Improved annual temperature cycle function for stream seasonal thermal regimes

Seasonal regimes of stream temperatures are important for ecological health as well as for societal water use. Seasonal regimes can be captured in the annual temperature cycle (the mean temperature for each day of the year) or in summary statistics such as seasonal mean temperatures, the former of which is the focus of this work. The annual temperature cycle is often characterized as a sine function, which performs satisfactorily for most streams. However, the sine function is unable to capture major seasonal variations, particularly for colder, drier, and high-elevation regions. Seasonal summary statistics are effective for classification but do not capture the full time series, preventing the use of lost time-series information, and lack context for the comparison of trends, hindering distinction between different causes of similar seasonal trends. We propose an improved function called the “three-sine model” to describe the stream annual temperature cycle with higher accuracy and demonstrate its use in two case studies. The three-sine model uses a cosine function over the entire year coupled with two seasonal anomaly sine functions. The three-sine model captures the stream annual temperature cycle with eight parameters, reveals distinct spatial trends, and outperforms the sinusoidal model for all elevations and 99% of streams. We conclude that this approach can support improved stream temperature analysis by capturing detailed seasonal trends in context.