Review of methods for the detection and estimation of trends with emphasis on water quality applications

Abstract

Methods for the detection and estimation of trends which are suitable for the type of data sets available from water quality and atmospheric deposition monitoring programmes are considered. Parametric and non-parametric methods which are based on the assumption of monotonic trend and which account for seasonality through blocking on season are described. The topics included are heterogeneity of trend, missing data, covariates, censored data, serial dependence and multivariate extensions. The basis for the non-parametric methods being the method of choice for current farge data sets of short to moderate length is reviewed. A more general definition of trend as the component of gradual change over time is consistent with another group of methods and some examples are given. Spatial temporal data sets and longer temporal records are also briefly considered. A broad overview of the topic of trend analysis is given, with technicalities left to the references cited. The necessity of defining what is meant by trend in the context of the design and objectives of the programme is emphasized, as is the need to model the variability in the data more generally.

Does it really rain more often on weekends than on weekdays? A case study for Slovenia

“…Various parametric and nonparametric tests can be used to detect the changes in the time series (e.g., Kendall 1975;Maidment 1993;Esterby 1996;Rao and Hamed 2001;Kundzewicz and Robson 2004;Khaliq et al 2009;Bezak et al 2015a). The nonparametric χ 2 test (Haan 2002) was used in the study to test the hypothesis about a non-uniform rainfall pattern.…”

Oxygen Demand Trends, Land Cover Change, and Water Quality Management for an Urbanizing Oregon Watershed

“…This is a critical limitation for my study because SOD has been identified as a significant source of oxygen demand for the Tualatin River (Rounds and Doyle 1997 The determination of long-tetm trends in water quality parameters has received substantial study throughout the last thitiy years from the techniques perspective (Hirsch and Slack 1984;Esterby 1996;Bekele and McFarland 2004) and with reference to case studies (e.g. Smith et al 1987;Lettenmaier et al 1991;Richards and Baker 2002).…”

“…They suggested that changes in cropland management and fertilizer applications are likely causes for this decrease. Trend estimates in water quality are confounded by discontinuous sampling intervals, sample detection limits, seasonality in water quality signals, variability related to discharge, and anthropogenic change in hydrologic systems (Hirsch et al 1991;Esterby 1996). As a result, much of the body of work concerning trend analysis has centered on capturing these sources of variability in order to an·ive at statistically robust estimates of change in water quality.…”

“…(1991) and Esterby (1996) LOWESS is a robust technique for creating a regression line that is based upon locally weighted averages about each x observation point (Cleveland 1979). …”

Detecting and Estimating Trends of Water Quality Parameters

“…Also useful for the detection of trends there are a variety of graphical techniques. For a detailed description of such methods readers may refer, for example, to texts such as Hirsch et al, 1982;Lettenmaier et al, 1982;Hirsch & Slack, 1984;van Belle & Hughes, 1984;Helsel, 1987;Lettenmaier, 1988;Hirsch et al, 1991;McLeod et al, 1991;Esterby, 1993Esterby, , 1996Reckhow et al, 1993;Kundzewicz & Robson (eds), 2000;Hess et al, 2001;Kundzewicz & Robson, 2004;Hesel & Frans, 2006;Visser et al, 2009. Several trend tests have also been described in statistical textbooks (e.g.…”