Large-Scale Modeling Of Unsaturated Flow By Using Mean Soil Water Content As Main Variable

Reasonably describing the large-scale unsaturated flow processes will be beneficial to groundwater resources assessment, agricultural water management, and environmental protection. Although the Richards'equation for unsaturated soil water flow has a solid physical foundation at the local scale, that equation could be restricted to large-scale application due to the variabilities of soil properties, boundary conditions and initial conditions. It is meaningful to model large-scale unsaturated flow and analyze the large-scale parameters.This work reviews the previous work about local-scale numerical models, variabilities of soil properties and large-scale modeling of unsaturated flow. It is found that, instead of pressure head, it is more reasonable to consider the mean soil water content as the primary variable of a large-scale equation. Based on the stochastic method, a series of large-scale models by using mean soil water content as main variable (i.e., theta-based) are constructed. The reference results calculated by Monte Carlo method are used to verify these large-scale models, and a field study is conducted to test the application of these large-scale models. The detailed studies and conclusions are presented as follows.Firstly, the numerical methods of the local-scale theta-based Richards'equation are summarized and improved, and a 2D local-scale theta-based model is constructed. These local-scale numerical models are the foundations of the large-scale numerical models.Secondly, based on the stochastic perturbation approach, a large-scale unsaturated flow model is derived in which the saturated hydraulic conductivity (Ks) is assumed to be a random field. This model is called LE in this paper. The governing equation of LE has a similar form as the local theta-based Richards'equation with different parameters. The large-scale parameters of LE (i.e., the large-scale relative diffusivity and the large-scale relative conductivity) can be expressed by the mean parameters plus the correction terms, which are affected by variability in the random soil parameters, Ks, and the flow process. Analytical solutions of the large-scale parameters are derived by a spectral approach for a synthetic, one-dimensional case. Based on a local-scale theta-based numerical method, a large-scale numerical model is constructed. Monte Carlo method are used to verify LE. The applicability of zero-order model with mean parameters (i.e., ME model) is discussed, and it is found that the variability of the input parameters hinders the mean flow—that is to say, larger variance of the input parameters would result in larger mean soil water content.Thirdly, on the basis of LE, another large-scale model is derived, which is named LE-e4 model in this paper. The large-scale parameters can be simply evaluated by the formula as [mean parameters] X [1+correction value]. The correction value shows positive proportional relation with variance of InKs, and it is related to soil properties as well. Monte Carlo simulations are used to verify LE-e4. The concept large-scale constitutive relation, including large-scale water retention curves or unsaturated hydraulic conductivity curves, is proposed. Based on this concept, validity and applicability of ME are discussed, and it is found that the difference between large-scale models (i.e., LE) and ME is if correction value is set to zero. If the soil type were close to clay, the error of the mean soil water content simulated by ME would be neglected, i.e., the correction value in the large-scale parameters could be set to zero.Fourthly, based on the work of LE and LE-e4, and the variabilities of boundary conditions and initial conditions are taken into account, a large-scale model (namely, LE-C) is established. The governing equation of LE-C still has a similar for as the local theta-based Richards'equation with different parameters. The large-scale parameters include several individual parts, i.e., mean parameters, soil properties variability factor, boundary condition variability factor, and initial condition variability factor. The variance models of boundary condition variability factor and initial condition variability factor is solved by numerical method, and the solutions are coupled to the large-scale numerical model. The validity of LE-C is investigated by Monte Carlo simulation. The study shows that both the mean value and variance of soil content can be evaluated by LE-C precisely, and the perturbation of boundary condition would be transmitted to internal flow zone with time, while the perturbation of initial condition would wears off when the state of flow is approaching to be steady.Fifthly, a ten days infiltration test is conducted in Wuhan University Water Conservancy and Water Environmental Laboratory (China), and the statistics of soil water content and parameters are analyzed. Under the condition of infiltration test, the mean value and variance are calculated by large-scale models (i.e., ME, LE, LE-e4 and LE-C). These results are compared with the results of Monte Carlo simulations and the measured values. Comparisons show that all of these large-scale model can be used to mean soil water content simulation. The ME is simplest and most efficient, but it cannot be used to calculate the variance of soil water content. LE-C shows the most accuracy in the mean soil water content simulation, and the variance of soil water content can be evaluated by LE-C.Sixthly, based on the combination of UCODE and large-scale numerical models, inverse models are constructed in this paper to optimize parameters of the large-scale constitutive relation. Inverse results show that theta-based numerical methods is more accurate than h-based numerical methods. The reason for the minimal differences of soil water content data simulated by these different models is that the large-scale constitutive relation curves described by the optimized parameters are close to each other.Lastly, the major research work and contributions are summarized, and the issues which need further investigation are presented. The possible extensions of the study and further research work are also issued.