本研究目的為建立一區域性地下水流模式之率定方法。首先,先對地下水區域進行主成分分析並找出其時空間變數,並以其為基準增設新輔助井,再以經驗正交函數法配合地下水流模式之蓄水量變化歷線與模擬誤差歷線,快速且準確地掌握各補注量與水文地質參數之時間與空間分布資訊,並針對地下水系統之地面水補注量以及水文地質參數進行修正,最後將該方法應用於名竹盆地。 本研究欲建立一地下水流數值模式率定方法,首先,先對原觀測井進行主成分分析,得到該區域之時空間變數分布,接著找出特徵值為0之交線,並於交點上新增輔助井。之後,設定目標函數使模擬水位與觀測水位之均方根誤差(RMSE值)最小,而本研究中選定之決策變數為水平水力傳導係數、垂直水力傳導係數以及各補注量之時空分布;限制式主要分為三條:(1)各補注量於率定過程中須符合質量守恆;(2)地下水位之模擬結果須符合地下水流控制方程式;(3)水平水力傳導係數與垂直水力傳導係數有一合理範圍之限制。求解流程首先為設定決策變數初始值,輸入地下水流模式進行地下水位之模擬,並計算其目標函數判斷是否達成停止條件,若否則計算蓄水量誤差歷線,並利用經驗正交函數分析地下水流模式之蓄水量模擬誤差歷線,計算決策變數之修正量,以進行各補注量與水文地質參數之修正,完成一次迭代過程,經過數次迭代求解達到停止條件後便完成地下水流參數優選模式之率定,獲得各淨補注量與水文地質參數之最佳時空分布。 本研究將所建立之參數率定模式應用於名竹盆地地下水流數值模式,其地下水流模式之模擬年限為2012年1月至2012年12月,以日為時間單位進行模擬,求解過程中同時針對兩層含水層中之水平水力傳導係數分區、垂直水力傳導係數分區以及第一含水層中之降雨補注量、邊界補注量、河水補注量時空分布進行率定計算修正量。率定結果發現,於模式迭代初期,其地下水位模擬誤差RMSE值下降幅度最大,於幾次迭代之後其地下水位模擬誤差RMSE值幾乎呈現穩定狀態不再下降而達到停止條件,完成模式率定。率定完成之水平水力傳導係數與垂直水力傳導係數皆在合理範圍內,其地下水流數值模式能夠準確模擬含水層(一)之水位變化趨勢與豐枯水期地下水位值;含水層(二)之地下水位模擬結果亦能大致抓到水位變化之趨勢,且在新增輔助井後,與無輔助井之模擬結果比較後可發現,地下水位模擬情形改善許多。顯示本研究方法能夠快速且準確的掌握地下水補注量與水文地質參數之時間與空間分布資訊,並反饋回地下水流數值模式中,以獲得準確且良好之地下水流數值模式。
This study is aimed to develop a regional groundwater numerical model calibration method. First, use principal component analysis (PCA) on the groundwater section to find out its temporal-spatial variable,and use it as a reference to create new assistance well. Then, applies empirical orthogonal function (EOF) with the change hydrograph of groundwater storage and simulated error hydrograph of groundwater level to quickly and accurately catch and calibrate the temporal-spatial distribuation of water recharge and hydrogeological parameters. The established method was applied on the groundwater system of Ming Chu Basin. This study is aimed to develop a groundwater numerical model calibration method. First, use principal component analysis (PCA) on the groundwater section to get its temporal-spatial variable distribution, and finding the line of eigenvalue=0, and create the new assistance well on it. After, setting the objective function is minimizing the the root mean square error (RMSE) of the simulated and observed groundwater level. The decision variables are horizontal hydraulic conductivity, vertical hydraulic conductivity and water recharge. There are three constraints of the optimization model: (1) the water recharge of groundwater system in every iteration of calibrating process must obey the mass balance; (2) the simulated groundwater level must follow the governing equation of groundwater flow; (3) the value of horizontal hydraulic conductivity and vertical hydraulic conductivity are restricted to a reasonable limits. The process of the optimization model sets the initial value of decision variables first, and inputs the variables to groundwater model. Thus, the groundwater level can be simulated and the objective function will be estimated. If the objective function doesn’t satisfy the stop condition, the simulated error hydrograph of groundwater level will be calculated and analyzed with EOF. Then, the modified decision variables is calculater according to the simulated error hydrograph of groundwater level end the result of EOF analysis. From iterations, the optimal temporal-spatial distribuation of surface water recharge and hydrogeological parameters can be obtain. This study applied the model on the calibration of the groundwater system in Ming Chu Basin. The simulated period is from January 2012 to December 2012 daily. The decision variables were selected in this study are horizontal hydraulic conductivity, vertical hydraulic conductivity of two acqufiers and rain water recharge, river water recharge and boundary water recharge of hydraulic conductivity in first acquifer. The result show that the RMSE is decreased dramatically in early iteration of the calibration and become smoothly after several iterations. The calibrated hydraulic conductivity and vertical leakence are in reasonable limits. The simulated groundwater level can reflect the approximately trendance in all acquifer and can capture the peak of the observed value in first acquifer. Hence, the established method of this study can effectively and accurately calibrate temporal-spatial distribution of surface water recharge and hydrogeological parameters.