The Application Of Markov Chain Monte Carlo Method (MCMC) In Parameter Uncertainty Analysis Of Van Genuchten Model

Soil water characteristic curve represents the function relation between the soil pressure head and water content. It is one of the most important hydraulic characteristics. In the study of soil water infiltration, evaporation, retention, soil erosion and solute transport process, soil water characteristic curve is an important tool to deduce parameters, therefore, the soil water characteristic curve is always the focus attention for soil physicists.Because of complex influence factors on the soil water characteristic curve, the relation between soil water and soil matrix potential has not been established, van Genuchten proposed the soil water characteristic curve equation matching the shape of most of soil water characteristic curve, so it has been widely applied. However, the van Genuchten formula is a complicated nonlinear equation, which has many parameters. Parameter fitting is a nonlinear problem, many scholars have done research on it, such as the least-squares method, nonlinear simplex method, simplex method, and so on. But these methods will meet for stopping or argument is negative and the computational efficiency is low, and so on.There are many models of describing the soil moisture curve. However, many uncertain factors exist in numerical solution process such as the uncertainty of parameters of the model, the input, the uncertainties of simplified practical problems of complex models and the uncertainty of the observation data, etc. Therefore, because of human factors and computational complexity, the use of the traditional method to solve the parameters of the van Genuchten equation is unfit. It is not easy to get the optimal solution.With the development of the computer technology and the improvement of Bayesian theory, Markov chain Monte Carlo (Markov chain Monte Carlo, MCMC) method has become an effective method to calculate the posterior distribution of random variables. It can easily handle the complex models. In this paper, Markov chain Monte Carlo simulation based on the adaptive algorithm is used to estimate the parameters of the van Genuchten equation, and to analyze the posterior distribution. The main study is:AM algorithm is chosen to solve the van Genuchten formula. Make observation and analysis the sampling process and the traces of mean value, variance to get uncertainty analysis. Through the numerical value corresponding to the points, the prediction of a given interval confidence level of parameters can be obtained. On the basis, the uncertainty can be quantified.Using M-H sampling algorithm to solve van Genuchten formula, the posterior distribution of model parameters can also be obtained. The two algorithms were analyzed and compared to find the more suitable algorithm to solve van Genuchten formula.The results show that AM sampling algorithm has more advantages in the ergodicity, convergence speed, accuracy and some level of confidence interval prediction than M-H sampling algorithm, is more suitable for calculation of van Genuchten model parameters.With the help of Hydrus-1D software, calculate the sensitivity of the van Genuchten parameters. Identify the parameter of maximum sensitivity coefficient, which has great influence on the uncertainty of simulation results. The results show that the sensitivity coefficient of parameter n is the largest and has great influence on the simulation result. So, the accuracy of the parameter n should be ensured during the experiments or data collection.Using MCMC method to deduce the van Genuchten model is a new attempt. The study shows that the application of the algorithm to solve the parameters of van Genuchten equal is effective. It is a new idea for solving the van Genuchten model.