區域性地下水系統水流模式率定方法之建立與應用－以濁水溪沖積扇為例

本研究目的為建立一區域性地下水流模式之率定方法，該方法可公式化為一優選模式，目標函數為使所有觀測井所對應之模擬與觀測蓄水量之均方根誤差 (RMSE) 最小；決策變數為水平水力傳導係數、垂直滲漏係數以及地面水補注量之時空分布；限制式包括：(1) 地面水補注量須符合質量守恆，(2) 地下水位之模擬結果須符合地下水流控制方程式，以及 (3) 水平水力傳導係數與垂直滲漏係數有一合理範圍。本研究為了有效地求解所建立之優選模式，乃利用經驗正交函數法(EOF) 分析地下水流模式之模擬蓄水量誤差歷線以建立一迭代演算法。演算法首先將決策變數初始值輸入地下水流模式進行地下水位之模擬，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計算決策變數之修正量以進行修正，如此完成一次迭代過程。經過數次迭代求解達到停止條件後便完成地下水流模式率定，獲得地面水補注量與水文地質參數之最佳時空分布。本研究將所建立之模式率定方法應用於濁水溪沖積扇，其地下水流模式之模擬年限為2012年1月至2014年12月，以月為模擬時間單位，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以及1,302個地面水補注量之時空分布進行率定。率定結果發現，於迭代初期，其蓄水量RMSE下降幅度最大，經歷5次迭代之後其誤差呈現較穩定下降狀態，最後於24次迭代後達到停止條件，完成模式率定。率定完成之地下水流模式能夠準確模擬各含水層之水位變化，顯示本研究方法能夠快速且準確地率定水文地質參數與地下水補注量之時間與空間分布。

關鍵字

地下水流模式率定；經驗正交函數；濁水溪沖積扇

並列摘要

This study aims to develop a methodology for regional groundwater flow model calibration. The proposed methodology was formulated as an optimization model. The objective function was to minimize the root mean square error (RMSE) of the simulated and observed groundwater storage associated with the observation wells. The decision variables were the horizontal hydraulic conductivity, the vertical leakance and the temporal-spatial distribution of surface water recharge. Three constraints included: (1) the surface water recharge of the groundwater system must obey mass balance; (2) the simulated groundwater level must follow the governing equation of groundwater flow; and (3) the value of horizontal hydraulic conductivity and vertical leakance are restricted to a reasonable range. To efficiently solve the optimization model an iterative algorithm was developed by applying empirical orthogonal function (EOF) analysis to the simulated error hydrograph of groundwater storage. The algorithm started with the initial value of decision variables. Groundwater level was simulated and the objective function was calculated. If the objective function does not satisfy the stop criterion, the simulated error hydrograph of groundwater storage will be calculated and the decision variables will be updated according to the EOF analysis. The optimal temporal-spatial distribution of surface water recharge and hydrogeological parameters can then be obtained through an iterative process. The proposed methodology was applied to the groundwater system of Chou-Shui River Alluvial Fan. The simulated period was from January 2012 to December 2014, and the time interval of the simulation was one month. The total number of hydraulic conductivity values in the four aquifers was 126, while there were 96 vertical leakance values, and 1,302 surface water recharge values. The results showed that the RMSE decreased dramatically in the early iteration stage of the calibration, became smooth after the fifth iteration, and finally stopped at the 24th iteration. The calibrated hydraulic conductivity and vertical leakance were within reasonable limits. The simulated groundwater level variations in all aquifers well-matched the observed ones. The methodology established in this study can thus effectively and accurately calibrate the temporal-spatial distribution of surface water recharge and the hydrogeological parameters.

並列關鍵字

groundwater flow model calibration ； empirical orthogonal function ； Chou-Shui River alluvial fan

國際替代計量

區域性地下水系統水流模式率定方法之建立與應用－以濁水溪沖積扇為例

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