Journal cover Journal topic
Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
Hydrol. Earth Syst. Sci., 20, 3411-3418, 2016
https://doi.org/10.5194/hess-20-3411-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
Technical note
24 Aug 2016
Technical note: Fourier approach for estimating the thermal attributes of streams
Masahiro Ryo1,2,3, Marie Leys1,3, and Christopher T. Robinson1,3 1Department of Aquatic Ecology, EAWAG, 8600 Duebendorf, Switzerland
2Department of Civil Engineering, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, 152-0033 Tokyo, Japan
3Institute of Integrative Biology, ETH-Zürich, 8092 Zürich, Switzerland
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.

Citation: Ryo, M., Leys, M., and Robinson, C. T.: Technical note: Fourier approach for estimating the thermal attributes of streams, Hydrol. Earth Syst. Sci., 20, 3411-3418, https://doi.org/10.5194/hess-20-3411-2016, 2016.
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We developed an analytical method to estimate thermal attributes (seasonal and diel periodicities as well as irregularities) in stream temperature at data-poor sites. We extrapolated the thermal attributes of a glacier-fed stream in the Swiss Alps using 2 years of hourly recorded temperature to the data-poor sites. The R scripts used in this study are available in the Supplement.
We developed an analytical method to estimate thermal attributes (seasonal and diel...
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