Data Assimilation For Unsaturated Flow In Soil

Unsaturated zone is an important part of hydrological cycle,and it is also the channel for surface pollutants to enter groundwater.Modeling matter and energy movement in the unsaturated zone has both theoretical and practical importance for agricultural water and soil resources management and pollution prevention and control.Numerical models are powerful tools for simulating unsaturated flow in soil,and one of the keys to successfully applying numerical models is to determine soil hydraulic parameters(such as saturated hydraulic conductivity and porosity).Traditional methods for directly measuring the soil hydraulic parameters are usually time-consuming,laborious,and costly,and can greatly disturb the soil.In addition,due to the heterogeneity of natural soil,the measured values at a certain point cannot represent the soil properties of the whole region.With the development of measurement and sensing technology,there are currently a variety of sensors that can monitor the movement of matter and energy in the soil online,which can easily obtain a large amount of data and have little disturbance to the soil.Effectively extracting information from these data and accurately inverting soil hydraulic parameters are of great significance for accurately simulating water movement,solute transport,and heat transfer in soil.Data assimilation methods can estimate soil hydraulic parameters by assimilating the observed data(such as pressure head,water content,solute concentration,and temperature).However,due to the CPU-intensive nature of unsaturated flow models,the spatial variability of soil,and the relative scarcity of observed data,challenges remain for existing data assimilation methods.Therefore,it is necessary to develop efficient data assimilation methods to estimate soil hydraulic parameters,reduce the uncertainty of unsaturated flow in soil,and thus provide quantitative support for the scientific management and protection of agricultural water and soil resources.Based on recent progress in uncertainty quantification and optimal experimental design,in this dissertation,Markov chain Monte Carlo(MCMC),ensemble Kalman filter(EnKF),and probabilistic collocation-based Kalman filter(PCKF)are respectively employed to estimate soil hydraulic parameters of heterogeneous unsaturated zone by assimilating the observed data such as pressure head,water content,solute concentration,and temperature.Moreover,optimal experimental design and uncertainty quantification methods are developed to improve the accuracy and computational efficiency of data assimilation.The specific research contents and conclusions of this dissertation are summarized as follows:1)Within the Bayesian framework,the data worth of soil water content and temperature in estimating unsaturated soil hydraulic and thermal parameters are systematically analyzed,and the global optimal design is carried out for these two types of observed data.However,one common issue in Bayesian methods(here specifically referred to as MCMC)is the considerably high computational cost since both the parameter estimation and the experimental design involve a large number of model evaluations.To address this issue,a new surrogate modeling method,i.e.,ANOVA(analysis of variance)-based transformed probabilistic collocation method(ATPCM),is developed in this dissertation.It is shown that,compared to the traditional PCM,ANOVA-based PCM,and transformed PCM,ATPCM can construct a more accurate surrogate model with a lower computational cost,avoiding the system model evaluations in the calculation of likelihood function,thereby greatly improving the computational efficiency;the surrogate model constructed by ATPCM is then utilized to accelerate the Bayesian data worth analysis for the most informative monitoring strategy,and thus improve the accuracy of parameter estimation.2)By combining EnKF with sequential optimal design,a sequential ensemble-based optimal design(SEOD)method is developed to improve the accuracy of EnKF in inverting soil hydraulic parameters.In the EnKF framework,Shannon entropy difference(SD),degrees of freedom for signal(DFS),and relative entropy(RE)are respectively used as the information metrics to quantify the information of candidate monitoring strategies,and then the genetic algorithm is applied to search for the optimal monitoring strategy with the highest amount of information.Finally,the observed data obtained from the optimal monitoring strategy are assimilated to estimate the unknown parameters.To verify the effectiveness of the method,one-dimensional and two-dimensional numerical examples of unsaturated flow are considered,and the optimal monitoring strategies based on different information metrics(i.e.,SD,DFS,and RE)are evaluated and compared with the conventional monitoring strategies.The results show that the optimal monitoring strategies are superior to the conventional monitoring strategies in both parameter estimation and state prediction;the small difference among the optimal monitoring strategies indicates that in the tested examples,the monitoring strategy is not very sensitive to the type of information metric.3)By combining the adaptive ANOVA-based PCKF with sequential optimal design,a sequential probabilistic collocation-based optimal design(SPCOD)method is developed to further improve the accuracy and efficiency of soil hydraulic parameter estimation.In the PCKF framework,SD is used as the information metric to quantify the information of candidate monitoring strategies,and then the genetic algorithm is applied to search for the optimal monitoring strategy with the highest amount of information.Finally,the observed data obtained from the optimal monitoring strategy are assimilated to estimate the unknown parameters.In order to verify the effectiveness of the method,two numerical examples of solute transport in unsaturated soil are considered,and the results provided by the optimal monitoring strategy are compared with those provided by the conventional monitoring strategies.The results show that,compared to the conventional monitoring strategies,the optimal monitoring strategy designed by SPCOD can provide more accurate parameter estimation and state prediction;compared with the SEOD method,SPCOD can provide a more robust and accurate monitoring design with the same computational cost.4)An ANOVA-based multi-fidelity probabilistic collocation method(AMF-PCM)is developed and used to quantify the uncertainty of coupled unsaturated flow and heat transport in soil.The central idea of AMF-PCM is to utilize a low-fidelity(LF)model to improve computational efficiency and multi-fidelity simulation framework to guarantee accuracy.In AMF-PCM,the system model(i.e.,high-fidelity,HF model)output is expressed as the sum of LF model output and correction function.For high-dimensional problems,we first respectively decompose the LF model output and the correction function using functional ANOVA,then perform the polynomial chaos expansion(PCE)on the low-order ANOVA components obtained from decomposition,and finally approximate the HF model output by summing the PCE representation of LF model output and correction function.To implement AMF-PCM,two typical ways(i.e.,simplifying the physics or using a coarser discretization)are used to build a computationally cheap LF model.The efficiency and accuracy of AMF-PCM are demonstrated by several numerical examples of coupled unsaturated flow and heat transport in soil with varying complexity.5)An adaptive multi-fidelity probabilistic collocation-based Kalman filter(AMF-PCKF)is developed to improve the applicability of PCKF in high-dimensional data assimilation problems.In the forecast step of AMF-PCKF,PCE expansion is performed on the system model(i.e.,HF model)output using AMF-PCM.To further improve the computational efficiency,some criterion is adopted to adaptively select the important ANOVA components for approximating the LF model output.In the analysis step of AMF-PCKF,the PCE coefficients of model parameters are updated by the observed data.To verify the effectiveness of the method,a water-gas two-phase flow experiment and a high-dimensional numerical example of coupled unsaturated flow and heat transport in soil are considered,and the results provided by AMF-PCKF are compared with those provided by EnKF with the same computational cost.The results show that AMF-PCKF can provide more accurate parameter estimation and state prediction than EnKF with the same computational cost,even when the number of unknown parameters is as high as 100.