反向推求地下水模式地下水文參數之研究

Abstract

地下水模式之模擬，需要許多輸入參數之設定，其中，流通係數、補注量是為其敏感參數之一，然而利用地下水模式模擬之結果優劣，則與輸入參數是否合宜有相當程度之關聯。 本研究先分析一維均質與非均質的飽和穩定地下水流問題，並分別以二個範例做說明。在均質問題中，定義執行度量函數 為模擬水位平均值、模擬水位與觀測水位平均值之均方根差值。另外並進行各參數(包括水力傳導係數、入滲率及邊界條件)之敏感度大小分析，即計算當各參數改變一個單位值時，其對執行度量函數 之影響為何；除此之外，並進行比較解析解與數值解之差異，以做為優化過程進行移步之依據。 本研究再利用啟發式演算法當中的禁忌演算法(Tabu Search algorithm)之優化方法，應用於地下水模式之參數推估及其辨識，其中並利用伴隨狀態方法(Adjoint State Method)轉換地下水模式之控制方程式，以改善且增強禁忌演算法之優化效能與效率，期望於有限之計算資源限制之下(如合理的計算時間，或是合理的計算機配備等)，能夠找到更合適之參數空間分佈進行模式輸入，模擬出最符合之地下水水流情形。 最後，優化過程中，利用禁忌演算法配合伴隨狀態方法與傳統禁忌演算法優選最佳參數效率之比較。

Transmissivity and Recharge are important and sensitive input parameters needing to be identified in groundwater model simulation. However, whether the simulation results are appropriate is strongly related with input parameters. An one dimensional homogenous and groundwater flow problem with the steady state in the confined aquifer is discussed in this study and two designed experiments are also showed to enhance this discussion. The definition of the performance measurement function is the average hydraulic head and root mean square error hydraulic head in the homogenous problem. Moreover, the sensitivity analyses of the parameters, such as the hydraulic conductivity, the infiltration rate, and boundary conditions are estimated for the analytical solutions and numerical solutions, and the result would be the base to decide move size of the optimal procedure. An optimal procedure is proposed in this study to apply Tabu Search to optimize the spatial distribution of the transmissivity and Adjoint State method is also used to enhance the efficiency of the optimization. In this way, the best spatial distribution of the transmissivity is expected to be identified under the limited computational effort, such as computing time and computing equipments. Furthermore, the groundwater flow can be simulated successfully. Finally, in optimal procedure, the solving efficiency of optimizing best parameter with Tabu search method cooperating with the adjoint state method and traditional Tabu search are compared.