Relationship between watershed topographic factors and the correction coefficients of the GRAPH rainfall-runoff model

網格式合理化法(Grid Rational Algorithm for Predicting Hydrograph；GRAPH)為近年來所發展的降雨－逕流模式，前人廣泛應用於台灣各集水區，因集水區地文、水文特性不一，在模式為清水流與不考慮臨前降雨、滲流及降雨損失之假設下，須以校正係數α、β進行修正。本研究彙整前人相關研究資料，結合地文資訊並以校正係數之平均數(Mα，Mβ)與標準差(Sα，Sβ)探討模式應用區位之特性。 利用7個集水區模擬所得之校正係數與集水區地文因子進行多變量統計，顯示4個主成份軸中12項地文因子解釋變異量為90%，再由特徵向量選取具顯著相關且作為同一主成份內原變數篩選依據之10項因子，將其加入判別分析，又函數結構矩陣中因細長比與圓比值權重小較不具區別能力故予以剔除，最後得8項具顯著區別能力之集水區地文因子，分別為(1)集水區周長(2)河川主流長度(3)集水區長度(4)集流時間(5)集水區面積(6)集水區寬度(7)平均坡度(8)平均初始逕流係數。 經K-Means群集法分群後，(Mα，Mβ，Sα，Sβ)可得六種組合以進行判別分析，由校正係數分布情形可歸納集水區特性如下：(1)水源涵養型集水區，如大南澳集水區；(2)崩塌型集水區，如烏溪、八掌溪與新武呂溪集水區；(3)人為干擾區位，如基隆河集水區；(4)堰塞型集水區，如濁水溪集水區；(5)泥岩型集水區，如二仁溪集水區。整體而言，地文因子用於校正係數分類變異之準確率達90%，顯示篩選出之地文因子與校正係數具高度相關，且以地文因子計算之區別分數可作為分類依據。The GRAPH (Grid Rational Algorithm for Predicting Hydrograph) model has been developed for rainfall-runoff simulation in recent years. Due to different characteristics in watershed topography and hydrology, and the model neglecting the situation of sediment transportation and antecedent precipitation; the simulation results of the model should be adjusted to fit the real world by means of correction coefficients. Coefficient α represents water resources conservation capability and the coefficient β can be regarded as the index of sediment concentration in the runoff. In this study, simulated data are collected from previous studies for discussing the relationship between grouping the variations of (α,β) and the correspondent watershed topographic factors by using multivariate analysis. Correction coefficients and topographic factors derived from seven watersheds were used in the multivariate analysis. The result shows that twelve topographic factors in four principal axes can explain 90% variability; ten factors with significant correction from eigenvector were further selected for discriminant analysis. Factor of elongation ratio and circularity ratio were deleted due to less discrimination in structure matrix ,there are still remain eight topographic factors (perimeter of watershed, length of main stream, length of watershed, time of concentration, area of watershed, width of watershed, average slope and average initial runoff coefficient) showing significant discrimination.Watershed characteristics through the distribution of correction coefficients describes as follows: (1)Watershed with more function of water cultivation such as Da-Nan-Ao;(2)Watershed vulnerable to landslide during storm period, higher landslide potential such as Wu River, Ba-zhang River and Xin-Wu-Liu River;(3)Watershed with artificial disturbance and the improper land use caused river blockage during storm period such as Keelung River;(4)Watershed with landslide-dammed such as Choshui River;(5)Watershed with mudstone such as Erhjin River. Accuracy rate of correction coefficients variation is 90% which classifies by topographic factors, and the result shows that there is highly correlation between each other. Topographic factors can be a basis of classification for calculating discriminative score.摘要 I ABSTRACT II 目錄 IV 表目錄 VI 圖目錄 VIII 壹、前言 1 貳、前人研究 3 一、水文模式及應用 3 （一）經驗型(線性) 4 （二）集塊－概念型(準非線性) 5 （三）分布－物理型(非線性) 5 （四）序率型 6 （五）模式比較 6 二、合理化公式 10 三、地文因子相關研究 12 四、多變量統計 14 參、研究材料及方法 18 一、研究試區概述 18 （一）各集水區概況 19 （二）水文資料 33 二、研究流程 36 三、分析方法 37 （一）集水區自動劃分 37 （二）集水區資訊分析 38 （三）降雨－逕流模式(GRAPH) 42 （四）多變量統計 50 肆、結果與討論 55 一、校正係數 55 二、選取事件與變數 56 （一）篩選暴雨事件 56 （二）選取變數 61 三、統計分析 63 （一）主成份分析 63 （二）群集分析 70 （三）判別分析 71 （四）結果分析 78 伍、結論與建議 84 一、結論 84 二、建議 85 參考文獻 8