應用短時距傅立葉轉換於地下水位資料補遺

Abstract

地下水為台灣重要的水資源，因此，自民國80年起政府陸續在全台地區建立地下水觀測站網，目前已累積大量水文地質相關資料，而其中地下水位資料更是其中最重要的資料，惟觀測資料常因儀器本身及管理上的不確定性而難免有所缺漏。有鑒於此，本研究乃整合線性回歸與短時距傅立葉轉換發展一項新的水位資料補遺方法，此新的補遺方法，能保留被補遺地下水位資料在時域及頻率域上的特徵。 此新的補遺方法主要有三個步驟；首先乃是應用線性回規方是以相關係數高之鄰近井日水位，內插補遺日水位時序資料以掌握主要的時空變化趨勢。接著在頻率域特徵方面，乃先將待補遺井資料進行短時距傅立葉轉換至時頻域，缺漏部分之時頻譜再以先前內插日水位之低頻部分時頻譜，及待補遺資料本身之高頻部分時頻譜補足，而得完整之時頻譜，接著再以傅立葉逆轉換，將補遺後之完整時頻譜轉換到時間域，完成時水位補遺。此補遺方法經檢驗及實際應用於嘉南平原北段地下水觀測資料之補遺，成果顯示此方法可保持各補遺水位資料的時間域與頻率域上的特徵，因此可應用於其他水文時序資料之補遺，方便後續資料探勘相關分析之進行。

Groundwater plays an important role on regional water supply, and observation wells are critical for groundwater related analysis and management. In Taiwan, a national wise groundwater observation network was completed in 2008 and a huge amount of groundwater levels data were collected. However, because of the uncertainty of data collecting instruments and wells maintenance, data miss is unavoidable. To addendum the missing groundwater levels data, this study developed a novel data addendum procedure based on the Linear Regression (LR) and Short-Time Fourier Transform (STFT). The proposed novel procedure can preserve the data features in time domain and frequency domain. The proposed method consists of three steps. The first step is to estimate the missing daily data by using a LR model based on the neighboring well data that has the highest correlation with the well data to be addendum. The process was expected to preserve the low frequency variation of the groundwater table below 1 cycle/week. The second step is to transform the time series data to be addendum into frequency domain via STFT. The resulting spectrum will have missing segment due to the missing data. The third step is to completed the spectrum and obtains the complete groundwater level data. To addendum the spectrum, the missing spectral segment was recovered by jointing the low frequency portion of the interpolated daily data and the high frequency part of the original data to be addendum. The complete groundwater level data was obtained by using Inversed STFT to the addendum spectrum. The proposed methodology was applied to addendum the groundwater levels data in northern part of Chianan Plain and the result shows that the addendum data can effectively preserve the data features in both time domain and frequency domain. The methodology can be applied to addendum other hydrological time series data to allow the application of data driven analysis.