本文旨在回顧並發展三種機率分佈模式，來描述阿里山的日雨型態，並說明這些模式的地形學隱義。多重線性模式是由一組乘冪定律所構成，其分段邊界是由一組特定的再現週期點所定義，精準描述了阿里山日雨規模和再現週期之間的關係。該模式所率定的再現週期點，可作為檢視氣候實況和氣候變遷的直觀參考。本文提出的非線性混成機率分佈模式，是由指數模式和乘冪定律混成，旨在取代不嚴格遵守機率密度函數定義的乘冪定律，以及不適用的指數模式；後者不適於描述季節性和地形影響強烈的臺灣日雨型態。此一嚴格遵守機率密度函數定義的模式，可以為描述日雨型態的參數建立一個相空間，從而讀者可以快速判釋日雨型態變化的整體動態，並且因其簡潔清晰的數學形式，適用在建立臺灣的土壤侵蝕指標。本文最後所提出的模式，基本上是把Kirkby早期用以描述日雨規模頻率的簡單指數模式，轉用為描述晴雨旋律。這一個轉用直接與Kirkby十餘年前所提的河段長度規模頻率有關，並且在迴旋的概念架構下，直接把河網機率分佈和降雨機率分佈聯繫起來，決定排水排砂的機率分佈型態。本文以石門水庫上游串聯的測站資料和DEM資料所粹取的參數，來說明前述概念架構的效用。本文以中央氣象局阿里山氣象站1937年2008年的日雨資料，來證實這三個模式的功效，進而討論它們在地形學上的隱義。
Three probability distribution models are proposed to describe the daily rainfall pattern in Alishan, Taiwan, namely the multilinear model, the non-linear hybrid probability distribution model, the exponential model. Their geomorphic implications are also addressed. The multi-linear model is consisted of power-laws separated by a set of daily rainfall magnitudes of certain return periods, which can be used as key factors to demonstrate the effect of climatic changes. The non-linear hybrid probability distribution model is proposed to substitute the power law and the exponential model, which is either mathematically incorrect or inappropriate when describing the daily rainfall pattern with strong seasonal and orographic effects. Through the non-linear hybrid model, a phase-space may be constructed. Its simplicity also offers the great potential of mathematically analysis on soil erosion in Taiwan. The last model proposed is an exponential model for analyzing weather spells, and it is explicitly linked with the frequency-magnitude of channel length. Through the concept of convolution and the probability distribution analysis, we may use parameters abstracted from the river channel network and the daily rainfall pattern to determine the daily water and sediment output at the drainage outlet. A case from Shimen drainage basin is demonstrated in the end.
