scholarly journals Comparison of Two Ensemble-Kalman Filter Based Methods for Estimating Aquifer Parameters from Real 3-D Hydraulic and Tracer Tomographic Tests

Geosciences ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. 462
Author(s):  
Emilio Sánchez-León ◽  
Carsten Leven ◽  
Daniel Erdal ◽  
Olaf A. Cirpka
Keyword(s):  
Kalman Filter ◽  
Hydraulic Conductivity ◽  
Ensemble Kalman Filter ◽  
Tracer Tests ◽  
Site Investigation ◽  
Concentration Data ◽  
Arrival Times ◽  
Hydraulic Tomography ◽  
Conservative Tracer ◽  
Observation Wells

Pumping and tracer tests are site-investigation techniques frequently used to determine hydraulic conductivity. Tomographic test layouts, in which multiple tests with different combinations of injection and observation wells are performed, gain a better insight into spatial variability. While hydraulic tomography has repeatedly been applied in the field, tracer tomography lags behind. In a previous publication, we presented a synthetic study to investigate whether the ensemble Kalman Filter (EnKF) or the Kalman Ensemble Generator (KEG) performs better in inverting hydraulic- and tracer-tomographic data. In this work, we develop an experimental method for solute-tracer tomography using fluorescein as a conservative tracer. We performed hydraulic- and tracer-tomographic tests at the Lauswiesen site in Germany. We analyzed transient drawdown and concentration data with the EnKF and steady-state hydraulic heads and mean tracer arrival times with the KEG, obtaining more stable results with the KEG at lower computational costs. The spatial distribution of the estimated hydraulic conductivity field agreed with earlier descriptions of the aquifer at the site. This study narrows the gap between numerical studies and field applications for aquifer characterization at high resolution, showing the potential of combining ensemble-Kalman filter based methods with data collected from hydraulic and solute-tracer tomographic experiments.

scholarly journals Comparison of Two Ensemble Kalman-Based Methods for Estimating Aquifer Parameters from Virtual 2-D Hydraulic and Tracer Tomographic Tests

Geosciences ◽  
2020 ◽  
Vol 10 (7) ◽  
pp. 276 ◽  
Author(s):  
Emilio Sánchez-León ◽  
Daniel Erdal ◽  
Carsten Leven ◽  
Olaf A. Cirpka
Keyword(s):  
Hydraulic Conductivity ◽  
Ensemble Kalman Filter ◽  
Tracer Tests ◽  
Tracer Test ◽  
Transient Signal ◽  
Concentration Data ◽  
Pumping Tests ◽  
Test Parameter ◽  
Arrival Times ◽  
Temporal Moments

We compare two ensemble Kalman-based methods to estimate the hydraulic conductivity field of an aquifer from data of hydraulic and tracer tomographic experiments: (i) the Ensemble Kalman Filter (EnKF) and (ii) the Kalman Ensemble Generator (KEG). We generated synthetic drawdown and tracer data by simulating two pumping tests, each followed by a tracer test. Parameter updating with the EnKF is performed using the full transient signal. For hydraulic data, we use the standard update scheme of the EnKF with damping, whereas for concentration data, we apply a restart scheme, in which solute transport is resimulated from time zero to the next measurement time after each parameter update. In the KEG, we iteratively assimilate all observations simultaneously, here inverting steady-state heads and mean tracer arrival times. The inversion with the dampened EnKF worked well for the transient pumping-tests, but less for the tracer tests. The KEG produced similar estimates of hydraulic conductivity but at significantly lower costs. We conclude that parameter estimation in well-defined hydraulic tests can be done very efficiently by iterative ensemble Kalman methods, and ambiguity between state and parameter updates can be completely avoided by assimilating temporal moments of concentration data rather than the time series themselves.

scholarly journals Jointly mapping hydraulic conductivity and porosity by assimilating concentration data via ensemble Kalman filter

2012 ◽  
Vol 428-429 ◽  
pp. 152-169 ◽  
Author(s):  
Liangping Li ◽  
Haiyan Zhou ◽  
J. Jaime Gómez-Hernández ◽  
Harrie-Jan Hendricks Franssen
Keyword(s):  
Kalman Filter ◽  
Hydraulic Conductivity ◽  
Ensemble Kalman Filter ◽  
Concentration Data

Simultaneous identification of contaminant source location, initial contaminant concentration, horizontal and vertical hydraulic conductivity in a three-dimensional coastal aquifer via ensemble Kalman filter 

2021 ◽  
Author(s):  
Arezou Dodangeh ◽  
Mohammad Mahdi Rajabi ◽  
Marwan Fahs
Keyword(s):  
Kalman Filter ◽  
Hydraulic Conductivity ◽  
Coastal Aquifers ◽  
Ensemble Kalman Filter ◽  
Coastal Aquifer ◽  
Three Dimensional ◽  
Source Location ◽  
Contaminant Concentration ◽  
Contaminant Source ◽  
Vertical Hydraulic Conductivity

<p>In coastal aquifers, we face the problem of salt water intrusion, which creates a complex flow field. Many of these coastal aquifers are also exposed to contaminants from various sources. In addition, in many cases there is no information about the characteristics of the aquifer. Simultaneous identification of the contaminant source and coastal aquifer characteristics can be a challenging issue. Much work has been done to identify the contaminant source, but in the complex velocity field of coastal aquifer, no one has resolved this issue yet. We want to address that in a three-dimensional artificial coastal aquifer.</p><p>To achieve this goal, we have developed a method in which the contaminant source can be identified and the characteristics of the aquifer can be estimated by using information obtained from observation wells. First, by assuming the input parameters required to simulate the contaminant transfer to the aquifer, this three-dimensional coastal aquifer that is affected by various phenomena such as seawater intrusion, tides, shore slope, rain, discharge and injection wells, is simulated and the time series of the output parameters including head, salinity and contaminant concentration are estimated. In the next step, with the aim of performing inverse modeling, random values ​​are added to the time series of outputs obtained at specific points (points belonging to observation wells) in order to rebuilt the initial conditions of the problem to achieve the desired unknowns (contaminant source and aquifer characteristics). The unknowns estimated in this study are the contaminant source location (x, y, z), the initial contaminant concentration, the horizontal and vertical hydraulic conductivity of the aquifer. SEAWAT model in GMS software environment has been used to solve the equations of flow and contaminant transfer and simulate a three-dimensional coastal aquifer. Next, for reverse modeling, one of the Bayesian Filters subset (ensemble Kalman filter) has been used in the Python programming language environment. Also, to reduce the code run time, the neural network model is designed and trained for the SEAWAT model.</p><p>This method is able to meet the main purpose of the study, namely estimating the value ​​of unknown input parameters, including the contaminant source location, the initial contaminant concentration, the horizontal and vertical hydraulic conductivity of the aquifer. In addition, that makes it possible to achieve a three-dimensional numerical model of the coastal aquifer that can be used as a benchmark to examine more accurately the impact of different phenomena simultaneously. In conclusion, we have developed an algorithm which can be used in the world's coastal aquifers to identify the contaminant source and estimate its characteristics.</p><p> </p><p>Key words: coastal aquifer, seawater intrusion, contaminants, groundwater, flow field, parameter estimation, ensemble kalman filter</p>

scholarly journals Joint inference of groundwater–recharge and hydraulic–conductivity fields from head data using the ensemble Kalman filter

2016 ◽  
Vol 20 (1) ◽  
pp. 555-569 ◽  
Author(s):  
D. Erdal ◽  
O. A. Cirpka
Keyword(s):  
Kalman Filter ◽  
Hydraulic Conductivity ◽  
Groundwater Recharge ◽  
Prior Knowledge ◽  
Ensemble Kalman Filter ◽  
Joint Estimation ◽  
Inversion Method ◽  
Estimation Of Parameters ◽  
Worst Case ◽  
Joint Inference

Abstract. Regional groundwater flow strongly depends on groundwater recharge and hydraulic conductivity. Both are spatially variable fields, and their estimation is an ongoing topic in groundwater research and practice. In this study, we use the ensemble Kalman filter as an inversion method to jointly estimate spatially variable recharge and conductivity fields from head observations. The success of the approach strongly depends on the assumed prior knowledge. If the structural assumptions underlying the initial ensemble of the parameter fields are correct, both estimated fields resemble the true ones. However, erroneous prior knowledge may not be corrected by the head data. In the worst case, the estimated recharge field resembles the true conductivity field, resulting in a model that meets the observations but has very poor predictive power. The study exemplifies the importance of prior knowledge in the joint estimation of parameters from ambiguous measurements.

scholarly journals Parallelized ensemble Kalman filter for hydraulic conductivity characterization

2013 ◽  
Vol 52 ◽  
pp. 42-49 ◽  
Author(s):  
Teng Xu ◽  
J. Jaime Gómez-Hernández ◽  
Liangping Li ◽  
Haiyan Zhou
Keyword(s):  
Kalman Filter ◽  
Hydraulic Conductivity ◽  
Ensemble Kalman Filter

On the use of the ground water fluxes for hydraulic tomography: Theoretical and field-based assessments

2020 ◽  
Author(s):  
Behzad Pouladiborj ◽  
Olivier Bour ◽  
Niklas Linde ◽  
Daniel Paradis ◽  
Jean-Marc Ballard ◽  
...  
Keyword(s):  
Hydraulic Conductivity ◽  
Fiber Optic ◽  
Joint Inversion ◽  
Temporal Trends ◽  
Quebec City ◽  
Water Fluxes ◽  
Hydraulic Tomography ◽  
Direct Push ◽  
Groundwater Flux ◽  
Observation Wells

<p>Hydraulic tomography is known for imaging hydraulic conductivity of aquifers. In hydraulic tomography, the aquifer is stressed sequentially at several locations with pumping or slug tests while hydraulic heads are observed in different points. These hydraulic head data along with a numerical model are then used to reconstruct the hydraulic conductivity distribution of the aquifer through inversion process. The reconstructed distribution usually represents smooth-low resolution model of hydraulic conductivity which may be suitable for representation of groundwater flow with limited applicability to transport problems. Here, we investigate the added value of using groundwater fluxes measurement for the reconstruction of hydraulic conductivity in tomographic experiment. Vertical profile of groundwater flux may be estimated using active fiber optic distributed temperature sensor (FO-DTS) methods with FO cables installed by direct push so as it is in direct contact with formation. In active FO-DTS, FO cable is heated and heat is transported by conduction and convection. So different water fluxes result in different temperature behavior. This study is carried out in two parts. First, we conducted a synthetic analyze where we used a sequence of synthetic multivariate Gaussian aquifers with different tomographic configurations and datasets. This analysis showed that joint inversion of groundwater fluxes and hydraulic heads leads to better hydraulic conductivity resolution than using hydraulic heads solely. Inversion of groundwater fluxes alone is also superior than using only hydraulic heads. Then, insights gained from the synthetic study were used to guide the implementation of a field study at the Saint-Lambert experimental site located 40 km south of Quebec City, Canada. The tomography experiment was performed between 3 wells closely spaced (between 5 and 9 m) and two active FO-DTS cables. FO cables were installed vertically by a direct push drilling technique at mid-point between the central pumping well and two observation wells. Discrete intervals along the observation wells were also isolated with packers to monitor temperature and hydraulic heads at different depths in these two screened observational wells. First, the aquifer was constrained to pumping continuously for 24 hours at a constant rate of 10 LPM with simultaneously recording temperature (passive mode) and hydraulic heads in 8 discrete well intervals and in the pumping well itself as well as along the 2 FO-DTS with approximate resolution of 25 cm. Then, by analyzing the piezo-metric heads and making sure that steady-state conditions were achieved, the pumping was held at the same rate but heat was injected to fiber optic cables (active mode) for another 64-hour period. After this period, heating and pumping were stopped. Preliminary results show the feasibility of the active FO-DTS in capturing varying groundwater fluxes with depth, as reflected in the different temporal temperature trend. These temperature trends will be used to estimate the vertical groundwater flux profile from these temperature temporal trends at a vertical resolution of approximately 25 cm. Then estimated fluxes will be used for hydraulic tomography. Those experimental results along with the synthetic analyze are shown to be promising in improving characterization of hydraulic conductivity of aquifers.</p>

scholarly journals Ensemble Kalman filter versus ensemble smoother for assessing hydraulic conductivity via tracer test data assimilation

2012 ◽  
Vol 9 (11) ◽  
pp. 13083-13115
Author(s):  
E. Crestani ◽  
M. Camporese ◽  
D. Baú ◽  
P. Salandin
Keyword(s):  
Spatial Distribution ◽  
Kalman Filter ◽  
Hydraulic Conductivity ◽  
Ensemble Kalman Filter ◽  
Tracer Test ◽  
State Variables ◽  
Modeling Framework ◽  
Gaussian Probability Density Function ◽  
Flow And Transport ◽  
Ensemble Smoother

Abstract. The significance of estimating the spatial variability of the hydraulic conductivity K in natural aquifers is relevant to the possibility of defining the space and time evolution of a non-reactive plume, since the transport of a solute 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 Kalman filter-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 non-Gaussianity 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.

scholarly journals Joint inference of groundwater-recharge and hydraulic-conductivity fields from head data using the Ensemble-Kalman filter

2015 ◽  
Vol 12 (6) ◽  
pp. 5565-5599 ◽  
Author(s):  
D. Erdal ◽  
O. A. Cirpka
Keyword(s):  
Kalman Filter ◽  
Hydraulic Conductivity ◽  
Groundwater Recharge ◽  
Prior Knowledge ◽  
Ensemble Kalman Filter ◽  
Joint Estimation ◽  
Inversion Method ◽  
Estimation Of Parameters ◽  
Worst Case ◽  
Joint Inference

Abstract. Regional groundwater flow strongly depends on groundwater recharge and hydraulic conductivity. Both are spatially variable fields, and their estimation is an ongoing topic in groundwater research and practice. In this study, we use the Ensemble Kalman filter as an inversion method to jointly estimate spatially variable recharge and conductivity fields from head observations. The success of the approach strongly depends on the assumed prior knowledge. If the structural assumptions underlying the initial ensemble of the parameter fields are correct, both estimated fields resemble the true ones. However, erroneous prior knowledge may not be corrected by the data. In the worst case, the estimated recharge field resembles the true conductivity field, resulting in a model that meets the observations but has very poor predictive power. The study exemplifies the importance of prior knowledge in the joint estimation of parameters from ambiguous measurements.

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