Modelling soil attribute depth functions with equal-area quadratic smoothing splines

Abstract

The objective of this paper is to test the ability of equal-area quadratic splines to predict soil depth functions based on bulk horizon data. In addition, the possibility of improving the prediction quality by the use of additional samples from the top and/or bottom of soil profiles along with horizon data is examined. The predictive performance of the splines is compared with that of exponential decay functions, and 1st and 2nd degree polynomials. In addition, the predictive quality of the conventional horizon data is examined. The measure of predictive performance used is the root mean square error values calculated from differences between the ‘true’ depth function and the fitted depth function. The ‘true’ depth functions were derived from the intensive sampling and laboratory analysis of soil profiles. Three soil profiles were sampled; a Red Podzolic Soil (Red Kurosol), Podzol (Aeric Podosol) and Krasnozem (Red Ferrosol). The soil attributes that were measured included; pH, electrical conductivity (EC), clay %, sand %, organic carbon %, gravimetric water content at −33 kPa and air dry. The results clearly indicated the superiority of equal-area quadratric splines in predicting depth functions. Such splines depend on a parameter, λ that controls goodness-of-fit vs. roughness. Their quality of fit varied with the λ value used and it was found that a λ value of 0.1 was the best overall predictor of the depth functions. The results also showed that using additional samples from the top and/or bottom of the soil profiles improved the prediction quality of the spline functions.