全域最佳解應用於地下水抽水源鑑定分析

Abstract

地下水為一珍貴的天然資源因此私人開發受法律條文限制，不可違法取用。當某一地下水發現遭受擅自取用，藉由觀測的地下水位來推求抽水源位置、抽水量、及抽取時間，則為需要探知的問題。因此本研究發展一個方法，藉由模擬退火演算法的優點，結合美國地質調查局所研發之三維地下水流模擬模式MODFLOW-2000，做為抽水源鑑定的工具，針對在監測井所量測得的地下水水位，推求地下水抽水源的位置、抽水量、及抽取時間。為驗證所發展方法的正確性，先假設某一抽水源抽取地下水，藉用MODFLOW-2000模式模擬該地下水系統的水力水頭分布。 隨後在利用所發展的方法，進行抽水源鑑求。首先選擇一個區域，設為可疑的抽水源區域。其次以模擬退火演算法，在可疑抽水源區域選定抽水源位置，並產生該抽水量及抽取時間的試誤解。最後再以MODFLOW-2000進行相關的水力模擬，以得到在各監測井的模擬地下水水位。當所得結果滿足所設定的目標函數時，亦即模擬水位高與實際水位高差值的平方和最小時，即表示求得正確的抽水源位置、抽水量、及抽取時間。由數值模擬的結果顯示，即便在均質含水層、非均質含水層、或是其觀測水位包含誤差，本研究所發展的方法，依然能得到精確的推估結果。

Groundwater is a precious water resource on earth. In the real world, if the groundwater is illegally pumped, the information including pumping source location, pumping rate, and pumping period are the important information and needed to be identified. Locating the unknown source is an inverse problem and can be considered as a pumping source identification problem. An approach, using the simulated annealing and a three-dimensional groundwater flow model (MODFLOW-2000) is developed to estimate the pumping source information. In order to verify the validity of the present approach, a pumping well is assumed to install at known location and withdraws the groundwater at a known pumping rate. After a specified time, the hydraulic head (hereafter called observed head) at observation wells can be simulated by MODFLOW. Then the proposed approach is chosen to estimate the pumping source information when minimizing the sum of square errors between the simulated heads and observed heads at the observed wells. In the estimation process, a series of trial solutions for source location, pumping rate, and pumping period are generated by simulated annealing (SA). Then the MODFLOW-2000 is employed with those generated source information to simulate the hydraulic distribution at observation wells. Those procedures are repeatedly until the sum of square error between simulated head and measured head is minimized. The proposed approach gives good estimated results in both synthetic and real problems even the measured heads contain measurement errors.