Premium
Smoothing Data with Cubic Splines 1
Author(s) -
Kimball B. A.
Publication year - 1976
Publication title -
agronomy journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.752
H-Index - 131
eISSN - 1435-0645
pISSN - 0002-1962
DOI - 10.2134/agronj1976.00021962006800010033x
Subject(s) - smoothing spline , smoothing , piecewise , spline (mechanical) , mathematics , monotone cubic interpolation , thin plate spline , box spline , spline interpolation , cubic function , mathematical analysis , statistics , physics , trilinear interpolation , bilinear interpolation , thermodynamics
Agronomic data frequently requires smoothing in order to obtain a reliable functional relationship for interpolating, predicting, or determining the rate of change of one variable with respect to another. To test whether cubic spline functions could provide satisfactory smoothing, the necessary equations were derived, computer programs written, and several sets of soil temperature and water content data were smoothed. Cubic spline smoothing displayed the following, advantages: 1) Because spline functions are defined piecewise, they can represent any variable arbitrarily well over wide ranges of the other. 2) The data can be obtained at unequal intervals, so high sampling rates can be used where changes are rapid and low rates where they are slow. 3) Additionally, the gradients derived from cubic spline functions are smoothly joined parabolas, not the abruptly joined straightline segments characteristic of parabolic spline smoothing.