異質性有效水文地質參數推估之研究

Abstract

地下含水層參數有不同尺度之異質性，模擬分析時，常利用均質的『有效參數』來描述異質含水層參數；有效參數是使模擬均質含水層的水流與實際異質性含水層的水流行為有大致相同之行為。本研究提出一個禁忌演算法結合伴隨狀態法的修正型模式(即修正型禁忌演算法，MTM)來推估非等向、異質性含水層的有效參數，並利用數個數值抽水試驗來驗證。針對不同條件(異質程度的含水層、抽水時間與抽水量)下，分別利用曲線法(TCM)、直線法(SLM)、達西定律與本研究所提出的MTM來推估其有效水文參數，進而分析與討論之。 結果顯示，MTM可以有效地推估出最具代表性且有效參數，其具有最小的洩降推估之均方根誤差。MTM可以降低TCM與SLM的人為誤差，進而推估精確之參數；且MTM所推估出來的參數接近幾何平均。針對MTM適用性的研究結果顯示：(1)當抽水時間段較短時，MTM所推估出來的有效參數比TCM與SLM所推估有效參數精確。(2)隨著含水層異質性的變異度增加，導致MTM推估之有效參數接近現地真實值(即達西定律所推估之有效參數)的抽水量之範圍減少。(3)含水層的較高異質程度導致參數推估的不確定性；同時，異質性的相關長度對參數推估精確度的影響程度也會變大。

Spatial heterogeneity is ubiquitous in nature; and variability of parameter in subsurface is extensive. The effective parameters are obtained by conceptualizing the heterogeneous soil formation as an equivalent homogeneous medium that will discharge approximately the same flux as the ensemble flux of the heterogeneous formations. This study proposed a modified form of Tabu Search (TS) embedded Adjoint State Method (ASM), entitled “Modified Tabu Search Method (MTM)”, to estimate effective parameters for anisotropic, heterogeneous aquifers. MTM is validated by several numerical pumping tests. Comparisons are made to other well-known techniques, the type-curve method (TCM), the straight-line method (SLM), and Darcy’s law, to provide insight into the challenge of determining the most effective parameter for an anisotropic aquifer at different scales of heterogeneity with considering varying pumping time and pumping rates. The results reveal that MTM can efficiently obtain the best representative and effective parameters in terms of the least mean square errors of the drawdown estimations. The use of MTM may involve less artificial errors than occur with TCM and SLM, and lead to better solutions. Therefore, effective transmissivity is more likely to be comprised of the geometric mean of all transmissivities within the cone of depression based on a precise estimation of MTM. Further investigation into the applicability of MTM shows: (1) While the duration of the pumping test is short, MTM proposed herein might successfully optimize the effective parameters batter than TCM and SLM. (2) With a larger variance of heterogeneity of an aquifer, the range of the pumping rate becomes smaller, leading to estimations by MTM closest to those estimated by Darcy’s law. (3) A higher level of heterogeneity in an aquifer can induce an uncertainty in estimations, while the changes in correlation length will affect the accuracy of MTM.