利用經驗正交函數法檢定含水層水文地質參數

Abstract

過去地下水流數值模式之建立，於補注量與抽水量之空間分布，仍有極大的改進空間，尤其以人為抽水量偏估最為嚴重，主要是因為私井的氾濫，實際量測資料與空間分布很難準確，而補注量的分配，大多是以河川模組或土壤質地、土地利用型態與邊界條件所配置，其中的猜測值仍佔多數，在諸多的不確定因素下，水文量的空間配置不僅變得更為複雜，且分配的正確與否也不得而知，在不確定的水文量時空分布下進行模式檢定，其正確性更是難以評估。 本研究旨在配合經驗正交函數法，並以屏東平原為例，首先設計一虛擬案例，利用經驗正交函數法分析屏東平原非受壓含水層之水文量淨值空間分布。虛擬案例將水文地質參數與抽補量視為已知，以模式模擬得觀測水位，計算蓄水量變化歷線，再利用經驗正交函數法進行水文量淨值的空間配置。在得到良好的水文量淨值空間配置下，再對虛擬案例模式進行參數率定，最終可評估最佳水文地質參數與真值的誤差。研究結果分為兩部分，第一部分為水文量淨值的空間分配，在時空配置完成後，模擬水位與觀測水位之均方根誤差(Root Mean Square Error)為1.97公尺，水文量淨值RMSE為9,310,648噸，與日平均蓄水量2.03億噸比較，約是其平均量之4.59%，由此可知經驗正交函數法能有效配置之水文量淨值之空間分布，整體誤差在接受範圍內；第二部分為水文地質參數之檢定，模式率定後的水位RMSE為1.11公尺，與原本誤差降低了0.86公尺，水文量淨值RMSE為5,222,030噸，較原先誤差降低約4,088,618噸，水文地質參數之率定值與初始設定值相差在兩個數量級內。虛擬案例顯示了本研究方法可有效配置水文量淨值之空間分布，在分配誤差較小的情況下，水文地質參數的誤差量也能有效控制。本研究進一步將虛擬案例應用於實際案例之屏東平原數值模式建置，以評估其可應用性。 實際案例旨要驗證虛擬案例的研究方法是否較以往模式設置更能找到較好的初始水文量空間分布，同樣以屏東平原為例，建構三種模式比較其優劣，分別是：(1)經驗正交函數抽補空間配置(2)補注量與抽水量空間平均配置(3)配合土壤質地分析補注空間配置。研究結果同樣分為兩部份，第一部分為水文量淨值的空間分配，配置完成後的水位RMSE分別為，模式(1)：6.31公尺，模式(2)：10.67公尺，模式(3)：10.43公尺，水文量淨值RMSE分別為，模式(1)：27,931,944噸，模式(2)：47,484,304噸，模式(3)：44,691,110噸，與日平均蓄水量2.19億噸比較，分別約是其平均量之12.75%、21.68%與20.41%，由此可知，以經驗正交函數法進行水文量空間配置，確實能有效減少整體的誤差量；第二部分為為水文地質參數之檢定，模式(1)率定後的水位RMSE為4.20公尺，較原先降低約2.11公尺，水文量淨值RMSE為19,552,360噸，較原先誤差降低約8,379,584噸，水文地質參數之率定值與初始設定值也相差在兩個數量級內，顯示本研究方法具有實際可行性，但於現地條件中，包含有受壓含水層與湧泉區域，僅需少許水量，水位便有明顯變化，故水位誤差較大。

The underground flow numerical model of the spatial distribution between recharging and pumping volume in the past few years still has a great space to improve, especially the artificial pumping volume which has the most serious bias. Due to the unchecked spreading of private wells, the accuracy of the field estimation and the spatial distribution is low. As for the recharging distribution, it is set by the river module, soil texture, land use patterns and the boundary conditions while the guess value is still the majority. As result, the accuracy of the model calibration at the unsure hydrological spatial and temporal distribution is hard to evaluate cause the complex hydrological space distribution which can’t be fully proved to be right. This study is based on the empirical orthogonal function method and takes Ping-Tung Plain as an example. The virtual case is designed at the very beginning to analyze the hydraulic value spatial distribution of the unconfined aquifer in Ping-Tung Plain by the empirical orthogonal function method. In this virtual case, the hydrogeological parameters are known. The modeling observation level can calculate the water storage changes hydrograph and be used to do the hydraulic net value space distribution by the empirical orthogonal function method. Then, at the appropriate hydraulic net value space distribution, the best hydrogeological parameters and the true value deviation can be evaluated after the parameter calibration of this virtual case. The result can be divided into two parts: First, the hydraulic net value space distribution. The root mean square error of simulated water levels and observation water level is 1.97 cm. The hydraulic net value RMSE is 9,310,648 tons which is 4.59% of the average value that compares with the daily average storage equals to 2.03 hundred million tons. From the above data, the empirical orthogonal function method can be proved to be the most effective way to do the hydraulic net value space distribution while the overall error is in the acceptable range; Second, the test of hydrogeological parameters. The water level RMSE after the model calibration equals to 1.11 m which is 0.86 m lower than the previous one and the hydraulic net value RMSE is 5,222,030 tons which is 4,088,618 tons lower than the previous one. Therefore, the calibration value of hydrogeological parameters and the initial value are different in two power orders. The virtual case shows that this study can set the hydraulic net value spatial distribution effective. And also, when the distribution error is low, the hydrogeological parameters can also be controlled effectively. This study takes further steps to apply this virtual case into the real case of numerical modeling in Ping-Tung Plain to evaluate the applicability. The real case is to verify the research method of the virtual case whether to find the better initial hydraulic spatial distribution then the previous methods or not. Therefore, three models are built to compare the advantages and disadvantages, which are (1) the recharging and pumping spatial distribution with the empirical orthogonal function, (2) the average recharging and pumping spatial distribution, (3) recharging spatial distribution with soil texture analysis. The result can also be divided into two parts: Fist, the hydraulic net value spatial distribution. The water levels RMSE after the distribution are (1) 6.31 m, (2) 10.67 m, (3) 10.43 m. The hydraulic net values RMSE are (1) 27,931,944 tons, (2) 47,484,304 tons, (3) 44,691,110 tons. The average values comparing with the daily average storage volume which equals to 2.19 hundred million tons are (1) 12.75%, (2) 21.68%, (3) 20.41%. As a result, the hydraulic spatial distribution by using the empirical orthogonal function method do effectively reduce the overall error; Second, the test of hydrogeological parameters. The water level RMSE after the model (1) calibration is 4.20 m which is 2.11 m lower than the previous one. And the hydraulic net value RMSE is 19,552,360 tons which is 8,379,584 tons lower than the previous one. As a result, the calibration value of hydrogeological parameters and the initial value are different in two power orders. This study shows that the research method has practical feasibility. But, in the field conditions which contain the confined aquifer and flooded areas, the water level has a significant change with only slight volume of water which shows that the water level deviation is larger.