Characterization Of Aquifer Heterogeneity Based On Multi-source Data Assimilation

The aquifer is inherently heterogeneous at different scales.Aquifer heterogeneity significantly impacts the processes of subsurface flow,solute and energy transport.As an import part of the aquifer,the streambed also shows significant heterogeneity.The streambed heterogeneity controls the surface water-groundwater exchange,which further influences biogeochemical cycles in the river system.Thus,accurate characterization of aquifer heterogeneity is vital for the management of regional water resources,as well as the protection of hydro-ecosystems.Information about the spatial variability of hydraulic parameters is traditionally obtained through the classical approaches,namely small-scale measurements of cores and slug/bail tests,which are expensive and time-consuming.Recent researches have focused on data assimilation methods,which inversely estimate the heterogeneous hydraulic parameters from easily obtained state variables(such as hydraulic head,solute concentration and temperature)in groundwater hydrology.Numerous studies have shown that the estimated hydraulic parameters through the data assimilation methods perform better than those obtained through traditional approaches in predicting the exchange flow and the related processes.To accurately characterize the heterogeneity of streambed hydraulic parameters and obtain an improved understanding of the interactions between surface water(SW)and groundwater(GW),we conducted the following analyses in this thesis:(1)We used an iterative ensemble smoother(IES)to quantify the spatial distribution of hydraulic parameters and 2-D exchange fluxes in streambeds by assimilating hydraulic head and temperature measurements.Four assimilation scenarios corresponding to different potential field applications were tested.In the first three scenarios,the heterogeneous hydraulic conductivity fields were first inferred from hydraulic head and/or temperature measurements,and then the flux fields were derived through Darcy's law using the estimated conductivity fields.The flux fields were estimated directly from the temperature measurements in the fourth scenario,which was more efficient and especially suitable for the situation that a complete knowledge of flow boundary conditions was unavailable.We concluded that,the best estimation could be achieved through jointly assimilating hydraulic head and temperature measurements,and temperature data were superior to the head data when they were used independently.Overall,the IES method provided more robust and accurate vertical flux estimations than those given by the widely used analytical solution-based methods.Furthermore,IES gave reasonable uncertainty estimations,which were unavailable in traditional methods.Since temperature can be accurately monitored with high spatial and temporal resolutions,the coupling of heat tracing techniques and IES provides promising potential in quantifying complex exchange fluxes under field conditions.(2)We proposed an efficient optimal design framework to collect the most informative diurnal temperature signal for Bayesian estimation of streambed hydraulic conductivities.The data worth(DW)was measured by the expected relative entropy from the prior to posterior distributions of conductivity fields.An adaptively refined Gaussian process(GP)surrogate was employed to alleviate the computational burden,resulting in at least three orders of magnitude of speed-up.The designed spatiotemporal monitoring networks in both numerical and sandbox experimental cases showed that,the most informative instants centered in a short period after the minimum/maximum temperature appeared.With the fixed number of measurements,extending the calibration period was more beneficial than increasing the monitoring frequency in improving the estimation results.To our best knowledge,this work is the first study on Bayesian monitoring design for streambed characterization with the heat tracing method.The method and results can provide guidance on selecting monitoring strategies under budget-limited conditions.(3)To improve the computational efficiency of data assimilation and experimental design,we proposed an adaptive GP based iterative ensemble smoother(GPIES)in this study.At each iteration of GPIES,the GP surrogate was adaptively refined by adding a few new base points chosen from the updated parameter realizations.Then the sensitivity information between model parameters and measurements was calculated from a large number of realizations generated by the GP surrogate with virtually no computational cost.Since the original model evaluations were only required for base points,whose number was much smaller than the ensemble size,the computational cost was significantly reduced,compared with the traditional IES.The applicability of GPIES in estimating heterogeneous conductivity was evaluated by two numerical cases and one sandbox experimental case.Results showed that GPIES achieved about one order of magnitude of speed-up compared with the standard IES,without sacrificing estimation accuracy.Although subsurface flow problems were considered in this study,the proposed method can be equally applied to other hydrological models.(4)To improve the applicability and computational efficiency of traditional filters and their variants,we proposed an adaptive GP based iterative smoother(GPIS)in this study.At each iteration,the sensitivity information was analytically derived from the GP surrogate and the updated parameter vector was treated as a new base point to refine the GP surrogate.Since the original model evaluations were still only required for base points,the computational cost of GPIS was much lower than that of the traditional IES and the recently proposed GPIES.The applicability of GPIS in estimating heterogeneous conductivity was evaluated by one synthetic case and one sandbox experimental case.The inversion results were compared with those of IES,IS and GPIES.Overall,GPIS showed superiority over the other three algorithms in terms of the computational efficiency and estimation accuracy.Furthermore,this method was nonintrusive so that it can be implemented easily.