Abstract
Based on the first linearized Boussinesq equation, the analytical solution of the transient groundwater model, which is used for describing phreatic flow in a semi-infinite aquifer bounded by a linear stream and subjected to time-dependent vertical seepage, is derived out by Laplace transform and the convolution integral. According to the mathematical characteristics of the solution, different methods for estimating aquifer parameters are constructed to satisfy different hydrological conditions. Then, the equation for estimating water exchange between stream and aquifer is proposed, and a recursion equation or estimating the intensity of phreatic evaporation is also proposed. A phreatic aquifer stream system located in Huaibei Plain, Anhui Province, China, is taken as an example to demonstrate the estimation process of the methods stated herein.
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References
Zheng W Z. Transient flow simulation and groundwater resources evaluation[M]. Beijing: Science Press, 1983 (in Chinese).
Mao C X. Analysis and control of seepage problems[M]. Beijing: Science Press, 1988 (in Chinese).
Sergio E S. Modeling groundwater flow under transient nonlinear free surface[J]. Journal of Hydrologic Engineering, 2003, 8(3):123–132.
Srivastava R. Aquifer response to linearly varying stream stage[J]. Journal of Hydrologic Engineering, 2003, 8(6):361–364.
Edenhofer J, Schmitz G H. Pressure distribution in a semi-infinite horizontal aquifer with steep gradients due to steady recharge and/or drainage: the exact explicit solution[J]. Transport in Porous Media, 2001, 45(3):345–364.
Mishra A, Hata T, Abdelhadi A W. Models for recession flows in the upper Blue Nile river[J]. Hydrological Processes, 2004, 18(15):2773–2786.
Szilagyi J, Parlange M B, Albertson J D. Recession flow analysis for aquifer parameter determination[J]. Water Resources Research, 1998, 34(7):1851–1857.
Basha H A, Maalouf S F. Theoretical and conceptual models of subsurface hillslope flows[J]. Water Resources Research, 2005, 41(7). DOI:10.1029/2004WR003769.
Troch P A, Van Loon A H, Hilberts A G J. Analytical solution of the linearized hillslope-storage Boussinesq equation for exponential hillslope width functions[J]. Water Resources Research, 2004, 40(8). DOI:10.1029/2003WR002850.
Woo S B, Philip L F L. Water table profiles and discharges for an inclined ditch-drained aquifer under temporally variable recharge[J]. Journal of Irrigation and Drainage Engineering, 2003, 129(2):93–99.
Tao Yuezan, Xi Daoying. Rule of transient phreatic flow subjected to vertical and horizontal seepage[J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(1):59–65.
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Communicated by LI Jia-chun
Project supported by National Natural Science Foundation of China (No. 40474065) and the National TCM Project in the 11th Five-Year Plan Period of China (No. 2006BAB01B01)
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Tao, Yz., Yao, M. & Zhang, Bf. Solution and its application of transient stream/groundwater model subjected to time-dependent vertical seepage. Appl Math Mech 28, 1173–1180 (2007). https://doi.org/10.1007/s10483-007-0905-y
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DOI: https://doi.org/10.1007/s10483-007-0905-y
Key words
- stream/groundwater aquifer
- time-dependent vertical seepage
- parameters of aquifer
- water quantity exchange
- phreatic evaporation