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About the Authors:
Stephen L. Katz
* E-mail: [email protected]
Affiliation: Channel Islands National Marine Sanctuary, National Oceanographic and Atmospheric Administration, Santa Barbara, California, United States of America
Stephanie E. Hampton
Affiliation: National Center for Ecological Analysis and Synthesis, University of California Santa Barbara, Santa Barbara, California, United States of America
Lyubov R. Izmest'eva
Affiliation: Scientific Research Institute of Biology, Irkutsk State University, Irkutsk, Russia
Marianne V. Moore
Affiliation: Department of Biological Sciences, Wellesley College, Wellesley, Massachusetts, United States of America
Introduction
Shifts in both magnitude and timing of temperature, precipitation and other climate variables associated with climate change have affected ecosystems, independently and in concert. Alterations in productivity and species ranges have been correlated with rising temperatures, and phenological changes have been evident as the timing of seasonal events has shifted across ecosystems [1]–[3]. It is increasingly appreciated that shifting abiotic and biotic seasonality manifests across a broad range of temporal scales related to climate variability, in addition to those associated with long-term warming, with cascading repercussions for ecosystems [1], [4]–[6]. Applying the tools of signal processing to evaluate patterns of seasonal variability in climate and local ecology may reveal important messages about how these systems are connected across space and what ecosystem level consequences may be expected.
Seasonal timing is defined in various ways across ecosystems and individual studies. Many ecologists define seasonal transitions by identifying biological threshold temperatures to be crossed [7], [8] and in the case of aquatic systems, the onset and deterioration of thermal stratification [9], [10] can be a useful seasonal indicator. Stine et al. [11], however, emphasize that the use of such thresholds in defining season can conflate changes in timing of season with changes in the annual mean, and these authors exploited an implementation of spectral analysis to describe season in time series data. In spectral analysis, the temporal positions of the harmonics (including harmonics with an annual frequency) contributing to the observed dynamics of a time series – phase (Φ) – are estimated over the length of the time series. If seasonal signals are non-stationary, in that they vary across a time series [12], the locally estimated phases will deviate from the phase estimated for the entire time series and the deviation can be expressed as a...