Bulk-density modelling using optimal power-transformation of measured physical and chemical soil parameters

Abstract

Listen

Translate article

Most of the existing bulk-density pedotransfer functions (PTFs) are formulated as linear (multiple) regression functions, with the requirements for multivariate normality and homoscedasticity. Bulk-density PTFs may or may not use transformed variables, such as natural logarithm (ln), in order to improve the normality and homoscedasticity. These transformations are often applied to explanatory variables and sometimes also to the bulk-density (ρb) response variable. The question remains whether we can develop better bulk-density predictive models by choosing better (optimal) normalising transformation and by transforming both response and explanatory variables. The main objective of this study was to develop new bulk-density models using optimally transformed soil parameters, including the models with optimally transformed ρb response variables. The specific aims were to develop new models with non-transformed and optimally transformed soil parameters and to compare them to each other and to selected calibrated models from the literature, using data from five Irish afforested mineral soils (Cambisols, Gleys, Leptosols, Luvisols and Podzols). The data used were dominated by Podzols and Cambisols. The novel approach taken in this study was to perform the optimal normalising transformation of variables by applying the power-transformation with parameter λ obtained with the help of a Box–Cox transformation, and to compare the transformed and non-transformed ρb models by computing the ‘corrected’ Akaike's Information Criterion (AICcorr). The comparison of models was done using AICcorr rather than applying a back-transformation for computing the model prediction-quality indices (such as R2) because the latter may not be suitable due to possible differences in variances of transformed and non-transformed ρb. Ten new models were developed with a help of stepwise multiple regression using physical and chemical soil parameters measured on composite soil samples by horizon from each study site, including models with optimally transformed bulk-density response variable (ρbλ). Modelling was performed separately using either soil organic carbon (SOC) or loss on ignition (LOIOM) as the main predictor. The results from this study indicate that the model-development and the predictive performance of the final bulk-density models may be improved by the use of optimally transformed data: the best new models in this study used λ power-transformation of variables, and loss on ignition (LOIOM) as a main predictor. The overall best new model was the new model in which both response variable ρb and explanatory variable LOIOM were λ power-transformed. Although the results from this study should be considered of an indicative nature due to limited number of sites, they show that the normality and homoscedasticity may need to be first tested before choosing the most suitable bulk-density PTFs for the new data. If applying the PTFs from this study to the new data, which also experience non-normality, it is recommended (in addition to usual model re-calibration) to first derive the new λ parameters by re-applying the Box–Cox transformation to the new data.