以平均含水量为主变量的非饱和水流运动宏观尺度模型研究

发布时间：2018-02-25 22:24

本文关键词： 土壤变异性 Richards方程含水量型方程宏观尺度模型本构关系非饱和带土壤水数值模拟　出处：《武汉大学》2016年博士论文　论文类型：学位论文

【摘要】：宏观尺度上非饱和水流运动过程是区域地下水资源、农业水分管理与环境保护领域的研究重点。尽管局部尺度上非饱和水流运动模型求解技术已经较为成熟,但由于非饱和带土壤水分运动参数、边界以及初值等因素具有明显的空间变异性,通过传统的确定性离散方法和Monte Carlo方法,很难将局部尺度模型应用于宏观尺度上非饱和水流运动过程的描述。根据区域非饱和土壤空间变异的基本特征,研究区域非饱和土壤中水分运动的宏观基本方程、宏观参数结构及其求解模型,对于区域地下水运动分析、地下水污染防护和农田水分管理具有重要的科学意义和实际应用价值。本文总结了近年来非饱和带局部尺度水分运动模型、土壤空间变异性以及宏观尺度模型等研究领域的成果,发现平均含水量更适宜作为宏观尺度模型的主变量。本文在从局部尺度模型出发,将非饱和带变异因素用随机场或随机变量进行描述,通过尺度提升方法(随机扰动法),建立了以平均含水量为主变量的宏观尺度模型,分析了宏观参数的参数结构,探索了宏观尺度模型的数值求解方法,并通过Monte Carlo方法和小区试验对所构建的模型进行验证。具体研究内容和主要结论如下：(1)总结并完善了局部尺度上以含水量为变量的一维非饱和水流运动数值模型,开发了以含水量为变量的二维非饱和运动数值模型,为宏观模型数值解法研究及Monte Carlo验证提供了基础。(2)将水力参数视为空间随机场,由局部尺度含水量型Richards方程出发,采用随机扰动法推导了以平均含水量为主变量的宏观尺度模型(即LE模型)。LE模型的控制方程在形式上与含水量型Richards方程相同,其中宏观参数则表示为平均参数加修正项的形式,而该修正项又与饱和水力传导度的统计特征及水流系统过程等因素相关。采用谱分析方法对宏观参数进行解析估计,并根据局部尺度含水量型迭代数值方法(Picard-6方法)构建了宏观方程的数值求解模型。在不同算例条件下,采用Monte Carlo方法参照解验证了LE模型的正确性。并与压力型宏观模型(LE-h模型)做对比,研究发现含水量型模型(LE模型)在模拟平均含水量时具有精度优势。讨论了平均模型(ME模型)的适用性和影响平均水流运动的因素,发现土壤水力参数的空间变异性会阻碍平均水流运动,即这些参数的方差越大,平均含水量则越大。(3)在LE模型的基础上,构建了LE-e4模型(或LE-e2模型),其中宏观参数可简单地采用[平均参数]×[1+修正值]进行估计。其中,修正值则与输入随机场的方差呈正比例关系,此外该值还和土壤性质有关。在不同算例条件下,以Monte Carlo的参照解对上述两模型进行了验证。提出了宏观本构关系曲线的概念,并以此进一步探讨了平均参数的适用性,指出宏观模型(LE、 LE-e4等)的实质是对平均模型中的平均参数进行了修正。当土壤粘性越强,平均模型(ME)模拟平均含水量的误差越小,即平均参数可以不修正。(4)以LE或LE-e4模型为基础,进一步将边界和初始条件的空间变异性进行随机描述,构建了宏观尺度上的LE-C模型。该模型的控制方程仍然具有含水量型Richards方程的形式,其宏观参数可表示为平均参数、土壤水力参数变异因素、边界条件变异因素和初始条件变异因素的叠加。研究了边界和初始条件变异因素对应的方差方程数值求解方法,并将其与宏观模型进行耦合求解。在不同算例条件下,以Monte Carlo提供的参照解验证了LE-C模型,研究结果表明：LE-C模型能够较好地估计含水量均值及其标准差,边界上的扰动随时间向内部传播,而初始条件扰动随时间逐渐消散。(5)开展了田间试验,将宏观尺度模型(ME、 LE、 LE-e4和LE-C)以实测参数进行正演模拟,模拟结果同含水量观测以及相同条件下的Monte Carlo模拟结果进行对比。在试验条件下,几种方法在模拟平均含水量方面的精度相当,ME方法计算效率最高,而LE-C方法能够较好地估计含水量方差。不同的宏观尺度模型可根据土壤粘性、变异性因素资料、是否需要求解含水量方差、求解效率等因素来进行选择。(6)本文还结合UCODE进行了宏观尺度模型的反演研究,从反演的角度证明了含水量型数值方法(Ross、 Picard-θ)的优势,发现了“异参同效”(同一模型不同参数组合模拟效果相同)和“异模同效”(不同模型模拟效果相同)现象,并分析其本质是宏观本构关系曲线互相接近。最后,对全文研究成果进行了归纳总结,提出研究中的不足之处,并对后续研究方向提出一些建议。
[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.

【学位授予单位】：武汉大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：S152.7

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