在時間序列的分析方法中，廣泛使用的方法係利用傅利葉分析，傅利葉分析主要是從時間域轉換成頻率域，但是在轉換成頻率域後會失去時間域的資訊，而且傅利葉分析有條件限制，分析的資料必須為平穩性或是具週期性才可使用傅利葉分析，但是受到氣候變遷影響，長期的資料大部分都不符合上述的條件，因此傅利葉分析方法並不適用。小波轉換的觀點是由法國學者Morlet首先提出，其除了可分析平穩性資料之外，還可以對於非平穩性與非週期性資料進行分析，並且有能力表現出局部的分析，如資料趨勢、異常的不連續點…等，其亦可以自行調整時間-頻率的大小得到所需的資訊。本研究首先以傅利葉轉換與小波轉換同時進行時間序列分量及其組合之分析，比較其優缺點與適用性。針對中央氣象局台北觀測站與台南觀測站自1897年至2004年之年雨量資料進行迴歸分析與小波分析，比較北部與西南部的長期趨勢與地域之差異性。結果發現降雨日數不分區域皆呈現減少趨勢而降雨強度皆呈現增加趨勢，1951年後之降雨量在北部為遞增，西南部則無明顯改變，台灣整體降水量呈現略微下降趨勢。再將台灣21個氣象局雨量觀測站與屏東雨量觀測站自1982年至2003年之長期月降雨量資料進行雨量分區，並以小波分析法分析其各區雨量站之降雨特性，藉以得到降雨特性之變化。結果發現北部的降雨強度逐漸增加以及西南部週期逐漸加大，週期逐漸加大代表未來處於乾旱的時間可能拉得更長，對於水利設施的設計與水資源管理上是一項嚴重的警訊。此外，台灣地區的降雨型態可能逐漸受到全球暖化的影響，降雨特徵亦受到許多因素的影響，例如：颱風、乾旱年、聖嬰與反聖嬰現象、火山爆發…等其他可能的因素。

　　Fourier analysis is commonly used to analyze time series and it assumes that data are stationary and periodic. However, actually data usually do not satisfy above conditions. Wavelet analysis was developed to analyze non-stationary and aperiodic data by Morlet, and obtaine the detailed information in time domain. Therefore, Wavelet analysis may be a better choice to analyze precipitation time series data than the Fourier analysis. In this study, wavelet transform and Fourier transform were used to analyze three components of time series. The results of the two analyses were compared. The results are helpful to explore the strong points of wavelet transform. Then, wavelet analysis and linear regression analysis are used to analyze long-term precipitation data of Taipei and Tainan stations to investigate the effects of geography . The results show that the precipitation days are decreasing and the intensity of precipitation is increasing in all regions. From 1951, the amount of precipitation was increased in northern Taiwan and decreased in southern Taiwan. SOM neural network is used to characterize the patterns of precipitation of 22 stations. The results show that the long-tern trend and periodic characteristics of Taiwan’s precipitation are function of time and regions. The intensity of precipitation shows to gradually increase in northern Taiwan and the periods of drought gradually enhance in southern Taiwan. Northern Taiwan seems to have more torrential rainfall events while southern Taiwan is facing more long-term droughts. This raises an alarm to water resources policies or hydrological design in the future. In addition, the precipitation types of Taiwan are possible influenced by the global climate change and other direct factors such as Typhoon and volcano eruption.

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