降雨量趨勢偵測與關聯耦合應用於水文頻率分析

氣候變遷對台灣造成多方面的衝擊，包括潛在降雨特性的改變導致更頻繁且嚴重的洪水或乾旱衝擊。Pettitt 檢定和 Mann-Kendall (MK) 檢定分別用以評估變遷點以及趨勢成分的量級。因此，Pettitt 檢定被視為變遷偵測的方法，而 MK 檢定被視為趨勢偵測的方法。然而，如果忽略針對時間序列相關性的處理，會導致 MK 檢定做出錯誤的結論。本文考慮強加線性趨勢於平穩一階自我迴歸模型的時間序列，提出可以控制型一誤差並且提高檢定力的修正趨勢移除—前置白化方法進行 MK 檢定。研究是否潛在氣候變遷於設計延時1、2、3、6、12、24與48小時的年最大降雨量序列以及鋒面雨、對流雨、颱風與梅雨事件所構成的事件最大降雨量序列。顯著趨勢經常存在於年最大降雨量序列，但極少存在於事件最大降雨量序列。根據超過百年紀錄的資料，於1947年以前，台中、台南、恆春、台東與花蓮各站設計延時1、2、3小時的年最大降雨量序列相同，揭露台灣中央氣象局可能曾更新雨量計設備。在1960至2020年間，台灣北部和南部在不同的設計延時的年最大降雨量序列顯示顯著遞增的趨勢。對流雨事件最大降雨量序列顯示顯著遞增的趨勢，且1940前後為變遷點。此外本文介紹基於關聯耦合的水文頻率分析，聚焦在 Kendall’s tau 和常態分數的相關性 (correlation of normal scores) 兩種和諧性測度 (concordance measure)。為了在相同的基準下比較候選關聯耦合族的相依結構，Kendall’s tau 在隨機抽樣的過程是固定的。透過模擬驗證和諧性測度確實反應相依結構的特性。應用推論邊緣函數法 (inference functions for margins method) 解聯合機率密度函數的參數及應用赤池訊息量準則 (AIC) 和貝葉斯信息量準則 (BIC) 進行模型挑選。針對颱風事件進行基於關聯耦合的水文頻率分析，颱洪災害事件可由最配適的存活關聯耦合的超越機率曲線求解，並利用設計生命週期的概念解釋颱洪災害事件。最終，發現台灣各區域具備相異的颱風事件特性。

關鍵字

變遷偵測；趨勢偵測；關聯耦合；設計生命水平；水文頻率分析

並列摘要

Climate change has negatively affected Taiwan in numerous ways, including altered rainfall characteristics that lead to devastating floods or more frequent and severe droughts. The Pettitt test and Mann–Kendall (MK) test are used to assess the change point (i.e., where a significant trend appears in data) and the magnitude of the trend component, respectively. Thus, the Pettitt test is used to detect changes and the MK test a trend detection method. However, the MK test may present incorrect results if serial correlation in a time series is ignored. For a stationary autoregression [AR(1)] model with a superimposed linear trend, we propose a modified trend-free prewhitening approach for the MK test to reduce type I error and achieve higher power. Next, we investigated whether climate change effects exist by considering the annual maximum series (AMS) of rainfalls of 1-, 2-, 3-, 6-, 12-, 24-, and 48-hour durations and the event maximum series (EMS) of four rainfall types: frontal rainfall, convective storm, typhoon, and meiyu (East Asian rains). Significant trends were frequently observed in AMS but not in EMS. Data covering over a century were analyzed, and the AMS of rainfalls of 1-, 2-, or 3-hour durations were the same in Taichung, Tainan, Hengchun, Taitung, and Hualien before 1947. This result was explained by changes in the rain gauge systems of Taiwan’s Central Weather Bureau around that year. From 1960-2020, northern and southern Taiwan both had significant increasing trends for the AMS of rainfalls of different durations. The EMS of rainfalls of convective storms indicates a significant increasing trend with change points around 1940. In addition, we conducted a copula-based hydrological frequency analysis in this paper. Kendall’s tau and correlation of normal scores are two types of concordance measures analyzed. For random sampling, Kendall’s tau was fixed to compare the dependence structure of all candidate copula families on the same basis. Through the use of simulations, the concordance measures were verified as reflecting the properties of the dependence structure. The inference function for margins method was applied to solve for the parameters of the joint density functions, and the Akaike and Bayes information criteria were used for model selection. For the copula-based hydrological frequency analysis of typhoon events, hazardous typhoon events were observed at the exceedance probability curve of the best-fit survival copula. We interpreted the hazardous typhoon events based on the concept of design life period. Finally, we discovered that the characteristics of typhoon events differed between regions in Taiwan.

並列關鍵字

Change detection ； Trend detection ； Copula ； Design life level ； Hydrological frequency analysis

參考文獻

Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In B. N. Petrov F. Csaki (Eds.), Proceedings of the 2nd international symposium on information theory (pp. 267–281). Akadémiai Kiadó.

Google Scholar

Blomqvist, N. (1950). On a measure of dependence between two random variables. The Annals of Mathematical Statistics, 21(4), 539–600. https://doi.org/10.1214/aoms/1177729754

Google Scholar

Chang, J., Li, Y., Wang, Y., Yuan, M. (2016). Copula-based drought risk assessment combined with an integrated index in the Wei River Basin, China. Journal of Hydrology, 540, 824–834. https://doi.org/10.1016/j.jhydrol.2016.06.064

Google Scholar

Cherubini, U., Gobbi, F., Mulinacci, S. (2016). Convolution copula econometrics (1st ed.). Springer. https://doi.org/10.1007/978-3-319-48015-2

Google Scholar

Cooley, D. (2013). Return periods and return levels under climate change. In A. AghaKouchak, D. Easterling, K. Hsu, S. Schubert, S. Sorooshian (Eds.), Extremes in a changing climate: Detection, analysis and uncertainty (pp. 97–114). Springer. https://doi.org/10.1007/978-94-007-4479-0_4

Google Scholar

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降雨量趨勢偵測與關聯耦合應用於水文頻率分析

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