Technical note: Fourier approach for estimating the thermal attributes of streams

Temperature models that directly predict ecologically important thermal attributes across spatiotemporal scales are still poorly developed. This study developed an analytical method based on Fourier analysis to estimate seasonal and diel periodicities, as well as irregularities in stream temperature, at data-poor sites. The method extrapolates thermal attributes from highly resolved temperature data at a reference site to the data-poor sites on the assumption of spatial autocorrelation. We first quantified the thermal attributes of a glacier-fed stream in the Swiss Alps using 2 years of hourly recorded temperature. Our approach decomposed stream temperature into its average temperature of 3.8 °C, a diel periodicity of 4.9 °C, seasonal periodicity spanning 7.5 °C, and the remaining irregularity (variance) with an average of 0.0 °C but spanning 9.7 °C. These attributes were used to estimate thermal characteristics at upstream sites where temperatures were measured monthly, and we found that a diel periodicity and the variance strongly contributed to the variability at the sites. We evaluated the performance of our predictive mechanism and found that our approach can reasonably estimate periodic components and extremes. We could also estimate the variability in irregularity, which cannot be represented by other techniques that assume a linear relationship in temperature variabilities between sites. The results confirm that spatially extrapolating thermal attributes based on Fourier analysis can predict thermal characteristics at a data-poor site. The R scripts used in this study are available in the Supplement.

Technical note: Fourier approach for estimating the thermal attributes of streams

Temperature models that directly predict ecologically important thermal attributes across spatio-temporal scales are still poorly developed. This study developed an analytical method to estimate seasonal and diel periodicities as well as irregularities in stream temperature at data-poor sites based on Fourier analysis. We first quantified the thermal attributes of a glacier-fed stream in the Swiss Alps using 2-years of hourly-recorded temperature. Stream temperature was accurately decomposed to an average 3.8 °C, diel periodicity spanning 4.9 °C, seasonal periodicity spanning 7.5 °C, and an irregularity having an average of 0.0 °C but spanning 9.7 °C. These thermal attributes then were used to estimate thermal attributes at spot-measured sites along the river, resulting in a different relative contribution (weighting) of attributes among sites. The results confirm that the developed method can infer stochastic behaviors in stream thermal attributes at spot-measured sites. Additional ways to further improve the methodological approach are discussed.