應用伴隨狀態方法結合共軛梯度法對傾斜滲漏含水層水文參數之推估

Application of Adjoint State Method With Conjugate Gradient Method to Estimate Hydrogeological Parameters in Inclined Leaky Aquifer

游勝凱(Sheng-Kai Yu)

指導教授 ： 譚義績

共同指導教授 ： 林俊男

國立臺灣大學/生物資源暨農學院/生物環境系統工程學研究所/碩士(2006年)

https://doi.org/10.6342/NTU.2006.01267

摘要

本文研究之目的在反向推求傾斜滲漏含水層之水文地質參數，反向推求過程中利用共軛梯度法的優化方式進行飽和非拘限且非水平含水層的參數推估。經由Boussinesq 方程式的特性來模擬飽和非拘限含水層的自由水面線。
利用伴隨狀態方法轉換地下水模式之控制方程式，以改善傳統差分法應用於共軛梯度法之求解梯度問題之效率，藉以增強共軛梯度法之反向推求效率，最後利用實驗室砂箱試驗之觀測資料驗證此參數推估模式。
期望參數推估模式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)，能夠找到更合適之水文地質參數，模擬出最符合之地下水水頭情形。

關鍵字

傾斜滲漏含水層 ； 共軛梯度法 ； 伴隨狀態方法

並列摘要

The purpose of this research is aimed on inverse estimating the hydrogeological parameter of an inclined leaky aquifer. The processes of inverse problem is used to simulate the free surface of groundwater flow in not horizontal and saturated unconfined aquifer, namely the Boussinesq equation.
An optimal procedure is proposed in this study to apply Conjugate Gradient Method to optimize the spatial distribution of the hydraulic conductivity and Adjoint State method is also used to enhance the efficiency of the optimization.
A sand box test is also designed to verify the proposed inversed model In this way, the best spatial distribution of the hydrogeological parameters 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.

並列關鍵字

Inclined Leaky Aquifer ； Conjugate Gradient Method ； Adjoint State Method

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