Techniques of trend analysis for monthly water quality data
TL;DR: The seasonal Kendall test as discussed by the authors is a nonparametric test for trend applicable to data sets with seasonality, missing values, or values reported as "less than" or values below the limit of detection.
Abstract: Some of the characteristics that complicate the analysis of water quality time series are non-normal distributions, seasonality, flow relatedness, missing values, values below the limit of detection, and serial correlation. Presented here are techniques that are suitable in the face of the complications listed above for the exploratory analysis of monthly water quality data for monotonie trends. The first procedure described is a nonparametric test for trend applicable to data sets with seasonality, missing values, or values reported as ‘less than’: the seasonal Kendall test. Under realistic stochastic processes (exhibiting seasonality, skewness, and serial correlation), it is robust in comparison to parametric alternatives, although neither the seasonal Kendall test nor the alternatives can be considered an exact test in the presence of serial correlation. The second procedure, the seasonal Kendall slope estimator, is an estimator of trend magnitude. It is an unbiased estimator of the slope of a linear trend and has considerably higher precision than a regression estimator where data are highly skewed but somewhat lower precision where the data are normal. The third procedure provides a means for testing for change over time in the relationship between constituent concentration and flow, thus avoiding the problem of identifying trends in water quality that are artifacts of the particular sequence of discharges observed (e.g., drought effects). In this method a flow-adjusted concentration is defined as the residual (actual minus conditional expectation) based on a regression of concentration on some function of discharge. These flow-adjusted concentrations, which may also be seasonal and non-normal, can then be tested for trend by using the seasonal Kendall test.
Citations
More filters
Book•
01 Jun 1989
TL;DR: The chemical composition of natural water is derived from many different sources of solutes, including gases and aerosols from the atmosphere, weathering and erosion of rocks and soil, solution or precipitation reactions occurring below the land surface, and cultural effects resulting from human activities.
Abstract: The chemical composition of natural water is derived from many different sources of solutes, including gases and aerosols from the atmosphere, weathering and erosion of rocks and soil, solution or precipitation reactions occurring below the land surface, and cultural effects resulting from human activities. Broad interrelationships among these processes and their effects can be discerned by application of principles of chemical thermodynamics. Some of the processes of solution or precipitation of minerals can be closely evaluated by means of principles of chemical equilibrium, including the law of mass action and the Nernst equation. Other processes are irreversible and require consideration of reaction mechanisms and rates. The chemical composition of the crustal rocks of the Earth and the composition of the ocean and the atmosphere are significant in evaluating sources of solutes in natural freshwater. The ways in which solutes are taken up or precipitated and the amounts present in solution are influenced by many environmental factors, especially climate, structure and position of rock strata, and biochemical effects associated with life cycles of plants and animals, both microscopic and macroscopic. Taken together and in application with the further influence of the general circulation of all water in the hydrologic cycle, the chemical principles and environmental factors form a basis for the developing science of natural-water chemistry. Fundamental data used in the determination of water quality are obtained by the chemical analysis of water samples in the laboratory or onsite sensing of chemical properties in the field. Sampling is complicated by changes in the composition of moving water and by the effects of particulate suspended material. Some constituents are unstable and require onsite determination or sample preservation. Most of the constituents determined are reported in gravimetric units, usually milligrams per liter or milliequivalents
6,271 citations
TL;DR: A large increase was seen in the number and proportion of hurricanes reaching categories 4 and 5 and the number of cyclones and cyclone days has decreased in all basins except the North Atlantic during the past decade.
Abstract: We examined the number of tropical cyclones and cyclone days as well as tropical cyclone intensity over the past 35 years, in an environment of increasing sea surface temperature. A large increase was seen in the number and proportion of hurricanes reaching categories 4 and 5. The largest increase occurred in the North Pacific, Indian, and Southwest Pacific Oceans, and the smallest percentage increase occurred in the North Atlantic Ocean. These increases have taken place while the number of cyclones and cyclone days has decreased in all basins except the North Atlantic during the past decade.
2,989 citations
TL;DR: In this paper, the effect of autocorrelation on the variance of the Mann-Kendall trend test statistic is discussed, and a modified non-parametric trend test is proposed.
2,252 citations
TL;DR: In this article, the power of the Mann-Kendall test and Spearman's rho test for detecting monotonic trends in time series data is investigated by Monte Carlo simulation.
1,642 citations
TL;DR: In this article, the authors investigated the effect of serial correlation on the performance of the Mann-Kendall (MK) statistic and showed that the presence of a trend alters the estimate of the magnitude of serial correlations.
Abstract: This study investigated using Monte Carlo simulation the interaction between a linear trend and a lag-one autoregressive (AR(1)) process when both exist in a time series. Simulation experiments demonstrated that the existence of serial correlation alters the variance of the estimate of the Mann–Kendall (MK) statistic; and the presence of a trend alters the estimate of the magnitude of serial correlation. Furthermore, it was shown that removal of a positive serial correlation component from time series by pre-whitening resulted in a reduction in the magnitude of the existing trend; and the removal of a trend component from a time series as a first step prior to pre-whitening eliminates the influence of the trend on the serial correlation and does not seriously affect the estimate of the true AR(1). These results indicate that the commonly used pre-whitening procedure for eliminating the effect of serial correlation on the MK test leads to potentially inaccurate assessments of the significance of a trend; and certain procedures will be more appropriate for eliminating the impact of serial correlation on the MK test. In essence, it was advocated that a trend first be removed in a series prior to ascertaining the magnitude of serial correlation. This alternative approach and the previously existing approaches were employed to assess the significance of a trend in serially correlated annual mean and annual minimum streamflow data of some pristine river basins in Ontario, Canada. Results indicate that, with the previously existing procedures, researchers and practitioners may have incorrectly identified the possibility of significant trends. Copyright 2002 Environment Canada. Published by John Wiley & Sons, Ltd.
1,573 citations
References
More filters
TL;DR: In this article, a simple and robust estimator of regression coefficient β based on Kendall's rank correlation tau is studied, where the point estimator is the median of the set of slopes (Yj - Yi )/(tj-ti ) joining pairs of points with ti ≠ ti.
Abstract: The least squares estimator of a regression coefficient β is vulnerable to gross errors and the associated confidence interval is, in addition, sensitive to non-normality of the parent distribution. In this paper, a simple and robust (point as well as interval) estimator of β based on Kendall's [6] rank correlation tau is studied. The point estimator is the median of the set of slopes (Yj - Yi )/(tj-ti ) joining pairs of points with ti ≠ ti , and is unbiased. The confidence interval is also determined by two order statistics of this set of slopes. Various properties of these estimators are studied and compared with those of the least squares and some other nonparametric estimators.
8,409 citations
"Techniques of trend analysis for mo..." refers background in this paper
...The problem of testing water quality monitoring data for trend in time has received considerable attention in the last decade (see, for example, Wolman [1971], Steele et al. [1974], Lettenmaier [1977], and Liebetrau [1979])....
[...]
...Examples of their combined use are presented by Smith et al. [1982]. The three procedures are as follows....
[...]
Book•
01 Jan 1948
TL;DR: The measurement of rank correlation was introduced in this paper, and rank correlation tied ranks tests of significance were applied to the problem of m ranking, and variate values were used to measure rank correlation.
Abstract: The measurement of rank correlation introduction to the general theory of rank correlation tied ranks tests of significance proof of the results of chapter 4 the problem of m ranking proof of the result of chapter 6 partial rank correlation ranks and variate values proof of the result of chapter 9 paired comparisons proof of the results of chapter 11 some further applications.
6,404 citations