Title

利用鍵結函數與最大熵定理於颱風降雨推估-以高屏溪流域為例

Translated Titles

Application of Copula and Maximum Entropy Method in Typhoon Rainfall Estimation in Kao-Ping River Basin

DOI

10.6342/NTU201602671

Authors

吳培瑞

Key Words

颱風降雨分類 ; 多元尺度分析 ; 最大熵機率密度函數 ; 高斯鍵結函數 ; 聯合機率密度函數 ; 貝式最大熵法 ; 颱風降雨推估 ; typhoon classification ; multidimensional scaling (MDS) ; maximum entropy probability density function ; Gaussian copula ; joint probability density function ; Bayesian maximum entropy (BME)

PublicationName

臺灣大學生物環境系統工程學研究所學位論文

Volume or Term/Year and Month of Publication

2016年

Academic Degree Category

碩士

Advisor

余化龍

Content Language

繁體中文

Chinese Abstract

颱風短時間內大量降雨時常造成巨大的災害,造成許多生命財產的損失,由於颱風降雨於集水區之時空分布不均,所以掌握降雨型態是非常重要的,因此分析颱風暴雨之時間空間關係為目前颱風降雨主要課題,每一場颱風的變異性相當高,但若能從颱風的時空分布尋找某些特徵,再從這些特徵建構出關連性,再由給定已知測站特定降雨量,以推估未設測站點可能降雨量,在未來決定水利設施尺寸或災害風險管理將會有些助益。 本研究主要分成三個部分,首先為颱風降雨分類,利用多維尺度分析法將高維度之七十六場發生於高屏溪流域之歷史颱風降雨事件投射至二維平面上,使觀察者易了解颱風之間的相對距離關係,再透過K-means分類法將颱風事件分為六群,利用颱風之資料透過最大熵機率密度函數法,由一到四階動差為限制條件以建立機率密度函數,可得到不同時間空間各測站之邊際分布,再將集水區內建立網格以推估未設測站,將網格的值內插取得一到四階動差,並透過高斯鍵結函數將同一時刻邊際函數鍵結以形成颱風時空間聯合機率密度函數。 建立聯合機率密度函數後,利用貝氏最大熵法進行颱風降雨推估,由聯合分布作為一般性知識,進行三個類別的颱風事件降雨推估,結果顯示第一、三、六群颱風的降雨型態,為該集水區主要降雨之時空分布型態,且第三類颱風事件之瑞伯颱風推估,該場事件之推估與實際降雨時空分布量值較為接近。

Topic Category 生物資源暨農學院 > 生物環境系統工程學研究所
生物農學 > 生物科學
Reference
  1. [3] Abramov, Rafail V. "An improved algorithm for the multidimensional moment-constrained maximum entropy problem." Journal of Computational Physics226.1 (2007): 621-644.
    連結:
  2. [4] Bárdossy, András. "Copula‐based geostatistical models for groundwater quality parameters." Water Resources Research 42.11 (2006).
    連結:
  3. [5] Bárdossy, András, and Jing Li. "Geostatistical interpolation using copulas."Water Resources Research 44.7 (2008).
    連結:
  4. [6] Bogaert, Patrick. "Spatial prediction of categorical variables: the Bayesian maximum entropy approach." Stochastic Environmental Research and Risk Assessment 16.6 (2002): 425-448.
    連結:
  5. [7] Brechmann, Eike Christain, and Claudia Czado. "Risk management with high-dimensional vine copulas: An analysis of the Euro Stoxx 50." Statistics & Risk Modeling 30.4 (2013): 307-342.
    連結:
  6. [8] Cheung, K. K. W., L-R. Huang, and C-S. Lee. "Characteristics of rainfall during tropical cyclone periods in Taiwan." Natural Hazards and Earth System Sciences 8.6 (2008): 1463-1474.
    連結:
  7. [9] Christakos, George. "A Bayesian/maximum-entropy view to the spatial estimation problem." Mathematical Geology 22.7 (1990): 763-777.
    連結:
  8. [10] De Michele, C., et al. "A multivariate model of sea storms using copulas."Coastal Engineering 54.10 (2007): 734-751.
    連結:
  9. [12] Dowson, D., and A. Wragg. "Maximum-entropy distributions having prescribed first and second moments (corresp.)." IEEE Transactions on Information Theory19.5 (1973): 689-693.
    連結:
  10. [13] Hao, Z., and V. P. Singh. "Single‐site monthly streamflow simulation using entropy theory." Water Resources Research 47.9 (2011).
    連結:
  11. [14] Kanevski, Mikhail, ed. Advanced mapping of environmental data. John Wiley & Sons, 2013.
    連結:
  12. [15] Kolovos, Alexander, et al. "Computational Bayesian maximum entropy solution of a stochastic advection‐reaction equation in the light of site‐specific information." Water resources research 38.12 (2002).
    連結:
  13. [16] Lin, Yuan-Chien, et al. "A space-time typhoon trajectories analysis in the vicinity of Taiwan." Stochastic Environmental Research and Risk Assessment 29.7 (2015): 1857-1866.
    連結:
  14. [17] Nelsen, Roger B. An introduction to copulas. Springer Science & Business Media, 2007.
    連結:
  15. [18] Renard, Benjamin, and Michel Lang. "Use of a Gaussian copula for multivariate extreme value analysis: some case studies in hydrology." Advances in Water Resources 30.4 (2007): 897-912.
    連結:
  16. [19] Turek, I. "A maximum-entropy approach to the density of states within the recursion method." Journal of Physics C: Solid State Physics 21.17 (1988): 3251.
    連結:
  17. [20] Wu, Zhijun, et al. "A fast Newton algorithm for entropy maximization in phase determination." SIAM review 43.4 (2001): 623-642.
    連結:
  18. [21] Zhang, L., and V. P. Singh. "Bivariate flood frequency analysis using the copula method." Journal of Hydrologic Engineering 11.2 (2006): 150-164.
    連結:
  19. [22] Zhang, L., and Vijay P. Singh. "Gumbel–Hougaard copula for trivariate rainfall frequency analysis." Journal of Hydrologic Engineering 12.4 (2007): 409-419.
    連結:
  20. [23] Zhang, Qiang, et al. "Copula‐based spatio‐temporal patterns of precipitation extremes in China." International Journal of Climatology 33.5 (2013): 1140-1152.
    連結:
  21. [24] Zhao, Lingling, et al. "Spatial pattern characterization and multivariate hydrological frequency analysis of extreme precipitation in the Pearl River Basin, China." Water resources management 26.12 (2012): 3619-3637.
    連結:
  22. [1] 朱宏杰、詹麗梅(2011). “侵台/近台颱風路徑分群及空間分析” Typhoon tracks clustering and spatial analysis near Taiwan
  23. [2] 吳瑞賢, et al. (2004). 歷年颱風降雨與災害特性分析之研究. 第八屆海峽兩 岸水利科技交流研討會: 339-410
  24. [11] Dong, J., T. Ochsner, and M. H. Cosh. "Bayesian Maximum Entropy Approach to Mapping Soil Moisture at the Field Scale." AGU Fall Meeting Abstracts. Vol. 1. 2012.