區域性地下水系統水流模式率定方法建立與應用-以濁水溪沖積扇與名竹盆地為例

本研究目的為建立一區域性地下水流模式之率定方法，而率定方法則採用最陡坡降法來對決策參數做修正，並加以實際運用於評估地層下陷區減少抽水量後水位抬升之變化以及地區可抽水量之評估。最陡坡降法以目標函數對決策變數的偏微分求得決策變數的修正量，但偏微分之結果並非解析解，因此利用物理概念配合特定數學函數對偏微分做近似，可快速求得5種決策變數:地面水淨補注量、深層抽水量、邊界淨流量、水平水力傳導係數以及垂直滲漏係數等參數修正量，並將該方法應用於濁水溪沖積扇與名竹盆地之地下水模型之率定。最後將率定完成之模型，用於名竹盆地之可抽水量評估以及濁水溪沖積扇地層下陷區減抽水位抬昇評估。本研究以優選模式建立地下水流數值模式率定方法，首先設定目標函數為使模擬與觀測之蓄水量誤差總和最小，而模式之決策變數為地面水補注量、邊界淨流量、深層抽水量、水平水力傳導係數以及垂直滲漏係數之時空分布。限制式設定為三條：(1)各系統流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)所有決策變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，並利用物理概念配合特定函數與蓄水量誤差歷線，計算決策變數之修正量，以進行上述參數之修正，以此算完成一次迭代過程。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，獲得地面水補注量、邊界淨流量、深層抽水量、水平水力傳導係數以及垂直滲漏係數之最佳並合理之時空分布。本研究將所建立之參數率定優選模式應用於濁水溪沖積扇地下水流數值模式率定，其地下水流模式之模擬年限為2012年1月至2014年12月，以月為時間單位進行模擬，求解過程中同時針對四層含水層共126個水平水力傳導係數分區、96個垂直滲漏係數分區、1080個地面水淨補注量之時空分布、3456個深層抽水量之時空分布以及1332個邊界淨流量時空分布進行率定計算修正量。率定結果發現第1層含水層因為可直接影響誤差之參數較多使誤差下降的較快，而較深層之誤差下降的相對較慢，但每一層含水層之水位誤差RMSE都能在1公尺上下。率定完成之水平水力傳導係數與垂直滲漏係數大多數皆在合理範圍內，而剩餘決策變數之通量也在合理認知範圍內。顯示本研究方法能夠快速且準確的掌握地下水之各種流通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，並將此模式應用於實際應用中。

關鍵字

濁水溪沖積扇；優選模式；參數率定

並列摘要

This study is aimed to develop a regional groundwater numerical model calibration method. After finsishing the model, I will apply it to evaluate the change of groundwater level when decreasing the volume of pumping in severe subsidence area, and possible volume of pumping in area. When I want to correct the parameters, I use Gradient method. It uses partial derivatives on objective function to decide the correction of parameters. However, the outcome of partial derivatives on objective function can’t be solved. So, I use physical principal and some mathematical function to approximate the the part of partial derivatives, and this can quickly find the correction of 5 parameters including net surface recharge, pumping in deep aquifer , net boundary flux , horizontal hydraulic conductivity, and vertical leakance. Finally, the established method was applied on the groundwater system of Chou-Shui River Alluvial Fan and Minzu Basin. With this model, we can estimate the pumping potential of Minzu Basin and the rise of groundwater in severe subsidence area of Chou-Shui River Alluvial Fan when decreasing the volume of pumping. The proposed groundwater parameters calibration method is based on an optimization model which the objective function is minimizing the the sum of square error of the simulated and observed error in groundwater storage. The decision variables are net surface recharge, volume of pumping in deep aquifer , net boundary flux ,horizontal hydraulic conductivity, and vertical leakance. There are three constraints of the optimization model: (1) the flow of groundeater system msut flow the conservation of mass(2) the simulated groundwater level must follow the governing equation of groundwater flow; (3) all decision variables 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. Applying the physical principal and some math function, the modified decision variables is calculater according to the simulated error hydrograph of groundwater level. From iterations, the optimal temporal-spatial distribuation of decision variables can be obtained. This study applied the optimization model on the calibration of the groundwater system in Chou-Shui River Alluvial Fan and Minzu Basin. The simulated period is from January 2012 to December 2014 monthly. The total variables of hydraulic conductivity in four acquifers are 126, of vertical leakance are 96. There are 1080 net surface recharge, 3456 pumping in deep aquifer and 1332 net boundary flux temporal-spatial distribuation in all stress period. The result show that the error in the aquifer drops down very quickly than deeper aquifers because lots of decision variavles can affect aquifer.However, the RMSE of groundwater level in all aquifers are still about 1 m. The calibrated hydraulic conductivity and vertical leakence are mostly in reasonable limits, and the other flow decision variables are still 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 groundwater flow and hydrogeological parameters. Finally, we can apply it in real situation and estimate it.