應用卡門濾波理論與遺傳演算法於地下水觀測井網設計

Abstract

本研究目的在發展一個整合卡門濾波、地下水數值模式與遺傳演算法之地下水觀測井網最佳設計模式。其中卡門濾波(Kalman Filtering)與地下水數值模式（MODFLOW）之整合，乃應用已發展之KALMOD模式， KALMOD主要功能在計算不同的觀測井網下，以觀測值更新的水位及其不確定性（以共變異矩陣代表），惟其無法進行最佳觀測系統（井網）之搜尋，因此本研究乃結合KALMOD與遺傳演算法，以降低更新後水位之不確定性為目標，發展最佳觀測井網設計模式。此井網設計模式的特色，在於不僅藉由數值模式描述地下水系統的物理機制，亦同時考量模式建構的不確定性，並且藉由卡門濾波理論可以使觀測系統在整個水位推估過程的角色有清楚的描述。本文並以假設的案例進行模式的驗證及探討影響井網佈置的因素，研究成果顯示，數值模式的精確度仍是觀測系統設計成敗的關鍵。

This study develops a groundwater monitoring network design model that integrates the Kalman Filtering, groundwater numerical model and a Genetic Algorithm. The KALMOD is an existing model that integrates the Kalman filter and MODFLOW. KALMOD functions primarily to calculate the head that is updated according to the data of a monitoring network and its uncertainty represented by the covariance. However, the KALMOD can not determine the optimal monitoring network. Therefore, this work combines it with a Genetic Algorithm to compute the optimal monitoring network automatically. The network design focuses mainly on reducing the uncertainty of the updated groundwater head at the monitoring sites. The proposed model can describe the physical conditions of a groundwater system through the numerical modeling and consider the modeling uncertainty. The Kalman Filtering also clearly identifies the role of the monitoring system. A hypothetical case is also presented to verify the effectiveness of the proposed model and investigate those factors affecting the network design. Simulation results demonstrate that success of the monitoring network design largely depends on the accuracy of the numerical model.