Joint inversion of contaminant source and aquifer parameters by assimilating ERT data with the ES-MDA algorithm
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Abstract:
Predicting the migration and transformation process of contaminants by utilizing numerical models is a commonly used method.The accuracy of model parameters could seriously affect the simulation results.While in practical site investigation,model parameters are often unavailable to obtain directly,thus it is needed to be estimated by solving the inverse problem of groundwater.In recent years,data assimilation has become a prevalent method for parametric uncertainty quantification.It can provide an estimate of the unknown model parameters by combining the observation data with the underlying dynamical principles governing the system.When solving high dimensional inversion problems,conventional observation methods can only provide sparse information (such as mass concentration and hydraulic head),so it can hinder the accuracy of the results.To deal with this issue,geophysical methods (such as electrical resistance tomography) are introduced to combine with the data assimilation because they can provide a large amount of continuous observation data. The groundwater flow and solute transport model was constructed with the MODFLOW and MT3DMS programs and KL expansion was introduced to implement the dimensionality reduction of the hydraulic conductivity field.An inversion method for groundwater model parameters based on the ensemble smoother with multiple data assimilation (ES-MDA) was proposed.The joint inversion of contaminant source strength and hydraulic conductivity field was realized by integrating conventional observation data (mass concentration and hydraulic head) and geophysical data (ERT data) collected through the electrical resistance tomography (ERT).Three numerical cases were designed based on the former ideas to compare the inversion accuracy with different types of observation data.All three cases were the ES-MDA algorithm as the data assimilation method,while Case 1 was integrated the mass concentration and hydraulic head as the observation data;Case 2 was integrated the ERT data as the observation data and Case 3 was integrated the three types of data simultaneously.The root-mean-square error (ERMS) was used to quantify the accuracy of the inversion results of the three cases. The results showed that the ERMS value for estimating the contaminant source strength got smaller (closer to zero) from Case 1 to Case 3,which exhibited that Case 3 obtained more accurate results by integrating multi-source observation data.As for the characterization of the hydraulic conductivity field,the posterior mean estimate of the log-conductivity field of Case 3 depicted the spatial distribution of the lnK field more accurately and its goodness of fit with the reference field was better than that of Case 1 and Case 2,which also demonstrated the advantage of using multi-source data as the observation. ES-MDA algorithm could be utilized to realize the joint inversion of contaminant source strength and hydraulic conductivity field by assimilating both conventional observation data (mass concentration and hydraulic head) and ERT data.The inversion results by assimilating ERT data showed better accuracy than the case with conventional observation data,which demonstrated that a large amount of continuous geophysical data could provide more effective information for the inversion.The inversion results could be further optimized by combing the ERT data with the conventional observation data of mass concentration and head.It also showed the importance of using multi-source observation data when dealing with inversion problems.
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