A soil water indicator for a dynamic model of crop and soil water interaction

Edwin Duque-Marín; Alejandro Rojas-Palma; Marcos Carrasco-Benavides; Edwin Duque-Marín; Alejandro Rojas-Palma; Marcos Carrasco-Benavides

doi:10.3934/mbe.2023618

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 8: 13881-13899. doi: 10.3934/mbe.2023618

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Research article

A soil water indicator for a dynamic model of crop and soil water interaction

1.
Doctorado en Modelamiento Matemático Aplicado, Facultad de Ciencias Básicas, Universidad Católica del Maule, Talca 3460000, Chile
2.
Departamento de Matemática, Física y Estadística, Facultad de Ciencias Básicas, Universidad Católica del Maule, Talca 3460000, Chile
3.
Departamento de Ciencias Agrarias, Facultad de Ciencias Agrarias y Forestales, Universidad Católica del Maule, Curicó 3340000, Chile

Academic Editor: Yang Kuang

Received: 15 December 2022 Revised: 16 May 2023 Accepted: 30 May 2023 Published: 19 June 2023

Water scarcity is a critical issue in agriculture, and the development of reliable methods for determining soil water content is crucial for effective water management. This study proposes a novel, theoretical, non-physiological indicator of soil water content obtained by applying the next-generation matrix method, which reflects the water-soil-crop dynamics and identifies the minimum viable value of soil water content for crop growth. The development of this indicator is based on a two-dimensional, nonlinear dynamic that considers two different irrigation scenarios: the first scenario involves constant irrigation, and the second scenario irrigates in regular periods by assuming each irrigation as an impulse in the system. The analysis considers the study of the local stability of the system by incorporating parameters involved in the water-soil-crop dynamics. We established a criterion for identifying the minimum viable value of soil water content for crop growth over time. Finally, the model was calibrated and validated using data from an independent field study on apple orchards and a tomato crop obtained from a previous field study. Our results suggest the advantages of using this theoretical approach in modeling the plants' conditions under water scarcity as the first step before an empirical model. The proposed indicator has some limitations, suggesting the need for future studies that consider other factors that affect soil water content.
- indicator,
- impulsive irrigation,
- mathematical model,
- vegetative growth,
- water scarcity
Citation: Edwin Duque-Marín, Alejandro Rojas-Palma, Marcos Carrasco-Benavides. A soil water indicator for a dynamic model of crop and soil water interaction[J]. Mathematical Biosciences and Engineering, 2023, 20(8): 13881-13899. doi: 10.3934/mbe.2023618

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Abstract

Water scarcity is a critical issue in agriculture, and the development of reliable methods for determining soil water content is crucial for effective water management. This study proposes a novel, theoretical, non-physiological indicator of soil water content obtained by applying the next-generation matrix method, which reflects the water-soil-crop dynamics and identifies the minimum viable value of soil water content for crop growth. The development of this indicator is based on a two-dimensional, nonlinear dynamic that considers two different irrigation scenarios: the first scenario involves constant irrigation, and the second scenario irrigates in regular periods by assuming each irrigation as an impulse in the system. The analysis considers the study of the local stability of the system by incorporating parameters involved in the water-soil-crop dynamics. We established a criterion for identifying the minimum viable value of soil water content for crop growth over time. Finally, the model was calibrated and validated using data from an independent field study on apple orchards and a tomato crop obtained from a previous field study. Our results suggest the advantages of using this theoretical approach in modeling the plants' conditions under water scarcity as the first step before an empirical model. The proposed indicator has some limitations, suggesting the need for future studies that consider other factors that affect soil water content.

References

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