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.     

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.     

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.     

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.     

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.     

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.     

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.     

APPROACHES TO MULTIVARIATE MODELING OF WATER RESOURCES TIME SERIES1

ABSTRACT: Alternative approaches suggested for modeling multiseries of water resources systems are reviewed and compared. Most approaches fall within the general framework of multivariate ARMA models. Formal modeling procedures suggest a three-stage iterative process, namely: model identification, parameter estimation and diagnostic checks. Although a number of statistical tools are already available to follow such modeling process, in general, it is not an easy task, especially if high order vector ARMA models are used. However, simpler ARMA models such as the contemporaneous and the transfer-function models may be sufficient for most applications in water resources. Two examples of modeling bivariate and trivariate streamflow series are included. Alternative modeling procedures are used and compared by using data generation techniques. The results obtained suggest that low order models, as well as contemporaneous ARMA models, reproduce quite well the main statistical characteristics of the time series analyzed. It is assumed that the same conclusions apply for most water resources time series.     

RESEARCH: Comparison of Temporal Trends in Ambient and Compliance Trace Element and PCB Data in Pool 2 of the Mississippi River, USA, 1985–1995

6+ ), copper (Cu), lead (Pb), mercury (Hg), nickel (Ni), selenium (Se), zinc (Zn), and polychlorinated biphenyls (PCBs). Water-column, bed-sediment, and fish-tissue (fillets) data collected by five government agencies comprised the ambient data set; effluent data from five registered facilities comprised the compliance data set. The nonparametric Mann-Kendall trend test indicated that 33% of temporal trends in all data were statistically significant (P < 0.05). Possible reasons for this were low sample sizes, and a high percentage of samples below the analytical detection limit. Trends in compliance data were more distinct; most trace elements decreased significantly, probably due to improvements in wastewater treatment. Seven trace elements (Cr, Cd, Cu, Pb, Hg, Ni, and Zn) had statistically significant decreases in wastewater and portions of either or both ambient water and bed sediment. No trends were found in fish tissue. Inconsistency in trends between ambient and compliance data were often found for individual constituents, making overall similarity between the data sets difficult to determine. Logistical differences in monitoring programs, such as varying field and laboratory methods among agencies, made it difficult to assess ambient temporal trends.     

NONPARAMETRIC STATISTICAL ANALYSIS OF ANNUAL PEAK FLOW DATA FROM A RECENTLY URBANIZED WATERSHED1

ABSTRACT. In order to demonstrate the feasibility of a nonparametric statistical application in investigating the hydrologic impact of the rapid land use change accompanying intense urbanization, annual maximum peak flow data from an actual example (the Northeast Branch Basin, a recently urbanized Washington, D.C., suburban watershed) were analyzed. Annual peak flow data from the Patuxent Basin above Unity, Maryland, a rural watershed in close proximity to the study area, were compared to data from the Northeast Branch for the Same period utilizing the Wilcoxon matched-pairs signed-ranks test. A change in central tendency of each series was noted at the 0.01 significance level; however, the change was negative in the rural basin and positive in the urbanized Northeast Branch Basin. This central tendency change was considered indicative of an average decrease in the size of rainstorms producing annual maximum peak discharges. Rainstorm data from the Northeast Branch Basin were divided into two equal periods (before urbanization and after) and the Wilcoxon test was applied. It was found that rainstorms producing maximum annual peak discharges in the urbanized period were indeed smaller than those in the prior period (0.01 level of significance); however, larger annual peaks were produced. It was concluded that nonparametric statistical methods can be used readily with conventional methods to isolate and clearly analyze the various problems in an actual urban hydrologic study.     

ROLE OF SYNTHETIC TIME SERIES IN HYDROMETEOROLOGICAL DATA ANALYSIS1

ABSTRACT: The use of synthetic time series (artificially simulated time series with specific and useful properties built into them) to increase the confidence in the statistical parameters of limited hydrometeorological time series is the subject matter of this paper. By constructing fourteen synthetic time series, a sensitivity analysis is performed to assess the net effect of nonstationarity, number of lags and small sample size on estimated spectral densities. Similarly, the effects of the harmonic-removal procedure on the resulting residual series and the confidence limits in cross spectral analysis are examined in the light of synthetic time series analysis. These analyses clearly indicate the useful supplemental role of synthetic time series in data analysis.     

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.     

Optimal Reorganization of NASA Earth Science Data for Enhanced Accessibility and Usability for the Hydrology Community

A long‐standing “Digital Divide” in data representation exists between the preferred way of data access by the hydrology community and the common way of data archival by earth science data centers. Typically, in hydrology, earth surface features are expressed as discrete spatial objects (e.g., watersheds), and time‐varying data are contained in associated time series. Data in earth science archives, although stored as discrete values (of satellite swath pixels or geographical grids), represent continuous spatial fields, one file per time step. This Divide has been an obstacle, specifically, between the Consortium of Universities for the Advancement of Hydrologic Science, Inc. and NASA earth science data systems. In essence, the way data are archived is conceptually orthogonal to the desired method of access. Our recent work has shown an optimal method of bridging the Divide, by enabling operational access to long‐time series (e.g., 36 years of hourly data) of selected NASA datasets. These time series, which we have termed “data rods,” are pre‐generated or generated on‐the‐fly. This optimal solution was arrived at after extensive investigations of various approaches, including one based on “data curtains.” The on‐the‐fly generation of data rods uses “data cubes,” NASA Giovanni, and parallel processing. The optimal reorganization of NASA earth science data has significantly enhanced the access to and use of the data for the hydrology user community.     

Nonparametric Monte Carlo Simulation for Flood Frequency Curve Derivation: An Application to a Korean Watershed1

Abstract: A mix of causative mechanisms may be responsible for flood at a site. Floods may be caused because of extreme rainfall or rain on other rainfall events. The statistical attributes of these events differ according to the watershed characteristics and the causes. Traditional methods of flood frequency analysis are only adequate for specific situations. Also, to address the uncertainty of flood frequency estimates for hydraulic structures, a series of probabilistic analyses of rainfall‐runoff and flow routing models, and their associated inputs, are used. This is a complex problem in that the probability distributions of multiple independent and derived random variables need to be estimated to evaluate the probability of floods. Therefore, the objectives of this study were to develop a flood frequency curve derivation method driven by multiple random variables and to develop a tool that can consider the uncertainties of design floods. This study focuses on developing a flood frequency curve based on nonparametric statistical methods for the estimation of probabilities of rare floods that are more appropriate in Korea. To derive the frequency curve, rainfall generation using the nonparametric kernel density estimation approach is proposed. Many flood events are simulated by nonparametric Monte Carlo simulations coupled with the center Latin hypercube sampling method to estimate the associated uncertainty. This study applies the methods described to a Korean watershed. The results provide higher physical appropriateness and reasonable estimates of design flood.     

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 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.     

DETECTABILITY OF STEP TRENDS IN THE RATE OF ATMOSPHERIC DEPOSITION OF SULFATE1

A method is presented to assist policy makers in determining the combination of number of sampling stations and number of years of sampling necessary to state with a given probability that a step reduction in atmospheric deposition rates of a given magnitude has occurred at a pre-specified time. This pre-specified time would typically be the time at which a sulfate emission control program took effect, and the given magnitude of reduction is some percentage change in deposition rate one might expect to occur as a result of the emission control. In order to determine this probability of detection, a stochastic model of sulfate deposition rates is developed, based on New York State bulk collection network data. The model considers the effect of variation in precipitation, seasonal variations, serial correlation, and site-to-site (cross) correlation. A nonparametric statistical test which is well suited to detection of step changes in such multi-site data sets is developed. It is related to the Mann-Whitney Rank-Sum test. The test is used in Monte Carlo simulations along with the stochastic model to derive statistical power functions. These power functions describe the probability of detecting (α=0.05) a step trend in deposition rate as a function of the size of the step-trend, record length before and after the step-trend, and the number of stations sampled. The results show that, for an area the size of New York State, very little power is gained by increasing the number of stations beyond about eight. The results allow policy makers to determine the tradeoff between the cost of monitoring and time required to detect a step-trend of a given magnitude with a given probability.     

Evidence for Changing Flood Risk in New England Since the Late 20th Century1

Abstract: Long‐term flow records for watersheds with minimal human influence have shown trends in recent decades toward increasing streamflow at regional and national scales, especially for low flow quantiles like the annual minimum and annual median flows. Trends for high flow quantiles are less clear, despite recent research showing increased precipitation in the conterminous United States over the last century that has been brought about primarily by an increased frequency and intensity of events in the upper 10th percentile of the daily precipitation distribution – particularly in the Northeast. This study investigates trends in 28 long‐term annual flood series for New England watersheds with dominantly natural streamflow. The flood series are an average of 75 years in length and are continuous through 2006. Twenty‐five series show upward trends via the nonparametric Mann‐Kendall test, 40% (10) of which are statistically significant (p < 0.1). Moreover, an average standardized departures series for 23 of the study gages indicates that increasing flood magnitudes in New England occurred as a step change around 1970. The timing of this is broadly synchronous with a phase change in the low frequency variability of the North Atlantic Oscillation, a prominent upper atmospheric circulation pattern that is known to effect climate variability along the United States east coast. Identifiable hydroclimatic shifts should be considered when the affected flow records are used for flood frequency analyses. Special treatment of the flood series can improve the analyses and provide better estimates of flood magnitudes and frequencies under the prevailing hydroclimatic condition.