Surface Fitting Using GCV Smoothing Splines on Supercomputers

Abstract

The task of fitting smoothing spline surfaces to meteorological data such as temperature or rainfall observations is computationally intensive. The Generalised Cross Validation (GCV) smoothing algorithm is O(n³) computationally, and memory requirements are 0(n²). Fitting a spline to a moderately sized data set of, for example. 1080 observations and calculating an output surface grid of dimension 220 × 220 involves approximately 5 billion floating point operations, and takes approximately 19 minutes of execution time on a Sun SPARC2 workstation. Since fitting a surface to data collected from the whole of Australia could conceivably involve data sets with approximately 10000 points, and because it is desirable to be able to fit surfaces of at least 1000 data points in 1 to 5 seconds for use in interactive visualisations, it is crucial to be able to take advantage of supercomputing resources. This paper describes the adaptation of the surface fitting program to different supercomputing platforms, and the results achieved.