Implementation of a sigmoid depth function to describe change of soil pH with depth

- We propose a new model to quantify soil pH distribution at depths in agricultural fields.
- Very simple model and easy to implement with small number of parameters
- It is based on the pedological and management characteristics of soil profile.
- Tested with a local (32) and global (432) soil profile dataset
- Compared with commonly used regression and spline based models

Soil pH controls the availability of the majority of plant nutrients, if not all, and determines the growth environment for plant roots. Profile depth functions have been used to represent the vertical distribution of soil attributes and to predict them at continuous depths. This paper proposes a new model to predict pH for a whole soil profile. Soil properties including pH are often similar within the plow layer from mixing during tillage and other agricultural operations. Similarly, soil pH below the root zone tends to be uniform due to low disturbance, leaving a transition zone from the bottom of the tillage layer to the bottom of the root zone due to depth-dependent root density and related soil processes. Keeping this physical description of agricultural field soil profile in mind, a closed form equation (model) was developed similar to a sigmoid curve. The model has 4 parameters including 1) soil pH at the top of a soil profile, 2) soil pH at the bottom of a soil profile, 3) hillslope parameter representing steepness of the curve that is determined by the length of the root zone, and 4) inflection point representing almost the midpoint of the transition zone or root zone. A total of 32 soil cores down to about 1.1 m depths were collected from an agricultural field of Macdonald farm, McGill University. The sub-samples were taken at every 10 cm and analyzed for soil pH in soil: water suspension in the laboratory. The measured pH was used to test the fitting performance of the sigmoid model. Additionally, a global dataset with 432 profiles with various soil classes, drainage types, land use, and altitude was also used to test the generality of the new model. The performance of this model was compared with the results of the commonly used 3rd order polynomial regression function and the equal-area quadratic spline function. Good performance of the sigmoid model with explicit physical explanation showed promise in predicting soil pH at depths. The spline function had the highest accuracy but lacked a general trend in its shape and parameters. The polynomial function had good accuracy and displayed a non-monotonic trend, which can also be used as a substitute for some profiles with complex variability.