臺灣博碩士論文加值系統

摘 要
本論文主要目的在於提出一套應用連續型降雨-逕流模式於未量測集水區的參數率定方法，以解決水資源計畫在規劃前期並無觀測流量記錄可供分析之窘境。論文內容主要分為兩個部份進行研究，第一部份先以已量測集水區為分析對象，探討如何提昇連續型降雨-逕流模式之模擬精度，第二部份則利用已量測集水區之分析結果，發展未量測集水區模式參數率定方法。
在第一部份之研究中，本研究參考歐洲廣泛使用之HBV模式架構，並成功地應用於高屏溪流域。由於降雨-逕流模式需要經由率定來決定模式參數，因此本研究首先探討採用不同目標函數對模式率定結果之影響。文中分別利用均方根誤差(RMSE)、平均絕對百分比誤差(MPE)與本研究所提出之多階段平均絕對百分比誤差(MSMPE)為目標函數進行分析。分析結果顯示：利用RMSE與MPE會分別偏重洪水流量與枯水流量之模擬；而採用MSMPE較能同時滿足洪、枯流量之模擬精度。由於同時針對不同高、低流量階段進行參數率定可視為多目標求解問題，因此本研究進一步結合多目標規劃與模糊集理論的觀點設計一個模糊多目標函數，來因應決策者針對不同高低流量決定可接受精度之需要。文中進一步探討：(1)不同目標函數的率定結果對模式內部水文機制之影響；(2)針對豐、枯水期修正模式參數對改善模擬流量歷線之程度與(3)以模糊控制器為架構發展流量誤差修正方法，該誤差修正方法可對率定時期外的模擬流量歷線提供良好的修正結果。
發展區域連續型降雨-逕流模式之前，有需要對模式參數之敏感度與互動性先進行瞭解。本研究利用熵值評估模式參數間的交互作用，並發現控制土壤含水層的參數間其交互作用甚劇。因此，對於要以特定一組參數值來代表該集水區實屬不易，此結果對於傳統方法所使用之參數區域化將造成相當的阻礙。
在第二部份之研究中，本文主要根據上述的分析結果，並發展一套未量測集水區模式參數率定方法。為擺脫傳統上利用已量測集水區率定的模式參數與集水區特性建立回歸關係以延伸至未量測集水區的方法，本研究先發展區域流量延時曲線，以求取未量測集水區之合成流量延時曲線，然後搭配以流量延時曲線為擬合目的之目標函數，來率定未量測集水區之連續型降雨-逕流模式。經由高屏溪兩個集水區之驗證顯示：本研究發展的未量測集水區模式參數率定方法可以合理率定未量測集水區之模式參數，並藉以模擬集水區出口之歷史流量序列。

ABSTRACT
The theme aims at developing a strategy for calibrating a continuous rainfall-runoff model at ungauged catchments, in which water resource projects may be planned and the flow series can be simulated at the early stage of planning. Two major parts are included in the study. To improve the performance of a continuous rainfall-runoff model at gauged catchments is the first part to be investigated. The second part is to develop a strategy for model calibration at ungauged catchments by utilizing the results of the former.
The HBV hydrological model, broadly used in Europe, was employed in the study and slightly modified for successful application in the Gao-Pen Creek Basin. Since the model parameters should be calibrated with objective functions, the first part of this study detected the effects of model calibration results by using various objective functions, including the root mean square error (RMSE), mean absolute percentage error (MPE), and multi-stage mean absolute percentage error (MSMPE). It concluded that using RMSE and MPE emphasized the high-flow and low-flow simulations, respectively. The MSMPE was found to simultaneously simulate all flow ranges well. Since various flow stages can be considered as various objectives, respectively, the study combined the concepts of the multi-objective programming and the fuzzy set theory to develop a fuzzy multi-objective function. The other subjects were further discussed in the study, which included (1) effects on the internal mechanisms of hydrological models by using various objective functions, (2) modification of model parameters for simultaneously simulating high and low flows, and (3) development of an error correction method on the basis of the fuzzy logic controller, which had a well performance for error correction outside the calibration period.
Before regionalizing the parameters of rainfall-runoff model, the sensitivities and interaction of parameters should be detected for further understanding. The study evaluated the interaction of parameters based on the entropy theory and found that the parameters for controlling soil moisture accounting had extreme interaction one another. It implies that it''s hard to find a representative parameter set for a basin and make the regionalization of parameters difficult.
Based on the above study results, the second part of this study developed a calibration strategy for a continuous rainfall-runoff model at ungauged catchments. This strategy differs to the traditional one, which relates the model parameters and catchment characteristics at gauge catchments for extrapolating the model parameters to ungauged catchments. In the strategy of the study, the regional flow duration curve was first constructed by which synthetic flow duration curves for ungauged catchments were calculated. The objective functions based on fitting synthetic flow duration curves were then used for model calibration at ungauged catchments. Two catchments in the basin of Gao-Ping Creek were used to verify the calibration strategy. It concluded that the strategy could calibrate the model parameters reasonably and the flow series could be simulated well at ungauged catchments.

目 錄
中文摘要…………………………………………………………………..0-1
英文摘要…………………………………………………………………..0-3
謝誌………………………………………………………………………..0-5
目錄………………………………………………………………………..0-6
圖目錄……………………………………………………………………..0-10
表目錄……………………………………………………………………..0-12
第一章 緒論……………………..………………………………………..1-1
1.1研究動機與目的………………………………………………...1-1
1.2文獻回顧………………………………………………………...1-4
1.3本文組織與研究內容…………………………………………...1-10
第二章 研究區域概況……………………………………………………2-1
2.1地理特性………………………………………………………...2-1
2.2地質條件………………………………………………………...2-3
2.3雨量空間分佈特性……………………………………………...2-3
2.4流量時間分佈特性……………………………………………...2-4
2.5水文站概況……………………………………………………...2-4
第三章 連續型降雨-逕流模式與最佳化參數率定方法………………..3-1
3.1 HBV模式架構………………………………………………….3-2
3.1.1土壤含水量估算部份……………………………………..3-3
3.1.2逕流反應部份……………………………………………...3-3
3.1.3連續方程式………………………………………………...3-5
3. 2最佳化參數率定方法…………………………………………...3-6
3.2.1自動全域最佳化技巧……………………………………...3-6
3.2.2 SCE法……………………………………………………..3-6
第四章目標函數對模式率定之影響……………………………………..4-1
4. 1研究區域概況……………………………………………………4-2
4.2目標函數………………………………………………………...4-3
4. 3模式參數率定與殘差分析………………………………………4-5
4.4分析結果與討論………………………………………………...4-6
4.4.1不同目標函數之分析結果………………………………...4-6
4.4.2參數對模式內部水文機制之影響………………………...4-11
4.4.3討論………………………………………………………...4-16
4. 5模糊多目標函數………………………………………………...4-17
4.5.1 隸屬函數………………………………………………….4-17
4.5.2 模糊多目標函數之建立………………………………….4-17
4.5.3 實例分析結果…………………………………………….4-22
4.6 結語……………………………………………………………..4-27
第五章 流量誤差修正方法………………………………………………5-1
5.1豐、枯水期之參數修正………………………………………...5-1
5.1.1分析結果…………………………………………………...5-2
5. 1.2討論………………………………………………………...5-9
5.2以模糊控制器建立流量誤差修正模式………………………...5-9
5.2.1模糊推理與模糊控制器…………………………………...5-10
5.2.2分析步驟…………………………………………………...5-13
5.2.3分析結果…………………………………………………...5-16
5.3結語……………………………………………………………...5-19
第六章 參數敏感度與互動性分析………………………………………6-1
6. 1參數敏感度分析………………………………………………...6-3
6.1.1局域敏感度分析…………………………………………...6-3
6.1.2全域敏感度分析…………………………………………...6-4
6.1.2分析結果…………………………………………………...6-6
6.2參數互動性之評估……………………………………………...6-8
6.2.1 熵理論……………………………………………………..6-8
6.2.2 分析結果…………………………………………………...6-9
6.3 結語……………………………………………………………..6-11
第七章 未量測集水區模式參數率定方法之建立………………………7-1
7.1未量測集水區模式參數率定方法……………………………...7-3
7.2流量延時曲線均一區之劃分……………………………………7-4
7.2.1主成份分析………………………………………………..7-7
7.2.2兩階段聚類分析…………………………………………..7-11
7.2.3模糊聚類分析方法………………………………………..7-15
7.2.4分析流程與結果…………………………………………..7-19
7.3區域流量延時曲線之推演……………………………………...7-26
7.3.1模糊線性回歸分析………………………………………..7-28
7.3.2分析結果與驗證…………………………………………..7-35
7.4結語……………………………………………………………...7-39
第八章 未量測集水區模式參數率定方法之驗證………………………8-1
8.1流量延時曲線貼近準則之定義………………………………...8-1
8.2 流量延時曲線貼近準則之分析結果…………………………..8-2
8.3流量延時曲線模糊貼近準則之定義…………………………...8-7
8.4 流量延時曲線模糊貼近準則之分析結果……………………..8-8
8.5未量測集水區參數率定方法之驗證……………………………8-11
8.6結語……………………………………………………………...8-13
第九章 結論、建議與未來研究課題……………………………………9-1
9.1結論……………………………………………………………...9-1
9.2建議與未來研究課題…………………………………………...9-5
參考文獻…………………………………………………………………..A-1
作者簡歷…………………………………………………………………..B-1

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