PARAMETRIC/NONPARAMETRIC MIXTURE DENSITY ESTIMATION WITH APPLICATION TO FLOOD-FREQUENCY ANALYSIS1

Much attention has been invested in the model choice problem for peak annual flows, in the context of flood frequency analysis. The authors would sidestep this dilemma through non-parametric density estimation methodology, but recognize that the standard nonparametric estimators preclude the use of prior information and related data, and furthermore have virtually no tail at all. Here we offer a remedy for these inadequacies by introducing an estimator which mixes parametric and nonparametric density estimates. We prove that our mixture rule is consistent. By this procedure, we do allow incorporation of prior information, experience, and regional data information, but nevertheless provide a safeguard against incorrect model choice.     

FLOOD FREQUENCY CHARACTERISTICS OF SOME ARIZONA WATERSHEDS1

The flood frequency characteristics of 18 watersheds in southeastern Arizona were studied using the log-Boughton and the log-Pearson Type 3 distribution. From the flood frequency study, a generalized envelope for Q₁₀₀ for watersheds 0.01 to 4000 mi² in area has been produced for southeastern Arizona. The generalized envelope allows comparisons to be made among the relative flood characteristics of the watersheds used in the study and provides a conservative estimate of Q₁₀₀ for ungaged watersheds in the region.     

REGIONALIZATION AND PREDICTION OF FLOODS IN THE FRASER RIVER CATCHMENT,B.C.1

Probability distributions that model the return periods of flood characteristics derived from partial duration series are proposed and tested in the Fraser River catchment of British Columbia. Theoretical distributions describing the magnitude, duration, frequency and timing of floods are found to provide a goof fit to the observed data. The five estimated parameters summarizing the flood characteristics of each basin are entered into a discriminant analysis procedure to establish flood regions. Three regions were identified, each displaying flood behavior closely related to the physical conditions of the catchment. Within each region, regression equations are obtained between parameter values and basin climatic and physiographic variables. These equations provide a satisfactory prediction of flood parameters and this allows the estimation of a comprehensive set of flood characteristics for areas with sparse hydrologic information.     

GENERALIZED SKEW COEFFICIENTS FOR FLOOD FREQUENCY ANALYSIS1

ABSTRACT: In order to promote a uniform and consistent approach for floodflow frequency studies, the U.S. Water Resources Council has recommended the use of the log-Pearson type III distribution with a generalized skew coefficient. This paper investigates various methods of determining generalized skew coefficients. A new method is introduced that determines generalized skew coefficients using a weighting procedure based upon the variance of regional (map) skew coefficients and the variance of sample skew coefficients. The variance of skew derived from sample data is determined using either of two non-parametric methods called the jackknife or bootstrap. Applications of the new weighting procedure are presented along with an experimental study to test various weighting procedures to derive generalized skew coefficients.     

NONPARAMETRIC STATISTICAL ANALYSIS OF ANNUAL PEAK FLOW DATA FROM A RECENTLY URBANIZED WATERSHED1

ABSTRACT. In order to demonstrate the feasibility of a nonparametric statistical application in investigating the hydrologic impact of the rapid land use change accompanying intense urbanization, annual maximum peak flow data from an actual example (the Northeast Branch Basin, a recently urbanized Washington, D.C., suburban watershed) were analyzed. Annual peak flow data from the Patuxent Basin above Unity, Maryland, a rural watershed in close proximity to the study area, were compared to data from the Northeast Branch for the Same period utilizing the Wilcoxon matched-pairs signed-ranks test. A change in central tendency of each series was noted at the 0.01 significance level; however, the change was negative in the rural basin and positive in the urbanized Northeast Branch Basin. This central tendency change was considered indicative of an average decrease in the size of rainstorms producing annual maximum peak discharges. Rainstorm data from the Northeast Branch Basin were divided into two equal periods (before urbanization and after) and the Wilcoxon test was applied. It was found that rainstorms producing maximum annual peak discharges in the urbanized period were indeed smaller than those in the prior period (0.01 level of significance); however, larger annual peaks were produced. It was concluded that nonparametric statistical methods can be used readily with conventional methods to isolate and clearly analyze the various problems in an actual urban hydrologic study.     

CATCHMENT RESPONSE TIME AS A PREDICTOR OF FLOOD QUANTILES1

ABSTRACT: A regression analysis using a generalized least squares approach on flow data from the driftless area of Wisconsin indicates that the ratio of drainage area to time-to-peak is a good predictor of flood quantiles. The estimation of time-to-peak (or some other measure of basin response time) requires direct measurement of river stage and possibly rainfall at the site of which the quantiles are to be estimated. The cost-effectiveness of such an approach must yet be determined.     

A UNIFYING SET OF PROBABILITY TRANSFORMS FOR STOCHASTIC HYDROLOGY1

Abstract: An ordered set of probability sensity functions was derived form transforms of the normal distribution. Variate transforms are based on orders of exponentiation. The set of distributions includes the log-normal. a partial basis for use of these functins in hydrology is demonstrated by establishing some required properties. A concept of mixed samples of zero and nonzero elements forming nonseparable sets of virtual and real elements is introduced to establish a physical lower limit of sampled diata independent of functional bounds.     

GAGE DENSITY AND LOCATION FOR ESTIMATING MEAN ANNUAL PRECIPITATION IN MOUNTAINOUS AREAS1

ABSTRACT: Data from a network of 45 shielded precipitation gages on the Reynolds Creek Experimental Watershed in Southwestern Idaho were analyzed to determine the optimum gage density for estimating mean annual precipitation. Four subsets of the 45 gage network were used to derive a curve of mean annual precipitation versus number of gages with a confidence band at the 95 percent level. When less than 20 gages were used in the estimate, the confidence interval widens rapidly. Estimates were improved by stratifying gages on the basis of plant cover class or by elevation bands. Sixty-four percent of the variation in mean annual precipitation was accounted for by elevation and cover class. The aspect and hydrologic soil classification were not statistically significant.     

ESTIMATING PROBABLE MAXIMUM FLOOD PROBABILITIES1

ABSTRACT: Methods of computing probabilities of extreme events that affect the design of major engineering structures have been developed for most failure causes, but not for design floods such as the probable maximum flood (PMF). Probabilities for PMF estimates would be useful for economic studies and risk assessments. Reasons for the reluctance of some hydrologists to assign a probability to a PMF are discussed, and alternative methods of assigning a probability are reviewed. Currently, the extrapolation of a frequency curve appears to be the most practical alternative. Using 46 stations in the Mid-Atlantic region, the log-gamma, log-normal, and log-Gumbel distributions were used to estimate PMF probabilities. A 600,000-year return period appears to be a reasonable probability to use for PMFs in the Mid-Atlantic region. The coefficient of skew accounts for much of the variation in computed probabilities.     

SPACE-TIME VALIDATION OF A THUNDERSTORM RAINFALL MODEL1

A probability model for predicting the occurrence and magnitude of thunderstorm rainfall developed in the southwestern United States was tested in the metropolitan Chicago area with reasonable success, especially for the moderate to the extreme runoff-producing events. The model requires the estimation of two parameters, the mean number of events per year and the conditional probability of rain given that an event has occurred. To tie in the data from more than one gage in an area, an event can be defined in several ways, such as the areal mean rainfall exceeding 0.50 inch and at least one gage receiving more than 1.0 inch. This type of definition allows both of the model parameters to be obtained from daily warm-season rainfall records. Regardless of the definition used a Poisson distribution adequately described the number of events per season. A negative binomial distribution was derived as representing the frequency density function for rainfall where several gages are employed in defining a storm. Chicago data fit both distributions very well at events with relatively high return periods. The results indicate the possibility of using the model on a regional basis where limited amount of data may be used to estimate parameters for extensive areas.     

NONPARAMETRIC STATISTICAL METHODS IN URBAN HYDROLOGIC RESEARCH1

ABSTRACT. In urban hydrologic studies, it is often necessary to determine the effect of changes in urban land use patterns on such runoff characteristics as flood peaks and flow volumes. Nonparametric statistical methods have certain properties that make them a valuable tool for detecting hydrologic change caused by a treatment, such as urbanization, that changes watershed over a period of time. As many hydrologists do not have a working familiarity with nonparametric methods, a number of them are used for illustrative purposes to analyze the effect of urbanization on 24 years of annual flood peaks for a Louisville, Kentucky, watershed. In the example, urbanization was found to increase the central tendency, but not the dispersion of the peaks. Peak flows modeled by holding watershed parameters constant were also found to be increasing because of an upward trend in precipitation. By following the numerical examples in the paper and looking up test statistics in referenced sources, the reader can easily apply these methods to other situations.     

TEMPORAL FLUCTUATIONS OF HEAVY RAINFALL MAGNITUDES IN NEW ORLEANS,LOUISIANA: 1871–19911

ABSTRACT: Recent occurrences of heavy rainfall in New Orleans, Louisiana, have led to speculation that the local heavy rainfall regime has changed. To objectively determine the validity of these speculations, changing magnitudes of storm rainfall were investigated through an examination of the annual maximum storm series from 1871 to 1991 at the New Federal site. Although a long-term trend was not found, the Wilcoxon test indicated that magnitudes during the last 14 years (from 1978–1991) differed significantly from the rest of the series.     

PERIODIC AUTOREGRESSIVE-MOVING AVERAGE (PARMA) MODELING WITH APPLICATIONS TO WATER RESOURCES1

Results involving correlation properties and parameter estimation for autoregressive-moving average models with periodic parameters are presented. A multivariate representation of the PARMA model is used to derive parameter space restrictions and difference equations for the periodic autocorrelations. Close approximation to the likelihood function for Gaussian PARMA processes results in efficient maximum-likelihood estimation procedures. Terms in the Fourier expansion of the parameters are sequentially included, and a selection criterion is given for determining the optimal number of harmonics to be included. Application of the techniques is demonstrated through analysis of a monthly streamflow time series.     

FLOOD FREQUENCY ANALYSIS FOR SMALL WATERSHEDS IN SOUTHERN ILLINOIS1

ABSTRACT: Twenty-two gaging stations were selected for developing a regional flood frequency curve for small (area less than 2 square miles) watersheds in southern Illinois. Five probability functions were compared, and the extreme value type I function was selected to develop the regional flood curve. The curve was generated with the index flood method and also another empirical method that related the function parameters to the watershed area. Estimated peak discharges with various return periods were compared with the results obtained from multiple regression analysis.     

Estimation of the shadow prices of pollutants with production/environment inefficiency taken into account: a nonparametric directional distance function approach

This paper deals with the estimation of the shadow prices of pollutants with a nonparametric directional distance function approach, where the inefficiency involved in the production process is taken into account unlike the previous studies. The directional vector, which is critical to the estimation and subject to the criterion for an appropriate efficiency rule proposed here, is calculated by using the annual plans of power plants in terms of production and environment. In the empirical study for Korea's electric power industry during the period of 1990-1995, we find that the average shadow prices of sulfur oxides (SOx), nitrogen oxides (NOx), and total suspended particulates (TSP) are approximately 10% lower than those calculated under the assumption of full efficiency. The methodology we propose and the findings obtained in the empirical study allow us to undertake better decision-making over a broad range of environmental policy issues.     

正交化方法在水质模型参数确定中的应用

本文根据常微分方程参数反问题的数学理论,将正交化方法同有限差分法结合用于确定水质模型参数,并与正则化方法、最速下降法和共轭梯度法作了比较。其计算结果对比表明,正交化方法具有快速、简便、可靠的特点。更适合于水质模型参数的确定。     

运用模糊数学法对焚烧烟气处理方法进行综合评价

运用模糊数学法的理论对城市生活垃圾及特种垃圾焚烧烟气的各种处理方法进行综合评价,提出合理的处理方法。     

有色金属行业CO2排放估算方法研究

通过对国内外有色金属行业温室气体排放估算方法研究现状的分析,将联合国政府间气候变化专门委员会(IPCC)温室气体排放清单指南、国际有色行业协会和环境科学研究中的一些常用算法,总结归纳应用于有色金属行业温室气体的排放量估算,从估算方法和结果上分析各种方法的优缺点和使用条件。以原铝生产CO2排放估算为例,对有色金属温室气体排放进行实证分析,为有色金属行业温室气体排放估算提供参选方法,促进有色金属工业的节能减排。