Mathematical modeling for water supply by means of natural supply sources: the case of Pachuca de Soto, Hidalgo

Numerous works have been published on modeling water supply systems with interacting natural supply sources, most often described by systems of differential equations. The underlying mathematical properties of those systems of differential equations, applied to water supply problems, have not been s...

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Bibliographic Details
Published in:Sustainable water resources management 2024-04, Vol.10 (2), p.63, Article 63
Main Authors: Gutiérrez-Corona, Josué N., Itzá-Ortiz, Benjamín A., Torres-Mendoza, Arturo, Tzatchkov, Velitchko G., Quezada-Téllez, Luis A.
Format: Article
Language:English
Subjects:
Decision making
Development Economics
Differential equations
Earth and Environmental Science
Earth Sciences
Groundwater
Groundwater recharge
Hydrogeology
Hydrology/Water Resources
Mass balance
Mathematical models
Mathematical properties
Modelling
Original Article
Parameter sensitivity
Parameters
Stability analysis
Surface water
Surface-groundwater relations
Sustainable Development
Water conveyance
Water Policy/Water Governance/Water Management
Water resources
Water resources management
Water supply
Water supply systems
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Summary:Numerous works have been published on modeling water supply systems with interacting natural supply sources, most often described by systems of differential equations. The underlying mathematical properties of those systems of differential equations, applied to water supply problems, have not been studied, however. In this paper, a novel mathematical model is proposed consisting of three coupled nonlinear non-autonomous differential equations, where the interaction of three main water sources (surface water, groundwater, and recharge water) is considered through a mass balance, with application to the water supply in the region of Pachuca de Soto, State of Hidalgo, Mexico. A stability analysis of the proposed system was developed, obtaining eight equilibrium points, only four of which turned out to be of physical relevance. One of them, called “the apocalyptic point”, shows that the three supply sources may decrease simultaneously and drastically. Numerical simulations were carried out for various parameters in 12 proposed scenarios for periods of time between 2000 and 2040. The system parameters were calibrated with available experimental data and the reliability of the model was validated through the mean squared error. The results show that the system is very sensitive to parameter variations, causing groundwater and recharge water to increase or decrease. It is also observed that the behavior of surface waters remains oscillatory. Due to its versatility, the model could be applicable to any other region. Therefore, it is expected to be a powerful tool for informed decision-making in water resources management.
ISSN:2363-5037
2363-5045
DOI:10.1007/s40899-024-01045-y