Research article

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


  • 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.

    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

    Related Papers:

  • 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.



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    [1] P. R. Shukla, J. Skea, E. Calvo Buendia, V. Masson-Delmotte, H. O. Pörtner, D. C.Roberts, et al., IPCC, 2019: Climate Change and Land: An IPCC Special Report on Climate Change, Desertification, Land Degradation, Sustainable Land Management, Food Security, and Greenhouse Gas Fluxes in Terrestrial Ecosystems, World Meteorological Organization: Geneva, Switzerland, 2019.
    [2] P. Ahmad, M. R. Wani, Physiological Mechanisms and Adaptation Strategies in Plants Under Changing Environment, Springer, New York, 2013.
    [3] J. C. Valverde-Otárola, D. Arias, Efectos del estrés hídrico en crecimiento y desarrollo fisiológico de Gliricidia sepium (Jacq.) Kunth ex Walp, Colombia forestal, 23 (2020), 20–34. https://doi.org/10.14483/2256201x.14786 doi: 10.14483/2256201x.14786
    [4] E. Duque-Marín, A. Rojas-Palma, M. Carrasco-Benavides, Mathematical modeling of fruit trees' growth under scarce watering, J. Phys. Conf. Ser., 2046 (2021), 012017. https://doi.org/10.1088/1742-6596/2046/1/012017 doi: 10.1088/1742-6596/2046/1/012017
    [5] Q. Shan, Z. Wang, H. Ling, G. Zhang, J. Yan, F. Han, Unreasonable human disturbance shifts the positive effect of climate change on tree-ring growth of Malus sieversii in the origin area of world cultivated apples, J. Clean. Prod., 287 (2021), 125008. https://doi.org/10.1016/j.jclepro.2020.125008 doi: 10.1016/j.jclepro.2020.125008
    [6] M. Lévesque, R. Siegwolf, M. Saurer, B. Eilmann, A. Rigling, Increased water-use efficiency does not lead to enhanced tree growth under xeric and mesic conditions, New Phytol., 203 (2014), 94–109. https://doi.org/10.1111/nph.12772 doi: 10.1111/nph.12772
    [7] R. Ogaya, A. Barbeta, C. Başnou, J. Peñuelas, Satellite data as indicators of tree biomass growth and forest dieback in a Mediterranean holm oak forest, Ann. Forest Sci., 72 (2015), 135–144. https://doi.org/10.1007/s13595-014-0408-y doi: 10.1007/s13595-014-0408-y
    [8] G. Arbat, J. Puig-Bargués, J. Barragán, J. Bonany, F. Ramírez de Cartagena, Monitoring soil water status for micro-irrigation management versus modelling approach, Biosyst. Eng., 100 (2008), 286–296. https://doi.org/10.1016/j.biosystemseng.2008.02.008 doi: 10.1016/j.biosystemseng.2008.02.008
    [9] A. Fares, A. K. Alva, Evaluation of capacitance probes for optimal irrigation of citrus through soil moisture monitoring in an entisol profile, Irrig. Sci., 19 (2000), 57–64. https://doi.org/10.1007/s002710050001 doi: 10.1007/s002710050001
    [10] A. Fernandes-Silva, M. Oliveira, T. A. Paço, I. Ferreira, Deficit irrigation in Mediterranean fruit trees and grapevines: Water stress indicators and crop responses, in Irrigation in Agroecosystems, IntechOpen, 2019. http://dx.doi.org/10.5772/intechopen.80365
    [11] H. E. Igbadun, A. A. Ramalan, E. Oiganji, Effects of regulated deficit irrigation and mulch on yield, water use and crop water productivity of onion in Samaru, Nigeria, Agr. Water Manage., 109 (2012), 162–169. https://doi.org/10.1016/j.agwat.2012.03.006 doi: 10.1016/j.agwat.2012.03.006
    [12] M. S. Hashem, T. Z. El-Abedin, H. M. Al-Ghobari, Assessing effects of deficit irrigation techniques on water productivity of tomato for subsurface drip irrigation system, Int. J. Agric. Biol. Eng., 11 (2018), 156–167. 10.25165/j.ijabe.20181104.3846 doi: 10.25165/j.ijabe.20181104.3846
    [13] V. Blanco, E. Torres-Sánchez, P. J. Blaya-Ros, A. Pérez-Pastor, R. Domingo, Vegetative and reproductive response of 'Prime Giant' sweet cherry trees to regulated deficit irrigation, Sci. Hortic., 249 (2019), 478–489. https://doi.org/10.1016/j.scienta.2019.02.016 doi: 10.1016/j.scienta.2019.02.016
    [14] M. Liu, Z. Wang, L. Mu, R. Xu, H. Yang, Effect of regulated deficit irrigation on alfalfa performance under two irrigation systems in the inland arid area of midwestern China, Agric. Water Manage., 248 (2021), 106764. https://doi.org/10.1016/j.agwat.2021.106764 doi: 10.1016/j.agwat.2021.106764
    [15] J. Lopez-Jimenez, A. Vande Wouwer, N. Quijano, Dynamic modeling of crop–soil systems to design monitoring and automatic irrigation processes: A review with worked examples, Water, 14 (2022), 889. https://doi.org/10.3390/w14060889 doi: 10.3390/w14060889
    [16] J. H. Thornley, I. R. Johnson, Plant and crop modelling, Clarendon Press, Oxford, 1990.
    [17] J. Prieto-Méndez, O. A. Acevedo-Sandoval, M. A. Méndez-Marzo, Indicadores e índices de calidad de los suelos (ICS) cebaderos del sur del estado de Hidalgo, México, Agronomía mesoamericana, 24 (2013), 83–91.
    [18] X. Chone, C. van Leeuwen, D. Dubourdieu, J. P. Gaudillère, Stem water potential is a sensitive indicator of grapevine water status, Ann. Bot., 87 (2001), 477–483.
    [19] N. Livellara, E. Saavedra, F. Salgado, Plant based indicators for irrigation scheduling in young cherry trees, Agric. Water Manage., 98 (2011), 684–690. https://doi.org/10.1016/j.agwat.2010.11.005 doi: 10.1016/j.agwat.2010.11.005
    [20] H. McCutchan, K. A. Shackel, Stem-water potential as a sensitive indicator of water stress in prune trees (Prunus domestica L. cv. French), J. Am. Soc. Hortic. Sci., 117 (1992), 607–611. https://doi.org/10.21273/JASHS.117.4.607 doi: 10.21273/JASHS.117.4.607
    [21] J. Marsal, G. Lopez, J. del Campo, M. Mata, A. Arbones, J. Girona, Postharvest regulated deficit irrigation in 'Summit'sweet cherry: fruit yield and quality in the following season, Irrig. Sci., 28 (2010), 181–189. https://doi.org/10.1007/s00271-009-0174-z doi: 10.1007/s00271-009-0174-z
    [22] V. Blanco, R. Domingo, A. Pérez-Pastor, P. J. Blaya-Ros, R. Torres-Sánchez, Soil and plant water indicators for deficit irrigation management of field-grown sweet cherry trees, Agric. Water Manage., 208 (2018), 83–94. https://doi.org/10.1016/j.agwat.2018.05.021 doi: 10.1016/j.agwat.2018.05.021
    [23] J. E. Fernández, M. V. Cuevas, Irrigation scheduling from stem diameter variations: A review, Agric Forest. Meteorol., 150 (2010), 135–151. https://doi.org/10.1016/j.agrformet.2009.11.006 doi: 10.1016/j.agrformet.2009.11.006
    [24] M. Carrasco-Benavides, J. Antunez-Quilobrán, A. Baffico-Hernández, C. Ávila-Sánchez, S. Ávila-Sánchez, S. Espinoza, et al., Performance assessment of thermal infrared cameras of different resolutions to estimate tree water status from two cherry cultivars: An alternative to midday stem water potential and stomatal conductance, Sensors, 20 (2020), 3596. https://doi.org/10.3390/s20123596 doi: 10.3390/s20123596
    [25] O. Diekmann, J. A. P. Heesterbeek, J. A. Metz, On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365–382. https://doi.org/10.1007/BF00178324 doi: 10.1007/BF00178324
    [26] P. Van den Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29–48. https://doi.org/10.1016/S0025-5564(02)00108-6 doi: 10.1016/S0025-5564(02)00108-6
    [27] P. D. Harrington, M. A. Lewis, A next-generation approach to calculate source–sink dynamics in marine metapopulations, Bull. Math. Biol., 82 (2020), 1–44. https://doi.org/10.1007/s11538-019-00674-1 doi: 10.1007/s11538-019-00674-1
    [28] A. Hurford, D. Cownden, T. Day, Next-generation tools for evolutionary invasion analyses, J. R. Soc. Interface, 7 (2010), 561–571. https://doi.org/10.1098/rsif.2009.0448 doi: 10.1098/rsif.2009.0448
    [29] S. Tang, Y. Xiao, R. A. Cheke, Dynamical analysis of plant disease models with cultural control strategies and economic thresholds, Math. Comput. Simul., 80 (2010), 849–921. https://doi.org/10.1016/j.matcom.2009.10.004 doi: 10.1016/j.matcom.2009.10.004
    [30] S. Gao, S. Luo, S. Yan, X. Meng, Dynamical behavior of a novel impulsive switching model for HLB with seasonal fluctuations, Complexity, 2018 (2018). https://doi.org/10.1155/2018/2953623 doi: 10.1155/2018/2953623
    [31] R. A. Taylor, E. A. Mordecai, C. A. Gilligan, J. R. Rohr, L. R. Johnson, Mathematical models are a powerful method to understand and control the spread of Huanglongbing, PeerJ, 4 (2016). https://doi.org/10.7717/peerj.2642 doi: 10.7717/peerj.2642
    [32] S. Gao, L. Xia, Y. Liu, D. Xie, A plant virus disease model with periodic environment and pulse roguing, Stud. Appl. Math., 136 (2016), 357–381. https://doi.org/10.1111/sapm.12109 doi: 10.1111/sapm.12109
    [33] D. S. Degefa, O. D. Makinde, D. T. Temesgen, Modeling potato virus Y disease dynamics in a mixed-cropping system, Int. J. Modell. Simul. 42 (2022), 370–387. https://doi.org/10.1080/02286203.2021.1919818 doi: 10.1080/02286203.2021.1919818
    [34] H. T. Alemneh, O. D. Makinde, D. M. Theuri, Mathematical modelling of msv pathogen inter- action with pest invasion on maize plant, Glob. J. Pure Appl. Math., 15 (2019), 55–79.
    [35] F. Ewert, R. P. Rötter, M. Bindi, H. Webber, M. Trnka, K. C. Kersebaum, et al., Crop modelling for integrated assessment of risk to food production from climate change, Environ. Modell. Softw., 72 (2015), 287–303. https://doi.org/10.1016/j.envsoft.2014.12.003 doi: 10.1016/j.envsoft.2014.12.003
    [36] J. L. Monteith, The quest for balance in crop modeling, Agron. J., 88 (1996), 695–697. https://doi.org/10.2134/agronj1996.00021962008800050003x doi: 10.2134/agronj1996.00021962008800050003x
    [37] P. Steduto, T. C. Hsiao, D. Raes, E. Fereres, AquaCrop-The FAO crop model to simulate yield response to water: I. Concepts and underlying principles, Agron. J., 101 (2009), 426–437. https://doi.org/10.2134/agronj2008.0139s doi: 10.2134/agronj2008.0139s
    [38] B. A. Keating, P. J. Thorburn, Modelling crops and cropping systems-Evolving purpose, practice and prospects, Eur. J. Agron., 100 (2018), 163–176. https://doi.org/10.1016/j.eja.2018.04.007 doi: 10.1016/j.eja.2018.04.007
    [39] G. Fischer, J. O. Orduz-Rogríguez, Ecofisiología en frutales, En: Fischer, Bogotá, 2012.
    [40] L. Edelstein-Keshet, Mathematical models in biology, Society for Industrial and Applied Mathematics, 2005.
    [41] E. Duque-Marín, A. Rojas-Palma, M. Carrasco-Benavides, Simulations of an impulsive model for the growth of fruit trees, J. Phys. Conf. Ser., 2153 (2022), 012018. https://doi.org/10.1088/1742-6596/2153/1/012018 doi: 10.1088/1742-6596/2153/1/012018
    [42] S. G. Hristova, D. D. Bainov, Bounded solutions of systems of differential equations with impulses, Ann. Pol. Math., 48 (1988), 191–206.
    [43] Y. Yang, Y. Xiao, Threshold dynamics for compartmental epidemic models with impulses, Nonlinear Anal. Real. World Appl., 13 (2012), 224–234. https://doi.org/10.1016/j.nonrwa.2011.07.028 doi: 10.1016/j.nonrwa.2011.07.028
    [44] S. K. Ooi, N. Cooley, I. Mareels, G. Dunn, K. Dassanayake, K. Saleem, Automation of on-farm irrigation: horticultural case study, IFAC Proc. Vol., 43 (2010), 256–261. https://doi.org/10.3182/20101206-3-JP-3009.00045 doi: 10.3182/20101206-3-JP-3009.00045
    [45] P. Filippucci, A. Tarpanelli, C. Massari, A. Serafini, V. Strati, M. Alberi, et al., Soil moisture as a potential variable for tracking and quantifying irrigation: A case study with proximal gamma-ray spectroscopy data, Adv. Water Resour., 136 (2020), 103502. https://doi.org/10.1016/j.advwatres.2019.103502 doi: 10.1016/j.advwatres.2019.103502
    [46] D. C. Harris, Nonlinear least-squares curve fitting with Microsoft Excel Solver, J. Chem. Educ., 75 (1998), 119. https://doi.org/10.1021/ed075p119 doi: 10.1021/ed075p119
    [47] D. G. Mayer, D. G. Butler, Statistical validatio, Ecol. Modell., 68 (1993), 21–32.
    [48] C. J. Willmott, On the validation of models, Phys. Geogr., 2 (1981), 184–194. https://doi.org/10.1080/02723646.1981.10642213 doi: 10.1080/02723646.1981.10642213
    [49] C. J. Willmott, S. M. Robeson, K. J. Matsuura, A refined index of model performance, Int. J. Climatol, 32 (2012), 2088–2094. https://doi.org/10.1002/joc.2419 doi: 10.1002/joc.2419
    [50] I. Lawrence, K. Lin, A concordance correlation coefficient to evaluate reproducibility, Biomet. Rics., (1989), 255–268.
    [51] R. R. Jiliberto, Deja a la estructura hablar: Modelización y análisis de sistemas naturales, sociales y socioecológicos, Ediciones UM, 2020.
    [52] S. M. Lane, Mathematical models: A sketch for the philosophy of mathematics, Am. Math. Mon., 88 (1981), 462–472. https://doi.org/10.1080/00029890.1981.11995299 doi: 10.1080/00029890.1981.11995299
    [53] J. Franklin, Philosophy and mathematical modelling. Teaching Mathematics and its Applications: An International Journal of the IMA, 2 (1983), 118–119.
    [54] S. M. Blower, H. Dowlatabadi, Sensitivity and uncertainty analysis of complex models of disease transmission: an HIV model, as an example, Int. Stat. Rev., 62 (1994), 229–243. https://doi.org/10.2307/1403510 doi: 10.2307/1403510
    [55] M. Martcheva, An introduction to mathematical epidemiology, Springer, New York, 2015.
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