Summary: What "well-known" and short parametrized mathematical function describes daily and hourly temperature for a given location?
If you look at the mean daily temperature graph for a given location, it looks like a sine wave with a period of one year.
Similarly, the hourly temperature for a given day for a given location also looks like a sine wave with a period of one day.
However, closer inspection (Fourier analysis) shows that they're not. There are fairly strong components of frequency 2/year and 3/year for the daily temperature, and the hourly temperature also has strong non-single-period terms.
Is there a parametrized function that reasonably describes the daily mean temperature and (a separate function) the hourly mean temperature? The parameters would be location-based.
I realize I can keep taking more Fourier terms to increase accuracy, but I was hoping for something more elegant. For example, maybe the graph is a parametrized version of sin^2(x) or some other "well-known" function.