Peak functions for modeling high resolution soil profile data

Parametric and non-parametric depth functions have been used to estimate continuous soil profile properties. However, some soil properties, such as those seen in weathered loess, have anisotropic peak-shaped depth distributions. These distributions are poorly handled by common parametric functions. And while nonparametric functions can handle this data they lack meaningful parameters to describe physical phenomena in the depth distribution of a property such as a peak, an inflection point, or a gradient. The objective of this work is to introduce the use of asymmetric peak functions to model complex and anisotropic soil property depth profiles. These functions have the advantages of providing parameters, which quantify or describe pedogenic processes. We demonstrate the application of the Pearson Type IV (PIV) and the logistic power peak (LPP) functions to high resolution soil property depth profiles measured by diffuse reflectance spectroscopy in a claypan soil landscape of Northeastern Missouri, USA. Both peak functions successfully fit clay, silt, and pH data for an example soil profile from a summit landscape position (R² = 0.90 for pH and 0.98 for silt and clay). The LPP function was further demonstrated to fit clay depth distribution for a shoulder, backslope, footslope, and a depositional landscape position (R² = 0.98, 0.96, 0.96, 0.91). Relationships between the fitted parameters of these profiles were useful to describe landscape trends in their morphological features and show promise to continuously describe pedogenic processes in three dimensions. Peak functions are a useful companion to high-resolution soil profile data collected by sensors and their combined use may allow more intensive mapping and better explanation of soil landscape variability.