以群集分析加強 van Genuchen 模式參數推估之研究

The purpose of this study is improving the ability of Continuous PTFs used to predict the parameters of van Genuchten model. This study focused on medium-texture soils. For solving the fuzzy area on a triangular texture figure, K-Means cluster analysis was used to classify samples according to particle size distribution rather than texture. Multiple leaner regression was used to develop models which included all samples and classified samples. The result showed that the classified models could improve the prediction in parameter α, however, they could do so in parameter n. Observation of each model revealed that the parameter n was affected by clay content. This study further compared continuous PTFs which were developed according to region, and the result showed that the models which were developed based on particle size distribution had better prediction. We also proved that classifying samples is necessary before developing a model.本研究旨在提升以連續土壤轉換函數 (Continuous PTFs) 預測van Genuchten 模式(vG-Model) 參數之能力。本研究針對中質地土壤進行分析，為解決三角質地圖界線上質地界定之模糊地帶，運用K-Means 群集分析法依據粒徑分布範圍做分類，取代依質地做分組。利用複線性迴歸分析發展分組前後之模式比較，結果顯示於參數α之預測，分組模式確實能提升整體預測力，而參數n 之預測，分組模式則未能精進預測能力；另發現黏粒含量 (C) 對於n 值具有 一定影響性，整體預測力與n 值本身具有不確定性有關。本研究進一步與國內以區域性發展之Continuous PTFs 比較，結果仍以粒徑分布範圍分組之模式預測力較佳，更印證模式發展前土樣分類之必要性

A Study of Using Continuous Pedotransfer Functions to Predict Parameters of van Genuchten Model.

本研究旨在以土壤質地為基礎，發展van Genuchten 模式(vG-Model)參數之連續土壤轉換函數(Continuous PTFs)，台灣土壤型態以壤土為主，故針對中質地土壤進行分析。藉由廣泛蒐集國內外文獻確立模式內使用之變數，運用K-Means法群集分析將土樣依砂粒與黏粒含量做分類，共分成兩組，再利用複線性迴歸分析發展模式，並與未分類土樣發展之模式比較其預測力。由驗證組之均方根誤差(RMSE)與無偏估線點位分布結果顯示依質地分類之Continuous PTFs確實能增進參數α之預測，進而探討模式變數發現重力水與α具有線性關係；參數n之模式則無明顯之效果，觀察其模式發現n值可能受黏粒含量(C)影響。將驗證組土樣依黏粒含量重新分組後再帶入模式，其RMSE與無偏估線點位對於C值大於8%之土樣確實有精進之效果，C值小於8%則無此現象，此與n值之模式發展具有不確定性有關，但黏粒含量對於此參數仍有相當之影響。本研究進一步比較質地發展之PTFs與前人研究依區域發展之PTFs比較，結果顯示質地分類發展之模式於預測參數α與n皆明顯較區域性發展之模式佳，更證實質地分類之必要性。本研究發展之模式如下所示： ln(α)=-3.2110-0.1871∙(BD∙FC)-1423.24∙〖FC〗^(-2) +0.14523∙(BD∙f)-0.1525∙〖OM〗^(-2) ln(n)=-0.0605+407.7189∙f^(-2)+0.0227∙〖OM〗^(-2) +0.00013∙(Sa∙C) ln(α)=-4.3389-0.1572∙(BD∙FC)+0.1259∙(BD∙f) -0.2197∙〖OM〗^(-2) ln⁡(n)=-0.1049+0.0272∙〖OM〗^(-2)+437.1857∙f^(-2) +0.00052∙(C∙FC) ln(α)=-5.6336- 0.0058∙〖FC〗^2+0.0052∙(f∙FC) ln⁡(n-1)=8.6704+5.1255∙〖BD〗^2+850.0738∙〖FC〗^(-2) -16.5089∙BD+0.01316∙(BD∙FC) +0.4315∙(C∙BD)-0.5646∙CThe purpose of this study is developing pedotransfer functions (PTFs) which were based on soil texture to derive parameters of van Genuchten Model(vG-Model). The study focused on loamy soil, because it is the main type of soil in Taiwan. Determining variables in PTFs by collecting literatures widely, then K-Means cluster analysis was used to classify samples according to the content of sand and clay. All samples were derived into two groups, multiple linear regression analysis was used to develop model for each group, and then compared the predictive ability with the model which was developed from all samples. By the calculation of root mean square error and the point distribution of unbiased estimate line which produced from validations showed that PTFs developed according to texture could surely improve the prediction of the parameter α. Further investigation showed that there might be linear relationship between soil gravity water and parameter α. There was no improvement in the prediction of parameter n. However, the result of observing the model showed that the parameter n might be affected by the content of clay. Taking validations to regroup according to the content of clay, and then put them in the model again. The result of root mean square error and the point distribution of unbiased estimate line showed that when the content of clay was greater than 8%, the improvement of the model was obvious, but when the contents of clay were less than 8%, it didn’t have any effect. This phenomenon was related with that the previous studies which pointed out there was uncertainty in developing the model of n, but the effect of clay was undeniable. This study further compared two PTFs which were developed according to texture and region, and the result showed that in prediction of parameter α and n, the former was better than the latter. And the result proved that it was necessary to classify samples by texture. PTFs were as follows: ln(α)=-3.2110-0.1871∙(BD∙FC)-1423.24∙〖FC〗^(-2) +0.14523∙(BD∙f)-0.1525∙〖OM〗^(-2) ln(n)=-0.0605+407.7189∙f^(-2)+0.0227∙〖OM〗^(-2) +0.00013∙(Sa∙C) ln(α)=-4.3389-0.1572∙(BD∙FC)+0.1259∙(BD∙f) -0.2197∙〖OM〗^(-2) ln⁡(n)=-0.1049+0.0272∙〖OM〗^(-2)+437.1857∙f^(-2) +0.00052∙(C∙FC) ln(α)=-5.6336- 0.0058∙〖FC〗^2+0.0052∙(f∙FC) ln⁡(n-1)=8.6704+5.1255∙〖BD〗^2+850.0738∙〖FC〗^(-2) -16.5089∙BD+0.01316∙(BD∙FC) +0.4315∙(C∙BD)-0.5646∙C目錄 摘要 I Abstract III 目錄 V 圖目錄 VII 表目錄 VIII 照片目錄 IX 常用符號表 X 第一章 前言 1 第二章 前人研究 3 第一節 土壤水分特性 3 第二節 van Genuchten Model 6 第三節 土壤轉換函數 9 第四節 土壤轉換函數之迴歸分析 12 第五節 群集分析 16 第三章 研究材料與方法 18 第一節 研究流程 18 第二節 研究材料 20 第三節 研究方法 22 第四章 結果與討論 30 第一節 壓力鍋排水實驗與vG-Model參數擬合結果 30 第二節 群集分析結果 34 第三節 連續土壤轉換函數─複線性迴歸分析 36 第四節 迴歸分析結果驗證與比較 42 第五節 參數n之分組PTFs與黏粒含量之探討 49 第六節 質地分組連續土壤轉換函數與前人研究之比較 52 第五章 結論與建議 55 參考文獻 57 中文部分 57 西文部分 58 附錄一 64 附錄二 67 圖目錄 圖2.1 毛細作用及吸附作用所形成之基質勢能示意圖 3 圖2.2 砂土與黏土水分特性曲線示意圖 4 圖3.1 研究流程圖 19 圖3.2 土壤點位分布 20 圖3.3 土壤質地分布圖(橘點─實驗組、藍點─驗證組) 21 圖3.4 土壤質地比例圖 21 圖4.1 擬合土壤水分特性曲線(苗栗武榮村1) 33 圖4.2 分組土樣質地分布情形(紫色Class1 橙色Class2) 35 圖4.3 擬合水分特性曲線(以尖石-玉峰4為例) 43 圖4.4 All與Class1驗證組無偏估線─ln(α) 47 圖4.5 All與Class2驗證組無偏估線─ln(α) 47 圖4.6 All與Class1驗證組無偏估線─ln(n) 47 圖4.7 All與Class2驗證組無偏估線─ln(n) 48 圖4.8 重力水與ln(α)之關係 48 圖4.9 All與Class1驗證組無偏估線─ln(n) 51 圖4.10 All與Class2驗證組無偏估線─ln(n) 51 圖4.11 吳晟哲(2010)與質地分組驗證組無偏估線─ln(α) 54 圖4.12 吳晟哲(2010)與質地分組驗證組無偏估線─ln(n) 54 表目錄 表2.1 PTFs分類 9 表2.2 Continuous PTFs變數統整 12 表4.1 實驗組水分特性曲線參數 31 表4.2 分組土樣粒徑分布統計資料 34 表4.3 VIF計算結果 37 表4.4 SPSS相關性分析結果 38 表4.5 迴歸分析比較 40 表4.6 複線性迴歸分析結果 41 表4.7 驗證組水分特性參數 42 表4.8 均方根誤差計算結果─ln(α) 45 表4.9 均方根誤差計算結果─ln(n) 46 表4.10 均方根誤差計算結果 50 表4.11 吳晟哲(2010)土壤轉換函數 52 表4.12 土壤轉換函數預測結果比較─ln(α) 53 表4.13 土壤轉換函數預測結果比較─ln(n) 53   照片目錄 照片3.1 壓力鍋系統示意圖 24 照片3.3 壓力鍋內部 25 照片3.2 土樣預濕照片 2