擴展式卡門濾波應用至水層參數之檢定

Abstract

本研究利用擴展式卡門濾波（Extended Kalman Filter）與三次仿樣（Cubic Spline）來推求得拘限含水層與自由含水層的水文地質參數。擴展式卡門濾波與Theis的解結合，並應用三次仿樣內插求得的等時距井洩降數據，經由疊代的方式，便可求得拘限含水層的水文地質參數。在自由含水層方面，同樣可運用此濾波與Neuman的解，求得自由含水層的參數。 此方法只需利用部分的洩降資料便可求得水層參數，而且可獲得不錯的精度，因此，長時間的抽水試驗或可減短。此外，最小平方法與牛頓法結合求解的結果，與此法做了比較，擴展式卡門濾波可有較大的初始猜測值範圍，即使其精度稍不如前者。最後，此一非線性的擴展式卡門濾波在決定自由含水層參數值時，在檢定初期比出水幾乎維持定值，直到洩降曲線變平緩後，比出水值先產生顯著的跳躍而後收斂趨於至一定值。此階段反應重力排水影響洩降曲線的現象，與自由含水層井洩降的物理行為相吻合。

A method using extended Kalman filter (EKF) and cubic spline is proposed to identify the aquifer parameters in both confined and unconfined aquifer systems. The Theis solution combined with EKF, using the interpolated drawdown data produced by cubic spline, can optimally determine the parameters for confined aquifer through the recursive filtering process. In an unconfined system, Neuman’s model is employed by the same manner as the Theis solution to determine the aquifer parameters. The proposed method can quickly identify the parameters, using only part of observed drawdown data and the obtained parameters are shown to achieve good accuracy. Thus, the lengthy pumping test can be shortened. In addition, the comparisons of analyzing results between using nonlinear least-squares combined with finite-difference Newton’s method (NLN) and EKF for various initial guess values are presented. The EKF is proven to have a wider range of initial guess values, though the accuracy of the result is not so good as that by using NLN. Finally, during the determination of aquifer parameters, specific yield almost maintains constant at the beginning of the identification process until the drawdown curve starts flattening. During the flat period, specific yield jumps initially and then approaches a certain value. This identification process reflects the effect of gravity drainage on the drawdown curve and conforms to the physical nature of the unconfined aquifer.