Long-Term and Seasonal Trends of Wastewater Chemicals in Lake Mead: An Introduction to Time Series Decomposition

ABSTRACT

A recent paper published time series of concentrations of chemicals in drinking water collected from the bottom of Lake Mead, a major American water supply reservoir. Data were compared to water level using only linear regression. This creates an opportunity for students to analyze these data further. This article presents a structured introduction to time series decomposition that compares long-term and seasonal components of a time series of a single chemical (meprobamate) with those of two supporting datasets (reservoir volume and specific conductance). For the chemical data, this must be preceded by estimation of missing datum points. Results show that linear regression analyses of time series data obscure meaningful detail and that specific conductance is the important predictor of seasonal chemical variations. To learn this, students must execute a linear regression, estimate missing data using local regression, decompose time series, and compare time series using cross-correlation. Complete R code for these exercises appears in the supplementary information. This article uses real data and requires that students make and justify key decisions about the analysis. It can be a guided or an individual project. It is scalable to instructor needs and student interests in ways that are identified clearly in this article.

KEYWORDS:

• Cross-correlation
• Environmental science
• Local regression
• Missing values
• Water quality
• Wastewater contaminant

Acknowledgments

Todd Tietjen and Peggy Roefer of the SNWA provided helpful discussion and database access, respectively. Glen van Brummelen and Jim Cohn (Quest University Canada) created the opportunity for the author to teach the statistics course in which this exercise was developed. Lucas Nguyen (Quest and Geosyntec Consultants, Inc.) made early contributions toward analyses of the chemical dataset. Lonnie Wake (Quest) provided helpful discussion at key points during conceptual development of this manuscript. The comments of Editor Dr. Bethany White and two anonymous reviewers allowed substantive improvements to the first version of the manuscript.

Funding

Part of this work was supported by a French Environmental Fellowship awarded to the author through the Harvard University Center for the Environment.

Supplementary Materials

Complete R code for this exercise is available as appendix, which can be accessed on the publisher's website.