, Bulletin 17B recommends combining the station skew with a regional skew using the inverse of their mean square errors (MSEs) as weights. While these weights can yield the minimum MSE skewness estimator, they do not provide the minimum MSE quantile estimators except when the true at-site skew is zero. In this paper, optimal weights which provide minimum MSE quantile estimators are derived. A Monte Carlo experiment illustrates the value of different weighting schemes and the value of using an informative regional skew. For reasonable values of the regional skew, the MSE of quantile estimators is reduced when the sample skew is combined with an informative regional skew. Modest improvements in the MSE of quantile estimates are obtained using optimal quantile weights rather than the MSE-skew weights. When the regional skew is actually very informative, there is a large loss of efficiency for positively skewed populations when either weight is incorrectly computed using a regional skew estimation error of 0.302 as recommended by the map in Bulletin 17B. Approximations for the MSE, variance, and bias of sample skewness estimators are provided with accuracies on the order of ±0.1%. In addition, a factor for unbiasing skewness estimators for |γ|≤1.414 is developed for use in regional skew studies. [ABSTRACT FROM AUTHOR]

Quantile estimation in rainfall/flood frequency analysis is very important in engineering design of water infrastructure. Many existing methods are based on parametric modeling with the assumption that the underlying probability distribution is known a priori. The estimation performance hence relies largely on the assumed distribution of the observations in addition to the historical measurements. If the distribution is not appropriate to describe the observations, the estimated parameters are prone to large errors. In this paper, artificial neural network and fuzzy logic based methods are used to obtain quantile estimates which avoid the difficult problem of distribution determination while increasing the accuracy of the estimated quantiles. A complete comparison with the conventional parametric methods is given through realistic annual maximum daily rainfall data and Monte Carlo simulations for various sample sizes. The results demonstrate that the artificial neural network techniques yield higher accuracy in quantile estimation than the conventional parametric methods for all sample sizes, particularly in the upper tail region of the frequency curve. [ABSTRACT FROM AUTHOR]

An at-site based rainfall frequency analysis was performed using hourly precipitation data for 53 selected stations in Indiana. The combined use of generalized extreme value and extreme value type I distributions was found to provide the best statistics, and was applied to construct the at-site estimates. This at-site result was then compared to other commonly used regional rainfall estimates, including Indiana Department of Natural Resources rainfall, Huff and Angel rainfall, and National Weather Service Atlas 14. Non-negligible differences between at-site and regional estimates were found even though Indiana was previously reported as a homogeneous region for rainfall. Results suggest that discretion is necessary when using regional rainfall estimates for site-specific problems. The at-site estimate was also applied to compute the depth ratios between different durations. This ratio exhibited significant variability with increasing return period implying that the use of a constant depth ratio to estimate rainfall might not be appropriate for larger return periods. [ABSTRACT FROM AUTHOR]

This study aims at deriving intensity-duration-frequency (IDF) curves from bivariate rainfall frequency analysis using the copula method, which does not assume the rainfall variables to be independent or normal or have the same type of marginal distributions. The bivariate distributions are then employed to determine conditional return periods and IDF curves needed for urban drainage design. The IDF curves are tested using rainfall data from catchments in Louisiana and are also compared with those of Technical Paper 40 (TP-40) of the U.S. National Weather Service as well as those published in the literature. [ABSTRACT FROM AUTHOR]

Since the adoption of the log-Pearson Type 3 (LP3) distribution byU.S. federal agencies, it has been widely used in hydrology, but itsproperties are not well understood. This paper explores thecharacteristics of the LP3 distribution in both real space and logspace, and their relationship. Comparisons with U.S. flood datasummaries reveal that the LP3 distribution provides a reasonablemodel of the distribution of annual flood series from unregulatedwatersheds for log space skews |γx|≤1.414 (though |γx|≤1 is more realistic), and for γx=0 with standard deviations in the range 0.1 to 1.0 with base-e natural logarithms (0.04 to 0.43 with base-10 common logarithms). L-moment ratio relationships for the LP3 distribution are also developed so they can be compared to summary statistics for a region, and to several other distributions frequently recommended for modeling hydrometeorological extremes. [ABSTRACT FROM AUTHOR]

Joint distributions of rainfall intensity, duration, and depth or those of rainfall intensity and duration, rainfall depth and duration, and rainfall intensity and depth are important in hydrologic design and floodplain management. Considering the dependence among rainfall intensity, depth, and duration, multivariate rainfall frequency distributions have been derived using one of three fundamental assumptions. Either the rainfall intensity, duration, and depth have been assumed independent, or they each have the same type of marginal probability distribution or they have been assumed to have the normal distribution or have been transformed to have the normal distribution. In reality, however, rainfall intensity, duration, and depth are dependent, do not follow, in general, the normal distribution, and do not have the same type of marginal distributions. This study aims at deriving trivariate rainfall frequency distributions using the Gumbel–Hougaard copula which does not assume the rainfall variables to be independent or normal or have the same type of marginal distributions. The trivariate distribution is then employed to determine joint conditional return periods, and is tested using rainfall data from the Amite River Basin in Louisiana. [ABSTRACT FROM AUTHOR]

In multivariate frequency analysis, when the number of variables increases, different mutual structures of dependence among the analyzed quantities are usually observed. To correctly model this behavior, a very flexible joint distribution function is needed. A quite simple approach to build such distributions is based on the copula function. Precisely, using the so-called fully nested or asymmetric Archimedean copulas, it is possible not only to focus attention on the structures of dependence overlooking the margins—a property common to all copulas—but also to analyze more complex asymmetric structures of dependence. The aim of this paper is to describe the inference procedure to carry out a trivariate frequency analysis via asymmetric Archimedean copulas. The writers highlight the differences between the symmetric Archimedean copulas and asymmetric ones, show the inference procedure, and carefully describe some goodness- of-fit tests proposed in the literature to choose the best fitting model when one uses the fully nested Archimedean copulas. Finally, the methodology is applied to observed hydrological data, and results are shown and commented on. [ABSTRACT FROM AUTHOR]

Using the Gumbel–Hougaard copula, trivariate distributions of flood peak, volume, and duration were derived, and then conditional return periods were obtained. The derived distributions were tested using flood data from the Amite River Basin in Louisiana. A major advantage of the copula method is that marginal distributions of individual variables can be of any form and the variables can be correlated. [ABSTRACT FROM AUTHOR]

This paper highlights the importance of taking into account the tail dependence in the context of bivariate frequency analysis based on copulas. Three nonparametric estimators of the tail-dependence coefficient are compared by simulations with seven families of copulas. We choose the two estimators most adapted to a bivariate frequency analysis of the annual maximum flows and the corresponding flow hydrograph volumes of the Loire River (France). In this example, the bivariate return period and the conditional density of the volume given that the flow exceeds a given threshold are computed. The results show, as can be expected, that out of the seven copula families tested, five overestimate the return periods of correlated extreme events. These results bring to the forefront the importance of taking into account the tail dependence in order to estimate the risk adequately. [ABSTRACT FROM AUTHOR]

This paper presents an introduction to inference for copula models, based on rank methods. By working out in detail a small, fictitious numerical example, the writers exhibit the various steps involved in investigating the dependence between two random variables and in modeling it using copulas. Simple graphical tools and numerical techniques are presented for selecting an appropriate model, estimating its parameters, and checking its goodness-of-fit. A larger, realistic application of the methodology to hydrological data is then presented. [ABSTRACT FROM AUTHOR]

The normal and lognormal distributions are frequently used in hydrology. As these distributions are in the form of integrals, they cannot be used for generation of normal and lognormal random numbers using inverse transforms. In this study, functions closely approximating the normal and lognormal distributions have been obtained and their use in hydrological studies is indicated. [ABSTRACT FROM AUTHOR]

The frequency distributions and record heaviest snowfalls from snowstorms across the nation are defined. Data for 1948–2001 from 204 first-order weather stations identified major snowstorms in the United States, and these storm values were analyzed to determine the 5- and 10-year return interval values, plus the record highest value at each station. These values, which are important in design and operational issues relating to heavy snow, have been used to develop nationwide patterns of these extreme events. A latitudinal distribution of low (south) to high values (north) exists in the central United States, but the mountain ranges of the west and east have higher extreme values associated with higher elevations. Maximum snowfalls exceed 140 cm in the highest elevation locales in the Cascade Mountains. The Great Lakes also enhance storm snowfall frequencies by 20–50% on their downwind sides. [ABSTRACT FROM AUTHOR]

A drought is usually represented by duration and severity, and may last several months or years. Multidimensional characteristics of a drought make univariate analysis unable to reveal the significant relationship among drought properties. Furthermore, historical records tend to be too short to fully evaluate drought characteristics. A practical method was proposed in this study to estimate the bivariate return period of droughts based on the use of synthetic data to overcome the above considerations. The bivariate return period of droughts is dependent on the drought interarrival time and the joint distribution of drought properties. A nonparametric method was employed in this study to estimate the joint distribution of drought properties. The historical droughts in the Conchos River Basin, Mexico were evaluated based on their return period estimated by the proposed method. The proposed method allowed a better understanding of the joint probabilistic behavior of droughts beyond the limitation of the univariate/parametric frequency analysis. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the seasonal characteristics of floods in Canada. Its principal objective is to judge the relevance of seasonal analysis and to attempt to present a unified set of methodologies for handling the problems of seasonally varied flows. Another objective is to broadly identify various regions of Canada for which seasonal analysis would be appropriate. Partial duration series and the exceedance model are used because they are well suited to this type of analysis. The focus will be on improved estimation of low-frequency/large-magnitude flood events. Two methods are investigated as a means for grouping flood series on a seasonal basis in a meaningful way: One method is based on flood generating phenomena, and the other divides the year into “homogeneous” periods, which could be called “seasons.” Seasonal analyses were performed on 166 hydrometric stations in all regions of Canada. Synthesis of the results has made it possible to broadly identify regions for which an analysis of seasonal flood variations may be the most relevant. In general, these are the southern regions of the country. Specifically, there is an indication from the results obtained for the Maritime provinces, southern Ontario and the Prairie provinces, that these regions are well suited to seasonal analysis. Also, the results show that frequency analysis for stations recording one or more rare events, or having flood subpopulations that are clearly distinct, may be significantly improved by using a seasonal approach. [ABSTRACT FROM AUTHOR]