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.

Detecting Trends Using Spearman's Rank Correlation Coefficient

“…A common characteristic of time series data is that the data tend to be serially correlatedÐthat is, the value of a data point tends to be related to previous data points collected in the series even after the underlying trend and any seasonal aects are accounted for (Montgomery and Reckhow, 1984;Gilbert, 1987;Berthouex and Brown, 1994). A common characteristic of time series data is that the data tend to be serially correlatedÐthat is, the value of a data point tends to be related to previous data points collected in the series even after the underlying trend and any seasonal aects are accounted for (Montgomery and Reckhow, 1984;Gilbert, 1987;Berthouex and Brown, 1994).…”

TIME SERIES ANALYSIS IN PERSPECTIVE1

“…Recently, there has been a marked increase in research related to nonparametric testing of trends in environmental series. Besides the paper of Hirsch and Gilroy (1985), readers may also wish to refer to work by authors such as Van Belle and Hughes (1984), Hirsch and Slack (1984), Montgomery and Reckhow (1984), and Lettenmaier (1976). Future research in the time series aspects of environmental impact assessment will probably entail developing more nonparametric tests for handling a wider variety of situations in trend detection and evaluation, rigourously comparing the capabilities of both parametric and nonparametric approaches, and providing criteria for optimally designing sampling schemes for water quality variables.…”

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

“…Sanders, et al (1983), describe the test in a water quality context. Montgomery (1984) and Lettenmaier (1976) suggest using the Mann-Whitney and Spearman Rho non-parametric tests for step and linear trends, respectively. Conover (1980) provides details of the tests.…”

“…A number of authors who have studied water quality trends over time point out the need for data to be "collected at a given location, by using consistent collection and measurement techniques on a regular schedule and over a substantial number of years" McLeod, et aL, 1983;Montgomery, 1984). An additional key assumption in testing for trends is that water quality observations are independent (unrelated to each other across time).…”

“…Water quality time series are almost certain to contain time dependenceeither seasonality, serial correlation, or both (Montgomery, 1984). A close review of the time series plot reveals considerable information regarding periodic behavior.…”