自組織映射圖於水文系統之研究

Abstract

自組織映射圖（self-organizing map, SOM）對於資料分析（data analysis）而言是一個有用的工具。大量的應用實例與前人的研究已經肯定自組織映射圖用於分析高維度、複雜的資料並由這些資料中萃取出有用資訊的能力。本論文之目的為建構以自組織映射圖網路為基礎的新方法來解決水文問題。在提出的方法中，自組織映射圖不僅可作為掘取並視覺化展示水文資料中有用特性的工具，亦可作為水文系統（hydrosystem）中分類與非線性回歸問題的資料前處理工具。本論文的內容可依據將提出的方法用於水文系統領域中的兩個問題而分為兩個部分，分述如下： 於論文的第一個部份，本研究嘗試以自組織映射圖網路為基礎發展一區域化（regionalization）推估方法，可用於推估未設測站處之水文特性（此處之水文特性係為設計雨型）。此推估方法包含了兩個部分：以SOM為基礎之群集分析方法（SOM-based clustering method）與未設站點指配方法（assigning method）。首先，使用SOM群集分析方法對各測站的設計雨型資料進行聚類分析。使用SOM群集分析方法可以建立各個測站之設計雨型資料間相互的拓樸（topological）關係，並可以幫助使用者客觀且可視化地決定資料之群集數目。接著，依據已分析之測站群集分布情形與欲推估之未設測站點的空間位置，透過分配方法可將該未設測站點指派至合適的群集中。當決定了該欲推估點合適的群集後，此群集中所有測站之設計雨型的平均值即令為此未設測站點之推估設計雨型。將此推估方法實際應用於北臺灣推估未設測站處之設計雨型，結果顯示本研究提出的推估方法可以提供合理的推估結果。而採用SOM為基礎之群集分析方法結合分配方法所得之推估結果會比採用慣用群集分析方法結合分配方法所得之推估結果有較佳的表現。 至於論文的第二個部份，本研究嘗試提出一複合式神經網路模式（hybrid neural network model），用來進行颱風時期之水文量預報工作（此處之水文量係為降雨深度）。此複合式神經網路結合了兩種不同類型的類神經網路，分別為自組織映射圖網路與多層感知機網路（multilayer perceptron network, MLPN）。在此複合式神經網路中，SOM為第一個部分，係為一個資料分析工具，可進行資料的群集分析（cluster analysis）與識別分析（discrimination analysis）工作。而MLPN則為此複合式神經網路的第二個部分，可進行輸入與輸出資料間的多變量非線性迴歸工作。藉由SOM資料分析技術，可找出輸入資料間的相互關係，並且可將具有相似特性的資料歸群於同一類，而將不同特性的資料分開。以SOM為基礎所發展的資料分析功能可提供更多的訊息，更進一步將有助瞭解颱風降雨的水文過程。接著，對於每個類別的資料再分別以不同的MLPN來建構與描述不同群集資料間不同的特性。亦即針對每一個不同的群集均架構一獨特的MLPN，如此將有助於後續的多變量非線性迴歸工作。將此模式實際應用於淡水河流域進行颱風降雨量預報之結果顯示，此方法相對於使用傳統單一MLPN所建置之多變量非線性迴歸模式有較佳的預報結果。

Self-organizing maps (SOM) are useful tools for unsupervised data analysis. Previous researches have shown the potential of the SOM in revealing information of high-dimensional and complex data. In this dissertation, new approaches configured with the SOM is proposed. In the proposed approaches, the SOM is used as a technique for extracting and visualizing salient features in hydrologic data and as a pre-processing tool for solving classification and nonlinear regression problems in hydrosystem. Two studies are conducted herein to demonstrate the superiority of the proposed approaches. In the first study, a regionalization approach based on the self-organizing map (SOM) is proposed to estimate design hyetographs at ungauged rainfall stations. The proposed approach contains two parts: a SOM-based clustering method and an assigning method. Firstly, the SOM-based clustering method is developed to group the design hyetographs at gauged sites. Using the SOM-based clustering method, the relative topological relationships of the design hyetographs at the gauged sites can be then established, and the number of clusters can be objectively decided by visual inspection. Furthermore, the assigning method is developed to assign an ungauged site to a specific cluster according to both the spatial information and the clustering results of gauged sites. After the ungauged site is assigned to the appropriate cluster, this cluster’s average design hyetograph is adopted as the estimated design hyetograph for the ungauged site. The proposed approach is applied to estimate the design hyetographs of ungauged sites in northern Taiwan. The results show that the approach performs better than methods based on conventional clustering techniques (namely the K-means and Ward’s methods). In the second study, an approach based on the self-organizing map (SOM) is proposed to construct a hybrid neural network model for short-term typhoon rainfall forecasting. Two different types of artificial neural networks, the self-organizing map (SOM) and the multilayer perceptron network (MLPN), are combined to develop the proposed model. The SOM is the first component in the proposed model and is used as the data analysis technique which can perform not only cluster analysis but also discrimination analysis. The MLPN is the second component is employed as the nonlinear regression technique to construct the relationships between the input and output (i.e. rainfall depth) data. Through the SOM-based data analysis technique, input data can be divided into distinct clusters and the relationships among data are then discovered. More insight into the typhoon-rainfall process can be revealed by the data analysis technique. For each cluster, a specific MLPN is then constructed. The data with different properties are separated into different clusters, which helps the multivariate nonlinear regression of each cluster. The proposed model is applied to the Tanshui River Basin to forecast the typhoon rainfall. The results show that the proposed model can forecast more precisely than the model which is developed by the conventional neural network approach and is recommended as an alternative to the conventional model for typhoon-rainfall forecasting.