The Uncertainty Analysis And Assessment Of Groundwater Flow Numerical Simulation

Water is the source of life,production,and ecological foundation.Groundwater is an important available freshwater resource,rational management and utilization of groundwater resources has become an important guarantee of sustainable socio-economic development.Groundwater field is a complex,open system,and some properties always do not represent concrete objects and need to be indirectly estimated by input and output measuremets.Natural hydrological process is conceptualized through relatively simple flow control equations in groundwater models.Moreover,observation data is always limited in the field hydrogeological conditions.Therefore,the predictive results of groundwater simulation are often deviate from true values,which is attribute to the uncertainty of groundwater numerical simulation.Recognizing the source of uncertainty and understanding it,this will help in improving the model structure and providing feedback for data collecting activities relating to model uncertainty analysis.The characteristics of probability distribution(COPD)of groundwater model outputs are the direct reflection of model uncertainties,which include probability density function(PDF)and numerical characteristics.An artificial groundwater model was built for producing groundwater outputs.The suitable probability density functions of outputs were selected by frequency analysis.After that,the stepwise regression and mutual entropy analysis were used to identify the affecting factors of the first two moments of GLS(mean and variance).Finally,classification tree analysis was used to identify the driving factors that lead the GLS to obey a specified distribution or not.Results indicate that the COPD of model outputs are mainly controlled by the probability distribution of input parameters.By contrast,the COPD of outputs remain nearly consistent in spite of different model layers in which the observation points are located.The mean and variance of outputs are both controlled by the distances of observation point from model's active boundaries.Moreover,the PDF's category of outputs is dominated by the average distance of observation point from pumping wells and the distances from model's active boundaries.Parameter uncertainty is the main component of groundwater numerical uncertainty.Four important methods which include GLUE,AM,SCEM-UA,and DREAM,are used for identifying parameters and predicting outputs for different dimensional problems.The results show that the model parameters and outputs derived by GLUE are uniformly distributed in larger ranges,in addition,the posterior distributions are influenced significantly by prior distribution.The posterior distribution derived from MCMC are distributed in narrower range,and the results from AM and SCEM-UA are liable to mislead.GLUE and AM methods are suitable for low-dimensional groundwater model parameter uncertainty,however,these two methods are not appropriate for high-dimensional problems,the posterior distributions are generated with serious deviations.By contrast,the parallel multi-chain MCMC methods(SCEM-UA,DREAM)are good at both low-dimensional and high-dimensional parameter uncertainty problems.Especially,the DREAM method is able to identify the model parameters and outputs effectively,and the posterior distributions have not misleading information.With incomplete information about hydrogeological conditions,conceptual model uncertainty is inevitable for groundwater numerical simulation and prediction. Based on different techniques to combine MC method and BMA,which include the approach to obtain integrated model likelihood and predictive distribution,five MC-BMA methods are proposed and compared.Thereinto,for the modified mefthod UpAM-Srum-BMA,integrated model likelihood is estimated to be the summation of likelihood values which are retained only when Markov Chain is updated.In addition,each retained simulator is weighted by its normalized likelihood value in forming predictive distributions.For illustrative purpose,a synthetical groundwater model is built.The results show that UpAM-Sun-BMA obtains the best comprehensive predictive efficiency for the ensemble predictions of groundwater budget terms,and is able to distinguish the performances of different model structures.However,the posterior weights of alternative conceptual models are fairly close when they are obtained by the others MC-BMA methods.Therefore,by considering predictive ability and convergence rate,UpAM-Sum-BMA is superior to the others MC-BMA methods.The uncertainty measurement is the essential content of uncertainty analysis,in addition,which is the precondition and guaranteed for scientific description,analysis and treatment of uncertainty.Parametric uncertainty is estimated by AM method,and conceptual model uncertainty is assessed in Bayesian model averaging framework.For quantifying predictive uncertainties,variance and information entropy methods are applied to measure the uncertainties of predictive distribution respectively for each groundwater outputs.Then,variance and information entropy methods are compared based on the results of uncertainty measurements.The results shows fthat variance and information entropy measuring methods are fairly consistent in estimating the uncertainties of predictive distributions for alternative conceptual models and BMA,except for the predictions deviate significantly from normal distribution.This is attributed to the intrinsic qualities of these two measuring methods,that variance is not a general mefthod for representing the concentration of a probability distribution.Nevertheless,variance is able to measure the uncertainties of normal distributions.Variance and information entropy measuring methods represent significantly differences in estimating each part of uncertainty of ensemble prediction,including within-model,between-model,and repeated uncertainties.This is attributed to the different definitions of these uncertainties for the two methods.By contrast,information entropy method is more appropriate in defining each part of uncertainty of ensemble prediction.By considering the theoretical basis of measuring method,definition for each part of uncertainty of ensemble prediction,and the consistence in uncertainty measurements,therefore,infoemation entropy method is more proper and accurate for measuring groundwater modeling uncertainties.