Mathematical Modelling and Simulation of Nitrate Leaching into Groundwater

Ochwach Jimrise; Okongo Mark; Ombaka Ochieng

doi:doi:10.11648/j.ijssam.20220704.12

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Mathematical Modelling and Simulation of Nitrate Leaching into Groundwater

Ochwach Jimrise, Okongo Mark, Ombaka Ochieng

Published in International Journal of Systems Science and Applied Mathematics (Volume 7, Issue 4)

Received: 28 August 2022 Accepted: 28 October 2022 Published: 22 November 2022

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Abstract

Nitrate leaching into groundwater is a complicated process that involves a number of different biochemical transformations. These biochemical transformations include immobilisation, mineralization, nitrification, volatilization, crop absorption, and nitrate leaching into groundwater. Groundwater nitrate contamination is a developing challenge that requires precise analytical and numerical solutions. Various approaches to measuring nitrate leaching have been developed from a range of measurement and modelling techniques, but all suffer from one limitation or another due to the complexities, challenges and assumptions made in quantifying nitrate leaching in groundwater. This calls for new approaches in which nitrate leaching can be analysed to gain a better understanding of nitrate fate and transport processes for the proper management of groundwater. The advection-dispersion equations are updated in this research work to simulate nitrogen leaching in soils with variable depth, duration, volumetric water content, and porosity. Graphical representations of numerical simulations of the concentration of nitrate in the soil at varying depths and times can be achieved with the help of MATLAB software. According to the findings of the study, the proportion of soil porosity to soil water volume is directly proportional to the amount of nitrate that leaches into the groundwater. Therefore, it is recommended that measures be taken to reduce the potential for groundwater contamination. These measures include reducing the amount of nitrogen used, avoiding overwatering, and developing a test that helps farmers measure the amount that is already present in the groundwater.

Published in	International Journal of Systems Science and Applied Mathematics (Volume 7, Issue 4)
DOI	10.11648/j.ijssam.20220704.12
Page(s)	74-84
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2022. Published by Science Publishing Group

Keywords

Mathematical Modelling, Nitrate, Modelling, Leaching, Advection-Dispersion, Groundwater

References

[1]	X. Su, H. Wang, Y. Zhang, Health risk assessment of nitrate contamination in groundwater: a case study of an agricultural area in northeast china, Water resources management 27 (8) (2013) 3025-3034. 23.
[2]	I. Marinov, A. M. Marinov, A coupled mathematical model to predict the influence of nitrogen fertilization on crop, soil and groundwater quality, Water resources management 28 (15) (2014) 5231-5246.
[3]	O. Ombaka, J. Gichumbi, C. Kinyua, Status of water quality of naka river in meru south, Kenya, International Journal of Modern Chemistry 3 (1) (2012) 23-38.
[4]	M. G. A. Eltarabily, A. M. Negm, Numerical simulation of fertilizers movement in sand and controlling transport process via vertical barriers, International Journal of Environmental Science and Development 6 (8) (2015) 559.
[5]	J. O. Ochwach, M. O. Okongo, S. W. Musundi, Modeling the impact of soil porosity on nitrate leaching to groundwater using the advection dispersion equation, OSR journal (2018).
[6]	D. J. Greenwood, K. Zhang, H. W. Hilton, A. J. Thompson, Opportunities for improving irrigation efficiency with quantitative models, soil water sensors and wireless technology, The Journal of Agricultural Science 148 (1) (2010) 1-16.
[7]	J. Dilip Kumar, K. Atul, Y. Raja Ram, Analytical solution to the onedimensional advection-diffusion equation with temporally dependent coefficients, Journal of Water Resource and Protection 2011 (2011).
[8]	G. Gurarslan, H. Karahan, D. Alkaya, M. Sari, M. Yasar, Numerical solution of advection-diffusion equation using a sixth-order compact finite difference method, Mathematical Problems in Engineering 2013 (2013).
[9]	T. F. Chan, Stability analysis of finite difference schemes for the advection-diffusion equation, SIAM journal on numerical analysis 21 (2) (1984) 272-284.
[10]	A. Toffoli, E. Bitner-Gregersen, A. R. Osborne, M. Serio, J. Monbaliu, M. Onorato, Extreme waves in random crossing seas: Laboratory experiments and numerical simulations, Geophysical Research Letters 38 (6) (2011).
[11]	D. Nielsen, M. Th. Van Genuchten, J. Biggar, Water flow and solute transport processes in the unsaturated zone, Water resources research 22 (9S) (1986) 89S-108S.
[12]	U. M. Sainju, R. Ghimire, G. P. Pradhan, Nitrogen fertilization i: Impact on crop, soil, and environment, Nitrogen Fixation (2019).
[13]	J. Refsgaard, M. Thorsen, J. B. Jensen, S. Kleeschulte, S. Hansen, Large scale modelling of groundwater contamination from nitrate leaching, Journal of hydrology 221 (3-4) (1999) 117-140.
[14]	J. Wu, D. Bernardo, H. P. Mapp, S. Geleta, M. L. Teague, K. B. Watkins, G. Sabbagh, R. Elliott, J. F. Stone, An evaluation of nitrogen runoff and leaching potential in the high plains, Journal of Soil and Water Conservation 52 (1) (1997) 73-80.
[15]	M. Pagliai, N. Vignozzi, Soil porosity as an indicator of soil health, Annals of arid zone 45 (3/4) (2006) 259.
[16]	M. T. Genuchten, F. J. Leij, T. H. Skaggs, N. Toride, S. A. Bradford, E. M. Pontedeiro, Exact analytical solutions for contaminant transport in rivers 1. the equilibrium advection-dispersion equation, Journal of Hydrology and Hydromechanics 61 (2) (2013) 146.
[17]	A. Gardenas, J. Hopmans, B. Hanson, J. Simnek, Two- dimensional modeling of nitrate leaching for various fertigation scenarios under microirrigation, Agricultural water management 74 (3) (2005) 219-242.
[18]	C. W. Culbertson, T. G. Huntington, J. M. Caldwell, C. O¡¯Donnell, Evaluation of aerial thermal infrared remote sensing to identify groundwater-discharge zones in the Meduxnekeag River, Houlton, Maine, US Department of the Interior, US Geological Survey, 2013.
[19]	D. Mulla, J. Strock, Nitrogen transport processes in soil: Nitrogen in agricultural systems, in: Agronomy Monograph Series No. 49: Nitrogen in Agricultural Systems, ASA-CSSA-SSSA, 2008, pp. 112-116.
[20]	R. Sobey, Fractional step algorithm for estuarine mass transport, International Journal for Numerical methods in fluids 3 (6) (1983) 567-581. 25
[21]	J. Miko lajk¡äow, Laboratory methods of estimating the retardation factor of migrating mineral nitrogen compounds in shallow groundwater, Geological Quarterly 47 (2003) 91-96.
[22]	E.Bosire, Numericalsimulationmodelfornitratefateand transport processes in groundwater around lake naivasha area, kenya, Ph.D. thesis, Kenyatta University (2009).
[23]	M. Ardestani, M. Sabahi, H. Montazeri, Finiteanalyticmethods for simulation of advection- dominated and pure advection solute transport with reaction in porousmedia, International Journal of Environmental Research 9 (1) (2015) 197-204.
[24]	M. Abramowitz, Handbook of mathematical functions, national bureau of standards, Applied Mathematics Series 2 (55) (1964).
[25]	H. S. Carslaw, J. C. Jaeger, Conduction of heat in solids, Conduction of heat in solids (1947).
[26]	F. J. Leij, M. T. van Genuchten, J. Dane, Mathematical analysis of one-dimensional solute transport in a layered soil profile, Soil Science Society of America Journal 55 (4) (1991) 944-953.
[27]	F. T. Lindstrom, R. Haque, V. H. Freed, L. Boersma, The movement of some herbicides in soils. linear diffusion and convection of chemicals in soils, Environmental science & technology 1 (7) (1967) 561-565.
[28]	M. T. Van Genuchten, Analytical solutions for chemical transport with simultaneous adsorption, zero-order production and first-order decay, Journal of hydrology 49 (3-4) (1981) 213-233.
[29]	J. A. Khazenzi, O. Osano, J. Wakhisi, P. Raburu, Risk among consumers of nitrate contaminated groundwater in langas, eldoret, kenya, Baraton Interdisciplinary Research Journal 3 (2) (2014) 41-50.
[30]	J. Crank, The mathematics of diffusion, 414 p (1975).
[31]	M. N. Almasri, J. J. Kaluarachchi, Modeling nitrate contamination of groundwater in agricultural watersheds, Journal of Hydrology 343 (3-4) (2007) 211-229. 26.
[32]	Y. Abrol, N. Raghuram, M. Sachdev, Agricultural nitrogen use and its environmental implications, IK International Pvt Ltd, 2007.
[33]	Vassiljev, A. Grimvall, M. Larsson, A dual-porosity model for nitrogen leaching from a watershed/un mod‘ele ‘a double porositÂ’e pour le lessivage de lâazote dâun bassin versant, Hydrological sciences journal 49 (2) (2004).

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APA Style

Ochwach Jimrise, Okongo Mark, Ombaka Ochieng. (2022). Mathematical Modelling and Simulation of Nitrate Leaching into Groundwater. International Journal of Systems Science and Applied Mathematics, 7(4), 74-84. https://doi.org/10.11648/j.ijssam.20220704.12

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ACS Style

Ochwach Jimrise; Okongo Mark; Ombaka Ochieng. Mathematical Modelling and Simulation of Nitrate Leaching into Groundwater. Int. J. Syst. Sci. Appl. Math. 2022, 7(4), 74-84. doi: 10.11648/j.ijssam.20220704.12

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AMA Style

Ochwach Jimrise, Okongo Mark, Ombaka Ochieng. Mathematical Modelling and Simulation of Nitrate Leaching into Groundwater. Int J Syst Sci Appl Math. 2022;7(4):74-84. doi: 10.11648/j.ijssam.20220704.12

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@article{10.11648/j.ijssam.20220704.12,
  author = {Ochwach Jimrise and Okongo Mark and Ombaka Ochieng},
  title = {Mathematical Modelling and Simulation of Nitrate Leaching into Groundwater},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {7},
  number = {4},
  pages = {74-84},
  doi = {10.11648/j.ijssam.20220704.12},
  url = {https://doi.org/10.11648/j.ijssam.20220704.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20220704.12},
  abstract = {Nitrate leaching into groundwater is a complicated process that involves a number of different biochemical transformations. These biochemical transformations include immobilisation, mineralization, nitrification, volatilization, crop absorption, and nitrate leaching into groundwater. Groundwater nitrate contamination is a developing challenge that requires precise analytical and numerical solutions. Various approaches to measuring nitrate leaching have been developed from a range of measurement and modelling techniques, but all suffer from one limitation or another due to the complexities, challenges and assumptions made in quantifying nitrate leaching in groundwater. This calls for new approaches in which nitrate leaching can be analysed to gain a better understanding of nitrate fate and transport processes for the proper management of groundwater. The advection-dispersion equations are updated in this research work to simulate nitrogen leaching in soils with variable depth, duration, volumetric water content, and porosity. Graphical representations of numerical simulations of the concentration of nitrate in the soil at varying depths and times can be achieved with the help of MATLAB software. According to the findings of the study, the proportion of soil porosity to soil water volume is directly proportional to the amount of nitrate that leaches into the groundwater. Therefore, it is recommended that measures be taken to reduce the potential for groundwater contamination. These measures include reducing the amount of nitrogen used, avoiding overwatering, and developing a test that helps farmers measure the amount that is already present in the groundwater.},
 year = {2022}
}

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TY  - JOUR
T1  - Mathematical Modelling and Simulation of Nitrate Leaching into Groundwater
AU  - Ochwach Jimrise
AU  - Okongo Mark
AU  - Ombaka Ochieng
Y1  - 2022/11/22
PY  - 2022
N1  - https://doi.org/10.11648/j.ijssam.20220704.12
DO  - 10.11648/j.ijssam.20220704.12
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 74
EP  - 84
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20220704.12
AB  - Nitrate leaching into groundwater is a complicated process that involves a number of different biochemical transformations. These biochemical transformations include immobilisation, mineralization, nitrification, volatilization, crop absorption, and nitrate leaching into groundwater. Groundwater nitrate contamination is a developing challenge that requires precise analytical and numerical solutions. Various approaches to measuring nitrate leaching have been developed from a range of measurement and modelling techniques, but all suffer from one limitation or another due to the complexities, challenges and assumptions made in quantifying nitrate leaching in groundwater. This calls for new approaches in which nitrate leaching can be analysed to gain a better understanding of nitrate fate and transport processes for the proper management of groundwater. The advection-dispersion equations are updated in this research work to simulate nitrogen leaching in soils with variable depth, duration, volumetric water content, and porosity. Graphical representations of numerical simulations of the concentration of nitrate in the soil at varying depths and times can be achieved with the help of MATLAB software. According to the findings of the study, the proportion of soil porosity to soil water volume is directly proportional to the amount of nitrate that leaches into the groundwater. Therefore, it is recommended that measures be taken to reduce the potential for groundwater contamination. These measures include reducing the amount of nitrogen used, avoiding overwatering, and developing a test that helps farmers measure the amount that is already present in the groundwater.
VL  - 7
IS  - 4
ER  -

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Author Information

Ochwach Jimrise

Department of Physical Science, Chuka University, Chuka, Kenya
Okongo Mark

Department of Physical Science, Chuka University, Chuka, Kenya
Ombaka Ochieng

Department of Physical Science, Chuka University, Chuka, Kenya

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APA Style

Ochwach Jimrise, Okongo Mark, Ombaka Ochieng. (2022). Mathematical Modelling and Simulation of Nitrate Leaching into Groundwater. International Journal of Systems Science and Applied Mathematics, 7(4), 74-84. https://doi.org/10.11648/j.ijssam.20220704.12

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ACS Style

Ochwach Jimrise; Okongo Mark; Ombaka Ochieng. Mathematical Modelling and Simulation of Nitrate Leaching into Groundwater. Int. J. Syst. Sci. Appl. Math. 2022, 7(4), 74-84. doi: 10.11648/j.ijssam.20220704.12

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AMA Style

Ochwach Jimrise, Okongo Mark, Ombaka Ochieng. Mathematical Modelling and Simulation of Nitrate Leaching into Groundwater. Int J Syst Sci Appl Math. 2022;7(4):74-84. doi: 10.11648/j.ijssam.20220704.12

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@article{10.11648/j.ijssam.20220704.12,
  author = {Ochwach Jimrise and Okongo Mark and Ombaka Ochieng},
  title = {Mathematical Modelling and Simulation of Nitrate Leaching into Groundwater},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {7},
  number = {4},
  pages = {74-84},
  doi = {10.11648/j.ijssam.20220704.12},
  url = {https://doi.org/10.11648/j.ijssam.20220704.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20220704.12},
  abstract = {Nitrate leaching into groundwater is a complicated process that involves a number of different biochemical transformations. These biochemical transformations include immobilisation, mineralization, nitrification, volatilization, crop absorption, and nitrate leaching into groundwater. Groundwater nitrate contamination is a developing challenge that requires precise analytical and numerical solutions. Various approaches to measuring nitrate leaching have been developed from a range of measurement and modelling techniques, but all suffer from one limitation or another due to the complexities, challenges and assumptions made in quantifying nitrate leaching in groundwater. This calls for new approaches in which nitrate leaching can be analysed to gain a better understanding of nitrate fate and transport processes for the proper management of groundwater. The advection-dispersion equations are updated in this research work to simulate nitrogen leaching in soils with variable depth, duration, volumetric water content, and porosity. Graphical representations of numerical simulations of the concentration of nitrate in the soil at varying depths and times can be achieved with the help of MATLAB software. According to the findings of the study, the proportion of soil porosity to soil water volume is directly proportional to the amount of nitrate that leaches into the groundwater. Therefore, it is recommended that measures be taken to reduce the potential for groundwater contamination. These measures include reducing the amount of nitrogen used, avoiding overwatering, and developing a test that helps farmers measure the amount that is already present in the groundwater.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Mathematical Modelling and Simulation of Nitrate Leaching into Groundwater
AU  - Ochwach Jimrise
AU  - Okongo Mark
AU  - Ombaka Ochieng
Y1  - 2022/11/22
PY  - 2022
N1  - https://doi.org/10.11648/j.ijssam.20220704.12
DO  - 10.11648/j.ijssam.20220704.12
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 74
EP  - 84
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20220704.12
AB  - Nitrate leaching into groundwater is a complicated process that involves a number of different biochemical transformations. These biochemical transformations include immobilisation, mineralization, nitrification, volatilization, crop absorption, and nitrate leaching into groundwater. Groundwater nitrate contamination is a developing challenge that requires precise analytical and numerical solutions. Various approaches to measuring nitrate leaching have been developed from a range of measurement and modelling techniques, but all suffer from one limitation or another due to the complexities, challenges and assumptions made in quantifying nitrate leaching in groundwater. This calls for new approaches in which nitrate leaching can be analysed to gain a better understanding of nitrate fate and transport processes for the proper management of groundwater. The advection-dispersion equations are updated in this research work to simulate nitrogen leaching in soils with variable depth, duration, volumetric water content, and porosity. Graphical representations of numerical simulations of the concentration of nitrate in the soil at varying depths and times can be achieved with the help of MATLAB software. According to the findings of the study, the proportion of soil porosity to soil water volume is directly proportional to the amount of nitrate that leaches into the groundwater. Therefore, it is recommended that measures be taken to reduce the potential for groundwater contamination. These measures include reducing the amount of nitrogen used, avoiding overwatering, and developing a test that helps farmers measure the amount that is already present in the groundwater.
VL  - 7
IS  - 4
ER  -

Copy | Download