應用重力模擬與地下水數值模式於比流出量推估 －以濁水溪沖積扇為例

Abstract

地下水補注量為地下水永續管理重要的資訊之一，而比出水量或儲水係數之不確定性則直接影響地下水補注量推估之正確性，然而現地比出水量與儲水係數僅能藉由複井抽水試驗取得，必需在試驗場址鑽鑿兩口水井，一用於抽水，另一則用於觀測，因此鑽探成本較單井試驗高，受到鑽井成本的限制，造成比出水量之現地試驗數量遠低於所需，使區域性地下水補注量之推估具有高度不確定性。 有鑑於此，本研究將以濁水溪沖積扇為研究區域，結合現地重力量測、重力模擬與地下水模擬，重力量測為非侵入式之調查方式，以取代傳統複井抽水試驗，進行比流出量之調查，降低地下水補注量推估之不確定性。本研究分別於溪州國小、土庫國中與客厝國小進行重力調查，量測2012年五月、八月與十月豐枯水期間的重力變化，量測重力值須先校正海潮、天文潮、大氣壓力與地層下陷等不同機制之影響，校正後之重力殘差即代表地下水量變化對重力之影響。其次，應用重力積分公式，搭配MODFLOW系統水量變化進行重力模擬，比較量測重力殘差與模擬重力變化幅度之比值，再據以調整比出水率參數值，反覆進行上述過程，直至模擬重力變化與重力殘差變化幅度吻合，即完成參數調查。 調查結果如下，由於溪州(1)為溪州國小鄰近之地下水觀測站，其曾進行複井抽水試驗，如複井試驗之結果如可與重力調查結果吻合，即表示重力量測與抽水試驗之高度關聯性。研究結果顯示，抽水試驗結果與本研究調查結果吻合，充分驗證本研究方法之可行性與正確性。在土庫國中與客厝國小方面，原量測重力殘差變化幅度對模擬重力變化幅度之比值分別為1.8與50倍，經將原參數值分別調大1.8倍與50倍後，模擬重力則與量測重力殘差吻合。經參數調整後，土庫國中鄰近區域之年淨抽水量由5.285(百萬噸)提高至7.232(百萬噸)，而客厝國小則由11.827 (百萬噸)改變至-3.584 (百萬噸)。 本研究成果顯示應用重力現地量測，配合地下水模擬與重力模擬，可取代傳統之複井抽水試驗，取得現地比出水量，相對於傳統需鑿設複井，花費大量鑽鑿成本，重力量測屬於非侵入式的地球物理量測方法，可節省大量成本，對於降低地下水參數及相關推估值之不確定，有極大助益。

In Taiwan, groundwater resources play a vital role on the regional supply management. Because the groundwater resources have been used without proper management in decades, several kinds of natural hazards, such as land subsidence, have been occurred. The Choshui alluvial fan is one of the hot spots in Taiwan. For sustainable management, accurately estimation of recharge is the most important information. The accuracy is highly related to the uncertainty of specific yield (Sy). Besides, because the value of Sy should be tested via a multi-well pumping test, the installation cost for the multi-well system limits the number of field tests. Therefore, the low spatial density of field test for Sy makes the estimation of recharge contains high uncertainty. Gravity measurement is a kind of physical geographical approach. Because gravity is a function of the mass of a material and the inverse square of the distance, the gravity measurement has the ability to observe the mass variation of the shallow groundwater system. Using the groundwater level observation and gravity measurement can be used for the calibration of Sy for a numerical model. Because the approach can observe the mass variation of groundwater without well installation, it can overcome the limitation of well construction for the Sy test. Four steps are used in the study. First, gravity variations of Si-jhou, Tu-ku and Ke-cuo are observed in May, August and November 2012. The measured values are required to remove the effect of other sources, such as ocean tide and land subsidence, and the removed values are called as gravity residual. Second, a numerical model, MODFLOW 2000, has been applied to simulate and calibrate the groundwater variation basing on the four values of Sy obtained from pumping tests. Although the groundwater levels are well-calibrated in the first version of MODFLOW with low spatial density of field test for Sy, the mass variation of groundwater might contain high uncertainty. Third, integrating the Newton gravity integral with the simulated water mass which obtained from the first version of MODFLOW may simulate the gravity variation of the system. Fourth, comparing the ratio between the variation ranges of gravity residual and the one of simulated gravity, the values of Sy can be modified basing on the ratio and assigned in the second version of MODFLOW. Because a multi-well pumping test has been applied on Si-jhou station, the values of Sy is 0.216. the gravity residual observed from Si-jhou and the measured Sy can be used to verify the proposed approach. Assigning the field test value of Sy in Si-jhou, the simulated gravity can fit the gravity residual well without parameter calibration. The study of Si-jhou is an evidence to verify the ability of the proposed approach. In Tu-ku and Ke-cuo station, the ratios between the variation ranges of gravity residuals and the ones of simulated gravities approximate 1.8 and 50. The values of Sy are modified as 1.8 and 50 times of the values assigned in the first version of MODFLOW. After the parameter re-assignment, the simulated gravities may fit the gravity residuals better in Tu-ku and Ke-cuo. The comparison of water balance between the two versions of MODFLOW indicates that the quantities of recharge for Tu-ku from -5.285 million tons increase to -7.232 million tons, and for Ke-cuo from 11.827 million tons to -3.584 million tons. The result show that using gravity measurement, groundwater simulation model and the one of simulated gravity, to replace the traditional multi-well pumping test, gravity measurement is a kind of non-intrusion physical geographical approach. Gravity measurement can saving a lot of cost, and also decrease the groundwater parameter uncertainty.