擴展式卡門濾波應用於滲漏水層參數之檢定

Abstract

本研究使用擴展式卡門濾波，檢定忽略及考慮滲漏層蓄水效應的滲漏水層參數。在忽略滲漏水層蓄水效應的例子中，針對拉格朗吉多項式內插得到等時距洩降資料，結合Hantush and Jacob的解透過卡門濾波遞迴演算的方式，可求得滲漏含水層三個參數的最佳值。在考慮滲漏層蓄水效應方面，同樣可運用結合卡門濾波與Neuman and Witherspoon的解，求得水層最佳的四個參數值。 本文所提方法可以快速的檢定得參數，利用部分觀測洩降數據就能得到良好的參數值，所以不必有長時間的抽水試驗。本研究方法可以應用在任意洩降時間段，因此在使用上沒有任何限制。檢定過程中，滲漏因子在最初時間段幾乎維持定值，此階段反應滲漏效應尚未影響水層的洩降，與受滲漏層影響的含水層抽水洩降的物理行為吻合。最後，為了瞭解數據若含有噪音對本方法分析結果的影響，本研究進行數據噪音的敏感度分析。分析的結果顯示，不論是白噪音或是有時間相關的噪音，對於檢定參數值的影響很小。

A method using extended Kalman filter (EKF) is presented to identify the aquifer parameters in leaky aquifer systems with and without considering the storage effect in the aquitard. In the case without considering the aquitard storage effect, the Hantush and Jacob’s solution combined with EKF can optimally determine the parameters for the leaky aquifer when analyzing the drawdown data interpolated by Lagrangian polynomial method. Coupled the Neuman and Witherspoon’s model, the EKF is also employed to estimate the four aquifer parameters. The proposed method can quickly identify the parameters, using only part of observed drawdown data and the obtained parameters are shown to have good accuracy. In field implementation, combined with on site water level measurement and data logger, the long time of pumping test can be shortened. In the process of parameter identification the leakage factor changes marginally for the first few observations, which may be attributed to the fact that there is a time lag between the start of pumping and the leakage effect on the drawdown. Finally, for the purpose of exploring the influence of white noises and temporal correlated noises in drawdown data, the results of sensitivity analysis show that the EKF approach is still applicable.