• 作者： 王如意
• 作者服務機構： 國立臺灣大學農工系
• 中文摘要： 頻率分析為水文研究一大課題，其為利用統計機率原理以分析水文事件，推求符合某工程壽命特定?歸週期設計水文量之大小，以做為水賽源規割開發之依據。 極端值分佈應用於水文頻率者有二，一為河川之年最大流量，另一為其年最小流量。前為洪水，後為乾涸，兩者皆為水文之極端“ 洪水頻率可應用最大極端值第一類漸近分佈法。將分析之統計樣本，求其平均值分及標準偏差，即可推算其洪水頻率方程式，且其理論最佳適合之洪水頻率直線可繪於極端機率紙上，俾供一般防洪工程設計之參考。 乾涸頻率乃應用最小極端值第三類漸近分佈法，其包括推求一形狀參數、一特徵乾涸量及一極小乾涸量。如=0，吾人可由乾涸流量資料之樣本平均值及標準偏差，求出及，則具二參數之乾涸頻率方程式即可求得矣。如＞0，吾人可假定估算之極小乾涸量宜小於最小觀測乾涸量，則形狀參數可由求知，且及為及之線性函數，即可求出具三參數之乾涸頻率方程式。理論之乾涸頻率，勿論＝0或＞0，皆可繪於極端對數機率紙上呈現一直線或圓滑曲線。一般言之，理論乾涸與實際乾涸頻率可得甚佳密合，適用於水資源規劃之乾洞預測。 本研究中，洪水頻率分析乃選擇具較長年數測站之年最大日流量之秒立米數為樣本；乾涸頻率乃根據上列測站之年最小日流量之秒立米數為分析對象。應用極端值分佈之理論，運用電子計算機之推算，求導本省集水區重要測站之洪水頻率與乾涸頻率方程式且點繪其水文頻率曲線。結果顯示，理論與實際甚為?合。
• 英文摘要： There are two main applications of theory of extreme values to hydrology:dealing with the maximum yearly and the minimum yearly discharges of a river.The former can be regarded as flood; the latter, as drought. Both flood and droughtare two hydrologic extremes. The frequency curve is an indispensable tool for analyzing hydrologic data. Forengineering purpose, the Gumbel's method of extreme values is one of the mostrepresentative methods for frequency analysis. The floods can be analyzed by the first asymptotic distribution of largest values.Equation of flood frequency is obtained by calculating the sample mean andstandard deviation of hydrologic data. A straight line can be plotted and a best-fitof theoretical frequency to actual floods can also be shown on the extremal proba-bility paper. The droughts are analyzed by the third asymptotic distribution of smallestvalues which contains a shape parameter, a location parameter and a minimumdrought . If =0, the two remaining parameters are estimated from the samplemean and the standard deviation. If >0, it is postulated that the estimate should be smaller than the smallest observed drought. An estimate for isobtained from the quotient. The estimation for and become linearfunctions of the mean and the smallest drought .The theoretical distributionof drought can be plotted as a straight line or a smooth curve on the extremallogarithmic probability paper. The theory gives an excellent fit to the observations,so it can safely be used for forecasting. In the present paper, flood frequency analysis is based on choosing annualmaximum daily discharge (cms) of stations with relatively longer period of recordsas sample; drought frequency analysis is based on annual minimum daily discharge(cms) of previously stations chosen as flood frequency studies. Method of Gumbel'sextreme values is applied for frequency analysis, electronic computer is used forsimplifying time-consuming procedures of calculation. Mathematical equations forflood frequency and drought frequency for each station are then derived, andfrequency curves for watersheds in Taiwan are also drawn. In general, the resultsprove quite satisfactory theoretically and practically.
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