Research Article
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Mathematical modeling of the groundwater level depending on the change of groundwater table height

Year 2021, Volume: 9 Issue: 1, 23 - 29, 17.06.2021
https://doi.org/10.33409/tbbbd.798562

Abstract

It is necessary to evaluate the change of the ground water table, the depth and level of groundwater for regulating the amount of
irrigation water in the agricultural areas, preventing salinization in the plant-root region, and planning the drainage system. In this
study, the variation of ground water table and its level depending on solution according to harmonic boundary condition of the
Boussinesq equation (nonlinear diffusion equation), derived from the Dupuit approximation and the Darcy law, were investigated.
It has been theoretically shown that the ground water table and its level depend on distance and time. The maximum variations of
ground water table and its level were calculated as 0.123 m and 2.123 m, at a distance of 0.5 m and at the 2nd hour, respectively. The
minimum changes were determined as -0.006 m and 1.994 m at a distance of 2.5 m and at the 2nd hour, respectively. It has been
determined that the fluctuation amplitude of the groundwater table is exponentially changed and the fluctuation in x> 2 m distance
approaches the "damping" process.

References

  • Boussinesq MJ, 1904. Recherches theoriques sur l’ecoulement des nappes d’eau infiltrées dans le sol et sur debit de sources. Journal de Mathématiques Pures et Appliquées 10: 5-78.
  • Childs EC, 1943. The water table , equipotentials, and streamlines in drained land. Soil Science, 56(5): 317-330.
  • Childs EC, 1945a. The water table , equipotentials, and streamlines in drained land: II. Soil Science, 59(4): 313-328.
  • Childs EC, 1945b. The water table , equipotentials, and streamlines in drained land: III. Soil Science, 59(5): 405-415. Coulibaly P, Anctil F, Aravena R, Bobee B, 2001. Artificial neural network modeling of water table depth fluctuations. Water Resources Research 37 (4): 885–896.
  • Coulibaly P, Baldwin CK, 2005. Nonstationary hydrological time series forecasting using nonlinear dynamic methods. Journal of Hydrology 307 (1): 164–174.
  • Cuthbert MO, 2010. An improved time series approach for estimating groundwater recharge from groundwater level fluctuations. Water Resources Research 46 (9): W09515.
  • Darcy H, 1856. Les fontaines publiques de la ville de Dijon. Dalmont, Paris, 647 p. Dumm LD, 1954. Drain spacing formula: new formula for determining depth and spacing of subsurface drains in irrigated lands. American Society of Agricultural Engineers, 35: 726–730.
  • Dumm LD, 1964. Transient flow concept in subsurface drainage: its validity and use. Transactions of the American Society of Agricultural Engineers, 7: 142-146.
  • Dupuit J, 1863. Études théoriques et pratiques sur le mouvement des eaux dans les canaux découverts et a travers les terrains perméables. Dunod, Paris, 364 p.
  • Ekberli İ, Gülser C, 2014. Estimatıon of soil temperature by heat conductivity equation. Vestnik Bashkir State Agrarian University (Вестник Башкирского Государственного Аграрного Университета), 2 (30):12-15.
  • Ekberli İ, Gülser C, 2018. Boussinesq denkleminin çözümüne bağlı olarak taban suyu seviyesi yüksekliğinin incelenmesi. Toprak Bilimi ve Bitki Besleme Dergisi, 6(2): 134-142.
  • Ekberli İ, Gülser C, 2018. Sulamada toprağın ıslanma derinliğinin belirlenmesi. Anadolu Tarım Bilimleri Dergisi, 33(2): 142-148. Ekberli İ, Sarılar Y, 2015. Toprak sıcaklığının profil boyunca sönme derinliğinin ve gecikme zamanının belirlenmesi. Ege Üniversitesi Ziraat Fakültesinin Dergisi, 52 (2): 219-225.
  • Faibishenko BA, 1986. Water-salt rejime of soils under irrigation. Agropromizdat, Moscow (in Russian), 304 p. Gülser C, Ekberli İ, 2002. Toprak sıcaklığının profil boyunca değişimi. Ondokuz Mayıs Üniversitesi Ziraat Fakültesinin Dergisi, 17(3): 43-47.
  • Gülser C, Ekberli İ, 2019. Toprak sıcaklığının tahmininde ısı taşınım denklemi ve pedotransfer fonksiyonun karşılaştırılması. Toprak Bilimi ve Bitki Besleme Dergisi, 7(2): 158-166.
  • Hayek M, 2019. Accurate approximate semi-analytical solutions to the Boussinesq groundwater flow equation for recharging and discharging of horizontal unconfined aquifers. Journal of Hydrology, 570: 411–422.
  • Jeong J, Park E, 2017. A shallow water table fluctuation model in response to precipitation with consideration of unsaturated gravitational flow. Water Resources Research 53: 3505-3512.
  • Kats DM, Shestakov VM, 1992. Melioration hydrogeology. Moscow State University Press, Mockow (in Russian), pp.71-92. Knotters M, Bierkens MFP, 2000. Physical basis of time series models for water table depths. Water Resources Research 36 (1): 181–188.
  • Kong J, Xin P, Hua G-F, Luo ZY, Shen C-J, Chen, D, Li L, 2015. Effects of vadose zone on groundwater table fluctuations in unconfined aquifers. Journal of Hydrology 528: 397-407.
  • Li X, Jin M, Zhou N, Huang J, Jiang S, Telesphore H, 2016. Evaluation of evapotranspiration and deepper colation under mulched drip irrigation in an oasis of Tarimbasin, China. Journal of Hydrology, 538: 677-688. Lockington DA, Parlange J.-Y, Parlange MB, Selker J, 2000. Similarity solution of the Boussinesq equation. Advances in Water Resources 23: 725-729.
  • Luthin JN (Editor), 1957. Drainage of Agricultural Lands. Agronomy Monographs, 7, American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America, Publisher Madison, Wisconsin, 620 p.
  • Mehdinejadiani B, Fathi P, 2020. Analytical solutions of space fractional Boussinesq equation to simulate water table profiles between two parallel drainpipes under different initial conditions. Agricultural Water Management, 240: 106324.
  • Neto DC, Chang HK, van Genuchten MT, 2015. A mathematical view of water table fluctuations in a shallow aquifer in Brazil. Groundwater, 54 (1): 82–91.
  • Okkonen J, Klöve B, 2010. A conceptual and statistical approach for the analysis of climate impact on ground water table fluctuation patterns in cold conditions. Journal of Hydrology, 388. 1-12.
  • Park E, Parker JC, 2008. A simple model for water table fluctuations in response to precipitation. Journal of Hydrology 356 (3): 344–349.
  • Rai SN, Manglik A, Singh VS, 2006. Water table fluctuation owing to time-varying recharge pumping and leakage. Journal of Hydrology 324 (1–4): 350–358.
  • Singh MP, Chauhan HS, Ram S, 1996. Unsteady state drainage in a vertically heterogeneous soil. Agricultural Water Management, 31: 285–293.
  • Singh RM, Singh KK, Singh SR, 2006. Falling water tables in a sloping/nonsloping aquifer under various initial water table profiles. Agricultural Water Management, 82(1-2): 210-222.
  • Su, N., 2017. The fractional Boussinesq equation of groundwater flow and its applications. Journal of Hydrology, 547: 403–412.
  • Tang G, Alshawabkeh AN, 2006. A semi-analytical time integration for numerical solution of Boussinesq equation. Advances in Water Resources,29: 1953-1968.
  • Telyakovskiy AS, Kurita S, Allen MB, 2016. Polynomial-based approximate solutions to the Boussinesq equation near a well. Advances in Water Resources 96: 68-73.
  • Uziak J, Chieng S, 1989. Drain-spacing formula for transient state flow with ellipse as an initial condition. Canadıan Agrıcultural Engıneerıng, 31: 101-105.
  • Yoon H, Jun SC, Hyun Y, Bae GO, Lee KK, 2011. A comparative study of artificial neural networks and support vector machines for predicting groundwater levels in a coastal aquifer. Journal of Hydrology 396 (1): 128–138.
  • Zavala M, Fuentes C, Saucedo H, 2007. Non-linear radiation in the Boussinesq equation of the agricultural drainage. Journal of Hydrology, 332: 374-380.

Taban suyu tablası yüksekliğinin değişimine bağlı olarak taban suyu seviyesinin matematiksel modellenmesi

Year 2021, Volume: 9 Issue: 1, 23 - 29, 17.06.2021
https://doi.org/10.33409/tbbbd.798562

Abstract

Tarım alanlarında sulama suyu miktarının düzenlenmesinde, bitki-kök bölgesi tuzlaşmasının önlenmesinde, drenaj sisteminin
planlanmasında taban suyu derinliği ve seviyesinin, taban suyu tablasının değişiminin değerlendirilmesi gerekir. Bu çalışmada,
Dupuit yaklaşımı ve Darcy yasasına bağlı olarak elde edilen Boussinesq denkleminin (doğrusal olmayan difüzyon denklemin),
harmonik sınır koşuluna bağlı çözümüne göre taban suyu tablası ve seviyesinin değişimleri incelenmiştir. Taban suyu tablası ve
seviyesinin mesafe ve zamana bağlı olduğu teorik olarak gösterilmiştir. Taban suyu tablası ve seviyesinin maksimum değişimleri
sırasıyla 0.123 m ve 2.123 m olarak, 0.5 m mesafede ve 2. saatte hesaplanmıştır. Minimum değişimler ise sırasıyla -0.006 m ve 1.994
m olarak 2.5 m mesafede ve 2. saatte belirlenmiştir. Taban suyu tablasının dalgalanma amplitütünün eksponansiyel olarak değiştiği
ve x>2 m mesafede dalgalanmanın “sönme” sürecine yaklaştığı belirlenmiştir.

References

  • Boussinesq MJ, 1904. Recherches theoriques sur l’ecoulement des nappes d’eau infiltrées dans le sol et sur debit de sources. Journal de Mathématiques Pures et Appliquées 10: 5-78.
  • Childs EC, 1943. The water table , equipotentials, and streamlines in drained land. Soil Science, 56(5): 317-330.
  • Childs EC, 1945a. The water table , equipotentials, and streamlines in drained land: II. Soil Science, 59(4): 313-328.
  • Childs EC, 1945b. The water table , equipotentials, and streamlines in drained land: III. Soil Science, 59(5): 405-415. Coulibaly P, Anctil F, Aravena R, Bobee B, 2001. Artificial neural network modeling of water table depth fluctuations. Water Resources Research 37 (4): 885–896.
  • Coulibaly P, Baldwin CK, 2005. Nonstationary hydrological time series forecasting using nonlinear dynamic methods. Journal of Hydrology 307 (1): 164–174.
  • Cuthbert MO, 2010. An improved time series approach for estimating groundwater recharge from groundwater level fluctuations. Water Resources Research 46 (9): W09515.
  • Darcy H, 1856. Les fontaines publiques de la ville de Dijon. Dalmont, Paris, 647 p. Dumm LD, 1954. Drain spacing formula: new formula for determining depth and spacing of subsurface drains in irrigated lands. American Society of Agricultural Engineers, 35: 726–730.
  • Dumm LD, 1964. Transient flow concept in subsurface drainage: its validity and use. Transactions of the American Society of Agricultural Engineers, 7: 142-146.
  • Dupuit J, 1863. Études théoriques et pratiques sur le mouvement des eaux dans les canaux découverts et a travers les terrains perméables. Dunod, Paris, 364 p.
  • Ekberli İ, Gülser C, 2014. Estimatıon of soil temperature by heat conductivity equation. Vestnik Bashkir State Agrarian University (Вестник Башкирского Государственного Аграрного Университета), 2 (30):12-15.
  • Ekberli İ, Gülser C, 2018. Boussinesq denkleminin çözümüne bağlı olarak taban suyu seviyesi yüksekliğinin incelenmesi. Toprak Bilimi ve Bitki Besleme Dergisi, 6(2): 134-142.
  • Ekberli İ, Gülser C, 2018. Sulamada toprağın ıslanma derinliğinin belirlenmesi. Anadolu Tarım Bilimleri Dergisi, 33(2): 142-148. Ekberli İ, Sarılar Y, 2015. Toprak sıcaklığının profil boyunca sönme derinliğinin ve gecikme zamanının belirlenmesi. Ege Üniversitesi Ziraat Fakültesinin Dergisi, 52 (2): 219-225.
  • Faibishenko BA, 1986. Water-salt rejime of soils under irrigation. Agropromizdat, Moscow (in Russian), 304 p. Gülser C, Ekberli İ, 2002. Toprak sıcaklığının profil boyunca değişimi. Ondokuz Mayıs Üniversitesi Ziraat Fakültesinin Dergisi, 17(3): 43-47.
  • Gülser C, Ekberli İ, 2019. Toprak sıcaklığının tahmininde ısı taşınım denklemi ve pedotransfer fonksiyonun karşılaştırılması. Toprak Bilimi ve Bitki Besleme Dergisi, 7(2): 158-166.
  • Hayek M, 2019. Accurate approximate semi-analytical solutions to the Boussinesq groundwater flow equation for recharging and discharging of horizontal unconfined aquifers. Journal of Hydrology, 570: 411–422.
  • Jeong J, Park E, 2017. A shallow water table fluctuation model in response to precipitation with consideration of unsaturated gravitational flow. Water Resources Research 53: 3505-3512.
  • Kats DM, Shestakov VM, 1992. Melioration hydrogeology. Moscow State University Press, Mockow (in Russian), pp.71-92. Knotters M, Bierkens MFP, 2000. Physical basis of time series models for water table depths. Water Resources Research 36 (1): 181–188.
  • Kong J, Xin P, Hua G-F, Luo ZY, Shen C-J, Chen, D, Li L, 2015. Effects of vadose zone on groundwater table fluctuations in unconfined aquifers. Journal of Hydrology 528: 397-407.
  • Li X, Jin M, Zhou N, Huang J, Jiang S, Telesphore H, 2016. Evaluation of evapotranspiration and deepper colation under mulched drip irrigation in an oasis of Tarimbasin, China. Journal of Hydrology, 538: 677-688. Lockington DA, Parlange J.-Y, Parlange MB, Selker J, 2000. Similarity solution of the Boussinesq equation. Advances in Water Resources 23: 725-729.
  • Luthin JN (Editor), 1957. Drainage of Agricultural Lands. Agronomy Monographs, 7, American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America, Publisher Madison, Wisconsin, 620 p.
  • Mehdinejadiani B, Fathi P, 2020. Analytical solutions of space fractional Boussinesq equation to simulate water table profiles between two parallel drainpipes under different initial conditions. Agricultural Water Management, 240: 106324.
  • Neto DC, Chang HK, van Genuchten MT, 2015. A mathematical view of water table fluctuations in a shallow aquifer in Brazil. Groundwater, 54 (1): 82–91.
  • Okkonen J, Klöve B, 2010. A conceptual and statistical approach for the analysis of climate impact on ground water table fluctuation patterns in cold conditions. Journal of Hydrology, 388. 1-12.
  • Park E, Parker JC, 2008. A simple model for water table fluctuations in response to precipitation. Journal of Hydrology 356 (3): 344–349.
  • Rai SN, Manglik A, Singh VS, 2006. Water table fluctuation owing to time-varying recharge pumping and leakage. Journal of Hydrology 324 (1–4): 350–358.
  • Singh MP, Chauhan HS, Ram S, 1996. Unsteady state drainage in a vertically heterogeneous soil. Agricultural Water Management, 31: 285–293.
  • Singh RM, Singh KK, Singh SR, 2006. Falling water tables in a sloping/nonsloping aquifer under various initial water table profiles. Agricultural Water Management, 82(1-2): 210-222.
  • Su, N., 2017. The fractional Boussinesq equation of groundwater flow and its applications. Journal of Hydrology, 547: 403–412.
  • Tang G, Alshawabkeh AN, 2006. A semi-analytical time integration for numerical solution of Boussinesq equation. Advances in Water Resources,29: 1953-1968.
  • Telyakovskiy AS, Kurita S, Allen MB, 2016. Polynomial-based approximate solutions to the Boussinesq equation near a well. Advances in Water Resources 96: 68-73.
  • Uziak J, Chieng S, 1989. Drain-spacing formula for transient state flow with ellipse as an initial condition. Canadıan Agrıcultural Engıneerıng, 31: 101-105.
  • Yoon H, Jun SC, Hyun Y, Bae GO, Lee KK, 2011. A comparative study of artificial neural networks and support vector machines for predicting groundwater levels in a coastal aquifer. Journal of Hydrology 396 (1): 128–138.
  • Zavala M, Fuentes C, Saucedo H, 2007. Non-linear radiation in the Boussinesq equation of the agricultural drainage. Journal of Hydrology, 332: 374-380.
There are 33 citations in total.

Details

Primary Language Turkish
Subjects Agricultural Engineering
Journal Section Articles
Authors

İmanverdi Ekberli 0000-0002-7245-2458

Coşkun Gülser

Publication Date June 17, 2021
Published in Issue Year 2021 Volume: 9 Issue: 1

Cite

APA Ekberli, İ., & Gülser, C. (2021). Taban suyu tablası yüksekliğinin değişimine bağlı olarak taban suyu seviyesinin matematiksel modellenmesi. Toprak Bilimi Ve Bitki Besleme Dergisi, 9(1), 23-29. https://doi.org/10.33409/tbbbd.798562
AMA Ekberli İ, Gülser C. Taban suyu tablası yüksekliğinin değişimine bağlı olarak taban suyu seviyesinin matematiksel modellenmesi. tbbbd. June 2021;9(1):23-29. doi:10.33409/tbbbd.798562
Chicago Ekberli, İmanverdi, and Coşkun Gülser. “Taban Suyu Tablası yüksekliğinin değişimine bağlı Olarak Taban Suyu Seviyesinin Matematiksel Modellenmesi”. Toprak Bilimi Ve Bitki Besleme Dergisi 9, no. 1 (June 2021): 23-29. https://doi.org/10.33409/tbbbd.798562.
EndNote Ekberli İ, Gülser C (June 1, 2021) Taban suyu tablası yüksekliğinin değişimine bağlı olarak taban suyu seviyesinin matematiksel modellenmesi. Toprak Bilimi ve Bitki Besleme Dergisi 9 1 23–29.
IEEE İ. Ekberli and C. Gülser, “Taban suyu tablası yüksekliğinin değişimine bağlı olarak taban suyu seviyesinin matematiksel modellenmesi”, tbbbd, vol. 9, no. 1, pp. 23–29, 2021, doi: 10.33409/tbbbd.798562.
ISNAD Ekberli, İmanverdi - Gülser, Coşkun. “Taban Suyu Tablası yüksekliğinin değişimine bağlı Olarak Taban Suyu Seviyesinin Matematiksel Modellenmesi”. Toprak Bilimi ve Bitki Besleme Dergisi 9/1 (June 2021), 23-29. https://doi.org/10.33409/tbbbd.798562.
JAMA Ekberli İ, Gülser C. Taban suyu tablası yüksekliğinin değişimine bağlı olarak taban suyu seviyesinin matematiksel modellenmesi. tbbbd. 2021;9:23–29.
MLA Ekberli, İmanverdi and Coşkun Gülser. “Taban Suyu Tablası yüksekliğinin değişimine bağlı Olarak Taban Suyu Seviyesinin Matematiksel Modellenmesi”. Toprak Bilimi Ve Bitki Besleme Dergisi, vol. 9, no. 1, 2021, pp. 23-29, doi:10.33409/tbbbd.798562.
Vancouver Ekberli İ, Gülser C. Taban suyu tablası yüksekliğinin değişimine bağlı olarak taban suyu seviyesinin matematiksel modellenmesi. tbbbd. 2021;9(1):23-9.