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.     

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.     

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.     

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.     

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.     

NONPARAMETRIC TEST PERFORMANCE FOR TRENDS IN WATER QUALITY WITH SAMPLING DESIGN APPLICATIONS1

ABSTRACT: In this paper four nonparametric tests for monotonic trend detection are compared with respect to their power and accuracy. The importance of comparing powers at equal empirical significance levels rather than nominal levels is stressed. Therefore, an appropriate graphical method is presented. The effect of the sampling frequency is also assessed using Monte Carlo simulations and a trajectory representation that visualizes the dynamics of the trade-off between the type I and type II errors. These methods are applied to compare four nonparametrical tests (seasonal Mann. Kendall, modified seasonal Mann-Kendall, covariance eigenvalue and covariance inversion) under several conditions. It is concluded with respect to the power that it is not worthwhile for the modified seasonal Mann-Kendall test applied to the AR(1) process considered in this paper to increase the sampling frequency from monthly to biweekly for detecting a monotonic trend of 5 percent, 10 percent, or 15 percent of the process variance. Under these conditions the seasonal Mann-Kendall test is highly liberal, while the covariance inversion and the covariance eigenvalue test are conservative. This research is situated in the development of an efficient sampling design for the Flemish water quality monitoring network.     

TREND ASSESSMENT OF WATER QUALITY TIME SERIES1

ABSTRACT A general methodology is described for identifying and statistically modeling trends which may be contained in a water quality time series. A range of useful exploratory data analysis tools are suggested for discovering important patterns and statistical characteristics of the data such as trends caused by external interventions. To estimate the entries in an evenly spaced time series when data are available at irregular time intervals, a new procedure based upon seasonal adjustment is described. Intervention analysis is employed at the confirmatory data analysis stage to rigorously model changes in the mean levels of a series which are identified using exploratory data analysis techniques. Furthermore, intervention analysis can be utilized for estimating missing observations when they are not too numerous. The effects of cutting down a forest upon various water quality variables and also the consequences of acid rain upon the alkalinity in a stream provide illustrative applications which demonstrate the effectiveness of the methodology.     

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.     

APPLICABILITY OF THE t-TEST FOR DETECTING TRENDS IN WATER QUALITY VARIABLES1

ABSTRACT: A major concern in managing water resources is whether or not water quality variables have changed over time or space. The two-sample Student's t-test is probably the most commonly used statistical test for this purpose. Given that the underlying assumptions of the test may often be violated by water quality variables, a major concern regarding applicability of the test arises. This paper reviews and synthesizes available information in order to examine the effects of non-normality, unequal variances, serial dependence, and seasonality on the performance of the two-sample t-test. The results suggest the t-test is robust for non-normal distributions if the distributions have the same shape (either symmetric or skewed) and sample sizes are equal. The t-test is also robust for unequal variances if the sample sizes are equal. The t-test appears not to be robust when: 1) samples come from two distributions of different shape, 2) samples have unequal variances and unequal sample sizes, 3) serial dependence in observations is present, or 4) seasonal changes, in concentration are present and not removed.     

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.     

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.     

A COMPARATIVE STUDY OF LINEAR AND NONLINEAR TIME SERIES MODELS FOR WATER QUALITY1

ABSTRACT: Surface water quality data are routinely collected in river basins by state or federal agencies. The observed quality of river water generally reflects the overall quality of the ecosystem of the river basin. Advanced statistical methods are often needed to extract valuable information from the vast amount of data for developing management strategies. Among the measured water quality constituents, total phosphorus is most often the limiting nutrient in freshwater aquatic systems. Relatively low concentrations of phosphorus in surface waters may create eutrophication problems. Phosphorus is a non-conservative constituent. Its time series generally exhibits nonlinear behavior. Linear models are shown to be inadequate. This paper presents a nonlinear state-dependent model for the phosphorous data collected at DeSoto, Kansas. The nonlinear model gives significant reductions in error variance and forecasting error as compared to the best linear autoregressive model identified.     

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.     

GOALS AND DATA COLLECTION DESIGNS FOR WATER QUALITY MONITORING1

ABSTRACT: Water quality monitoring cannot address every information need through one data collection procedure. This paper discusses the goals and related procedures for designing water quality monitoring programs. The discussion focuses on the broad information needs of those agencies operating water quality networks. These information needs include the ability to assess trends and environmental impacts, determine compliance with objectives or standards, estimate mass transport, and perform general surveillance. Each of these information needs has different data requirements. This paper outlines these goals and discusses factors to consider in developing a monitoring plan on a site by site basis.     

ANTIDEGRADATION WATER QUALITY CRITERIA FOR THE DELAWARE RIVER: A DISTRIBUTION-FREE STATISTICAL APPROACH1

ABSTRACT: Existing water quality for the Middle Delaware Scenic and Recreational River is significantly better than is required by current standards, leaving a potential for degradation. A method is presented for deriving candidate antidegradation water quality criteria for this segment of the Delaware River using statistical analysis of historic (ambient) water quality data. Data for 34 water quality parameters are first evaluated for data density, serial correlation, trend, seasonality, and other factors. These preliminary analyses are based on observation of data plots and application of distribution-free statistical techniques that are insensitive to outliers and are robust to relatively mild violations of basic assumptions. Data for 12 of the parameters have sufficient density for further analysis and can reasonably be modeled as independent and identically distributed over time (either seasonally or for the entire data sets). For these 12 parameters, distribution-free statistical methods are developed and used to derive intervals within which there is high confidence (usually greater than 95 percent) that the quantiles with potential use as anti-degradation criteria (the 0.85^th, 0.90^th, and 0.95^th quantiles in this study) for a particular parameter lie.     

ANTIDEGRADATION WATER QUALITY CRITERIA FOR THE DELAWARE RIVER: A DISTRIBUTION-FREE STATISTICAL APPROACH1

ABSTRACT: Existing water quality for the Middle Delaware Scenic and Recreational River is significantly better than is required by current standards, leaving a potential for degradation. A method is presented for deriving candidate antidegradation water quality criteria for this segment of the Delaware River using statistical analysis of historic (ambient) water quality data. Data for 34 water quality parameters are first evaluated for data density, serial correlation, trend, seasonality, and other factors. These preliminary analyses are based on observation of data plots and application of distribution-free statistical techniques that are insensitive to outliers and are robust to relatively mild violations of basic assumptions. Data for 12 of the parameters have sufficient density for further analysis and can reasonably be modeled as independent and identically distributed over time (either seasonally or for the entire data sets). For these 12 parameters, distribution-free statistical methods are developed and used to derive intervals within which there is high confidence (usually greater than 95 percent) that the quantiles with potential use as anti-degradation criteria (the 0.85^th, 0.90^th, and 0.95^th quantiles in this study) for a particular parameter lie.     

ESTABLISHING STATISTICAL DESIGN CRITERIA FOR WATER QUALITY MONITORING SYSTEMS: REVIEW AND SYNTHESIS1

ABSTRACT: Regulatory water quality management has placed fairly extensive information expectations on routine, fixed-station monitoring without a corresponding emphasis being placed on the need to design monitoring systems to meet these expectations. To correct the situation there is increasing interest in developing more quantitative monitoring system design procedures which incorporate the statistical nature of sampling. In examining the development of such quantitative criteria, this paper describes the roles of statistics in a systematic approach to monitoring - initial design and routine reporting of results - and reviews the use of statistics in each. The paper emphasizes the need to tie the two together, via statistical design criteria, in order for the identified information expectations to be met in a statistically sound manner. However, the use of statistics in water quality monitoring is noted as currently being as much an art as it is a science.     

MINE DRAINAGE AND ROCK TYPE INFLUENCES ON EASTERN OHIO STREAM WATER QUALITY1

ABSTRACT: Stream water during fair weather (base flow) is largely ground water discharge, which has been in contact with minerals of the underlying aquifer. Base flow water quality should therefore reflect aquifer mineralogy as well as upstream land use. Three upstream mining categories (unmined lands, abandoned coal mines, and reclaimed coal mines) differed in pH, specific conductance, sulfate, iron, aluminum, and alkalinity for 122 streams in eastern Ohio. Aquifer rock type influenced pH, specific conductance, sulfate, iron, and alkalinity. Reclamation returned many components of acid mine drainage to near unmined levels, although sulfate and specific conductance were not improved. Acid mine drainage problems were less severe in watersheds underlain by the calcareous Monogahela Formation. These results should ayply to other Appalachian coal regions having similar rock units. The water quality data distributions were neither consistently normal nor lognormal. Statistical tests utilizing ranks of the water quality data, instead of the data themselves, proved useful in analyzing the influences of mining category and rock type.     

CONTROLLING GROUND WATER DEGRADATION IN THE TULARE LAKE BASIN1

ABSTRACT This study examined the feasibility of extending the Accelerated Salt Transport (ASTRAN) method of groud water quality control to a complex, closed basin which is experiencing ground water quality degradation from irrigated agriculture (e.g., the Tulare Lake Basin in the Southern portion of the California Central Valley). A linear programming model was constructed and parametric analysis conducted which produced results with a “general appraisal” (or “level B”) degree of accuracy. The study concluded that a drainage water export drain is required in order to implement a long-term solution but that ground water degradation can be mitigated by a combination of the ASTRAN method and other measures even with existing entitlements and legal constraints.