# What are the considerations for spline-interpolating a whole dataset?

In Clinton, et al. 2010, the authors use splines to interpolate 100 equally spaced data points per year from only about a dozen actual measurements.

The 12 (or possibly less for the NDVI data) annual obser- vations of precipitation and NDVI were not enough for the computation of the various metrics. This is due to the statisti- cal nature of the metrics, which are only calculable with more data points. To interpolate over times of missing data and to obtain more data points annually, we fit splines to the complete series (2001–2005) for both NDVI and precipitation. We used one-dimensional thin plate splines, or Duchon’s splines, as implemented by JSpline+ (Rozhenko, 2009). Hermance et al. (2007) demonstrated the use of splines for such a purpose. Our method is similar to using a smoothing spline with penal- ized roughness (Hastie et al., 2001). Once a spline has been fit to the series, an arbitrary number of equally spaced data points can be generated. We generated 100 data points in each year, for a total of 500 data points in each series.

That technique sounds so dodgy, except I guess in this case it's plausible because NDVI ought to be a fairly smooth phenomenon. I think what bothers me is using interpolation to generate a whole dataset, rather than a couple of missing values. This strikes me as a change-of-support problem, but in time instead of space, a kind of downscaling.

Are there any rules of thumb about how many "data" values you can comfortably interpolate from how many actual measurement? What are the issues around generating more "data" than the information might support? Would measures of local variation or roughness in the original data indicate whether splined data is a good idea?

• The spline interpolant is a function defined over some region in $\mathbb{R}^n$, so you ask the wrong question. It does'nt matter at how many points you calculate the spline interpolant, it is defined everywhere. You ought to ask if interpolation makes sense at all given how few data points you have. – kjetil b halvorsen Apr 7 '17 at 17:43
• That is what I am asking. Care to answer? – J Kelly Apr 8 '17 at 1:56