This study used the marginal likelihood and Bayesian posterior model probability for evaluation of model complexity in order to avoid using over-complex models for numerical simulations. It focused on investigation of...This study used the marginal likelihood and Bayesian posterior model probability for evaluation of model complexity in order to avoid using over-complex models for numerical simulations. It focused on investigation of the impacts of prior parameter distributions(involved in calculating the marginal likelihood) on the evaluation of model complexity. We argue that prior parameter distributions should define the parameter space in which numerical simulations are made. New perspectives on the prior parameter distribution and posterior model probability were demonstrated in an example of groundwater solute transport modeling with four models, each simulating four column experiments. The models had different levels of complexity in terms of their model structures and numbers of calibrated parameters. The posterior model probability was evaluated for four cases with different prior parameter distributions. While the distributions substantially impacted model ranking, the model ranking in each case was reasonable for the specific circumstances in which numerical simulations were made. For evaluation of model complexity, it is thus necessary to determine the parameter spaces for modeling, which can be done by conducting numerical simulation and usineg engineering judgment based on understanding of the system being studied.展开更多
The traditional advection-dispersion equation(ADE) and the mobile-immobile model(MIM) are widely used to describe solute transport in heterogeneous porous media. However, the fitness of the two models is casedependent...The traditional advection-dispersion equation(ADE) and the mobile-immobile model(MIM) are widely used to describe solute transport in heterogeneous porous media. However, the fitness of the two models is casedependent. In this paper, the transport of conservative,adsorbing and degradable solutes through a 1 m heterogeneous soil column under steady flow condition was simulated by ADE and MIM, and sensitivity analysis was conducted. Results show that MIM tends to prolong the breakthrough process and decrease peak concentration for all three solutes, and tailing and skewness are more pronounced with increasing dispersivity. Breakthrough curves of the adsorbing solute simulated by MIM are less sensitive to the retardation factor compared with the results simulated by ADE. The breakthrough curves of degradable solute obtained by MIM and ADE nearly overlap with a high degradation rate coefficient, indicating that MIM and ADE perform similarly for simulating degradable solute transport when biochemical degradation prevails over the mass exchange between mobile and immobile zones. The results suggest that the physical significance of dispersivity should be carefully considered when MIM is applied to simulate the degradable solute transport and/or ADE is applied to simulate the adsorbing solute transport in highly dispersive soils.展开更多
基金supported by the U.S.Department of Energy Early Career Research Program Award(Grant No.DE-SC0008272)U.S.National Science Foundation(Grant No.1552329)
文摘This study used the marginal likelihood and Bayesian posterior model probability for evaluation of model complexity in order to avoid using over-complex models for numerical simulations. It focused on investigation of the impacts of prior parameter distributions(involved in calculating the marginal likelihood) on the evaluation of model complexity. We argue that prior parameter distributions should define the parameter space in which numerical simulations are made. New perspectives on the prior parameter distribution and posterior model probability were demonstrated in an example of groundwater solute transport modeling with four models, each simulating four column experiments. The models had different levels of complexity in terms of their model structures and numbers of calibrated parameters. The posterior model probability was evaluated for four cases with different prior parameter distributions. While the distributions substantially impacted model ranking, the model ranking in each case was reasonable for the specific circumstances in which numerical simulations were made. For evaluation of model complexity, it is thus necessary to determine the parameter spaces for modeling, which can be done by conducting numerical simulation and usineg engineering judgment based on understanding of the system being studied.
基金funded by Projects of the National Natural Science Foundation of China (51379207, 51321001)
文摘The traditional advection-dispersion equation(ADE) and the mobile-immobile model(MIM) are widely used to describe solute transport in heterogeneous porous media. However, the fitness of the two models is casedependent. In this paper, the transport of conservative,adsorbing and degradable solutes through a 1 m heterogeneous soil column under steady flow condition was simulated by ADE and MIM, and sensitivity analysis was conducted. Results show that MIM tends to prolong the breakthrough process and decrease peak concentration for all three solutes, and tailing and skewness are more pronounced with increasing dispersivity. Breakthrough curves of the adsorbing solute simulated by MIM are less sensitive to the retardation factor compared with the results simulated by ADE. The breakthrough curves of degradable solute obtained by MIM and ADE nearly overlap with a high degradation rate coefficient, indicating that MIM and ADE perform similarly for simulating degradable solute transport when biochemical degradation prevails over the mass exchange between mobile and immobile zones. The results suggest that the physical significance of dispersivity should be carefully considered when MIM is applied to simulate the degradable solute transport and/or ADE is applied to simulate the adsorbing solute transport in highly dispersive soils.
