Mathematical model to describe litter decomposition rate in semiarid regions

Abstract

Although semiarid regions present a poor rainfall distribution throughout the year, the most frequently used mathematical model describing the litter decomposition rate (LDR) predicts the same behavior of crop residues behavior in dry and rainy seasons. The aim of this study was to design a mathematical model to describe the LDR by a means of piecewise continuous function depending on the rainfall quantity. A field experiment was conducted from October 2009 to September 2010 at Brejo Paraibano, Paraíba, Brazil. The experimental design was completely randomized in a 6 × 12 factorial arrangement, with six plant residues, brachiaria (Brachiaria decumbens Stapf), corn (Zea mays L.), sorghum (Sorghum bicolor (L.) Moench), jack bean (Canavalia ensiformis L.), pigeonpea (Cajanus cajan (L.) Hunth), and leucaena (Leucaena leucocephala Lam.), and 12 collection periods. Using data obtained from an experimental field, a mathematical model was developed. The proposed model is based on the concept of infinite series. It was verified that in dry seasons the LDR can be well described by a linear function whereas in rainy ones an exponential function describes it better. Statistical analysis showed good agreement between the experimental data and the theoretical model. For the model, the decomposition coefficients for each culture and each period are proposed.