Groundwater Model Evaluation Based On Bayesian Theory

Due to the complexity of groundwater system and the limitation of human cognition,there are always differences between groundwater model and real groundwater system,which leads to the deviation between the simulation results and the real observation results,and affects the reliability of groundwater simulation.This deviation can be attributed to the uncertainty of groundwater simulation.In recent years,numerical simulation technology has been widely used in the fields of groundwater resource evaluation and management,groundwater contaminant source dentification,and groundwater pollution remediation and treatment.How to control the uncertainty of groundwater numerical simulation and improve the reliability of simulation and prediction results has become a hot topic and difficult problem in the field of groundwater research.A set of possible groundwater models can be built to describe the same groundwater system,which is caused by the uncertainty of model structure,such as different characterizations of aquifer spatial structure,different definitions of pollutant chemical reaction model and so on.Moreover,different models may have inconsistent simulation and prediction performance.Multiple model analysis methods based on Bayesian theory,such as Bayesian model averaging(BMA)and Bayesian model selection(BMS),have become the main methods for quantitative analysis and control of the uncertainty of groundwater model structure.The key of Bayesian multiple model analysis method is how to evaluate models,i.e.calucalte model posterior weights scientifically,efficiently and accurately.In this study,two key links in model evaluation,i.e.estimation of model marginal likelihood and assignment of model prior weight,are studied and innovated,and are applied to groundwater contaminant source identification.The research results are as follows:(1)The nested sampling algorithm based on Adaptive Metropolis(NSE?AM)was proposed in this study to calculate the marginal likelihood of model.In order to slove the inefficiency of local constrained sampling in the NSE,the Adaptive Metropolis algorithm is applied to improve the constrained local sampling.Thus,the NSE?AM algorithm was proposed.By calculating the marginal likelihoods of several linear,non-linear analytical functions and a set of groundwater models with different structures,and compared with the original nested sampling algorithm based on Metropolis Hasting(NSE?MH),the result showed that NSE?AM is better than NSE?MH in accuracy,convergence and stability,but the stability is not improved significantly.(2)The nested sampling algorithm based on MT-DREAM_(zs)(NSE?MT)was proposed in this study to calculate the marginal likelihood of model.In order to furture improve the efficiency of local constrained sampling in the NSE,the MT-DREAM_(zs)algorithm was applied to update the constrained local sampling.Thus,the NSE?MT algorithm was proposed.Through a series of benchmark tests,NSE?MT was compared with existing algorithms(AME,NSE?MH,NSE?DR,POLYCHORD and GAME)in terms of accuracy,stability and convergence.The results showed that NSE?MT outperforms NSE?MH and NSE?DR in the accuracy,stability and convergence.And NSE?MT outperforms GAME and POLYCHORD in the convergence.However,NSE?MT is less accurate than GAME and POLYCHORD for high-dimensional and multimodal complex problems.(3)Bayesian model selection was applied for groundwater contaminant source identification.In order to solve the problem of multiple models in groundwater contaminant source identification,model selection is based on marginal likelihood of models,and the contaminant source is identified by using the posterior distribution of contaminant source characteristics.Through two case studies,which include a three-dimensional heterogeneous groundwater solute transport model and a laboratory column groundwater nano-Ti O₂ transport experiment,the important influence of model structure uncertainty on groundwater contaminant source identification and the necessity of model evaluation were verified.(4)The correlation matrix method was proposed to assign prior weights to groundwater models in Bayesian model averaging(BMA).In order to overcome the defect of using uniform model prior weights in traditional multiple model analysis,weighting schemes based on the correlation matrix were proposed,which can effectively penalize models for being highly correlated and improve the prediction performance of BMA.Through two case studies,which include the three-dimensional heterogeneous groundwater flow model under ideal conditions and the snowmelt runoff model of Tizinafu river basin in southern Xinjiang,the proposed method was verified.