Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/34977
標題: 結合頻率分析與地理統計方法推估降雨空間分佈之研究-以雪霸國家公園 為例
A Study of Estimation Rainfall Spatial Analysis Distribution by Combing Frequency and Geostatistics Approach - Sueh-Pa National Park as an Example
作者: Huang, China-Ching
黃家慶
關鍵字: Frequency;地理統計;Geostatistics;頻率分析
出版社: 水土保持學系所
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摘要: 
因地球暖化之影響,氣候益趨異常化且水文事件極端化,雪霸國家公園因常遭豪雨侵襲造成道路崩塌,於水保與水利工程設計時,由於雨量站不足且分佈不均,造成無法引可靠降雨資料之窘境,並常造成極嚴重之災害。為尋求園區內降雨空間分佈適宜之方法,本研究以雪霸國家公園為範圍,採用雲形曲線法(Spline)、距離反比權重法(IDW)、克利金法(Kriging)推估降雨之空間分佈,並比較三種方法之優劣,找出適用於本區之地理統計方法,並以此方法分析本區之最大降雨-深度-面積延時曲線,當園區需設計水利工程時,此曲線可分析水利工程結構物之合理最大水深以供參考。
本研究將降雨分成長時之年降雨及短時之日暴雨兩種,分別討論之;(一)年降雨方面,蒐集研究區2000年之年雨量,以上述三法推估年降雨空間分佈,並將推估之結果以地理資訊系統與傳統之徐昇氏多邊形法計算平均年雨量,以比較其結果。(二)暴雨方面,蒐集研究區24、48、72降雨延時之最大累積雨量,且將此資料以時下最常採用之甘保氏極端值第一類分佈法與對數皮爾遜第三類分佈法分析5、10、20、50、100頻率年各站之暴雨量,並將此暴雨量做為屬性值,以上述三法推估暴雨空間分佈。(三)最後以RMS(均方根)分析年降雨與暴雨空間分佈之結果,找出最適合用於推估降雨空間分佈之方法。(四)以上述方法分析園區之最大降雨-深度-面積延時曲線。
本研究之結論有五:(1)年降雨空間分佈以距離反比權重法與克利金法較佳。但三法分析之平均年雨量差異不大,不過都比徐昇式多邊形法之結果準確。(2)暴雨空間分佈以克利金法較佳,其平均相對誤差僅7%,另兩法約14%。(3)距離反比權重法雖在年降雨空間分佈中比雲形曲線法好,但暴雨空間分佈之結果為最差,符合Gotway 等人(1996年)之理論,惟距離反比權重法穩定性差,且易受因子之影響。 (4)使用RMS法分析後以克利金法之結果最佳。(5)以頻率分析方法結合克利金法可推求研究區之DAD曲線,此DAD曲線可簡易計算出水利工程結構物之最大將雨水深。
建議有四:(1)由上述之結論,本研究建議未來需分析降雨空間分佈時應多蒐集屬性值(樣本點),且應採用克利金法推估之。(2)以克利金法分析暴雨時,會使雨量估計值之範圍變廣,故暴雨頻率分析應採用對數皮爾遜第三類分佈法。(3)用本研究提供之方法,可簡易求得DAD曲線,未來有此等需求時,方能節省許多時間。(4) 園區內需分析排水溝等水利工程結構物之排水量時,可參考本研究分析之DAD曲線與Hortan公式分析之結果,應可簡易計算出合理之最大降雨深度。

In these recent years, because of global warming influence, the climate became more anomalous and hydrology events became more extreme, it caused rainfall distribution in Taiwan area to be more unbalanced, and brought about an extremely severe disaster. In search of the most suitable ways for rainfall spatial distribution in Shei-Pa National Park, this research will take Shei-Pa National Park as the boundary, and use Spline , IDW(Inverse Distance Weighted), Kriging method to estimate the distribution of rainfall space, also compare the merits and demerits of these three methods, and find out the most suitable analysis method that used in this area and Hydrological observation station where is located at severe shortage area.

This study will divide the rainfall into long time annual rainfall and short time daily cloudburst, and will be discussed separately, (1) for annual rainfall side, collect in the study area of annual rainfall in year 2000, and estimate its annual rainfall space distribution by using those three methods above, and also use geographical information system and traditional Thiessen Polygons method to calculate the average of annual rainfall volume, for comparing its results. (2) For cloudburst side, collect in the study area of the highest accumulated rainfall volume for 24, 48, 72 delayed rainfall volume, and also use the most extreme value of Gumbel type I distribution method and Log-Pearson Type III distribution method to analyze among 5, 10, 20, 50, 100 rainfall frequency for each year, and also take this rainfall volume as property value, and use those three methods above to estimate the distribution of cloudburst space. (3) Finally, using RMS to analyze annual rainfall and cloudburst space distribution result, and also find out the most suitable method that used in the distribution of rainfall space, and analyze DAD(Depth Area Duration) of this area and also K, n value of Hortan formula.

The conclusions of this study are :
(1). IDW(Inverse Distance Weighted) and Kriging method are better used in analyzing of annual rainfall space distribution, but the average of annual rainfall volume that analyzed by three methods are almost same, but it is more accurate than the results of analysis by Thiessen Polygons method.
(2). Kriging method is better used in analyzing of cloudburst space distribution, its average relative error is only 7%, while by using those two other methods it will be 14%.
(3). Although IDW(Inverse Distance Weighted) method is better than Spline method in annual rainfall space distribution, but the results of cloudburst space distribution are the worst, conform to Gotway and other people theory, only the stability of IDW(Inverse Distance Weighted) method is bad, and can be easily influenced by the factors.
(4). The annual rainfall space distribution uses 11 sample size, while cloudburst space distribution used 14 sample size, the both sample sizes are different, and cloudburst space distribution relative error is the lowest(only 10%), we can know that if sample sizes are more, the results will be more accurate.
(5). Kriging method result is the best after using RMS analysis method.

There are two suggestions :
(1). The average relative error is only 13.3% by using Kriging analysis method, while by using RMS analysis method, its residual is 76. Therefore, this study suggests using Kriging analysis method in annual and daily rainfall space distribution analysis. (2). When cloudburst is analyzed by using Kriging method, it can cause the boundary of estimate will be wider, thus cloudburst frequency analysis should use Log-Pearson Type III distribution method.
URI: http://hdl.handle.net/11455/34977
其他識別: U0005-2807201018594100
Appears in Collections:水土保持學系

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