改良式降低變異數分析於地下水觀測井網規劃之應用

Abstract

本研究是以改良式降低變異數分析的方法（MVRA）來解決考慮區域性不確 定性之地下水觀測井網規劃問題，包括決定最佳設井位置及最佳數量。本 法是根據降低變異數分析繼續發展，增加設井位置在不同區域有不同權重 （如土地利用、鄰域影響等）之考慮，最佳設井位置乃選擇具最大加權總 變異數降低量（因新增一井所增加的資訊利益）之位置，演算過程中並根 據各點淨期望利益（因新增一井所增加的經濟利益減掉相對增加的量測費 用）不小於零的限制式，來決定所需的設井數量。本研究以FORTRAN 語言 發展此程式模組，文中並探討可能設井位置之密度對於最佳井位分佈之影 響，以作為採用格點間距之參考，根據分析結果，最佳的格點間距與影響 範圍（ range）、已知點的幾何分佈以及區域的大小有關。已知點為對稱 分佈且區域面積尺度相對於影響範圍較大時，採用格點間距等於影響範圍 即可以得到最佳井位；若為不對稱分佈則可能需要採用比影響範圍更小的 格點間距。在實例演算中，選擇雲林地區為研究場址，分別執行當各可能 設井位置有相同權重或因其所在區域而有不同權重之兩個範例，獲致合理 的分析結果。 This research develop a new algorithm, Modified Variance Reduction Analysis (MVRA), to solve a problem of groundwater monitoring network planning. The algorithm can obtain the optimal well location and well numbers for a planning area with uncertain geophysical structure. This method is the extention of Variance Reduction Analysis and can consider different weightings associated with distinct parts of the study area. The weightings, which specified subjectively by the user, may depends on the consideration of land use and the influence of neighborhood region, and it can affect the selection of well locations. The optimal well locations are determined by comparing the weighted total variance reduction (the maximum information gain). The well number is determined by the net expected benefits which is the difference of the economic gain to the monitoring cost. A new well is not suitable when the net expected benefits become negative. The model is programmed by the FORTRAN language. The relation between the grid space for the potential location of monitoring wells and the resulting monitoring network have been studied. According to the analysis, the best grid space is determined by the range of semi-variogram, geometric distribution of existing monitoring wells and the area of study region. Under some minor assumptions, when the existing wells have symmetric distribution and the area of study is much larger than the range,the optimal monitoring netework can be obtained with the grid space equals to range. However, if the existing wells is non-symmetric, the grid space must be smaller than the range. There two application examples. One have uniform weighting and the other have non-uniform weighting for all the potential location of monitoring wells. The applications of this model to the Yun-Lin area demonstrate a resonable result.