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 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.

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 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 An efficient ensemble Kalman Filter implementation via shrinkage covariance matrix estimation: exploiting prior knowledge

2021 ◽  
Vol 25 (3) ◽  
pp. 985-1003
Author(s):  
Santiago Lopez-Restrepo ◽  
Elias D. Nino-Ruiz ◽  
Luis G. Guzman-Reyes ◽  
Andres Yarce ◽  
O. L. Quintero ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Prior Knowledge ◽  
Covariance Matrix ◽  
Ensemble Kalman Filter ◽  
General Circulation ◽  
Circulation Model ◽  
Covariance Matrix Estimation ◽  
Practical Implementation ◽  
Matrix Estimation ◽  
The Impact

AbstractIn this paper, we propose an efficient and practical implementation of the ensemble Kalman filter via shrinkage covariance matrix estimation. Our filter implementation combines information brought by an ensemble of model realizations, and that based on our prior knowledge about the dynamical system of interest. We perform the combination of both sources of information via optimal shrinkage factors. The method exploits the rank-deficiency of ensemble covariance matrices to provide an efficient and practical implementation of the analysis step in EnKF based formulations. Localization and inflation aspects are discussed, as well. Experimental tests are performed to assess the accuracy of our proposed filter implementation by employing an Advection Diffusion Model and an Atmospheric General Circulation Model. The experimental results reveal that the use of our proposed filter implementation can mitigate the impact of sampling noise, and even more, it can avoid the impact of spurious correlations during assimilation steps.

scholarly journals Improving the joint estimation of CO<sub>2</sub> and surface carbon fluxes using a Constrained Ensemble Kalman Filter in COLA (v1.0)

2021 ◽  
Author(s):  
Zhiqiang Liu ◽  
Ning Zeng ◽  
Yun Liu ◽  
Eugenia Kalnay ◽  
Ghassem Asrar ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Grid Point ◽  
Carbon Sources ◽  
Co2 Concentration ◽  
Carbon Fluxes ◽  
Joint Estimation ◽  
Observation Window ◽  
Surface Carbon ◽  
Carbon Dioxide Co2

Abstract. Atmospheric inversion of carbon dioxide (CO2) measurements to understand carbon sources and sinks has made great progress over the last two decades. However, most of the studies, including four-dimension variational (4D-Var), Ensemble Kalman filter (EnKF), and Bayesian synthesis approaches, obtains directly only fluxes while CO2 concentration is derived with the forward model as post-analysis. Kang et al. (2012) used the Local Ensemble Transform Kalman Filter (LETKF) that updates the CO2, surface carbon fluxes (SCF), and meteorology field simultaneously. Following this track, a system with a short assimilation window and a long observation window was developed (Liu et al., 2019). However, this system faces the challenge of maintaining global carbon mass. To overcome this shortcoming, here we introduce a Constrained Ensemble Kalman Filter (CEnKF) approach to ensure the conservation of global CO2 mass. After a standard LETKF procedure, an additional assimilation process is applied to adjust CO2 at each model grid point and to ensure the consistency between the analysis and the first guess of global CO2 mass. In the context of observing system simulation experiments (OSSEs), we show that the CEnKF can significantly reduce the annual global SCF bias from ~0.2 gigaton to less than 0.06 gigaton by comparing between experiments with and without it. Moreover, the annual bias over most continental regions is also reduced. At the seasonal scale, the improved system reduced the flux root-mean-square error from priori to analysis by 48–90 %, depending on the continental region. Moreover, the 2015–2016 El Nino impact is well captured with anomalies mainly in the tropics.

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

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.

Dynamic Fracture Characterization From Tracer-Test and Flow-Rate Data With Ensemble Kalman Filter

SPE Journal ◽  
2018 ◽  
Vol 23 (02) ◽  
pp. 449-466 ◽  
Author(s):  
Siavash Hakim Elahi ◽  
Behnam Jafarpour
Keyword(s):  
Kalman Filter ◽  
Hydraulic Conductivity ◽  
Test Data ◽  
Ensemble Kalman Filter ◽  
Tracer Test ◽  
Natural Fracture ◽  
Production Data ◽  
Matrix Properties ◽  
Half Length

Summary Hydraulic fracturing is performed to enable production from low-permeability and organic-rich shale-oil/gas reservoirs by stimulating the rock to increase its permeability. Characterization and imaging of hydraulically induced fractures is critical for accurate prediction of production and of the stimulated reservoir volume (SRV). Recorded tracer concentrations during flowback and historical production data can reveal important information about fracture and matrix properties, including fracture geometry, hydraulic conductivity, and natural-fracture density. However, the complexity and uncertainty in fracture and reservoir descriptions, coupled with data limitations, complicate the estimation of these properties. In this paper, tracer-test and production data are used for dynamic characterization of important parameters of hydraulically fractured reservoirs, including matrix permeability and porosity, planar-fracture half-length and hydraulic conductivity, discrete-fracture-network (DFN) density and conductivity, and fracture-closing (conductivity-decline) rate during production. The ensemble Kalman filter (EnKF) is used to update uncertain model parameters by sequentially assimilating first the tracer-test data and then the production data. The results indicate that the tracer-test and production data have complementary information for estimating fracture half-length and conductivity, with the former being more sensitive to hydraulic conductivity and the latter being more affected by fracture half-length. For characterization of DFN, a stochastic representation is adopted and the parameters of the stochastic model along with matrix and hydraulic-fracture properties are updated. Numerical examples are presented to investigate the sensitivity of the observed production and tracer-test data to fracture and matrix properties and to evaluate the EnKF performance in estimating these parameters.

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