Assessment of finite difference models for water content determination in soils of the semi-arid region of Brazil
DOI:
https://doi.org/10.24221/jeap.9.4.2024.7361.309-324Palavras-chave:
Potencial matricial, Conteúdo de água no solo, Diferenças finitas, Método explícito, Método implícito, SemiáridoResumo
The water content in soil and its variation with depth are critical for numerous processes, significantly influencing plant growth, soil mechanics, and physical and chemical properties. In the semi-arid region of northeastern Brazil, where the Caatinga biome is located, accurate estimation of soil water content is crucial due to severe water scarcity and highly variable precipitation patterns. This study aimed to evaluate the sensitivity and accuracy of a computational model for predicting soil matric potential and water content. The model solves the Richards’ equation using three finite difference methods: explicit, implicit, and Crank-Nicolson. The methods were applied to three soil textures (sandy loam, silt, and clay), and a preliminary analysis was performed to identify the optimal time (dt) and spatial (dz) steps for achieving relative differences below 1%. The model predicted acceptable soil matric potential and water content behavior, particularly for sandy loam, which required finer steps (1 second, 1 cm) compared to silt and clay (10 seconds, 5 cm). Two test cases from the literature were used for further validation. Finally, the model was applied to soil textures typical of northeastern Brazil, confirming its ability to capture the dynamics of soil water content in this region. The results highlight the applicability of this computational approach to semi-arid soils, contributing to improved water management and crop production strategies.Downloads
Referências
Althoff, D.; Rodrigues, L. N.; Silva, D. D. 2021. Addressing hydrological modeling in watersheds under land cover change with deep learning. Advances in Water Resources, 154, 103965. https://doi.org/10.1016/j.advwatres.2021.103965
Arioli, M.; Scott, J. 2014. Chebyshev acceleration of iterative refinement. Numerical Algorithms, 66, (3), 591-608. https://doi.org/10.1007/s11075-013-9750-7
Assouline, S.; Sela, S.; Dorman, M.; Svoray, T. 2024. Runoff generation in a semiarid environment: The role of rainstorm intra-event temporal variability and antecedent soil moisture. Advances in Water Resources, 188, 104715. https://doi.org/10.1016/j.advwatres.2024.104715
Bittelli, M.; Campbell, G. S.; Tomei, F. 2015. Soil Physics with Python. In Soil Physics with Python. Oxford University Press. 460p. https://doi.org/10.1093/acprof:oso/9780199683093.001.0001
Brito, T. R.; Lima, J. R. D. S.; Oliveira, C. L.; Souza, R. M. S.; Antonino, A. C. D.; Medeiros, E. V.; Souza, E. S.; Alves, E. M. 2020. Mudanças no Uso da Terra e Efeito nos Componentes do Balanço Hídrico no Agreste Pernambucano. Revista Brasileira de Geografia Física, 13, (2), 870-886. https://doi.org/10.26848/rbgf.v13.2.p870-886
Carsel, R. F.; Parrish, R. S. 1988. Developing joint probability distributions of soil water retention characteristics. Water Resources Research, 24, (5), 755-769. https://doi.org/10.1029/WR024i005p00755
Celia, M. A.; Bouloutas, E. T.; Zarba, R. L. 1990. A general mass-conservative numerical solution for the unsaturated flow equation. Water Resources Research, 26, (7), 1483-1496. https://doi.org/10.1029/WR026i007p01483
Chapra, S. C.; Canale, R. P. 2016. Metodos Numericos para Ingenieros. McGraw-Hill, Seventh Edition. 864p.
Chavarria, G.; Santos, H. P. 2012. Plant Water Relations: Absorption, Transport and Control Mechanisms. In Advances in Selected Plant Physiology Aspects. InTech. 29p. https://doi.org/10.5772/33478
Cirilo, J. A. 2008. Políticas públicas de recursos hídricos para o semi-árido. Estudos Avançados, 22, (63), 61-82. https://doi.org/10.1590/S0103-40142008000200005
Daneshi, A.; Brouwer, R.; Najafinejad, A.; Panahi, M.; Zarandian, A.; Maghsood, F. F. 2020. Modelling the impacts of climate and land use change on water security in a semi-arid forested watershed using InVEST. Journal of Hydrology, 593, 125621. https://doi.org/10.1016/j.jhydrol.2020.125621
Farthing, M. W.; Ogden, F. L. 2017. Numerical Solution of Richards’ Equation: A Review of Advances and Challenges. Soil Science Society of America Journal, 81, (6), 1257-1269. https://doi.org/10.2136/sssaj2017.02.0058
Fredlund, D. G.; Xing, A. 1994. Equations for the soil-water characteristic curve. Canadian Geotechnical Journal, 31, (4), 521-532. https://doi.org/10.1139/t94-061
Hillel, D. 1998. Environmental soil physics. Academic Press, First Edition. 771p.
Leal, I. R.; Silva, J. M. C.; Tabarelli, M.; Lacher, T. E. 2005. Changing the Course of Biodiversity Conservation in the Caatinga of Northeastern Brazil. Conservation Biology, 19, (3), 701-706. https://doi.org/10.1111/j.1523-1739.2005.00703.x
List, F.; Radu, F. A. 2016. A study on iterative methods for solving Richards’ equation. Computational Geosciences, 20, (2), 341-353. https://doi.org/10.1007/s10596-016-9566-3
Liu, F.; Qian, H.; Wang, G.; Gao, Y.; Shi, Z. 2024. New insights into the parameterization of the dry surface layer and its hydrogeochemical mechanism: An experimental study. Advances in Water Resources, 190, 104738. https://doi.org/10.1016/j.advwatres.2024.104738
Lott, P. A.; Walker, H. F.; Woodward, C. S.; Yang, U. M. 2012. An accelerated Picard method for nonlinear systems related to variably saturated flow. Advances in Water Resources, 38, 92-101. https://doi.org/10.1016/j.advwatres.2011.12.013
Miranda, J. H.; Duarte, S. N.; Libardi, P. L.; Folegatti, M. V. 2005. Simulação do deslocamento de potássio em colunas verticais de solo não-saturado. Engenharia Agrícola, 25, (3), 677-685. https://doi.org/10.1590/S0100-69162005000300013
Mualem, Y. 1976. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resources Research, 12, (3), 513-522. https://doi.org/10.1029/WR012i003p00513
Shukla, P. R.; Skea, J.; Buendia, E. C.; Masson-Delmotte, V.; Pörtner, H. O.; Roberts, D. C.; Zhai, P.; Slade, R.; Connors, S.; Diemen, R.; Ferrat, M.; Haughey, E.; Luz, S.; Neogi, S.; Pathak, M.; Petzold, J.; Pereira, J. P.; Vyas, P.; Huntley, E.; … Malley, J. 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. Disponível em: https://www.ipcc.ch/srccl
PBMC. 2014. Painel Brasileiro de Mudanças Climáticas. Base científica das mudanças climáticas. Volume 1 - Primeiro Relatório de Avaliação Nacional. Disponível em: https://repositorio.mctic.gov.br/handle/mctic/4306
Pedrozo, H. A.; Rosenberger, M. R.; Schvezov, C. E. 2015. Comparison of Finite Difference Models Applied to Soil Infiltration. RECyT, 17, (23), 36-44.
Pedrozo, H. A.; Rosenberger, M. R.; Schvezov, C. E. 2016. Stability analysis of the solution of the one-dimensional Richards equation by the finite difference method. AIP Conference Proceedings, 1738, 480008. https://doi.org/10.1063/1.4952244
Rad, A. M.; Ghahraman, B.; Khalili, D.; Ghahremani, Z.; Ardakani, S. A. 2017. Integrated meteorological and hydrological drought model: A management tool for proactive water resources planning of semi-arid regions. Advances in Water Resources, 107, 336-353. https://doi.org/10.1016/j.advwatres.2017.07.007
Richards, L. A. 1931. Capillary conduction of liquids through porous mediums. Physics, 1, (5), 318-333. https://doi.org/10.1063/1.1745010
Schneider, R. 2003. Explicit and Implicit Finite-Difference Methods for the Diffusion Equation in Two Dimensions. Forschungszentrum Karlsruhe GmbH, Karlsruhe. Disponível em: https://www.osti.gov/etdeweb/biblio/20414585
Sishodia, R. P.; Shukla, S.; Graham, W. D.; Wani, S. P.; Jones, J. W.; Heaney, J. 2017. Current and future groundwater withdrawals: Effects, management and energy policy options for a semi-arid Indian watershed. Advances in Water Resources, 110, 459-475. https://doi.org/10.1016/j.advwatres.2017.05.014
Soares, W. A.; Silva, S. R.; Lima, J. R. 2020. Land-use change effect on the hydro-dynamic characteristics of soil in the Brazilian semi-arid region. Ambiente e Agua - An Interdisciplinary Journal of Applied Science, 15, (2), e2368. https://doi.org/10.4136/ambi-agua.2368
Genuchten, M. T. 1980. A Closed-form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils. Soil Science Society of America Journal, 44, (5), 892-898. https://doi.org/10.2136/sssaj1980.03615995004400050002x
Vasconcellos, C. A.; Amorin, J. C. 2001. Numerical Simulation of Unsaturated Flow in Porous Media Using a Mass-Conservative Model. 16th Brazilian Congress of Mechanical Engineering, Uberlândia, Brasil.
Vieira, R. M. S. P.; Tomasella, J.; Alvalá, R. C. S.; Sestini, M. F.; Affonso, A. G.; Rodriguez, D. A.; Barbosa, A. A.; Cunha, A. P. M. A.; Valles, G. F.; Crepani, E.; Oliveira, S. B. P.; Souza, M. S. B.; Calil, P. M.; Carvalho, M. A.; Valeriano, D. M.; Campello, F. C. B.; Santana, M. O. 2015. Identifying areas susceptible to desertification in the Brazilian northeast. Solid Earth, 6, (1), 347-360. https://doi.org/10.5194/se-6-347-2015
Wendland, E.; Pizarro, M. L. P. 2010. Modelagem computacional do fluxo unidimensional de água em meio não saturado do solo. Engenharia Agrícola, 30, (3), 424-434. https://doi.org/10.1590/S0100-69162010000300007
Wu, L.; He, B.; Peng, J. 2024. Analysis of Rainfall-Caused Seepage into Underlying Bedrock Slope Based on Seepage Deformation Coupling. International Journal of Geomechanics, 24, (5), 04024076. https://doi.org/10.1061/IJGNAI.GMENG-9175
Zhu, S. R.; Wu, L. Z.; Shen, Z. H.; Huang, R. Q. 2019. An improved iteration method for the numerical solution of groundwater flow in unsaturated soils. Computers and Geotechnics, 114, 103113. https://doi.org/10.1016/j.compgeo.2019.103113
Downloads
Publicado
Como Citar
Edição
Seção
Licença
Copyright (c) 2024 Daniel Milian Pérez, Abel Gámez Rodríguez, Yaicel Ge Proenza, Frederico Dias Nunes, Antonio Celso Dantas Antonino, José Romualdo de Sousa Lima, Severino Martins dos Santos Neto, Artur Paiva Coutinho, Marcus Metri Correa
Este trabalho está licenciado sob uma licença Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Material protegido por direitos autorais e plágio. No caso de material com direitos autorais ser reproduzido no manuscrito, a atribuição integral deve ser informada no texto; um documento comprobatório de autorização deve ser enviado para a Comissão Editorial como documento suplementar. É da responsabilidade dos autores, não do JEAP ou dos editores ou revisores, informar, no artigo, a autoria de textos, dados, figuras, imagens e/ou mapas publicados anteriormente em outro lugar. Se existir alguma suspeita sobre a originalidade do material, a Comissão Editorial pode verificar o manuscrito por plágio. Nos casos em que trechos já publicados em outro documento for confirmado, o manuscrito será devolvido sem revisão adicional e sem a possibilidade de nova submissão. Autoplágio (ou seja, o uso de frases idênticas de documentos publicados anteriormente pelo mesmo autor) também não é aceitável.
Direitos autorais: Autor
Material protected by copyright and plagiarism rights. In the case of copyrighted material being reproduced in a manuscript, full attribution should be informed in the text; an authorization document is proving to be sent to the Editorial Board as a supplementary document. It is the responsibility of the authors, not JEAP or editors or reviewers, to inform, in the article, the authors of texts, data, graphics, images and maps previously published elsewhere. If there is any suspicion about the originality of the material, the Editorial Board can check the manuscript for plagiarism. Where plagiarism is confirmed, the document will be returned without further review and the possibility of a new submission. Self-plagiarism (i.e., the use of the same phrases previously published documents by any of the authors) is not acceptable.
Copyright: Author
