scholarly journals Implementation of the Kalman Filter for a Geostatistical Bivariate Spatiotemporal Estimation of Hydraulic Conductivity in Aquifers

Water ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 3136
Author(s):  
Hugo Enrique Júnez-Ferreira ◽  
Julián González-Trinidad ◽  
Carlos Alberto Júnez-Ferreira ◽  
Cruz Octavio Robles Rovelo ◽  
G.S. Herrera ◽  
...  
Keyword(s):  
Spatial Distribution ◽  
Kalman Filter ◽  
Hydraulic Conductivity ◽  
Flow Model ◽  
Hydraulic Head ◽  
Spatiotemporal Data ◽  
Hydraulic Parameters ◽  
Synthetic Experiment ◽  
Heterogeneous Aquifer ◽  
Estimate Error

The estimation of the hydraulic parameters of an aquifer such as the hydraulic conductivity is somehow complicated due to its heterogeneity, on the other hand field and laboratory tests are both time consuming and costly. The use of geostatistical-based techniques for data assimilation could represent an alternative tool that allows the use of space-time aquifer behaviour to characterize hydraulic conductivity heterogeneity. In this paper, a spatiotemporal bivariate methodology was implemented combining historical hydraulic head data with hydraulic conductivity sparse data in order to obtain an estimate of the spatial distribution of the latter variable. This approach takes advantage of the correlation between the hydraulic conductivity (K) and the hydraulic head (H) behaviour through time. In order to evaluate this approach, a synthetic experiment was constructed through a transitory numerical flow-model that simulates hydraulic head values in a horizontally-heterogeneous aquifer. Geostatistical tools were used to describe the correlation between simulated spatiotemporal data of hydraulic head and the spatial distribution of the hydraulic conductivity in a group of model nodes. Subsequently, the Kalman filter was used to estimate the hydraulic conductivity values at nonsampled sites. The results showed acceptable differences between estimated and synthetic hydraulic conductivity data, with low estimate error variances (predominating the 1 m2/day2 value for K for all the cases, however, the smallest number of cells with values above 2 m2/day2 correspond to the bivariate spatiotemporal case) and the best agreement between the estimated errors and the selected model variance (SMSE values of 0.574 and 0.469) were found for the bivariate cases, which suggests that the implemented methodology could be used for reducing calibration efforts, particularly when the hydraulic parameters data are scarce.

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

2013 ◽  
Vol 17 (4) ◽  
pp. 1517-1531 ◽  
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. 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 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.

Spatial Variation of Aquifer Parameters from Coastal Aquifers of Sindhudurg District, Maharashtra Using Pore-water Resistivity and Bulk Resistivity

2018 ◽  
Vol 1 (1) ◽  
pp. 28-40
Author(s):  
Suneetha Naidu ◽  
Gautam Gupta
Keyword(s):  
Hydraulic Conductivity ◽  
Pore Water ◽  
Coastal Aquifers ◽  
Hydraulic Parameters ◽  
Formation Factor ◽  
Bulk Resistivity ◽  
Good Correspondence ◽  
Aquifer System ◽  
Transverse Resistance ◽  
Water Resistivity

Estimation of hydraulic parameters in coastal aquifers is an important task in groundwater resource assessment and development. An attempt is made to estimate these parameters using geoelectrical data in combination with pore-water resistivity of existing wells. In the present study, 29 resistivity soundings were analysed along with 29 water samples, collected from the respective dug wells and boreholes, in order to compute hydraulic parameters like formation factor, porosity, hydraulic conductivity and transmissivity from coastal region of north Sindhudurg district, Maharashtra, India. The result shows some parts of the study area reveal relatively high value of hydraulic conductivity, porosity and transmissivity. Further, a negative correlation is seen between hydraulic conductivity and bulk resistivity. The hydraulic conductivity is found to vary between 0.014 and 293 m/day, and the transmissivity varied between 0.14 and 11,722 m2/day. The transmissivity values observed here are in good correspondence with those obtained from pumping test data of Central Ground Water Board. These zones also have high aquifer thickness and therefore characterize high potential within the water-bearing formation. A linear, positive relationship between transverse resistance and transmissivity is observed, suggesting increase in transverse resistance values indicate high transmissivity of aquifers. These relations will be extremely vital in characterization of aquifer system, especially from crystalline hard rock area.

scholarly journals Geological and groundwater flow model of a submarine groundwater discharge site at Hanko (Finland), northern Baltic Sea

2021 ◽  
Author(s):  
Samrit Luoma ◽  
Juha Majaniemi ◽  
Arto Pullinen ◽  
Juha Mursu ◽  
Joonas J. Virtasalo
Keyword(s):  
Hydraulic Conductivity ◽  
Groundwater Flow ◽  
Baltic Sea ◽  
Submarine Groundwater Discharge ◽  
Flow Model ◽  
Groundwater Discharge ◽  
Coarse Grained ◽  
Local Geometry ◽  
Groundwater Flow Model ◽  
Submarine Groundwater

AbstractThree-dimensional geological and groundwater flow models of a submarine groundwater discharge (SGD) site at Hanko (Finland), in the northern Baltic Sea, have been developed to provide a geological framework and a tool for the estimation of SGD rates into the coastal sea. The dataset used consists of gravimetric, ground-penetrating radar and shallow seismic surveys, drill logs, groundwater level monitoring data, field observations, and a LiDAR digital elevation model. The geological model is constrained by the local geometry of late Pleistocene and Holocene deposits, including till, glacial coarse-grained and fine-grained sediments, post-glacial mud, and coarse-grained littoral and aeolian deposits. The coarse-grained aquifer sediments form a shallow shore platform that extends approximately 100–250 m offshore, where the unit slopes steeply seawards and becomes covered by glacial and post-glacial muds. Groundwater flow preferentially takes place in channel-fill outwash coarse-grained sediments and sand and gravel interbeds that provide conduits of higher hydraulic conductivity, and have led to the formation of pockmarks on the seafloor in areas of thin or absent mud cover. The groundwater flow model estimated the average SGD rate per square meter of the seafloor at 0.22 cm day−1 in autumn 2017. The average SGD rate increased to 0.28 cm day−1 as a response to an approximately 30% increase in recharge in spring 2020. Sensitivity analysis shows that recharge has a larger influence on SGD rate compared with aquifer hydraulic conductivity and the seafloor conductance. An increase in recharge in this region will cause more SGD into the Baltic Sea.

Quantitative investigations of the hydraulic connection between a large reservoir and a buried valley aquifer in southern Alberta

2005 ◽  
Vol 42 (5) ◽  
pp. 1461-1473 ◽  
Author(s):  
B D Smerdon ◽  
C A Mendoza ◽  
A M McCann
Keyword(s):  
Groundwater Flow ◽  
Flow Model ◽  
Hydraulic Head ◽  
Water Levels ◽  
Groundwater Flow Model ◽  
Reservoir Level ◽  
Hydraulic Connection ◽  
Southern Alberta ◽  
Approximate Location ◽  
Pumping Rates

Quantitative investigations, including two aquifer tests and development of a three-dimensional (3D) groundwater flow model, were required to determine the hydraulic connection between an irrigation reservoir and a buried valley aquifer in southern Alberta. Evidence of seepage was detected in the buried valley aquifer 10 km east of the Pine Coulee reservoir at the onset of filling in 1999, when the reservoir level exceeded an elevation of 1035 m above sea level (a.s.l.). Concern for an increase in the local water table and the creation of artesian conditions in the aquifer prompted this study to determine the approximate location of a seepage window that appeared to be connecting the reservoir and aquifer. Observations of hydraulic head in the aquifer during the pumping tests revealed a barrier boundary when the reservoir level was at an elevation of 1035 m a.s.l. and a recharge boundary condition when the elevation exceeded 1039 m a.s.l. These data were used to calibrate a 3D groundwater flow model, which was needed to determine the hydraulic properties and approximate location of the leakage zone. The quantitative investigation showed that seepage likely occurred through the sideslopes of the flooded coulee, rather than through the low-permeability coulee floor sediments or the embankment dam. Further simulations illustrated the expected seepage rates at various reservoir supply levels and the pumping rates required for relief wells installed in the buried valley aquifer to maintain historic aquifer hydraulic head. A brief postanalysis indicated that the forecasted pumping rates were only 15% lower than have been required to maintain preconstruction water levels in the buried valley aquifer.Key words: dams, seepage analysis, groundwater modelling, buried valley aquifer, pumping test.

Simulating transient infiltration in unsaturated soils

1998 ◽  
Vol 35 (6) ◽  
pp. 1093-1100 ◽  
Author(s):  
J R McDougall ◽  
I C Pyrah
Keyword(s):  
Hydraulic Conductivity ◽  
Unsaturated Soils ◽  
Flow Model ◽  
Unsaturated Flow ◽  
Surface Region ◽  
Infiltration Rate ◽  
Soil Suction ◽  
Wetting Front ◽  
Near Surface ◽  
Unsaturated Hydraulic Conductivity

Transient responses to various infiltration events have been examined using an unsaturated flow model. Numerical simulations reveal a range of infiltration patterns which can be related to the ratio of infiltration rate to unsaturated hydraulic conductivity. A high value of this ratio reflects a prevailing hydraulic conductivity which cannot readily redistribute the newly infiltrated moisture. Moisture accumulates in the near-surface region before advancing down through the soil as a distinct wetting front. In contrast, low values of the ratio of rainfall to unsaturated hydraulic conductivity show minimal moisture accumulation, as the relatively small volumes of infiltrating moisture are readily redistributed through the soil profile.Key words: numerical modelling, infiltration, unsaturated soil, soil suction, groundwater.

scholarly journals Simultaneous estimation of land surface scheme states and parameters using the ensemble Kalman filter: identical twin experiments

2011 ◽  
Vol 15 (8) ◽  
pp. 2437-2457 ◽  
Author(s):  
S. Nie ◽  
J. Zhu ◽  
Y. Luo
Keyword(s):  
Parameter Estimation ◽  
Soil Moisture ◽  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Land Surface ◽  
Estimation Method ◽  
State Parameter ◽  
Hydraulic Parameters ◽  
Constrained Estimation ◽  
Estimated Parameters

Abstract. The performance of the ensemble Kalman filter (EnKF) in soil moisture assimilation applications is investigated in the context of simultaneous state-parameter estimation in the presence of uncertainties from model parameters, soil moisture initial condition and atmospheric forcing. A physically based land surface model is used for this purpose. Using a series of identical twin experiments in two kinds of initial parameter distribution (IPD) scenarios, the narrow IPD (NIPD) scenario and the wide IPD (WIPD) scenario, model-generated near surface soil moisture observations are assimilated to estimate soil moisture state and three hydraulic parameters (the saturated hydraulic conductivity, the saturated soil moisture suction and a soil texture empirical parameter) in the model. The estimation of single imperfect parameter is successful with the ensemble mean value of all three estimated parameters converging to their true values respectively in both NIPD and WIPD scenarios. Increasing the number of imperfect parameters leads to a decline in the estimation performance. A wide initial distribution of estimated parameters can produce improved simultaneous multi-parameter estimation performances compared to that of the NIPD scenario. However, when the number of estimated parameters increased to three, not all parameters were estimated successfully for both NIPD and WIPD scenarios. By introducing constraints between estimated hydraulic parameters, the performance of the constrained three-parameter estimation was successful, even if temporally sparse observations were available for assimilation. The constrained estimation method can reduce RMSE much more in soil moisture forecasting compared to the non-constrained estimation method and traditional non-parameter-estimation assimilation method. The benefit of this method in estimating all imperfect parameters simultaneously can be fully demonstrated when the corresponding non-constrained estimation method displays a relatively poor parameter estimation performance. Because all these constraints between parameters were obtained in a statistical sense, this constrained state-parameter estimation scheme is likely suitable for other land surface models even with more imperfect parameters estimated in soil moisture assimilation applications.

scholarly journals Analysis of Groundwater Response to Oscillatory Pumping Test in Unconfined Aquifers: Consider the Effects of Initial Condition and Wellbore Storage

2018 ◽  
Author(s):  
Ching-Sheng Huang ◽  
Ya-Hsin Tsai ◽  
Hund-Der Yeh ◽  
Tao Yang
Keyword(s):  
Water Table ◽  
Integral Transform ◽  
Pumping Test ◽  
Hydraulic Head ◽  
Analytical Models ◽  
Hydraulic Parameters ◽  
Storage Effect ◽  
Initial Condition ◽  
Wellbore Storage ◽  
Present Solution

Abstract. Oscillatory pumping test (OPT) is an alternative to constant-head and constant-rate pumping tests for determining aquifer hydraulic parameters without water extraction. There is a large number of analytical models presented for the analyses of OPT. The combined effects of wellbore storage and initial condition regarding the hydraulic head prior to OPT are commonly neglected in the existing models. This study aims to develop a new model for describing the hydraulic head fluctuation induced by OPT in an unconfined aquifer. The model contains a typical flow equation with an initial condition of static water table, inner boundary condition specified at the rim of a finite-radius well for incorporating wellbore storage effect, and linearized free surface equation describing water table movement. The analytical solution of the model is derived by the Laplace transform and finite integral transform. Sensitivity analysis is carried out for exploring head response to the change in each of hydraulic parameters. Results suggest that head fluctuation due to OPT starts from the initial condition and gradually tends to simple harmonic motion (SHM) after a certain pumping time. A criterion for estimating the time to have SHM since OPT is graphically presented. The validity of assuming an infinitesimal well radius without wellbore storage effect is investigated. The present solution agrees well to head fluctuation data observed at the Boise hydrogeophysical research site in southwestern Idaho.

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>

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