Abstract

An observational time series can normally be viewed as consisting of two general components: one that we are interested in (signal), and another that we are not (noise) and that usually obscures the signal. For analysis of data sets capturing the temporal evolution of complex, open, multi-faceted systems—such as those routinely encountered in environmental and engineering geoscience—the operational definitions of signal and noise will frequently be extremely context-dependent, reflecting whatever happen to be the scientific interests of, or the societal questions posed to, a particular researcher. As such, either signal or noise may be mechanistic, random, or both in origin. Further, signal and noise may often be of comparable strength. In this paper, existing concepts are compiled and integrated to offer a flexible and general metric for the strength of an arbitrarily defined signal embedded within an observational time series. One potential application is the estimation of the relative importance or clarity of a specified physical process or effect. Brief, illustrative examples are drawn from geoscientific trend analysis. The results of these preliminary studies suggest that signal-to-noise ratios can be a useful, robust, and readily applied descriptive aid to support experimental characterization of geophysical patterns (as applied here to ecological low-flow data from the Cowichan region of British Columbia), exploration of fundamental relationships (suggesting a non-linear relationship between data set length and trend clarity on the basis of numerical experiments), and science communication (following from a straightforward analogy to consumer electronics).

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