| Title |
Development of an Analytical Model for Estimating Streamflow Depletion in a Finite-Width Stream due to Groundwater Pumping |
| Authors |
이정우(Lee, Jeongwoo) ; 정일문(Chung, Il-Moon) ; 홍성훈(Hong, Sung Hun) |
| DOI |
https://doi.org/10.12652/Ksce.2026.46.4.0313 |
| Keywords |
하천수 감소량, 유한폭 하천, 지하수 양수, 푸리에-라플라스 변환, 해석적 모형 Streamflow depletion, Finite-width stream, Groundwater pumping, Fourier-Laplace transform, Analytical model |
| Abstract |
Analytical solutions for a line-width stream in an unbounded aquifer have been widely used to estimate streamflow depletion induced by groundwater pumping. However, these solutions neglect stream width by treating the stream as a line, limiting their applicability to wide streams. To address this limitation, this study develops an analytical model for estimating streamflow depletion under finite-width stream conditions. A two-dimensional unsteady groundwater flow equation was formulated by incorporating a source term representing stream leakage and a sink term representing groundwater pumping. An analytical solution for groundwater drawdown was derived using the Fourier-Laplace transform. Based on this, streamflow depletion was formulated in the Laplace domain as an integral over stream width, and the corresponding time-domain solution was obtained via numerical inverse Laplace transform. The developed analytical solution was validated by comparison with numerical results obtained using MODFLOW. The effect of stream width was then evaluated under various hydrogeological conditions, including transmissivity, storage coefficient, streambed hydraulic conductivity, and the distance from the stream boundary to the pumping well. The results showed that the difference between the two analytical solutions decreased as the pumping duration increased. Overall, however, the line-with solution tended to overestimate streamflow depletion compared with the finite-width solution. Furthermore, it is found to be appropriate when the distance between the stream boundary and the pumping well exceeds approximately twice the stream width. The proposed analytical model is applicable to streams of any width, making it a more versatile and widely applicable analytical tool. |