Fitting curves to cyclic data

A common problem in hydrology is to fit a smooth curve to cyclic or periodic data, either to define the most probable values of the data or to test some principle that one wishes to demonstrate.  This study treats of those problems where the length or period of the cycle is know beforehand - as a day, year, or meander length for example.  Curve-fitting can be made by free-hand drawing, and where the data are closely aligned this method offers the simplest and most direct course.  However, there are many problems where the best fit is far from obvious, and analytical methods may be necessary.