Nonlinear modeling of liming reaction and extractable base curves¹

Ajuste não linear de curvas de reação de calcário e bases trocáveis

HIGHLIGHTS:

Statistically nonlinear models were proposed for pH as a function of lime doses.

Statistically nonlinear models were proposed for exchangeable Ca⁺² + Mg⁺² as a function of lime doses.

The use of a statistical index combined with constraints on extrapolation values enabled the se-lection of the best-fitting models.

ABSTRACT

Modeling the response of soils to liming is important for understanding neutralization reactions and predicting lime residual effects. Models based on simple or quadratic polynomial equations are the most used due to their simplicity and ease of fitting; however, they fail to reproduce a realistic soil response to liming, indicating a decrease in pH as the lime dose is increased after reaching a maximum point. Thus, several nonlinear functions were tested and compared to polynomial models, using a dataset from a liming test conducted on a sandy clay loam soil in a farm. The best-fitting models for pH data were the Mitscherlich, three-parameter logistic, and Morgan-Mercer-Flodin models. The best-fitting models for exchangeable Ca⁺² + Mg⁺² data were Skaggs et al., Gompertz, and Morgan- Mercer-Flodin. The use of the proposed T index, which ranks models based on their residual standard error and Akaike information criterion values, combined with constraints on extrapolation values, was useful for selecting models that are statistically robust and empirically coherent.

Key words:
pH correction; nonlinear functions; liming effect; soil correction