Smoothing data series by means of cubic splines: quality of approximation and introduction of an iterative spline approach
arxiv: Mathematics::Numerical Analysis | Computer Science::Graphics
Cubic splines with equidistant spline sampling points are a common method in atmospheric science for the approximation of undisturbed background conditions by means of filtering superimposed fluctuations from a data series. Often, not only the background conditions are of scientific interest but also the residuals – the subtraction of the spline from the original time series.
Based on test data sets, we show that the quality of approximation is not increasing continuously with increasing number of spline sampling points/decreasing distance between two spline sampling points. Splines can generate considerable artificial oscillations in the data.
We introduce an iterative spline approach which is able to significantly reduce this phenomenon. We apply it not only to the test data but also to TIMED-SABER temperature data and choose the distance between two spline sampling points in a way that we are sensitive for a large spectrum of gravity waves.