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

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.