| The simulation of unsaturated flow is of great significance in agricultural production and environmental protection, since many importance processes, e.g., rainfall infiltration, solute (including contaminant and plant nutrient) transport and plant growth, take place in the unsaturated zone. Due to its importance, there are increasing interests of modeling water movement in unsaturated zone, where the accurate acquisition of soil unsaturated hydraulic parameters is a precondition of reliable predictions.Generally, the unsaturated soil hydraulic parameters can be obtained by fitting water content and matric potential measurements of soil samples. However, this process is time and labor consuming. Furthermore, it suffers from the scale effect, i.e., the lab-obtained parameters are not suitable for field modeling. Recently, due to the rapid development of sensor and computer techniques, the combination of on-site measurements and simulation-based inversion for soil unsaturated hydraulic parameters are becoming increasingly popular in unsaturated flow modeling. Based on searching for one set of parameters that best fits the measurements, traditional optimization methods can not quantify the uncertainty of the parameters. Recently, the Bayesian inversion methods are receiving increasing attention where the parameters are modeled as random variables and described with their probabilistic distribution functions. Through sampling the posterior (i.e., conditional) distributions of model parameters, Markov Chain Monte Carlo (MCMC) algorithm can be used as an efficient method for parameter estimation. Recently, one state-of-the-art MCMC algorithm, DREAM (ZS) has been utilized in many fields for its high efficiency.In this paper, using numerical simulations and column experiments, we compared the performance of optimization and DREAM (ZS) in estimating unsaturated heterogeneous hydraulic parameters. The main work included:(1) We used traditional lab-based methods, i.e., cutting-ring infiltration method to obtain the saturated conductivity and soil moisture pressure membrane method to obtain the unsaturated soil hydraulic parameters. And these results were used as initial values for the Levenberg-Marquardt (LM) algorithm and prior information for MCMC algorithm.(2) Through numerical case studies, we compared the performance and applicability of LM and MCMC algorithms in estimating soil hydraulic parameters.(3) We designed and conducted layered sand and soil column experiments, respectively. Based on the results of numerical case studies, we proposed a method that can provide the prior distribution for Bayesian method, i.e., using the results of LM algorithm to provide the prior information for Bayesian method, and fitting the matric potential measurements to verify the effectiveness of proposed methods.It can be concluded that:(1) Based on the research about the inverse problem of unsaturated flow in layered soil, it was shown that both LM and MCMC algorithms could provide reasonable results, which resulted acceptable water transport predictions.(2) The popular LM algorithm could provide one single set of model parameter estimation with very few model runs, which takes very little time. However, this method was sensitive to the initial guess of parameters, and the obtained predictions occasionally deviated from the measurements. Meanwhile, the single value result could not provide the uncertain quantification of model parameters, which might cause risk in prediction.(3) The MCMC algorithm could provide state predictions that better fit measurements. More importantly, it accurately quantified the uncertainty of the parameters, which could avoid the potential risk introduced by making predictions via a single estimated value. However, the MCMC algorithm was with higher computational cost compared to LM algorithm. As the simulation conducted in this study was not CPU-demanding, the MCMC algorithm was recommended here. |
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