Analysis Of Groundwater Model Structural Uncertainty Based On Gaussian Process Regression

In the establishment of groundwater model,the actual groundwater system is usually simplified,but the simplified model makes the result of groundwater simulation and prediction uncertain.The sources of uncertainty are composed of model parameter uncertainty,model structural uncertainty and uncertainty from observation datas.Nowadays,the main analysis method for groundwater model structural uncertainty is Bayesian model averaging(BMA)method.But BMA suffers from the difficulty of model weight esitmation,which makes its application infeasible.Recently analysis method for groundwater model structural uncertainty based on data-driven model is paid great attention,such as Gaussian process regression(GPR).In this paper,GPR is used to analyse the structural uncertainty in groundawater simulation.Main results are as follows.Fisrstly,the analysis method for model structural uncertainty based on GPR is established by combining the DREAMzs algorithm with GPR,which makes the parameters of groundwater model and hyperparameters of GPR identified simultaneously.Based on the method,a synthetic numerical simulation of seawater intrusion in karst fissure area and a solute transport column experiment are taken as case studies to analyze the uncertainty of groundwater model parameters and prediction results.In contrast with the uncertainty analysis without considering model structural error,the impact of parameter compensation is significantly reduced by considering model structural error.Moreover,the model prediction performance is also improved.Secondly,the performance of analysis of model structural uncertainty based on GPR with single-kernel,double-kernel and multi-kernel functions is systematically compared and evaluated.Square exponential,Matern and rational quadratic kernel functions are combined,including the combination of single,double and multiple kernel functions.Through three cases of groundwater analytical solutions,different combinations of kernel functions are used to analyze the structural uncertainty of groundwater model based on GPR.By comparing and analyzing the quantitative evaluation indexes under different kernel conditions,it is found that the rational quadratic kernel is the best because of its shape hyperparameter making the kernel structure adjustable and the square exponential function is also pretty good among the GPR results of all kernel functions.What's more,if the type of cases are similar,the kernel function may have similar results.Becasuse too many hyperparameters of double-kernel or multi-kernel functions lead to overfitting,the prediction results of GPR based on those kernel functions are worse than those of single kernel functions.Thirdly,as for complex groundwater model uncertainty analysis with uncertainty transfering between multiple submodels and multi-source datas,Stacked GPR is applied to a hierarchical synthetic solute transport model.Uncertainty of groundwater model parameters and prediction is analyzed respectively based on Stacked GPR and single GPR.The results show that most physical parameters are identified pretty well and the prediction results of each layer based on Stacked GPR are better than those of each layer based on single GPR.In addition,compared with single GPR,the absolute error of prediction value based on Stacked GPR is generally smaller in the entire area,but the introduction of structural error terms in flow submodels of Stacked GPR will change the model boundary conditions and increases the uncertainty of the input of solute transport submodel.It makes that the absolute error of C(concentration)prediction value is larger in the areas without observation points or around hydrogeological boundaries,the increase of prediction indexes is not obvious and the posterior distribution of a few parameters is biased.