ESTIMATING THE MEAN AND VARIANCE OF CENSORED PHOSPHORUS CONCENTRATIONS IN FLORIDA RAINFALL1

ABSTRACT: The total phosphorous (TP) concentrations in the South Florida rainfall have been recorded in weekly intervals with a detection limit (D_L) of 3.5 μg/L. As a large amount of the data is reported as below the D_L, appropriate statistical methods are needed for data analysis. Thus, an attempt was made to identify an appropriate method to estimate the mean and variance of the data. In particular, a method to separate the statistics for the below D_L portion from the estimated population statistics is proposed. The estimated statistics of the censored data are compared with the statistics of the uncensored data available from the recent years’ laboratory records. It was found that the one-step restricted maximum likelihood method is the most accurate for the wet TP data, and that the proposed method to combine the estimated statistics for TP < D_L portion and the sample statistics for TP ≥ D_L portion improves estimates compared to the conventional maximum likelihood estimates.     

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.     

ESTIMATING MEAN AND VARIANCE FOR ENVIRONMENTAL SAMPLES WITH BELOW DETECTION LIMIT OBSERVATIONS1

ABSTRACT: Left-censoring of data sets complicates subsequent statistical analyses. Generally, substitution or deletion methods provide poor estimates of the mean and variance of censored samples. These substitution and deletion methods include the use of values above the detection limit (DL) only, or substitution of 0, DL/2 or the DL for the below DL values during the calculation of mean and variance. A variety of statistical methods provides better estimators for different types of distributions and censoring. Maximum likelihood and order statistics methods compare favorably to the substitution or deletion methods. Selected statistical methods applicable to left-censoring of environmental data sets are reviewed with the purpose of demonstrating the use of these statistical methods for coping with Type I (and Type II) left-censoring of normally and log-normally distributed environmental data sets. A PC program (UNCENSOR) is presented that implements these statistical methods. Problems associated with data sets with multiple DLs are discussed relative to censoring methods for life and fatigue tests as recently applied to water quality data sets.     

USING UNCENSORED TRACE-LEVEL MEASUREMENTS TO DETECT TRENDS IN GROUND WATER CONTAMINATION1

ABSTRACT: Environmental decision making involving trace-levels of contaminants can be complicated by censoring, the practice of reporting concentrations either as less than the limit of detection (LOD) or as not detected (ND) when a test result is less than the LOD. Censoring can result in data series that are difficult to meaningfully summarize, graph, and analyze through traditional statistical methods. In spite of the relatively large measurement errors associated with test results below the LOD, simple and meaningful analyses can be carried out that provide valuable information not available if data are censored. For example, an indication of increasing levels of contamination at the fringe of a plume can act as an early warning signal to trigger further study, an increased sampling frequency, or a higher level of remediation at the source. This paper involves the application of nonparametric trend analyses to uncensored trace-level groundwater monitoring data collected between March 1991 and August 1994 on dissolved arsenic and chromium for seven wells at an industrial site in New York.     

A TAU-LIKE TEST FOR TREND IN THE PRESENCE OF MULTIPLE CENSORING POINTS1

ABSTRACT: A common problem arises in testing for trends in water quality when observations are reported as “less than detection limit.” If a single detection limit is used for the entire study, existing non-parametric statistical methods, modified for ties, are applicable. If, however, the detection limit varies during the course of the study, resulting in multiple detection limits, then the commonly used trend detection methods are not appropriate. A statistic similar to Kendall's tau, but based on expected ranks, is proposed. Monte Carlo simulations show that the normal approximation to the distribution of this statistic is quite good, even for small samples and a large proportion of censored observations. The statistic is also shown to have greater power than the ad-hoc method of treating all observations less than the target censored observation as tied.     

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.     

小流域水质评价方法对比研究

为分析小流域水质评价方法的准确度和适应度,以小安溪流域2017年和2018年的监测数据为基础,利用单因子评价法、综合指数评价法、内梅罗污染指数法和加拿大水质指数法进行水质评价,利用等标水质分析的思想对比了四种方法的评价准确度。评价结果显示:单因子评价法更适合评价水质分布较均匀的流域,内梅罗污染指数法要更为客观一些,加拿大水质指数法更适合较大的、评价指标较多的流域。综合指数评价法是最适合小流域水质评价的。其结果为小流域水质评价方法选择提供了借鉴。     

Water Quality and Land Use Changes in the Alafia and Hillsborough River Watersheds,Florida, USA1

Abstract: Spatial distribution of land use can have a substantial effect on surface and groundwater quality. Our objective was to test for trends in flow components and water quality related to changes in land use in the Alafia and Hillsborough River watersheds in Florida, USA, over the period 1974‐2007. In addition, water quality statistics were evaluated in the perspective of numeric water quality criteria and proposed reclassification of segments of the Alafia River. Trends in 10 water quality parameters and three discharge variables were evaluated using a nonparametric trend detection test. Results of land use analysis indicated substantial urbanization and loss of agricultural land in the study area. Discharge variables did not exhibit significant trends, whereas trends in the majority of water quality concentrations were negative or nonsignificant with total nitrogen and total Kjeldahl nitrogen as exceptions showing positive trends. Changes in nutrient pathways could not be clearly identified. Considering recently promulgated numeric nutrient criteria and standards for dissolved fluoride, much of the Alafia River was found to be out of compliance. While there were land use changes and changes in water quality over the study period, it was difficult to identify a direct cause‐effect relationship. Responses to regulatory efforts, such as the Clean Water Act and improvements in phosphate mining practices, may have had greater impacts on water quality than changes in land use.     

Estimating irrigation water demand in the Moroccan Drâa Valley using contingent valuation

Irrigation water management is crucial for agricultural production and livelihood security in Morocco as in many other parts of the world. For the implementation of an effective water management, knowledge about farmers' demand for irrigation water is crucial to assess reactions to water pricing policy, to establish a cost-benefit analysis of water supply investments or to determine the optimal water allocation between different users. Previously used econometric methods providing this information often have prohibitive data requirements. In this paper, the Contingent Valuation Method (CVM) is adjusted to derive a demand function for irrigation water along farmers' willingness to pay for one additional unit of surface water or groundwater. An application in the Middle Draa Valley in Morocco shows that the method provides reasonable results in an environment with limited data availability. For analysing the censored survey data, the Least Absolute Deviation estimator was found to be a more suitable alternative to the Tobit model as errors are heteroscedastic and non-normally distributed. The adjusted CVM to derive demand functions is especially attractive for water scarce countries under limited data availability.     

STOCHASTIC WATER QUALITY ANALYSIS USING RELIABILITY METHOD1

ABSTRACT: This study developed a QUAL2E‐Reliability Analysis (QUAL2E‐RA) model for the stochastic water quality analysis of the downstream reach of the main Han River in Korea. The proposed model is based on the QUAL2E model and incorporates the Advanced First‐Order Second‐Moment (AFOSM) and Mean‐Value First‐Order Second‐Moment (MFOSM) methods. After the hydraulic characteristics from standard step method are identified, the optimal reaction coefficients are then estimated using the Broyden‐Fletcher‐Goldfarb‐Shanno (BFGS) method. Considering variations in river discharges, pollutant loads from tributaries, and reaction coefficients, the violation probabilities of existing water quality standards at several locations in the river were computed from the AFOSM and MFOSM methods, and the results were compared with those from the Monte Carlo method. The statistics of the three uncertainty analysis methods show that the outputs from the AFOSM and MFOSM methods are similar to those from the Monte Carlo method. From a practical model selection perspective, the MFOSM method is more attractive in terms of its computational simplicity and execution time.     

Assessment of groundwater quality by means of self-organizing maps: application in a semiarid area

The Kohonen neural network was applied to hydrochemical data from the Detritic Aquifer of the Lower Andarax, situated in a semiarid zone in the southeast of Spain. An activation map was obtained for each of the sampling points, in which the spatial distribution of the activated neurons indicated different water qualities. To extract the information contained in the activation maps, they were divided into nine quadrats. Cartesian coordinates were assigned to each quadrant (x, y), and for each sampling point, three derived variables were selected, which were assigned the values x and y of the corresponding quadrat. A classification was defined based on this simple matrix system which allows an easy and rapid means of evaluating the water quality. This assessment highlights the various processes that affect groundwater quality. The method generates output that is easier to interpret than from traditional statistical methods. The information is extracted from the activation maps without significant loss of information. The method is proposed for assessing water quality in hydrogeochemically complex areas, where large numbers of observations are made.     

A spatial-statistical approach for modeling the effect of non-point source pollution on different water quality parameters in the Velhas river watershed--Brazil

In this article, a methodology for evaluating the effect of land use/land cover on the quality of nearby stream water in a semiarid environment is described and tested on a large watershed in Southeastern Brazil. The approach aims at identifying the width of the riparian area having the strongest effect on different water quality parameters. The land use/land cover data were generated from remotely sensed data while water quality point data were supplied by a government agency. Testing was conducted for both the rainy and dry seasons in an effort to understand the direct effect of surface runoff. The approach combines cartographic modelling using a geographical information system (GIS) and statistics to establish the strength of the relationship between water quality, land use and the distance from the stream. Results suggest a strong relationship between land use/land cover and turbidity, nitrogen and fecal coliforms. They also suggest that each of these parameters has a unique behavior when distance from the stream is considered. Finally, although it was expected that the models would apply better during the wet season, some parameters had the opposite behavior and displayed a better fit during the dry season.     

STATISTICAL METHODS AND SAMPLING DESIGN FOR ESTIMATING STEP TRENDS IN SURFACE-WATER QUALITY1

ABSTRACT: This paper addresses two components of the problem of estimating the magnitude of step trends in surface water quality. The first is finding a robust estimator appropriate to the data characteristics expected in water-quality time series. The Hodges-Lehmann class of estimators is found to be robust in comparison to other nonparametric and moment-based estimators. A seasonal Hodges-Lehmann estimator is developed and shown to have desirable properties. Second, the effectiveness of various sampling strategies are examined using Monte Carlo simulation coupled with application of this estimator. The simulation is based on a large set of total phosphorus data from the Potomac River. To assure that the simulated records have realistic properties, the data are modeled in a multiplicative fashion incorporating flow, hysteresis, seasonal, and noise components. The results demonstrate the importance of balancing the length of the two sampling periods and balancing the number of data values between the two periods. The inefficiency of sampling at frequencies much in excess of 12 samples per year is demonstrated. Rotational sampling designs are discussed, and efficient designs, at least for this river and constituent, are shown to involve more than one year of active sampling at frequencies of about 12 per year.     

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.     

USE OF MICROCOMPUTERS FOR THE MANAGEMENT OF WATER QUALITY DATA1

ABSTRACT: Information on raw water quality, treatment process removal efficiency, and distribution system monitoring is essential to the proper management and operation of a water utility system. Microcomputer hardware and software systems using commercially available data base management systems (DBMS) have emerged within the last few years as an effective means of managing, analyzing, and displaying water quality data. Understanding hardware, software, and training requirements is essential to the proper use of these systems. Three types of data base design are common: relational, hierarchical, and network. Only the relational type of data base architecture is widely implemented on microcomputer DBMS. In this paper two examples of the application of DBMS to water utility problems are presented. One example deals with collection and analysis of data concerning the water quality of the Mississippi River. The second example deals with the DBMS as a means of analyzing water quality data in the North Penn Water Authority (NPWA) distribution system.