An Adaptive Surrogate Based Method For Groundwater Data Assimilation

Accurate characterization of subsurface hydraulic parameters is vital to the modeling of groundwater flow and contaminant transport.However,the hydraulic conductivities of aquifers are usually associated with natural spatial heterogeneity.Limited by manpower and resources,the amount of borehole measurements of hydraulic conductivity is usually limited.Therefore,the prediction of groundwater flow and contaminant transport inevitably involves with some degree of uncertainty.Data assimilation methods can be used to fuse information from head data,inversely estimate parameters and reduce the uncertainty in groundwater modeling.With the development of measuring and sensing technology,various monitoring data are becoming more and more accessible in real-time on site.The booming of data technology requires more accurate and efficient data assimilation methods urgently.The iterative ensemble smoother(IES)has been widely used in data assimilation problems for groundwater,soil water and petroleum reservoir models.IES is essentially a method based on Monte Carlo simulation and requires a large number of realizations to ensure the accuracy of the results.However,a large-scale groundwater model with numerous nodes usually needs a long period of simulation time.Thus a large ensemble size will lead to unaffordable computational burden,which hinders the fast and accurate parameter inversion and rational decision making for the assessment and management of groundwater resources.To address the above issues,this thesis developed an IES algorithm based on the adaptive surrogate system for the inversion of spatial heterogeneous conductivity field of groundwater flow models.The numerical and field case studies were implemented to illustrate the validity of proposed algorithm.The research results are helpful to accurately and efficiently fuse groundwater monitoring data,to reduce the uncertainties in groundwater modeling,and have important theoretical significance for the rational management of groundwater resources.The main contents and results of this thesis are as follows:(1)An algorithm that seamlessly couples the adaptive polynomial chaos expansion(PCE)surrogate with the IES data assimilation framework has been developed.The core idea of this method is to explore the target parameter space by using the surrogate model through iterations,and to adaptively refine the surrogate model based on the preliminary inversion results.In this way,the true parameters can be gradually approached.In the actual implementation,the Karhunen-Loève(KL)expansion is firstly used to reduce the dimensionality of heterogeneous conductivity field.The training parameter set is generated based on the Gaussian random variables after dimension reduction.Then the sparse PCE is constructed to approximate the groundwater model and serves as the surrogate in IES.During the data assimilation,a small number of posterior realizations are used to adjust the training set and improve the surrogate.Since a much smaller number of groundwater model evaluations are required,the computational cost can be significantly reduced compared to the traditional IES algorithm.(2)A 2-D numerical case study was implemented to validate the proposed method in the inversion of moderately heterogeneous conductivity field.The results showed that,the surrogate could be improved with the adjustment of training set and adaptively approached the original model outputs with true parameters.The detailed comparison with the traditional IES showed that the inversion results of this method were similar in terms of accuracy,but the computational cost(i.e.,the number of original model evaluations)was reduced by an order of magnitude.(3)A real-world field study was implemented to verify the performance of this method in the inversion of highly heterogeneous 3-D conductivity field.The results showed that,with the increasing heterogeneity,the difficulty in constructing the surrogate model increased,and the advantages of the proposed method over IES were reduced as well.However,the new method could still achieve the similar accuracy of IES with 1/3 computational cost.The inversion results were also in good agreement with the geological survey results.