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.     

INTERVENTION ANALYSIS OF WATER QUALITY RECORDS1

The impoundment of the Kootenai River by Libby Dam caused changes in discharge and water quality in the river downstream from Lake Koocanusa. The changes observed downsteam were largely attributable to the depth of withdrawal from the reservoir and the reservoir's ability to store and mix various influent water masses. The preimpoundment and postimpoundment time series of discharge and six water quality variables were autocorrelated and exhibited strong seasonality. Intervention analysis, a technique employing Box-Jenkins time series models, was used to quantify the nature and magnitude of the changes in water quality after the construction of Libby Dam. The models were developed with data from June 1967 through February 1981 and were able to satisfactorily forecast riverine conditions from March 1981 through January 1982.     

MULTIVARIATE TREND TESTING OF LAKE WATER QUALITY1

ABSTRACT: Multivariate methods of trend analysis offer the potential for higher power in detecting gradual water quality changes as compared to multiple applications of univariate tests. Simulation experiments were used to investigate the power advantages of multivariate methods for both linear model and Mann-Kendall based approaches. The experiments focused on quarterly observations of three water quality variables with no serial correlation and with several different intervariable correlation structures. The multivariate methods were generally more powerful than the univariate methods, offering the greatest advantage in situations where water quality variables were positively correlated with trends in opposing directions. For illustration, both the univariate and multivariate versions of the Mann-Kendall based tests were applied to case study data from several lakes in Maine and New York which have been sampled as part of EPA's long term monitoring study of acid precipitation effects.     

SELECTING TREND TESTS FOR WATER QUALITY SERIES WITH SERIAL CORRELATION AND MISSING VALUES1

ABSTRACT: The use of nonparametric tests for monotonic trend has flourished in recent years to support routine water quality data analyses. The validity of an assumption of independent, identically distributed error terms is an important concern in selecting the appropriate nonparametric test, as is the presence of missing values. Decision rules are needed for choosing between alternative tests and for deciding whether and how to pre-process data before trend testing. Several data pre-processing procedures in conjunction with the Mann-Kendall tau and the Seasonal Kendall test (with and without serial correlation correction) are evaluated using synthetic time series with generated serial correlation and missing data. A composite test (pre-testing for serial correlation followed by one of two trend tests) is evaluated and was found to perform satisfactorily.     

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.     

AN EVALUATION OF WEEKLY AND MONTHLY TIME SERIES FORECASTS OF MUNICIPAL WATER USE1

ABSTRACT: A cascade model for forecasting municipal water use one week or one month ahead, conditioned on rainfall estimates, is presented and evaluated. The model comprises four components: long term trend, seasonal cycle, autocorrelation and correlation with rainfall. The increased forecast accuracy obtained by the addition of each component is evaluated. The City of Deerfield Beach, Florida, is used as the application example with the calibration period from 1976–1980 and the forecast period the drought year of 1981. Forecast accuracy is measured by the average absolute relative error (AARE, the average absolute value of the difference between actual and forecasted use, divided by the actual use). A benchmark forecast is calculated by assuming that water use for a given week or month in 1981 is the same as the average for the corresponding period from 1976 to 1980. This method produces an AARE of 14.6 percent for one step ahead forecasts of monthly data and 15.8 percent for weekly data. A cascade model using trend, seasonality and autocorrelation produces forecasts with AARE of about 12 percent for both monthly and weekly data while adding a linear relationship of water use and rainfall reduces the AARE to 8 percent in both cases if it is assumed that rainfall is known during the forecast period. Simple rainfall predictions do not increase the forecast accuracy for water use so the major utility of relating water use and rainfall lies in forecasting various possible water use sequences conditioned on sequences of historical rainfall data.     

A WATER QUALITY ASSESSMENT OF DEVELOPMENT IN THE SENEGAL RIVER BASIN1

A study was made to determine the impact on water quality due to water resource development in a large river basin in a semi-arid region of West Africa. Mathematical modeling and the examination of case histories were used to project impacts. The impacts associated with changes in water quality were shown to be slight assuming that modern basin and agricultural management practices are adopted. Analytical techniques normally implemented in studies of more highly developed basins are useful for analysis of water quality impacts in relatively undeveloped basins.     

USE OF FIRST-ORDER UNCERTAINTY ANALYSIS TO OPTIMIZE SUCCESSFUL STREAM WATER QUALITY SIMULATION1

ABSTRACT: A first-order uncertainty technique is developed to quantify the relationship between field data collection and a modeling exercise involving both calibration and subsequent verification. A simple statistic (LTOTAL) is used to quantify the total likelihood (probability) of successfully calibrating and verifying the model. Results from the first-order technique are compared with those from a traditional Monte Carlo simulation approach using a simple Streeter-Phelps dissolved oxygen model. The largest single difference is caused by the filtering or removal of unrealistic outcomes within the Monte Carlo framework. The amount of bias inherent in the first-order approach is also a function of the magnitude of input variability and sampling location. The minimum bias of the first-order technique is approximately 20 percent for a case involving relatively large uncertainties. However the bias is well behaved (consistent) so as to allow for correct decision making regarding the relative efficacy of various sampling strategies. The utility of the first-order technique is demonstrated by linking data collection costs with modeling performance. For a simple and inexpensive project, a wise and informed selection resulted in an LTOTAL value of 86 percent, while an uninformed selection could result in an LTOTAL value of only 55 percent.     

A MONTHLY TIME SERIES MODEL OF MUNICIPAL WATER DEMAND1

A multivariate time series model is formulated to study monthly variations in municipal water demand. The left hand side variable in the multivariate regression model is municipal water demand (gallons per connection per day) and the right hand side contains (explanatory) variables which include price (constant dollars), average temperature, total precipitation, and percentage of daylight hours. The application of the regression model to Salt Lake City Water Department data produced a high multiple correlation coefficient and F-statistic. The regression coefficients for the right hand side variables all have the appropriate sign. In an ex post forecast, the model accurately predicts monthly variations in municipal water demand. The proposed monthly multivariate model is not only found useful for forecasting water demand, but also useful for predicting and studying the impact of nonstructural management decisions such as the effect of price changes, peak load pricing methods, and other water conservation programs.     

NATIONWIDE ASSESSMENT OF URBAN RUNOFF IMPACT ON RECEIVING WATER QUALITY1

ABSTRACT: Urban stormwater runoff has been recognized as a potential major contributor of pollution to receiving waters. However the projected high costs of control have prompted an examination of the extent to which these impacts have been documented. A nationwide search was conducted for case studies demonstrating a cause-effect linkage between urban runoff and impairment of beneficial uses in receiving waters. The results indicate that numerous definitions of “impacts” are being used and that few substantive data exist to support many of these allegations. Results of a preliminary impact assessment are presented for the 248 urbanized areas of the United States. Then, the results of more recent efforts to assess these impacts in several case studies are described. This assessment demonstrates the critical need for additional short-term and long-term sampling programs.     

MODELING HYDROLOGIC TIME SERIES FROM THE ARCTIC1

The general intervention model is applied to hydrologic and meteorologjc time series from the Canadian Arctic. The authors show how the model is able to account for environmental interventions, missing observations in the data, changes in data collection procedures, the effects of external inputs, as well as seasonality and autocorrelation. Methods for identifying transfer functions by making use of a physical understanding of the processes involved are demonstrated and sample applications of the general intervention model to Arctic data are shown.     

SAMPLING FREQUENCY SELECTION FOR REGULATORY WATER QUALITY MONITORING1

ABSTRACT: The selection of sampling frequencies in order to achieve reasonably small and uniform confidence interval widths about annual sample means or sample geometric means of water quality constituents is suggested as a rational approach to regulatory monitoring network design. Methods are presented for predicting confidence interval widths at specified sampling frequencies while considering both seasonal variation and serial correlation of the quality time series. Deterministic annual cycles are isolated and serial dependence structures of the autoregressive, moving average type are identified through time series analysis of historic water quality records. The methods are applied to records for five quality constituents from a nine-station network in Illinois. Confidence interval widths about annual geometric means are computed over a range of sampling frequencies appropriate in regulatory monitoring. Results are compared with those obtained when a less rigorous approach, ignoring seasonal variation and serial correlation, is used. For a monthly sampling frequency the error created by ignoring both seasonal variation and serial correlation is approximately 8 percent. Finally, a simpler technique for evaluating serial correlation effects based on the assumption of AR(1) type dependence is examined. It is suggested that values of the parameter p₁, in the AR(1) model should range from 0.75 to 0.90 for the constituents and region studied.     

ESTIMATION OF COASTAL WATER CONTAMINATION LONG-TERM TREND USING SEASONAL LINEAR MODELS1

ABSTRACT: Bivalves are used as bioindicators to assess trends of the chemical quality of coastal and marine environments due to their ability to concentrate chemicals. These shellfish are subject to seasonal physiological changes influencing the chemical concentration. Using quarterly data, we model concentration via linear regression with a biologically based seasonal component. This was applied to cadmium concentration measured in the blue mussel (Mytilus edulis) at three sites in the Seine estuary (Normandy, France). In this case we have a high concentration season from January to June and a “low concentration” season from July to December. This season definition was checked a posteriori, using box-and-whisker plots and a statistical test of comparison of pair-wise adjusted least-squares mean differences, and it appears to be very reasonable. We averaged data by season and across sites. Our final model (R²= 0.846 with N= 27 observations) includes highly significant terms: a season effect, which accounts for 45% of the total variability, a linear and a quadratic time term. Outliers were identified by high Studentized residual values and attributed to bias in the temporal sampling schemes. The methodology developed will further be used with other shellfish and/or other trace elements and organic chemicals.     

MULTIVARIATE NONPARAMETRIC TESTS FOR TREND IN WATER QUALITY1

ABSTRACT: National and state fixed station stream quality monitoring networks have now been in existence for over ten years. The resulting data bases provide opportunities and challenges for statistical trend assessment. Although nonparametric tests have been developed that are well suited to such problems, the interpretation of variations in trend significance between seasons and variables remains a problem. One recently developed test is based on the sum of Mann-Kendall statistics over seasons or variables, with the test statistic variance computed as the sum of the covariances of the individual Mann-Kendall statistics. In this method, up- and downtrends can cancel, giving an overall indication of no trend. A related test which is sensitive to trend regardless of direction has been shown to behave poorly for typical stream quality record lengths. An alternative formulation which is sensitive to up- and downtrends and has power approaching that of the covariance sum method, is described. In addition, a variation of a contrast test for discriminating trend directions and magnitudes among variables or seasons where correlation between seasons or variables is present is described, and tests of its performance reported.     

CONSIDERATIONS OF SCALE IN WATER QUALITY MONITORING AND DATA ANALYSIS1

ABSTRACT: An assumption of scale is inherent in any environmental monitoring exercise. The temporal or spatial scale of interest defines the statistical model which would be most appropriate for a given system and thus affects both sampling design and data analysis. Two monitoring objectives which are strongly tied to scale are the estimation of average conditions and the evaluation of trends. For both of these objectives, the time or spatial scale of interest strongly influences whether a given set of observations should be regarded as independent or serially correlated and affects the importance of serial correlation in choosing statistical methods. In particular serial correlation has a much different effect on the estimation of long-term means than it does on the estimation of specific-period means. For estimating trends, a distinction between serial correlation and trend is scale dependent. An explicit consideration of scale in monitoring system design and data analysis is, therefore, most important for producing meaningful statistical information.     

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.     

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.     

DESIGN OF AN INDEX OF WATER QUALITY1

ABSTRACT: This paper describes the formulation of an Index of Water Quality to evaluate the level of pollution in fresh water. A Four-Round Delphi equation, using a panel of seven nationally recognized water scientists, was performed to ascertain the pollutants to be included in the index, the relationship between the quantity of these pollutants in the water and the resulting quality of the water, and the importance of each pollution variable to each water use as well as to overall pollution. A multiplicative index was used to bring the pollutants together into one system.     

DATA REQUIREMENTS OF A WATER QUALITY MANAGEMENT PROGRAM1

ABSTRACT: Routine data collection currently consumes a large amount of the total resources devoted to water quality management. All too often data collection becomes an end in itself, with little thought given to the purpose of the data collection. The problem generally stems from a lack of proper routine surveillance system design and a failure on the part of the designers to initially identify the data needs of the management program. This study attempts, in a general way, to delineate the data needs of a water quality management program. This first required an identification of the activities involved in water quality management. The activities were then discussed in terms of the types of information needed to successfully complete their assigned tasks. Several detailed examples are given. The results of the discussion are summarized and several strategies are proposed to relate the results to surveillance system design.     

QUANTIFICATION FOR VISUALIZATION OF TIME TREND1

ABSTRACT: A method for quantifying fluctuations in time-series data was developed and tested to aid the process of visualization. The methodology is based on free-form sliding polynomials and identifies (a) short-period variability about the mean value, (b) a long-term trend or cycle, and (c) random errors residual to these two structured components. Consistent results were obtained for designed synthetic data and natural data from seven sites in Georgia. Statistics of fit of the analytical model for the natural data were not significant on a site-by-site basis. An unexpected finding for the study was obtained when the statistical results for the seven data sets for temperature were pooled. The smoothing model yielded consistent long-term trends even though the individual station results were not significant. Also, the correlation coefficients, while low, showed a statistically significant trend toward higher values toward the northwest and away from the Georgia coast line. This study thus supports the concept that multiple-site, and regionally based, analyses are necessary for the detection of trends. Secondarily, such consistency of results strengthens the conclusion that the proposed smoothing method is an effective procedure in the presence of varying amounts of random content in the natural data sets.