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

Abstract. 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.