台灣地區不同延時低流量最佳分佈之探討

The Optimal Distribution Functions of Various Duration Low Flows in Taiwan

蕭政宗(Jenq-Tzong Shaiu) ； 張雅閔(Ya-Min Chang)

《農業工程學報》 54卷2期 (2008/06) Pp. 35-51

https://doi.org/10.29974/JTAE.200806.0004

摘要

本文研究目的爲探討台灣地區各河川不同延時低流量之特性，包括不同延時低流量之機率分佈、特定延時最佳機率分佈及其在區域變化的趨勢等。本文首先蒐集台灣地區北部、中部、南部及東部區域紀錄期間超過20年且連績不間斷的日流量資料共58站，並以年最小l日、2日、3日、7日、30日、60日、90日及180日流量爲不同延時之低流量，以K-S及卡方(chi-square)適合度檢定法檢定適合不開延時低流搬之機率分佈，再以最小均方根誤差爲標準選取各站不鬨延時低流澱之量佳分佈，進而探討最佳分佈在不同延時及區域的變化特性。本文以五種三參數機率分佈來代表河川不同延時之低流量，分別爲通用羅吉斯分佈(generalized logistic distribution, GLO)、通用極端續分佈(generalized extreme-value distribution, GEV)、三參數對數常態分佈(thee-parameter lognormal distribution, LN3)、皮爾遜第Ⅲ型分佈(Pearson type Ⅲ distribution PE3)及通用帕雷托分佈(generalized Pareto distribution, GPA)，經以K-S及卡方適合度檢定此五種分佈可適用於絕大部分台灣地贏不同延時之低流量，其中GLO、GEV及LN3之通過率高達95%以上，最適於代表台灣地區不同延時之低流量。至於台灣地區各流量站不同延時低流量佳機率分佈則以GLO所佔比例較高，約有36%~43%，其次爲PE3及GEV，約有10%~29%。低流量最佳機率分佈區域間之趨勢並不明顯，在北、中及南區以GLO爲最佳機率分佈所佔比例較高，在東區則較爲分歧，並左無一明顯高比例之機率分佈存在。

關鍵字

低流量 ； 機率分佈函數 ； 線性動差

並列摘要

This study aims to explore the low-flow characteristics in Taiwan which include distribution functions of low flow the best data-fit distribution functions and the corresponding spatial patterns for various durations. A total of 58 daily streamflow records with record length exceeding 20 years we collected from Northern, Central, Southern, and Eastern regions in Taiwan The annual minimum 1-, 2-, 3-, 7-, 30-, 60-, 90-, and 180- day flows are considered as the annual low flows for various durations. The K-S and chi-square goodness-of-fit test are employed to detect the distribution functions unsuitable to represent low flows. The minimum root mean square error is then used as a criterion to determine the optimal distribution funetions for various duration low flows. In this study, five three-parameter distribution functions, including generalized logistic distribution (GLO), generalized extreme-value distribution (GEV) three-parameter lognonnal distribution (LN3), Pearson type Ⅲ distribution (PE3), and generalized Pareto distribution (GPA). are adopted to fit low flows. Generally, these five distributions are suitable to represent the low flows in Taiwan regardless of durations. Over 95% of low flows for various durations in Taiwan can by the distributions of GLO, GEV, and LN3. However, no single distribution. function dominates the optimal distributions (Unction. Approximate 36~43% of streamflow gauge stations of low flows are best fitted by the OLO. The PF3 and GEV are the optimal distributions to represent low flows tot another 10-29% of streamflow gauge stations. The spatial pattern for the optimal low-flow distribution functions is not significant. In Northern, Central, and Southern regions, the GLO has the highest percentage. However, no single distribution dominates the optimal low flow distribution in Eastern region.

並列關鍵字

Low flow ； Probability distribution functions ； L-moment