DATA ANALYSIS OF WATER QUALITY TIME SERIES IN LAKE ERIE1

ABSTRACT: A comprehensive data analysis study is carried out for detecting trends and other statistical characteristics in water quality time series measured in Long Point Bay, Lake Erie. In order to glean an optimal amount of useful information from the available data, the exploratory and confirmatory data anslysis stages are adhered to. To test a range of hypotheses regarding the statistical properties of the time series, a wide variety of both parametric and nonparametric techniques are employed. A particularly useful nonparametric method for discovering trends is the seasonal Mann-Kendall test.     

TIME SERIES ANALYSIS IN PERSPECTIVE1

ABSTRACT: By employing a set of criteria for classifying the capabilities of time series models, recent developments in time series analysis are assessed and put into proper perspective. In particular, the inherent attributes of a wide variety of time series models and modeling procedures presented by the authors of the 18 papers contained in this volume are clearly pointed out. Additionally, it is explained how these models can address many of the time series problems encountered when modeling hydrologic, water quality and other kinds of time series. For instance, families of time series models are now available for modeling series which may contain nonlinearities or may follow nonGaussian distributions. Based upon a sound physical understanding of a problem and results from exploratory data analyses, the most appropriate model to fit to a data set can be found during confirmatory data analyses by following the identification, estimation and diagnostic check stages of model construction. Promising future research projects for developing flexible classes of time series models for use in water resources applications are suggested.     

DESIGN CONSIDERATIONS FOR AMBIENT STREAM QUALITY MONITORING1

ABSTRACT: Existing ambient water quality monitoring programs have resulted in data which are often unsuitable for assessment of water quality trends. A primary concern in designing a stream quality monitoring network is the selection of a temporal sampling strategy. It is extremely important that data for trend assessment be collected uniformly in time. Greatly superior trend detection power results for such a strategy as compared to stratified sampling strategies. In general, it is desirable that sampling frequencies be at least monthly but not greater than biweekly; higher sampling frequencies usually result in little additional information. An upper limit on trend detectability exists such that for both five and ten year base periods it is often impossible to detect trends in time series where the ratio of the trend magnitude to time series standard deviation is less than about 0.5. For the same record lengths trends in records with trend to standard deviation ratios greater than about one can usually be detected with very high power when a uniform sampling strategy is followed.     

TECHNIQUES FOR DETECTING TRENDS IN LAKE WATER QUALITY1

ABSTRACT: With the advent of standards and criteria for water quality variables, there has been an increasing concern about the changes of these variables over time. Thus, sound statistical methods for determining the presence or absence of trends are needed. A Trend Detection Method is presented that provides: 1) Hypothesis Formulation - statement of the problem to be tested, 2) Data Preparation - selection of water quality variable and data, 3) Data Analysis - exploratory data analysis techniques, and 4) Statistical Tests - tests for detecting trends. The method is utilized in a stepwise fashion and is presented in a nonstatistical manner to allow use by those not well versed in statistical theory. While the emphasis herein is on lakes, the method may be adopted easily to other water bodies.     

An imprecise fuzzy risk approach for water quality management of a river system

Uncertainty plays an important role in water quality management problems. The major sources of uncertainty in a water quality management problem are the random nature of hydrologic variables and imprecision (fuzziness) associated with goals of the dischargers and pollution control agencies (PCA). Many Waste Load Allocation (WLA) problems are solved by considering these two sources of uncertainty. Apart from randomness and fuzziness, missing data in the time series of a hydrologic variable may result in additional uncertainty due to partial ignorance. These uncertainties render the input parameters as imprecise parameters in water quality decision making. In this paper an Imprecise Fuzzy Waste Load Allocation Model (IFWLAM) is developed for water quality management of a river system subject to uncertainty arising from partial ignorance. In a WLA problem, both randomness and imprecision can be addressed simultaneously by fuzzy risk of low water quality. A methodology is developed for the computation of imprecise fuzzy risk of low water quality, when the parameters are characterized by uncertainty due to partial ignorance. A Monte-Carlo simulation is performed to evaluate the imprecise fuzzy risk of low water quality by considering the input variables as imprecise. Fuzzy multiobjective optimization is used to formulate the multiobjective model. The model developed is based on a fuzzy multiobjective optimization problem with max–min as the operator. This usually does not result in a unique solution but gives multiple solutions. Two optimization models are developed to capture all the decision alternatives or multiple solutions. The objective of the two optimization models is to obtain a range of fractional removal levels for the dischargers, such that the resultant fuzzy risk will be within acceptable limits. Specification of a range for fractional removal levels enhances flexibility in decision making. The methodology is demonstrated with a case study of the Tunga–Bhadra river system in India.     

MFAM模型在河流水质污染模拟及预测中的应用

文中以时间序列分析为基础，介绍了均值生成函数这一崭新概念，并且经成份因子提取分析推导建立了模拟序列的数字模型（简记为MFAM），经对黄河下游花园口断面的1988-1989年实测水质污染指标溶解氧（DO），氨氧，化学耗氧量（COD），五日生化需氧量（BOD5）等序列模拟，结果表明MFAM模型能较好地模拟河流水质污染指标的变化趋势，拟合平均误差只有5.2-6.4%，MFAM模型应用于预测1990-1991年水质污染指标变化，结果表明预测精度达85%以上，文中最后得出结论：MFAM模型应用于河流污染模拟和预测，是完全可行且十分方便。     

GENERATION OF SYNTHETIC AND MISSING CLIMATIC DATA FOR PUERTO RICO1

ABSTRACT: Climatic data such as temperature, solar radiation, relative humidity, and wind speed have been widely used to estimate evapotranspiration. Moat of the solar radiation data and portions of the relative humidity data are either not available or missing from the records in Puerto Rico. Depending upon the availability and data characteristics of records, three methods (including a regression technique, an averaging of historical data, and a regional average) were used to generate missing data, and a time series analysis was used to synthesize a series of climatic data. The limitations and applicability of each method are discussed. The results showed that the time series analysis method can be successfully used to synthesize a series of monthly solar radiations for several stations. The regression technique and the regional average can be successfully applied to generate missing monthly solar radiation data. The regression technique and the averaging of historical data have been satisfactorily used to interpolate missing monthly relative humidity. The explained variance (R²) varied from 0.68 to 0.88, which are both significant at the 0.05 level of significance.     

NONPARAMETRIC APPROACHES TO ENVIRONMENTAL IMPACT ASSESSMENT1

ABSTRACT: The interesting developments in non-parainetric testing and estimation methods presented in the upcoming sequence of nine papers are evaluated, compared, and put into proper perspective. Because a deterioration in water quality constitutes a direct threat to human health, it is of utmost importance to have flexible non-parametric methods available for detecting and describing trends in water quality time series. A distinct advantage of nonparametric tests is that they are usually very effective when applied to “messy” environmental data which may, for example, contain many missing observations and not be normally distributed. By applying their enhanced approaches for nonparametric methods to water quality time series, as well as employing well designed simulation experiments, the authors of the papers clearly demonstrate the efficacy of utilizing nonparametric tests in environmental impact assessment.     

A Hydrologic Data Screening Procedure for Exploring Monotonic Trends and Shifts in Rainfall and Runoff Patterns

A thorough understanding of past and present hydrologic responses to changes in precipitation patterns is crucial for predicting future conditions. The main objectives of this study were to determine temporal changes in rainfall‐runoff relationship and to identify significant trends and abrupt shifts in rainfall and runoff time series. Ninety‐year rainfall and runoff time series datasets from the Gasconade and Meramec watersheds in east‐central Missouri were used to develop data screening procedure to assess changes in the rainfall and runoff temporal patterns. A statistically significant change in mean and variance was detected in 1980 in the rainfall and runoff time series within both watersheds. In addition, both the rainfall and runoff time series indicated the presence of nonstationary attributes such as statistically significant monotonic trends and/or change in mean and variance, which should be taken into consideration when using the time series to predict future scenarios. The annual peak runoff and the annual low flow in the Meramec watershed showed significant temporal changes compared to that in the Gasconade watershed. Water loss in both watersheds was found to be significantly increasing which is potentially due to the increase in groundwater pumping for water supply purposes.     

SUPPLEMENTATION OF MISSING VALUES IN WATER QUALITY DATA1

ABSTRACT The problem of estimating missing values in water quality data using linear interpolation and harmonic analysis is studied to see which one of these two methods yields better estimates for the missing values. The data used in this study consisted of midnight values of dissolved oxygen from the Ohio River collected over a period of one year at Stratton station. Various hypothetical cases of missing data are considered and the two methods of supplementing missing values are evaluated using statistical tests. The results indicate that when the percentage of missed data points exceeded ten percent of the total number in the original sample, harmonic analysis usually yielded better estimates for both the regularly and irregularly missed cases. For data that exhibit cyclic variation, examples of which are dissolved oxygen concentration and water temperature, harmonic analysis as a data generation technique appears to be superior to linear interpolation.     

TESTING FOR TREND IN LAKE AND GROUND WATER QUALITY TIME SERIES1

ABSTRACT: The detection of gradual trends in water quality time series is increasing in importance as concern grows for diffuse sources of pollution such as acid precipitation and agricultural non-point sources. A significant body of literature has arisen dealing with trend detection in water quality variables that exhibit seasonal patterns. Much of the literature has dealt with seasonality of the first moment. However, little has been mentioned about seasonality in the variance, and its effect upon the performance of trend detection techniques. In this paper, eight methods of trend detection that arise from both the statistical literature as well as the water quality literature have been compared by means of a simulation study. Varying degrees of seasonality in both the variances and the means have been introduced into the artificial data, and the performances of these procedures are analyzed. Since the focus is on lake and ground water quality monitoring, quarterly sampling and short to moderate record lengths are examined.     

PAST AND FUTURE OF ANALYSIS OF WATER RESOURCES TIME SERIES1

ABSTRACT: water resources supply and demand time series consist of several or all of the four basic characteristics: tendency, intermittency, periodicity and stochasticity. Their importance changes from one type of variables to another. Historic developments of analysis of time series in hydrology have varied significantly over the past, from the stress on search for periodicities and persistence in annual series to the emphasis on the series stochastic properties. Supply and demand series are often highly interrelated, which fact is most often neglected in planning water resources systems in general, and water storage capacities in particular. The future of series analysis in water resources will likely be by a joint use of physically-based structural analysis and the use of advanced methods of treating data by stochastic processes, statistical estimation and inference techniques. The most intriguing challenge of the future of this analysis may be the treatment of nonnormal, nonlinear and in general nonstationary hydrologic and water use time series. The proper treatment of complex multivariate processes will also challenge the specialists, especially for the purposes of transfer of information between data on variables at given points, or between data at several points of a given variable, or both.     

STATISTICAL CHARACTERISTICS OF COAL-MINE DISCHARGES ON WESTERN PENNSYLVANIA REMINING SITES1

ABSTRACT: Under an approved remining program, a coal mine operator can remine abandoned sites without legally assuming treatment responsibilities of the previously degraded water, as long as these discharging waters are not further degraded. Determination of discharge degradation caused by remining of abandoned coal mines requires knowledge of mine water quality and discharge flow rate characteristics both before and after remining. Normality tests performed on the water quality and flow data from 57 mine discharges indicate generally nonnormal distributions and extreme right-skewness. Exploratory data analysis (notched box-and-whisker plots) of the differences among medians indicates that the water quality of underground mines was more highly degraded in terms of acidity, iron, and sulfate concentrations than that from surface mines. Spearman's rank correlation tests, normality testing, and exploratory data analysis indicate that discharge flow rate is the primary controlling factor on the variability of pollution load rate. Reduction of recharge from the surface and adjacent unmined strata should decrease the mine discharge flow rate and in turn the pollution load.     

A METHOD FOR OBTAINING SLOPE INFORMATION FOR HYDROLOGIC MODELS1

: A method is described for obtaining surface slope information for analysis with other land resource and water quality data in hydrologic models of nonpoint sources of water pollution. The method described requires a point sampling scheme, topographic maps, and a coordinate digitizer. Sample point elevation, slope direction, and slope magnitude are calculated from locations of the sample point and the nearest upper and lower contour lines. Details of the data collection methodology and associated problems are discussed.     

NONPARAMETRIC TESTS FOR TREND DETECTION IN WATER QUALITY TIME SERIES1

ABSTRACT: A review of nonparametric tests for trend leads to the conclusion that Mann-Whitney, Spearman, and Kendall tests are the best choice for trend detection in water quality time series. Recently these tests have been adapted to account for dependence and seasonality in such series (Lettenmaier, 1976; Hirsch, et al., 1972; Hirsch and Slack, 1984). For monotonic trends, a procedure allowing to select the pertinent tests considering the characteristics of time series is proposed and the practical limitations of the tests are also brought out. This procedure has been applied to identify the appropriate trend detection test for the time series of nine water quality parameters at Lake Laflamme (Québec). When a time series can be tested with the Mann-Whitney, Kendall, Spearman, or Lettenmaier (1976) test, the number of observations required to detect trends of a given magnitude, for selected significance and power levels can be calculated with the power function of the t test. When the test proposed by Hirsch, et al. (1984), Hirsch and Slack (1984), or Farrell (1980) need to be used, the number of observations can only be estimated approximately from the results of empirical power studies.     

VISUALIZATION OF TRENDS AND FLUCTUATIONS IN CLIMATIC RECORDS1

ABSTRACT: Small systematic changes in climatic records are often poorly visualized by standard time series plots because they are usually hidden by the magnitude and variability of the data values themselves. A visualization approach based on the rescaled adjusted partial sums (RAPS) which overcomes the above-stated shortcomings is presented. This visualization highlights trends, shifts, data clustering, irregular fluctuations, and periodicities in the record. Additional information on the number, magnitude, shape, frequency, and timing of fluctuations and trends can also be inferred. The visualization approach can be used for preliminary visual inspection of a time series, to gain a feel for the data, and/or to guide and focus subsequent statistical tests and analyses. It is not intended as a substitute for standard statistical analysis. Alternatively, the visualization approach can be used to display findings of a time series analysis. The capabilities and limitations of the approach are discussed and illustrated for two time series of annual rainfall values.     

Detecting acid precipitation impacts on lake water quality

The United States Environmental Protection Agency is planning to expand its long-term monitoring of lakes that are sensitive to acid deposition effects. Effective use of resources will require a careful definition of the statistical objectives of monitoring, a network design which balances spatial and temporal coverage, and a sound approach to data analysis. This study examines the monitoring objective of detecting trends in water quality for individual lakes and small groups of lakes. Appropriate methods of trend analysis are suggested, and the power of trend detection under seasonal (quarterly) sampling is compared to that of annual sampling. The effects of both temporal and spatial correlation on trend detection ability are described.     

WATER QUALITY PREDICTION WITHIN AN INTERBASIN TRANSFER SYSTEM1

ABSTRACT A methodology for predicting the spatial and temporal levels of conservative water quality constituents within a multibasin water resource system is presented. Dissolved solids, sulfates, and chlorides are the constituents used during this investigation; however, any other conservative ion or mineral can be incorporated into the simulation model. The methodology is tested on the proposed Texas Water System. The water quality model, QNET-I, utilizes monthly canal and river flows and reservoir storage levels calculated by the Texas Water Development Board's systems simulation model. Discharge-concentration relationships are developed for each source of water in the system, including significant waste-water discharges. Reservoirs in the system are assumed to be completely mixed with respect to conservative constituents. A mass balance analysis is performed for each node and each month during the simulation period. The output from the water quality simulation is a table of the concentrations of the conservative water quality constituents at each demand point in the system and in each reservoir and canal for every month the system is in operation. The desired quality of the water at the demand locations is used to determine the economic utility of transporting and mixing water from various sources.     

WATER QUALITY TRENDS AT INFLOWS TO EVERGLADES NATIONAL PARK1

ABSTRACT: Water quality data collected at inflows to Everglades National Park (ENP) are analyzed for trends using the seasonal Kendall test (Hirsch et al., 1982; Hirsch and Slack, 1984). The period of record is 1977–1989 for inflows to Shark River Slough and 1983–1989 for inflows to Taylor Slough and ENP's Coastal Basin. The analysis considers 20 water quality components, including nutrients, field measurements, inorganic species, and optical properties. Significant (p<0.10) increasing trends in total phosphorus concentration are indicated at eight out of nine stations examined. When the data are adjusted to account for variations in antecedent rainfall and water surface elevation, increasing trends are indicated at seven out of nine stations. Phosphorus trend magnitudes range from 4 percent/year to 21 percent/year Decreasing trends in the Total N/P ratio are detected at seven out of nine stations. N/P trend magnitudes range from -7 percent/year to -15 percent/year. Trends in water quality components other than nutrients are observed less frequently and are of less importance from a water-quality-management perspective. The apparent nutrient trends are not explained by variations in marsh water elevation, antecedent rainfall, flow, or season.     

A Sensitivity and Error Analysis Framework for Lake Eutrophication Modeling1

ABSTRACT: A framework for sensitivity and error analysis in mathematical modeling is described and demonstrated. The Lake Eutrophication Analysis Procedure (LEAP) consists of a series of linked models which predict lake water quality conditions as a function of watershed land use, hydrolgic variables, and morphometric variables. Specification of input variables as distributions (means and standard errors) and use of first-order error analysis techniques permits estimation of output variable means, standard errors, and confidence ranges. Predicted distributions compare favorably with those estimated using Monte-Carlo simulation. The framework is demonstrated by applying it to data from Lake Morey, Vermont. While possible biases exist in the models calibrated for this application, prediction variances, attributed chiefly to model error, are comparable to the observed year-to-year variance in water quality, as measured by spring phosphorus concentration, hypolimnetic oxygen depletion rate, summer chlorophyll-a, and summer transparency in this lake. Use of the framework provides insight into important controlling factors and relationships and identifies the major sources of uncertainty in a given model application.