PARAMETER ESTIMATION FOR TPLN DISTRIBUTION FOR FLOOD FREQUENCY ANALYSIS1

ABSTRACT: The principle of maximum entropy (POME) was used to derive an alternative method for parameter estimation for the three parameter lognormal (TPLN) distribution. Six sets of annual peak discharge data were used to evaluate this method and compare it with the methods of moments and maximum likelihood estimation.     

熵法估参在环境监测数据频率分析中的应用

以最大信息熵原理为理论基础的熵法估参方法，是一种具有严格物理和数学意义的新型参数估计方法，本文针对珠江广州河段主要污染物含量长年监测数据，对比熵法与传统方法矩法对四参数Г分布的估参结果，并以频率绝对离盖和最小为准则进行判定，结果表明，熵法估参结果与矩法总体上相当接近，且大部分样本的熵法估计参数优于矩法，在环境监测数据频率分析中具有实用性和推广价值。     

ESTIMATING PARAMETERS OF EV1 DISTRIBUTION FOR FLOOD FREQUENCY ANALYSIS1

ABSTRACT: The parameters of the extreme value type 1 distribution were estimated for 55 annual flood data sets by seven methods. These are the methods of (1) moments, (2) probability weighted moments, (3) mixed moments, (4) maximum likelihood estimation, (5) incomplete means, (6) principle of maximum entropy, and (7) least squares. The method of maximum likelihood estimation was found to be the best and the method of incomplete means the worst. The differences between the methods of principle of maximum entropy, probability weighted moments, moments, and least squares were only minor. The difference between these methods and the method of maximum likelihood was not pronounced.     

EVALUATION OF PROBABILITY DENSITY FUNCTIONS IN PRECIPITATION MODELS FOR THE PACIFIC NORTHWEST1

ABSTRACT: Recent work has found that a one-parameter Weibull model of wet day precipitation amount based on the Weibull distribution provides a better fit to historical daily precipitation data for eastern U.S. sites than other one-parameter models. The general two-parameter Weibull distribution was compared in this study to other widely used distributions for describing the distribution of daily precipitation event sizes at 99 sites from the U.S. Pacific Northwest. Surprisingly little performance was sacrificed by reducing the two-parameter Weibull to a single-parameter distribution. Advantages of the single-parameter model included requiring only the mean wet day precipitation amount for calibration, invertibility for simulation purposes, and ease of analytical manipulation. The fit of the single-parameter Weibull to the 99 stations included in this study was significantly better than other single-parameter models tested, and performed as well as the widely endorsed, more cumbersome, two-parameter gamma model. Both the one-and two-parameter Weibull distributions are shown to have b-moments that are consistent with historical precipitation data, while the ratio of b-skew and b-variance in the gamma model is inconsistent with the historical recerd by this measure. In addition, it was found that the two-parameter gamma distribution was better fit using the method of moments estimators than maximum likelihood estimates. These findings suggested that the distribution in precipitation among sites in the Pacific Northwest with dramatically different settings are nearly identical if expressed in proportion to the mean site event size.     

THE FLEXIBLE TOLERANCE METHOD FOR ESTIMATING HYDROLOGIC PARAMETERS IN THE ROOT ZONE1

In this study, a constrained minimization method, the flexible tolerance method, was used to solve the optimization problems for determining hydrologic parameters in the root zone: water uptake rate, spatial root distribution, infiltration rate, and evaporation. Synthetic soil moisture data were first generated using the Richards' equation and its associated initial and boundary conditions, and these data were then used for the inverse analyses. The results of inverse simulation indicate the following. If the soil moisture data contain no noise, the rate of estimated water uptake and spatial root distribution parameters are equal to the true values without using constraints. If there is noise in the observed data, constraints must be used to improve the quality of the estimate results. In the estimation of rainfall infiltration and surface evaporation, interpolation methods should be used to reduce the number of unknowns. A fewer number of variables can improve the quality of inversely estimated parameters. Simultaneous estimation of spatial root distribution and water uptake rate or estimation of evaporation and water uptake rate is possible. The method was used to estimate the water uptake rate, spatial root distribution, infiltration rate, and evaporation using long‐term soil moisture data collected from Nebraska's Sand Hills.     

KRIGED ESTIMATES OF TRANSMISSIVITY IN THE MESILLA BOLSON,NEW MEXICO1

ABSTRACT: Kriging utilizes a statistically based procedure of spatial interpolation that incorporates the spatial correlation structure of the phenomenon, and provides an error estimate. Kriging was applied to a total of 141 transmissivity values in an attempt to quantify the transmissivity distribution of the Santa Fe aquifer in Mesilla Bolson. New Mexico. The analysis produced contour maps of estimated transmissivity values and associated estimation variances. Through variogram analysis and fitting of an exponential variogrsm to 141 natural log of transmissivity (InT) values, the range was determined to be 3 miles, the average variance 2.74 (σ_InT= 1.65) with a mean of 8.65. Kriged estimates were generally lower when compared to estimates based on available transmissivity maps.     

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.     

ESTIMATION OF THE HIEC1 LOSS PARAMETERS FOR ROUTING THE PROBABLE MAXIMUM FLOOD1

ABSTRACT: Twenty storm events were used to select design values of the HEC1 loss parameters STRTL and CNSTL in order to route the probable maximum flood, PMF, through the Englewood watershed, Ohio. The parameter STRTL represents the initial volume of water lost due to interception and incomplete saturation of the soil prior to the storm. The parameter CNSTL represents a continuous loss rate and depends only on the watershed. When optimized from each storm event, STRTL varied between 0.0 and 3.4 inches with an average of 1.0 inch; CNSTL varied between 0.02 and 0.26 inch/hour, and it followed a normal probability distribution with a mean of about 0.1 inch/hour. The absence of correlation between optimum CNSTL values and each of total rainfall, total loss, and runoff duration supported the selection of the mean CNSTL as a design value. PMF routing through the Englewood watershed revealed that the PMF at the outlet is not sensitive to STRTL, but highly affected by CNSTL variations. The insensitivity to STRTL was due to the presence of a dam at the outlet of the watershed that caused the buildup of water in the watershed, thereby masking the storage effect of STRTL. The peak PMF increased by about 27 percent when the design CNSTL was decreased to 0.05 inch! hour, and decreased by about 18 percent when the design CNSTL was increased to 0.15 inch/hour.     

AN ILLUSTRATION OF MODEL STRUCTURE IDENTIFICATION1

ABSTRACT: The purpose of this article is to discuss the importance of uncertainty analysis in water quality modeling, with an emphasis on the identification of the correct model specification. A wetland phosphorus retention model is used as an example to illustrate the procedure of using a filtering technique for model structure identification. Model structure identification is typically done through model parameter estimation. However, due to many sources of error in both model parameterization and observed variables and data, error-in-variable is often a problem. Therefore, it is not appropriate to use the least squares method for parameter estimation. Two alternative methods for parameter estimation are presented. The first method is the maximum likelihood estimator, which assumes independence of the observed response variable values. In anticipating the possible violation of the independence assumption, a second method, which coupled a maximum likelihood estimator and Kalman filter model, was presented. Furthermore, a Monte Carlo simulation algorithm is presented as a preliminary method for judging whether the model structure is appropriate or not.     

Wind power potential assessment for three buoys data collection stations in the Ionian Sea using Weibull distribution function

The present article utilizes wind measurements from three buoys data collection stations in Ionian Sea to study the wind speed and power characteristics using the Weibull shape and scale parameters. Specifically, the site dependent, annual, and monthly mean patterns of mean wind speed, Weibull parameters, frequency distribution, most probable wind speed, maximum energy carrying wind speed, wind power density and wind energy density characteristics have been analyzed. The Weibull distribution was found to represent the wind speed distribution with more than 90% accuracy, in most of the cases. Moreover, the correlation between the percentages of times the wind speed was above cut-in-speed and the measured mean wind speed for the three selected sites, as the correlation between the aforementioned percentages and the scale parameter c were examined and were found linear. At all these sites, no definite increasing or decreasing trends in annual mean wind speed values could be detective over the data reporting period. The mean values of wind speed, scale parameter, most probable wind speed, maximum energy carrying wind speed, wind power and wind energy density values showed higher values during winter time and lower in summer time in Pylos and Zakynthos. Moreover, Pylos and Zakynthos were found to be the best sites from wind power harnessing point of view.     

Effects of palm oil mill effluent media on cell growth and lipid content of Nannochloropsis oculata and Tetraselmis suecica

In this study, palm oil mill effluent (POME) was used as an alternative medium for algal biomass and lipid production. The influence of different concentrations of filtered and centrifuged POME in sea water (1, 5, 10 and 15%) on microalgal cell growth and lipid yield were investigated. Both Nannochloropsis oculata and Tetraselmis suecica had enhanced cell growth and lipid accumulation at 10% POME with maximum specific growth rate (0.21 d^–1 and 0.20 d^–1) and lipid content (39.1 ± 0.73% and 27.0 ± 0.61%), respectively, after 16 days of flask cultivation. The total Saturated Fatty Acid (SFA) (59.24%, 68.74%); Monounsaturated Fatty Acid (MUFA) (15.14%, 12.26%); and Polyunsaturated Fatty Acid (PUFA) (9.07%, 8.88%) were obtained for N. oculata and T. suecica, respectively, at 10% POME. Algal cultivation with POME media also enhanced the removal of Chemical Oxygen Demand (COD) (93.6–95%), Biological Oxygen Demand (BOD) (96–97%), Total Organic Compound (TOC) (71–75%), Total Nitrogen (TN) (78.8–90.8%) and oil and grease (92–94.9%) from POME.     

ON THE ESTIMATION OF DIRECT IRRIGATION BENEFITS1

For optimal allocation of resources, it is critical to arrive at proper estimations of direct benefits created by irrigation projects. This paper reviews critically the traditinal procedures of estimating the direct irrigation benefits and, in this context, presents formulas to show the extent of bias in them. The paper further discusses the implications of shifts in demand over time for biases in the estimation of direct benefits through traditional procedures and provides altenate procedures for the proper estimation of direct irrigation benefits. In this context, it throws some light on the exact distribution of benefits between consumers and producers.     

MEASUREMENT OF HYDRAULIC CONDUCTIVITY AND DIFFUSIVITY FOR PREDICTING THE PROCESS OF SOIL WATER INFILTRATION FROM A TRICKLE SOURCE1

ABSTRACT: Two soil water functions, hydraulic conductivity K(θ) and diffusivity D(θ), were estimated by two methods In one method D(θ) was estimated according to Bruce and Klute (1956), and K(θ) was calculated from D(θ) and the retention curve. In the second, K(θ) was obtained by field estimation, with D(θ) being calculated from K(θ) and the retention curve. The criterion of reliability for both methods was agreement between experimental and predicted distribution of soil water content. The prediction was made using the functions K(θ) and D(θ) as soil water parameters in both methods. Theoretical and experimental agreement was generally good. The first method, however, was found to be best for high soil water content and the second for low soil water content. In addition, the water content at the end of the monotonic increase of function D(θ) (estimated according to Bruce and Klute 1956) was found to be about the upper limit of field soil water content. It can be used as a boundary condition in the numerical solution of a cylindrical model of infiltration from a trickle source. It was concluded that the best agreement between theory and experiment can be found when the combined values of D(θ) and K(θ) from both methods of estimation are used.     

Fitting a Gamma Distribution Over a Synthetic Unit Hydrograph1

ABSTRACT: Several methods for synthetic unit hydrographs are available in the literature. Most of these methods involve the hand fitting of a curve over a set of a few hydrograph points, which can sometimes be a subjective task. Besides, the user often finds it difficult or simply neglects to adjust the generated unit graph to a runoff volume of one unit (inch, cm, or mm). It is the purpose of this paper to present to the design hydrologist a simple method to fit a smooth gamma distribution over a single point specified by the unit hydrograph peak and the time to peak with a guaranteed unit depth of runoff.     

Magnetic composite prepared from palm shell-based carbon and application for recovery of residual oil from POME

Magnetic separation combined with adsorption by activated carbon has been found to be a useful method for removing pollutants. In this paper, the use of palm shell as a source of activated carbon for the removal and recovery of oil from palm oil mill effluent (POME) is studied. In the first part of the study, the properties of samples of activated carbon prepared from palm shell under a variety of different conditions were characterized for their hydrophobicity, surface areas and pore size distribution. The most effective of the activated carbon samples was prepared by impregnation with ZnCl(2) followed by combined physical/chemical activation under carbon dioxide flow at 800 °C. Four grams of these samples adsorbed 90% of the oil from 50 mL POME. In the second part, the palm shell-based carbon samples were given magnetic properties by the technique of iron oxide deposition. Ninety-four percent of the activated carbon/iron oxide composite containing the adsorbed oil could be extracted from the POME by a magnetic bar of 0.15 T. Four grams of the composite can remove 85% of oil from 50 mL POME and a total of 67% of the initial oil can then be recovered by hexane extraction. Powder X-ray diffractometry showed the presence of magnetite and maghemite in the activated carbon/iron oxide composite.     

PREDICTION OF MEAN ANNUAL FLOWS IN THE FRASER RIVER CATCHMENT,BRITISH COLUMBIA1

ABSTRACT: A method of predicting annual flows is presented and is applied to the Fraser River catchment. Statistical tests show the annual flow records to be stationary and aerially independent and can be adequately approximated by Gaussian distributions. Estimates are made of the Gaussian parameters for each subbasin. The spatial variations of these parameters are described by third order trend surfaces. The fitted surfaces can then be used to predict parameters of ungaged basins using the latitude and longitude of the basin centroids. The predicted parametric values are substituted into the Gaussian distribution to generate flows of various return periods.     

The valuation of historical sites: a case study of Valdivia,Chile

The economic valuation of cultural heritage is an area of increasing interest and an important research topic in the emerging field of cultural economics. Many services and values associated with cultural heritage are not traded in markets, and their estimation requires methods developed for the valuation of non-market goods, such as those used in environmental economics. This paper applies the contingent valuation method with double dichotomous choice to estimate the value of historical sites in the city of Valdivia, Chile. The valuation exercise was implemented by designing a hypothetical guided walking tour to a cluster of historical sites in the city centre, and surveying tourists visiting the city during the summer of 2004. Parametric and non-parametric statistical methods were used to estimate the survival distribution and the mean and median estimates of the willingness-to-pay (WTP). The study emphasizes the importance of explicitly treating heterogeneous preferences and the sensitivity of the survival distribution to the estimation methods used.     

A COMPARISON OF STATISTICAL TESTS ON THE EXTREME-VALUE TYPE-1 DISTRIBUTION1

ABSTRACT: The effects of the selections of plotting position formulae and class division schemes on goodness of fit tests are investigated for the extreme-value type-1 distribution using annual flood and annual maximum daily rainfall data. It was found that the plotting position formulae have a minor influence on the tests which involve their use, while the class division schemes may have a pronounced effect on the X²-test. The study also recommended the maximum likelihood method for fitting purposes and a new test which is independent of the afore-mentioned selections for judging the goodness of fit.     

COUPLING OF NONPARAMETRIC FREQUENCY AND L-MOMENT ANALYSES FOR MIXED DISTRIBUTION IDENTIFICATION 1

ABSTRACT: Both L-moment and nonparametric frequency analyses were performed on a series of annual maximum floods from New Brunswick, Canada. The L-moment analysis concluded that the data were generated from a unimodal Generalized Extreme Value (GEV) distribution. However, the nonparametric frequency analysis indicated that a majority of stations followed nonunimodal mixed distributions since peak flows occur during different seasons and are the result of different generating mechanisms. The coupling of L-moment and nonparametric analyses facilitates mixed distribution identification. Thus, the nonparametric method helps in identifying underlying probability distribution, especially when samples arise from mixed distributions.