REGIONAL FLOOD EQUATIONS FOR THE PROVINCES OF ONTARIO AND QUEBEC1

ABSTRACT: When nonparametric frequency analysis was performed on 183 stations from Ontario and Quebec, unimodal and multimodal maximum annual flood density functions were discovered. In order to determine generating mechanisms, a monthly partitioning of the annual maximum floods was undertaken. The timing of the floods revealed that the unimodal distributions reflected a single flood generating mechanism while the multi-modal densities reflected two or more mechanisms. Based on the division of the flood series by mechanisms, nine homogeneous regions were delineated. L-moment distributional homogeneity tests along with smaller standard errors for the regional equations supported the delineation.     

MULTIVARIATE EXTREME VALUE DISTRIBUTION WITH MIXED GUMBEL MARGINALS1

ABSTRACT: Bivariate and trivariate distributions have been derived from the logistic model for the multivariate extreme value distribution. Marginals in the models are extreme value type I distributions for two-component mixture variables (mixed Gumbel distribution). This paper is a continuation of the previous works on multivariate distribution in hydrology. Interest is focused on the analysis of floods which are generated by different types of storms. The construction of their corresponding probability distributions and density functions are described. In order to obtain the parameters of such a bivariate or trivariate distribution, a generalized maximum likelihood estimation procedure is proposed to allow for the cases of samples with different lengths of record. A region in Northern Mexico with 42 gauging stations, grouped into two homogeneous regions, has been selected to apply the models. Results produced by the multivariate distributions have been compared with those obtained by the Normal, log-Normal-2, log-Normal-3, Gamma-2, Gamma-3, log-Pearson-3, Gumbel, TCEV and General Extreme Value distributions. Goodness of fit is measured by the criterion of standard error of fit. Results suggest that the proposed models are a suitable option to be considered when performing flood frequency analysis.     

BIVARIATE FREQUENCY ANALYSIS OF FLOODS USING COPULAS1

Abstract: Bivariate flood frequency analysis offers improved understanding of the complex flood process and useful information in preparing flood mitigation measures. However, difficulties arise from limited bivariate distribution functions available to jointly model the correlated flood peak and volume that have different univariate marginal distributions. Copulas are functions that link univariate distribution functions to form bivariate distribution functions, which can overcome such difficulties. The objective of this study was to analyze bivariate frequency of flood peak and volume using copulas. Separate univariate distributions of flood peak and volume are first fitted from observed data. Copulas are then employed to model the dependence between flood peak and volume and join the predetermined univariate marginal distributions to construct the bivariate distribution. The bivariate probabilities and associated return periods are calculated in terms of univariate marginal distributions and copulas. The advantage of using copulas is that they can separate the effect of dependence from the effects of the marginal distributions. In addition, explicit relationships between joint and univariate return periods are made possible when copulas are employed to construct bivariate distribution of floods. The annual floods of Tongtou flow gauge station in the Jhuoshuei River, Taiwan, are used to illustrate bivariate flood frequency analysis.     

Nonparametric Monte Carlo Simulation for Flood Frequency Curve Derivation: An Application to a Korean Watershed1

Abstract: A mix of causative mechanisms may be responsible for flood at a site. Floods may be caused because of extreme rainfall or rain on other rainfall events. The statistical attributes of these events differ according to the watershed characteristics and the causes. Traditional methods of flood frequency analysis are only adequate for specific situations. Also, to address the uncertainty of flood frequency estimates for hydraulic structures, a series of probabilistic analyses of rainfall‐runoff and flow routing models, and their associated inputs, are used. This is a complex problem in that the probability distributions of multiple independent and derived random variables need to be estimated to evaluate the probability of floods. Therefore, the objectives of this study were to develop a flood frequency curve derivation method driven by multiple random variables and to develop a tool that can consider the uncertainties of design floods. This study focuses on developing a flood frequency curve based on nonparametric statistical methods for the estimation of probabilities of rare floods that are more appropriate in Korea. To derive the frequency curve, rainfall generation using the nonparametric kernel density estimation approach is proposed. Many flood events are simulated by nonparametric Monte Carlo simulations coupled with the center Latin hypercube sampling method to estimate the associated uncertainty. This study applies the methods described to a Korean watershed. The results provide higher physical appropriateness and reasonable estimates of design flood.     

COMPARISON OF DESIGN STORM CONCEPTS USING CONTINUOUS SIMULATION WITH SHORT DURATION STORMS1

ABSTRACT: The objectives of this paper were to test the ability of various design storm distributions to simulate the actual rainfall pattern and to compare the runoff rates used in the design of stormwater management devices in the State of Florida using continuous simulation approach. The analyses were performed for four gaged stations to evaluate the applicability of design storm distributions in different parts of the State of Florida. The approach used in this study compared the peak runoff rates from design storms based on the various distributions to those that would result from actual rainfall events. A series of continuous runoff rates were developed through the use of actual fifteen-minute recorded rainfall data, Horton type infiltration decay and recovery rate, and a continuous simulation model. The runoff rates were analyzed using frequency distributions to obtain peak runoff rates associated with different return periods based on the assumption that the continuous simulation approach closely predicts the actual runoff rates from the gaged stations. The results show that the behavior of the design storm distributions varies for different watershed characteristics in different parts of the state. The study also suggests that in general the Florida Department of Transportation and the Suwanne River Water Management (FDOT/ SRWMD) distributions appeared to agree with the continuous simulation results.     

DEVELOPMENT OF A BACTERIAL TRANSPORT MODEL FOR COARSE SOILS1

ABSTRACT: A bacterial transport model, developed to analyze bacterial translocation in coarse-grained soils, is presented. The complex governing equation is presented first, followed by analyses of each of the major processes influencing bacterial transport. These analyses suggest simplification of the governing equation is feasible when input data on specific processes are limited or unavailable. Model parameters, including bacterial die-off, bacterial distribution, input bacterial concentration, and saturated hydraulic conductivity, were randomly generated using a procedure known to produce either a normal or log-normal distribution of random numbers. Monte Carlo simulations were completed, and the resulting output was used to generate cumulative frequency distributions showing the probability of bacterial transport beyond various soil depths. Results from these simulations indicate that bacteria have a high probability of traveling through coarse-grained soils when low clay content and soil water temperatures limit bacterial retention and die-off.     

REGIONALIZATION AND PREDICTION OF ANNUAL FLOODS IN THE FRASER RIVER CATCHMENT,BRITISH COLUMBIA1

A method of predicting probability distributions of annual floods is presented and is applied to the Fraser River catchment of British Columbia. The Gumbel distribution is found to adequately describe the observed flood frequency data. Using the estimated Gumbel parameters, discriminant analysis is performed to separate basins into flood regions. Within each region, regression analysis is used to relate physiographic and climatic variables to the means and standard deviations of the annual flood series. The regression equations are applied to four test basins and the results indicate that the method is suitable for an estimation of annual floods.     

A COMPARISON OF METHODS FOR ESTIMATING LOW FLOW CHARACTERISTICS OF STREAMS1

ABSTRACT: Four methods for estimating the 7-day, 10-year and 7-day, 20-year low flows for streams are compared by the bootstrap method. The bootstrap method is a Monte Carlo technique in which random samples are drawn from an unspecified sampling distribution defined from observed data. The nonparametric nature of the bootstrap makes it suitable for comparing methods based on a flow series for which the true distribution is unknown. Results show that the two methods based on hypothetical distributions (Log-Pearson III and Weibull) had lower mean square errors than did the Box-Cox transformation method or the Log-Boughton method which is based on a fit of plotting positions.     

Predicting Periphyton Cover Frequency Distributions across New Zealand's Rivers

Regression models of mean and mean annual maximum (MAM) cover were derived for two categories of periphyton cover (filaments and mats) using 22 years of monthly monitoring data from 78 river sites across New Zealand. Explanatory variables were derived from observations of water quality variables, hydrology, shade, bed sediment grain size, temperature, and solar radiation. The root mean square errors of these models were large (75‐95% of the mean of the estimated values). The at‐site frequency distributions of periphyton cover were approximated by the exponential distribution, which has the mean cover as its single parameter. Independent predictions of cover distributions at all sites were calculated using the mean predicted by the regression model and the theoretical exponential distribution. The probability that cover exceeds specified thresholds and estimates of MAM cover, based on the predicted distributions, had large uncertainties (~80‐100%) at the site scale. However, predictions aggregated by classes of an environmental classification accurately predicted the proportion of sites for which cover exceeded nominated criteria in the classes. The models are useful for assessing broad‐scale patterns in periphyton cover and for estimating changes in cover with changes in nutrients, hydrological regime, and light.     

A COMPARISON OF TRANSFORMATION METHODS FOR FLOOD FREQUENCY ANALYSIS1

ABSTRACT: The SMEMAX transformation, its modified versions and power transformation were applied to 55 long-term records of annual maximum flood flows tested previously for independence, homogeneity and completeness. Even though SMEMAX transformation reduced the coefficient of skewness to near zero for flood data, their distribution was not a true normal distribution. In almost all cases, the coefficient of kurtosis was quite different from 3.0 of the normal distribution. Empirical criteria showed that SMEMAX transformation performed well only for 40 (70 percent) of the 55 stations tested. Its performance level dropped, especially for stations which had both the coefficient of skewness and kurtosis greater than 3.0 and 10.0, respectively. Power transformation was generally better in transforming the flood data to a normal distribution. It performed well for 50 (90 percent) of the 55 stations tested. The coefficient of skewness in case of the data transformed by power transformation was much closer to the zero value than in the case of SMEMAX transformed series. The SMEMAX transformation and its two modified versions yielded identical results when flood frequency analysis was performed. Computationally, all three methods were equally simple and easy to apply for flood frequency analysis. In some cases, the coefficient of kurtosis for the transformed distributions obtained both by SMEMAX and power transformations deviated farther from that for the normal distribution than for the parent distribution.     

Analysis of Extreme Summer Rainfall Using Climate Teleconnections and Typhoon Characteristics in South Korea1

Abstract: It is now widely acknowledged that climate variability modulates the frequency of extreme hydrological events. Traditional methodologies for hydrologic frequency analysis are not devised to account for variation in the exogenous teleconnections. Flood frequency analysis is further plagued by the assumptions of stationary in the causal structure as well as ergodicity. Here, we propose a dynamical hierarchical Bayesian analysis to account for exogenous forcing that govern the summer season rainfall. The precursors for Korean summer rainfall at different frequencies are identified utilizing wavelet and independent component analyses. The sea surface temperatures, the ensemble of rainfall predictions by General Circulation Model, in addition to the typhoon attributes were found to have direct correlation with extreme rainfall events and were used as inputs to the logistic regression model. The model parameters are estimated using Markov Chain Monte Carlo and the resulting posterior distributions associated with individual inputs are analyzed to advance our understanding of the spatiotemporal impact of the teleconnections. Eight rainfall stations throughout Korea are considered in this analysis. We demonstrate that the probability of occurrence of extreme events could be successfully projected at a 90% rate of correct classification of extreme events.     

HEAVY RAINFAL RELATIONS OVER CHICAGO AND NORTHEASTERN ILLINOIS1

ABSTRACT: Detailed studies of rainfall frequency and pattern relations were made over the Chicago urban region and the surrounding six Illinois counties (Cook, DuPage, Kane, Will, Lake, and McHenry). These studies utilized raingage records from an urban network of National Weather Service raingages in the region, primarily for the period 1949 to 1974. Frequency distributions of point rainfall were obtained for periods from 5 minutes to 72 hours and recurrence intervals of 6 months to 50 years. These results indicated a spatial pattern of short-duration heavy rainfall frequencies related to urban-lake effects, particularly in the huge industrial region over the southern portion of Chicago. The time distribution within heavy rainstorms over the urban region was determined, and it was found that the point rainfall relations over the urban region were similar to a 12-year sample of a dense raingage network over a rural area in central Illinois. The characteristics of heavy rainfall over northeast Illinois were also studied through the use of heavy, 1-day storms. A total of 87 storms, capable of producing local flooding, were analyzed to determine 1) the frequency distribution of storm centers, 2) seasonal and diurnal distribution of storms, and 3) orientation and movement of storms.     

AN APPLICATION OF COMPUTER GRAPHICS TO ANALYSIS OF EXTREMES1

ABSTRACT: A convenient method for the statistical analysis of hydrologic extremes is to use probability papers to fit selected theoretical distributions to extremal observations. Three commonly accepted statistical distributions of extreme hydrologic events are: the double exponential distribution, the bounded exponential distribution, and the Log Pearson Type III distribution. In most cases, probability papers are distribution specific. But, for the Log Pearson Type III distribution, the probability paper is characterized by a population-specific parameter, namely, the coefficient of skewness. It is not practicable to procure probability papers for all possible values of this parameter. Therefore, a computer program is developed to generate population-specific probability papers and to perform statistical analysis of the data using computer graphics. Probability papers covering return periods up to 1000 years or more are generated for the three distributions mentioned above. Using a plot routine, available extremal observations are plotted on selected probability papers and a linear regression analysis is used to fit a straight line to the data. Predictions of hydrologic extremes for higher recurrence intervals can be made by extrapolating the fitted straight lines.     

Assessing Uncertainty in Estimates of Nitrogen Loading to Estuaries for Research, Planning, and Risk Assessment

Parametric (propagation for normal error estimates) and nonparametric methods (bootstrap and enumeration of combinations) to assess the uncertainty in calculated rates of nitrogen loading were compared, based on the propagation of uncertainty observed in the variables used in the calculation. In addition, since such calculations are often based on literature surveys rather than random replicate measurements for the site in question, error propagation was also compared using the uncertainty of the sampled population (e.g., standard deviation) as well as the uncertainty of the mean (e.g., standard error of the mean). Calculations for the predicted nitrogen loading to a shallow estuary (Waquoit Bay, MA) were used as an example. The previously estimated mean loading from the watershed (5,400 ha) to Waquoit Bay (600 ha) was 23,000 kg N yr⁻¹. The mode of a nonparametric estimate of the probability distribution differed dramatically, equaling only 70% of this mean. Repeated observations were available for only 8 of the 16 variables used in our calculation. We estimated uncertainty in model predictions by treating these as sample replicates. Parametric and nonparametric estimates of the standard error of the mean loading rate were 12–14%. However, since the available data include site-to-site variability, as is often the case, standard error may be an inappropriate measure of confidence. The standard deviations were around 38% of the loading rate. Further, 95% confidence intervals differed between the nonparametric and parametric methods, with those of the nonparametric method arranged asymmetrically around the predicted loading rate. The disparity in magnitude and symmetry of calculated confidence limits argue for careful consideration of the nature of the uncertainty of variables used in chained calculations. This analysis also suggests that a nonparametric method of calculating loading rates using most frequently observed values for variables used in loading calculations may be more appropriate than using mean values. These findings reinforce the importance of including assessment of uncertainty when evaluating nutrient loading rates in research and planning. Risk assessment, which may need to consider relative probability of extreme events in worst-case scenarios, will be in serious error using normal estimates, or even the nonparametric bootstrap. A method such as our enumeration of combinations produces a more reliable distribution of risk.     

Examining Flood Frequency Distributions in the Midwest U.S.1

Villarini, Gabriele, James A. Smith, Mary Lynn Baeck, and Witold F. Krajewski, 2011. Examining Flood Frequency Distributions in the Midwest U.S. Journal of the American Water Resources Association (JAWRA) 47(3):447‐463. DOI: 10.1111/j.1752‐1688.2011.00540.x Abstract: Annual maximum peak discharge time series from 196 stream gage stations with a record of at least 75 years from the Midwest United States is examined to study flood peak distributions from a regional point of view. The focus of this study is to evaluate: (1) “mixtures” of flood peak distributions, (2) upper tail and scaling properties of the flood peak distributions, and (3) presence of temporal nonstationarities in the flood peak records. Warm season convective systems are responsible for some of the largest floods in the area, in particular in Nebraska, Kansas, and Iowa. Spring events associated with snowmelt and rain‐on‐snow are common in the northern part of the study domain. Nonparametric tests are used to investigate the presence of abrupt and slowly varying changes. Change‐points rather than monotonic trends are responsible for most violations of the stationarity assumption. The abrupt changes in flood peaks can be associated with anthropogenic changes, such as changes in land use/land cover, agricultural practice, and construction of dams. The trend analyses do not suggest an increase in the flood peak distribution due to anthropogenic climate change. Examination of the upper tail and scaling properties of the flood peak distributions are examined by means of the location, scale, and shape parameters of the Generalized Extreme Value distribution.     

Evidence for Changing Flood Risk in New England Since the Late 20th Century1

Abstract: Long‐term flow records for watersheds with minimal human influence have shown trends in recent decades toward increasing streamflow at regional and national scales, especially for low flow quantiles like the annual minimum and annual median flows. Trends for high flow quantiles are less clear, despite recent research showing increased precipitation in the conterminous United States over the last century that has been brought about primarily by an increased frequency and intensity of events in the upper 10th percentile of the daily precipitation distribution – particularly in the Northeast. This study investigates trends in 28 long‐term annual flood series for New England watersheds with dominantly natural streamflow. The flood series are an average of 75 years in length and are continuous through 2006. Twenty‐five series show upward trends via the nonparametric Mann‐Kendall test, 40% (10) of which are statistically significant (p < 0.1). Moreover, an average standardized departures series for 23 of the study gages indicates that increasing flood magnitudes in New England occurred as a step change around 1970. The timing of this is broadly synchronous with a phase change in the low frequency variability of the North Atlantic Oscillation, a prominent upper atmospheric circulation pattern that is known to effect climate variability along the United States east coast. Identifiable hydroclimatic shifts should be considered when the affected flow records are used for flood frequency analyses. Special treatment of the flood series can improve the analyses and provide better estimates of flood magnitudes and frequencies under the prevailing hydroclimatic condition.     

An Analysis of the Wind Energy Potential of Elazig,Turkey

Abstract

In this study, the wind energy potential of Elazig is statistically analyzed based on hourly measured wind speed data over the five-year period from 1998 to 2002. The probability density distributions are derived from cumulative distribution functions. Two probability density functions are fitted to the measured probability distribution on a yearly basis. The wind energy potential of the location is studied based on the Weibull and Rayleigh distributions. It was found that the numerical values of both Weibull parameters (k and c) for Elazig vary over a wide range. The yearly values of k range from 1.653 to 1.878 with an average value of 1.819, while those of c are in the range of 2.757–2.994 m/s with an average value of 2.824 m/s. In addition, yearly mean wind speed and mean power density of Elazig is found as 2.79 m/s and 38.76 W/m², respectively. The wind speed distributions are represented by Weibull distribution and also by Rayleigh distribution, with a special case of the Weibull distribution for k = 2. As a result, the Rayleigh distribution is found to be suitable to represent the actual probability of wind speed data for Elazig.     

中国南方酸雨的分布特征及其成因分析

本文阐述了酸雨的危害、近几年中国南方地区酸雨的污染的时空分布状况、酸雨的成因等3方面的内容。研究表明：我国南方酸雨区的酸雨污染状况基本上处在一个稳定的时期。降水pH〈5的区域有从长江中上游向长江中下游发展的趋势;在时间分布上,秋季冬季降水pH低,酸雨发生的频率高;春季夏季降水pH高,酸雨发生的频率低。在酸雨的成因上,着重讨论了大气性质、污染物的迁移和扩散、气候条件、大气中颗粒物浓度以及土壤性质对酸雨形成的影响。