Dynamic Time Warping for Quantitative Analysis of Tracer Study Time-Series Water Quality Data

Hyoungmin Woo, Dominic L. Boccelli, James G. Uber, Robert Janke, Yuan Su

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Conservative chemicals (such as sodium chloride) have been utilized to perform tracer studies within drinking water distribution systems. The resulting signals from a tracer study can provide significant quantitative information to assess the ability of a given network model to represent the underlying hydraulic and transport characteristics of the network. Often, however, the resulting observed water quality time-series data are simply visually inspected to assess the ability of the network model to accurately predict water quality transport. The use of standard quantitative metrics, such as arrival times, sum of squared errors (SSE), and correlation analysis at different time lags to assess the differences between the observed and predicted time-series, can provide some useful information but are not sufficient for paired data signals. In this study, the use of dynamic time warping (DTW) - an approach for estimating the similarity between two time series of data - is presented as a method for quantitative analysis of observed and model-predicted conservative chemical time-series data. DTW uses dynamic programming to match the elements of two time series, in a sequential approach, to minimize the SSE of the two signals. Whereas the SSE provides one goodness-of-fit metric, the resulting length of the warping path also provides additional information as to the degree of the alignment between the two data streams.

Original languageEnglish (US)
Article number04019052
JournalJournal of Water Resources Planning and Management
Issue number12
StatePublished - Dec 1 2019


  • Correlation analysis
  • Dynamic time warping (DTW)
  • Sum of squared errors (SSE)
  • Tracer study
  • Water distribution system

ASJC Scopus subject areas

  • Geography, Planning and Development
  • Civil and Structural Engineering
  • Water Science and Technology
  • Management, Monitoring, Policy and Law


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