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## Ciencia del suelo

*versión On-line* ISSN 1850-2067

#### Resumen

SALAZAR ESPINOZA, Paulina Alejandra; GOMEZ FERNANDEZ, Juan Alfredo y NUNEZ RAMOS, Pedro Antonio. Mathematical model applied to the dynamica of nitrogen in soils under pasture in southern Chile.* Cienc. suelo* [online]. 2011, vol.29, n.2, pp.213-222.
ISSN 1850-2067.

The fertilization efficiency program in pasture systems for improving livestock feeding is very important for for farmers in southern Chile. This paper reformulates a mathematical simulation model proposed to describe the concentration of total nitrogen (NT) in soil, in order to fit real experimental data. The objective was to determine the appropriate fertilization strategies in pastures and their direct use by livestock. Critical assumptions consisted, first, in that the concentration of TN in the soil depends on the concentration of its three major components: organic nitrogen (N-NO), nitrate nitrogen (N-NO_{3}-) and ammonium nitrogen (N-NH_{4}+) and second, that the behavior of the concentration of these components depends strongly on the season of the year and, therefore, the coefficients in the model must be different for each season and third, that only the first 10 cm of the soil profile are meaningful for pasture growth. The modified model consists of a system of partial differential equations (PDE), which consists of EDP's for N-NO and N-NO_{3}-, while N-NH_{4}+ was interpolated by a polynomial with the degree varying with the season. The model parameters were calculated solving a functional least squares sum of residuals, using the experimental data. We used optimization methods to solve the problem of least squares. The model used initial data and boundaries approximated by polynomials for each season of the year. The resulting parameters were two: A Quasi-Newton (BFGS) and a Genetic Algorithm (GA). The combination of these algorithms was used to avoid possible local minima and to find a global minimum. The GA was used systematically to find good reference points, which gave BFGS as the initial solution. This combination worked well as all the parameters found globally minimized the residual sum of squares. The results showed that the proposed model was significantly adapted to the data (with a 3% maximum error); therefore, the parameters obtained can be considered for the model for the soil type and season accordingly.

**Palabras clave
:
**Mathematical model; Pasture; Nitrogen; Grazing.