本文關(guān)鍵詞： 土壤變異性 Richards方程 含水量型方程 宏觀尺度模型 本構(gòu)關(guān)系 非飽和帶 土壤水 數(shù)值模擬　出處：《武漢大學》2016年博士論文　論文類型：學位論文

【摘要】：宏觀尺度上非飽和水流運動過程是區(qū)域地下水資源、農(nóng)業(yè)水分管理與環(huán)境保護領(lǐng)域的研究重點。盡管局部尺度上非飽和水流運動模型求解技術(shù)已經(jīng)較為成熟,但由于非飽和帶土壤水分運動參數(shù)、邊界以及初值等因素具有明顯的空間變異性,通過傳統(tǒng)的確定性離散方法和Monte Carlo方法,很難將局部尺度模型應用于宏觀尺度上非飽和水流運動過程的描述。根據(jù)區(qū)域非飽和土壤空間變異的基本特征,研究區(qū)域非飽和土壤中水分運動的宏觀基本方程、宏觀參數(shù)結(jié)構(gòu)及其求解模型,對于區(qū)域地下水運動分析、地下水污染防護和農(nóng)田水分管理具有重要的科學意義和實際應用價值。本文總結(jié)了近年來非飽和帶局部尺度水分運動模型、土壤空間變異性以及宏觀尺度模型等研究領(lǐng)域的成果,發(fā)現(xiàn)平均含水量更適宜作為宏觀尺度模型的主變量。本文在從局部尺度模型出發(fā),將非飽和帶變異因素用隨機場或隨機變量進行描述,通過尺度提升方法(隨機擾動法),建立了以平均含水量為主變量的宏觀尺度模型,分析了宏觀參數(shù)的參數(shù)結(jié)構(gòu),探索了宏觀尺度模型的數(shù)值求解方法,并通過Monte Carlo方法和小區(qū)試驗對所構(gòu)建的模型進行驗證。具體研究內(nèi)容和主要結(jié)論如下：(1)總結(jié)并完善了局部尺度上以含水量為變量的一維非飽和水流運動數(shù)值模型,開發(fā)了以含水量為變量的二維非飽和運動數(shù)值模型,為宏觀模型數(shù)值解法研究及Monte Carlo驗證提供了基礎。(2)將水力參數(shù)視為空間隨機場,由局部尺度含水量型Richards方程出發(fā),采用隨機擾動法推導了以平均含水量為主變量的宏觀尺度模型(即LE模型)。LE模型的控制方程在形式上與含水量型Richards方程相同,其中宏觀參數(shù)則表示為平均參數(shù)加修正項的形式,而該修正項又與飽和水力傳導度的統(tǒng)計特征及水流系統(tǒng)過程等因素相關(guān)。采用譜分析方法對宏觀參數(shù)進行解析估計,并根據(jù)局部尺度含水量型迭代數(shù)值方法(Picard-6方法)構(gòu)建了宏觀方程的數(shù)值求解模型。在不同算例條件下,采用Monte Carlo方法參照解驗證了LE模型的正確性。并與壓力型宏觀模型(LE-h模型)做對比,研究發(fā)現(xiàn)含水量型模型(LE模型)在模擬平均含水量時具有精度優(yōu)勢。討論了平均模型(ME模型)的適用性和影響平均水流運動的因素,發(fā)現(xiàn)土壤水力參數(shù)的空間變異性會阻礙平均水流運動,即這些參數(shù)的方差越大,平均含水量則越大。(3)在LE模型的基礎上,構(gòu)建了LE-e4模型(或LE-e2模型),其中宏觀參數(shù)可簡單地采用[平均參數(shù)]×[1+修正值]進行估計。其中,修正值則與輸入隨機場的方差呈正比例關(guān)系,此外該值還和土壤性質(zhì)有關(guān)。在不同算例條件下,以Monte Carlo的參照解對上述兩模型進行了驗證。提出了宏觀本構(gòu)關(guān)系曲線的概念,并以此進一步探討了平均參數(shù)的適用性,指出宏觀模型(LE、 LE-e4等)的實質(zhì)是對平均模型中的平均參數(shù)進行了修正。當土壤粘性越強,平均模型(ME)模擬平均含水量的誤差越小,即平均參數(shù)可以不修正。(4)以LE或LE-e4模型為基礎,進一步將邊界和初始條件的空間變異性進行隨機描述,構(gòu)建了宏觀尺度上的LE-C模型。該模型的控制方程仍然具有含水量型Richards方程的形式,其宏觀參數(shù)可表示為平均參數(shù)、土壤水力參數(shù)變異因素、邊界條件變異因素和初始條件變異因素的疊加。研究了邊界和初始條件變異因素對應的方差方程數(shù)值求解方法,并將其與宏觀模型進行耦合求解。在不同算例條件下,以Monte Carlo提供的參照解驗證了LE-C模型,研究結(jié)果表明：LE-C模型能夠較好地估計含水量均值及其標準差,邊界上的擾動隨時間向內(nèi)部傳播,而初始條件擾動隨時間逐漸消散。(5)開展了田間試驗,將宏觀尺度模型(ME、 LE、 LE-e4和LE-C)以實測參數(shù)進行正演模擬,模擬結(jié)果同含水量觀測以及相同條件下的Monte Carlo模擬結(jié)果進行對比。在試驗條件下,幾種方法在模擬平均含水量方面的精度相當,ME方法計算效率最高,而LE-C方法能夠較好地估計含水量方差。不同的宏觀尺度模型可根據(jù)土壤粘性、變異性因素資料、是否需要求解含水量方差、求解效率等因素來進行選擇。(6)本文還結(jié)合UCODE進行了宏觀尺度模型的反演研究,從反演的角度證明了含水量型數(shù)值方法(Ross、 Picard-θ)的優(yōu)勢,發(fā)現(xiàn)了“異參同效”(同一模型不同參數(shù)組合模擬效果相同)和“異模同效”(不同模型模擬效果相同)現(xiàn)象,并分析其本質(zhì)是宏觀本構(gòu)關(guān)系曲線互相接近。最后,對全文研究成果進行了歸納總結(jié),提出研究中的不足之處,并對后續(xù)研究方向提出一些建議。
[Abstract]:The macro scale unsaturated flow is the process of regional groundwater resources, focus on agricultural water management and environmental protection field. Although the local scale unsaturated flow model technology has been more mature, but due to the unsaturated soil water movement parameters, boundary and initial factors have significant spatial variability, through the determination of discrete Monte method and traditional Carlo method, it is difficult to apply the local scale model in macroscopic scale unsaturated flow process. According to the basic characteristics of regional spatial variability of unsaturated soil, the study area non macro basic equation of water movement in soil, the macro parameters of structure and model analysis for regional groundwater movement and it has important scientific significance and practical application value of groundwater protection and farmland water management. This article summarizes the past Years of unsaturated water movement model with local scale, soil spatial variability and macro scale model research results, found that the average moisture content is more suitable as the main variable of macro scale model. In this paper, starting from the local scale model, the non mutation factor used is described with the airport or random variable by saturation. Scale lifting method (random perturbation method), established a macro scale model is based on the average moisture content of main variables, parameters of structure analysis of the macro parameters, explore the numerical method of macro scale model, and through the Monte Carlo method and experiment to verify the model. The concrete research contents and main conclusions are as follows: (1) summarize and improve the local scale in water saturated flow numerical variables one dimensional motion model, developed the variable two-dimensional unsaturated water transport to The dynamic numerical model, provides the basis for macro model research on numerical solution and Monte Carlo verification. (2) the hydraulic parameters are considered as random field, by the local scale water type Richards equation, using the random perturbation method is derived for the average moisture content was the main variable macro scale model (LE model) control equation the.LE model in the same form and content type Richards equation, which is expressed as the average macroscopic parameters parameters and the modified terms, and the correction and the statistical characteristics of saturated hydraulic conductivity and water system process related factors. Methods for analytical estimation of macro parameters by spectrum analysis, and according to the local scale water type iterative numerical method (Picard-6 method) was constructed. The numerical model of macroscopic equations in different example under the conditions of reference solutions to validate the LE model by Monte Carlo method. And with the pressure type macro model (LE-h model) comparative study found that water content model (LE model) has the advantage of accuracy in simulating the average moisture content is discussed. The average model (ME model) and the applicability of the influencing factors of the average flow, found that the spatial variability of soil hydraulic parameters will hinder the average flow exercise, the variance of these parameters is larger, the average moisture content is greater. (3) based on the LE model, constructed the LE-e4 model (or LE-e2 model), which can use the simple macro parameters [mean]] * [1+ parameter correction value is estimated. The corrected value is input with the airport is proportional to the variance of the value, and is related to soil properties. Examples in different conditions, with the Monte Carlo reference solutions to validate the above two models. Put forward the concept of constitutive relation curve, and further discusses the average. Is the number of points out that the macro model (LE, LE-e4) is the essence of the average parameter average correction model. When the soil viscosity is strong, the average error between the simulation model (ME) the average water content is small, can not modify the average parameters. (4) in LE or LE-e4 mode as the foundation, will further describe the spatial variability of the random boundary and initial conditions, LE-C model is constructed on the macro scale. The governing equation of the model still has a water content of Richards type equations, the macroscopic parameters can be expressed as the average parameters of soil hydraulic parameters variation factors, superposition boundary conditions and initial conditions of variation the variation of factors. The variance equation numerical methods for solving the corresponding boundary and initial condition variance, and its coupling with macro model. Examples in different conditions, using Monte Carlo provided reference for validation The LE-C model, the results show that the LE-C model can be used to estimate the mean water content and standard deviation, the disturbance on the boundary with time to internal communication, and initial condition perturbations with time gradually dissipated. (5) carried out a field experiment, the macro scale model (ME, LE, LE-e4 and LE-C) on the measured parameters the forward simulation, the simulation results with the water content and the observation of Monte under the same conditions the simulation results of Carlo were compared. Under the experimental conditions, the average water content of several methods in the simulation precision of the ME method, the highest efficiency, while the LE-C method can accurately estimate the variance. Macro scale model according to the different the viscous soil, material variability factors, whether need to solve the water content variance, to select factors of solving efficiency. (6) this paper combines UCODE studied inverse model from the macro scale, inversion The angle proved that the numerical method of water content type (Ross, Picard- 0) advantage, found "equifinality" (a model with different parameters to simulate the effect of the same) and different modes and effect "(different model to simulate the effect of the same phenomenon, and analyze its essence) is the macroscopic constitutive relation curves are close to each other finally, the research results are summarized and put forward the deficiencies in the research, and puts forward some suggestions for the future research direction.

【學位授予單位】：武漢大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：S152.7

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