Abstract:Abstract. Groundwater flow models are important tools in assessing baseline conditions and investigating management alternatives in groundwater systems. The usefulness of these models, however, is often hindered by insufficient knowledge regarding the magnitude and spatial distribution of the spatially-distributed parameters, such as hydraulic conductivity (K), that govern the response of these models. Proposed parameter estimation methods frequently are demonstrated using simplified aquifer representations, w… Show more
“…In Li et al (2012), the EnKF was used to map the hydraulic conductivity and porosity fields by assimilating dynamic piezometric data and multiple concentration data. In Bailey and Baú (2012), the ES was iteratively applied to estimate the parameters of a geostatistical model through assimilation of water table elevation data. Tong et al (2012) used the EnKF in a synthetic two-dimensional aquifer to estimate the hydraulic conductivity by assimilating solute concentration data measured in a large number of observation wells.…”
Abstract. Estimating the spatial variability of hydraulic conductivity K in natural aquifers is important for predicting the transport of dissolved compounds. Especially in the nonreactive case, the plume evolution is mainly controlled by the heterogeneity of K. At the local scale, the spatial distribution of K can be inferred by combining the Lagrangian formulation of the transport with a Kalman-filter-based technique and assimilating a sequence of time-lapse concentration C measurements, which, for example, can be evaluated on site through the application of a geophysical method. The objective of this work is to compare the ensemble Kalman filter (EnKF) and the ensemble smoother (ES) capabilities to retrieve the hydraulic conductivity spatial distribution in a groundwater flow and transport modeling framework. The application refers to a two-dimensional synthetic aquifer in which a tracer test is simulated. Moreover, since Kalmanfilter-based methods are optimal only if each of the involved variables fit to a Gaussian probability density function (pdf) and since this condition may not be met by some of the flow and transport state variables, issues related to the nonGaussianity of the variables are analyzed and different transformation of the pdfs are considered in order to evaluate their influence on the performance of the methods. The results show that the EnKF reproduces with good accuracy the hydraulic conductivity field, outperforming the ES regardless of the pdf of the concentrations.
“…In Li et al (2012), the EnKF was used to map the hydraulic conductivity and porosity fields by assimilating dynamic piezometric data and multiple concentration data. In Bailey and Baú (2012), the ES was iteratively applied to estimate the parameters of a geostatistical model through assimilation of water table elevation data. Tong et al (2012) used the EnKF in a synthetic two-dimensional aquifer to estimate the hydraulic conductivity by assimilating solute concentration data measured in a large number of observation wells.…”
Abstract. Estimating the spatial variability of hydraulic conductivity K in natural aquifers is important for predicting the transport of dissolved compounds. Especially in the nonreactive case, the plume evolution is mainly controlled by the heterogeneity of K. At the local scale, the spatial distribution of K can be inferred by combining the Lagrangian formulation of the transport with a Kalman-filter-based technique and assimilating a sequence of time-lapse concentration C measurements, which, for example, can be evaluated on site through the application of a geophysical method. The objective of this work is to compare the ensemble Kalman filter (EnKF) and the ensemble smoother (ES) capabilities to retrieve the hydraulic conductivity spatial distribution in a groundwater flow and transport modeling framework. The application refers to a two-dimensional synthetic aquifer in which a tracer test is simulated. Moreover, since Kalmanfilter-based methods are optimal only if each of the involved variables fit to a Gaussian probability density function (pdf) and since this condition may not be met by some of the flow and transport state variables, issues related to the nonGaussianity of the variables are analyzed and different transformation of the pdfs are considered in order to evaluate their influence on the performance of the methods. The results show that the EnKF reproduces with good accuracy the hydraulic conductivity field, outperforming the ES regardless of the pdf of the concentrations.
“…The latter is referred to as return mass (RM) throughout the remainder of this paper. The ES scheme is used due to its computational efficiency (Bailey and Baù, 2012), a particularly constraining requirement when dealing with physically-based distributed, data-intensive models such as reactive transport models. The methodology is applied to a 1-year transient simulation for a synthetic aquifer system characterized by a comprehensive suite of hydrological and chemical forcing terms, processes, and system parameters that approaches a real-world setting.…”
“…Rasmussen et al (2015) used the ensemble transform Kalman filter (ETKF) to assimilate groundwater head and stream discharge in a catchment-scale integrated hydrological model for both state updating and parameter estimation. Other studies that focus on joint state updating and parameter estimation in integrated hydrological modelling include Bailey and Baù (2012), in which a smoother was used to calibrate hydraulic conductivity using streamflow and head observations, and Kurtz et al (2013), which used head observations to calibrate heterogenous riverbed conductivities.…”
Abstract. The use of bias-aware Kalman filters for estimating and correcting observation bias in groundwater head observations is evaluated using both synthetic and real observations. In the synthetic test, groundwater head observations with a constant bias and unbiased stream discharge observations are assimilated in a catchment-scale integrated hydrological model with the aim of updating stream discharge and groundwater head, as well as several model parameters relating to both streamflow and groundwater modelling. The coloured noise Kalman filter (ColKF) and the separate-bias Kalman filter (SepKF) are tested and evaluated for correcting the observation biases. The study found that both methods were able to estimate most of the biases and that using any of the two bias estimation methods resulted in significant improvements over using a bias-unaware Kalman filter. While the convergence of the ColKF was significantly faster than the convergence of the SepKF, a much larger ensemble size was required as the estimation of biases would otherwise fail. Real observations of groundwater head and stream discharge were also assimilated, resulting in improved streamflow modelling in terms of an increased Nash-Sutcliffe coefficient while no clear improvement in groundwater head modelling was observed. Both the ColKF and the SepKF tended to underestimate the biases, which resulted in drifting model behaviour and sub-optimal parameter estimation, but both methods provided better state updating and parameter estimation than using a bias-unaware filter.
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