自組特徵映射網路結合非線性自回歸模式預測屏東平原地下水位

Self-Organizing Map and Nonlinear Autoregression Networks for Forecasting Groundwater Levels at Pingtung Plain

黃健維(Chien-Wei Huang)

指導教授 ： 張斐章

國立臺灣大學/生物資源暨農學院/生物環境系統工程學研究所/碩士(2016年)

https://doi.org/10.6342/NTU201601833

摘要

本研究以屏東平原作為研究區域，蒐集1999年至2014年雨量、流量、抽水量、地下水位等資料，首先以主成分分析萃取枯水時期地下水資料特性，分析結果發現由兩個主成分可以解釋70%的資料特性，且由主成分的權重分布與主成分分數的分析結果發現東區與西區有不同的特性存在。第二部分探討不同水文因子與地下水之相關性，由分析結果發現以單水文因子分析難以解釋區域性地下水的變動關係，僅能推論雨量為影響地下水變動之重要因子。第三部分透過自組特徵映射網路(SOM)將月地下水資料進行分類並建立水位分布圖，其分類結果和主成分分析結果一致，發現該區域地下水位在2005年前後有明顯差異，且能獲得水位在空間分布上的情形，隨後透過含外變數非線性自迴歸模式(R-NARX)針對各含水層平均水位進行預測，各分區在T+1測試階段的表現上R^2皆能高達0.81以上，T+2測試階段R^2亦能有0.70左右，顯示R-NARX透過自身回饋水位資訊能對平均水位有良好的預測結果。最後將R-NARX模式所預測之平均水位透過SOM水位分布圖進行內、外插修正後，即可得到屏東平原各地下水觀測站水位，再以克利金法推估整體水位空間分布並完成區域地下水預測模式的建置，作為屏東平原水資源調配之參考依據。

關鍵字

主成分分析 ； 自組特徵映射網路 ； 外變數非線性自迴歸模式 ； 區域地下水水位預測模式

並列摘要

In this study, Pingtung Plain was the study area and the investigative data collected during 1999 and 2014 consisted of rainfall, flow, groundwater extraction and groundwater level. First, we extracted groundwater characteristics in dry seasons from historical data by using the principle component analysis (PCA). The results showed that two principal components could explain 70% of data characteristics. Besides, the analytical results on the weight distribution and scores of principal components indicated that there were distinguishable features between the eastern and the western zones of the study area. Second, we investigated the correlations between different hydrological factors and groundwater levels. The results indicated that it was difficult to explain the regional groundwater level variations based on one single hydrological factor and we only could infer rainfall was an important factor affecting groundwater level variations. Third, we used the Self-Organizing Map (SOM) to classify monthly groundwater level data for constructing groundwater level distribution maps. We found that significant differences in groundwater levels occurred around 2005 in the study area, which were consistent with the results of the PCA, and therefore we could obtain the spatial distribution of groundwater levels. Fourth, we used the Nonlinear Autoregressive with Exogenous Inputs (R-NARX) to forecast the average groundwater level in each layer of the aquifer. The results showed that the R^2 value reached as high as 0.81 at T+1 and remained around 0.70 at T+2 in the testing phrases for each zone. It demonstrated that the R-NARX could well forecast the average groundwater levels by using the feedback information of groundwater level. Finally, based on the SOM groundwater level distribution maps we interpolated and extrapolated the forecasted average groundwater levels obtained from the R-NARX to derive the groundwater level of each monitoring well in the study. We then used the Kriging method to estimate the spatial distribution of groundwater levels in the whole study area for completing the construction of the regional groundwater level forecast model, which can provide valuable information for the management of water resources.

並列關鍵字

Principle component analysis (PCA) ； Self-Organizing Map (SOM) ； Nonlinear Autoregressive with Exogenous Inputs (NARX) ； Regional groundwater level forecast model.

參考文獻

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