考虑河床渗透性影响的基流退水过程解析模型

摘要:
基流退水过程分析是流域尺度平均水文地质参数估计的有效方法之一, 但传统基流退水过程模型未考虑河床的渗透性, 其对参数估计的影响并不清楚。针对这个问题, 建立了降水入渗及河水位波动驱动下, 考虑河床渗透性影响的潜水含水层地下水流数学模型, 运用格林函数方法推导出水位及流量的解析解, 并利用数值模拟验证了解析解。结果表明, 在降水入渗强度波动的驱动下, 河床渗透性越小, 降水入渗引起更高的地下水位上升, 更低的基流量峰值, 更慢的基流退水过程; 河水位波动驱动下, 河床渗透性更低时, 地下水位对河水位波动的响应更弱, 地表水-地下水交互通量更小; 河床渗透性显著影响基流退水曲线, 退水早期, 低渗透性的河床导致曲线斜率远大于3, 而退水后期, 曲线斜率趋近于1, 且其不受河床渗透性影响。当河床渗透性较差时, 由于忽略了河床渗透性的影响, 传统模型会过高估计基流量, 过低估计含水层的渗透系数。
- 基流退水过程 /
- 含水层补给 /
- 河水位波动 /
- 河床渗透性 /
- 解析解
Abstract: Objective
Baseflow recession analysis is an effective approach to estimating watershed-scale hydrogeological parameters. However, the traditional baseflow recession model did not consider the effects of semipervious riverbanks, and their influence on parameter estimation is unclear.
Methods
To address this issue, a mathematical model for groundwater flow in an unconfined aquifer with time-dependent recharge and river stages is presented. The effects of the semipervious riverbank are specifically taken into consideration. The analytical solutions of the hydraulic head and discharge are derived by using Green's function method, and their validities are tested by numerical simulations.
Results
The results show that, forced by the fluctuating recharge rate, the lower riverbank permeability leads to a higher peak of hydraulic heads, a lower baseflow, and slower baseflow recessions. For the case forced by the fluctuating river stages, the lower riverbank permeability leads to the weaker responses of water flow to the fluctuated river stage and the lower fluxes of surface water-groundwater interaction. The riverbank permeability significantly affects the baseflow recession curves. During early stage, the low riverbank permeability caused the power index of the recession curve to be larger than 3. For later stage, the power index approaches 1, which is not affected by the riverbank permeability.
Conclusion
For a low riverbank permeability, the traditional model will overestimate the baseflow and underestimate the hydraulic conductivities of aquifers because it neglects the effects of riverbank permeability.
- baseflow recession /
- aquifer recharge /
- river stage fluctuation /
- riverbank permeability /
- analytical solution
注释:

(所有作者声明不存在利益冲突)

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图 1 潜水含水层剖面地下水流的概念模型

h(x, t)为地下水的水头；K为含水层渗透系数；W(t)为含水层随时间变化的补给率；S_y为给水度；K_b为河床渗透系数；b为河床厚度；h_b(t)为随时间波动的河床水位

Figure 1. Schematic diagram of groundwater flow in a cross-section of unconfined aquifers

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图 2 入渗补给波动下地下水位及基流的解析解和数值解对比

a.2次降水入渗补给事件；b.不同位置的地下水位；c.基流；W_D为降水入渗补给强度；h_D为河床水位；Q_D为基流量

Figure 2. Comparison of the analytical solution and the numerical solution for hydraulic heads and baseflow induced by time-varying recharge

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图 3 河水位波动下地下水位及基流解析解和数值解对比

a.河水位及不同位置地下水位；b.基流

Figure 3. Comparison of the analytical solution and the numerical solution for hydraulic heads and baseflow induced by time-varying river stages

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图 4 地下水位和基流在不同α影响下对补给波动的响应

a.2次降水入渗补给事件；b.x_D=0.5处地下水位；c.基流

Figure 4. Responses of hydraulic heads and baseflow induced by time-varying recharge

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图 5 x_D=0.5处地下水位和基流在不同α影响下对河水位波动的响应

a.河水位及不同α的地下水位；b.不同α的基流

Figure 5. Responses of hydraulic heads at x_D=0.5 and baseflow induced by time-varying river stages

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图 6 地下水位在不同α影响下对河水位波动的响应

a.α=0.1；b.α=1；c.α=10；d.无河床影响解

Figure 6. Responses of hydraulic heads induced by time-varying river stages for different α

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图 7 基流在W_D=0，h_bD=0.6时不同α影响下的变化

Figure 7. Change in baseflow with time for different α when W_D=0 and h_bD=0.6

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图 8 不同α的影响下-dQ_D/dt_D与Q_D的双对数坐标图

Figure 8. log-log plots for -dQ_D/dt_D vs. Q_D for different α

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图 9 不同α的退水曲线指数b随时间的变化

Figure 9. Changes in exponent b of the baseflow recession hydrograph with time at different α

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