A Geostatistical Inverse Method for Variably Saturated Flow in the Vadose Zone

Yeh, Tian Chyi Jim; Zhang, Jinqi

doi:10.1029/96wr01497

Cited by 88 publications

(56 citation statements)

References 32 publications

(34 reference statements)

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“…For applications to groundwater systems, the majority of methodologies are demonstrated using two-dimensional (2-D) confined groundwater flow models (e.g., Gailey et al, 1991;Hantush and Mariño, 1997;Hendricks Franssen et al, 1999;Drécourt et al, 2006;Hendricks Franssen and Kinzelbach, 2008;Fu and Gómez-Hernández, 2009;Bailey and Baù, 2010). Several studies have employed threedimensional steady-state flow models (Chen and Zhang, 2006;Liu et al, 2008), and several have estimated hydraulic parameters in variably-saturated flow conditions (Yeh and Zhang, 1996;Zhang and Yeh, 1997;Li and Yeh, 1999), although for the latter applications were limited to small 2-D vertical-plane systems. In general, however, critical components of hydrology in watershed systems, e.g., infiltration and percolation in variably-saturated porous media, ponding and overland flow, and stream channel flow have been neglected.…”

Section: R T Bailey and D Baù: Estimating Geostatistical Parametersmentioning

confidence: 99%

Estimating geostatistical parameters and spatially-variable hydraulic conductivity within a catchment system using an ensemble smoother

Bailey

Baù

2012

Hydrol. Earth Syst. Sci.

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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, when in reality the groundwater regime in a given watershed is influenced by strongly-coupled surface-subsurface processes. Furthermore, parameter estimation methodologies that rely on a geostatistical structure of K often assume the parameter values of the geostatistical model as known or estimate these values from limited data.In this study, we investigate the use of a data assimilation algorithm, the Ensemble Smoother, to provide enhanced estimates of K within a catchment system using the fullycoupled, surface-subsurface flow model CATHY. Both water table elevation and streamflow data are assimilated to condition the spatial distribution of K. An iterative procedure using the ES update routine, in which geostatistical parameter values defining the true spatial structure of K are identified, is also presented. In this procedure, parameter values are inferred from the updated ensemble of K fields and used in the subsequent iteration to generate the K ensemble, with the process proceeding until parameter values are converged upon. The parameter estimation scheme is demonstrated via a synthetic three-dimensional tilted v-shaped catchment system incorporating stream flow and variably-saturated subsurface flow, with spatio-temporal variability in forcing terms. Results indicate that the method is successful in providing improved estimates of the K field, and that the iterative scheme can be used to identify the geostatistical parameter values of the aquifer system. In general, water table data have a much greater ability than streamflow data to condition K. Future research includes applying the methodology to an actual regional study site.

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Section: R T Bailey and D Baù: Estimating Geostatistical Parametersmentioning

confidence: 99%

Estimating geostatistical parameters and spatially-variable hydraulic conductivity within a catchment system using an ensemble smoother

Bailey

Baù

2012

Hydrol. Earth Syst. Sci.

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“…Harter and Yeh [1996b] used the cokriging technique to investigate effects of conditioning using head and conductivity measurements on solute transport in the vadose zone. The technique was also employed by Yeh and Zhang [1996] to estimate parameters of unsaturated conductivity based on moisture content and head measurements. Tong [1996] applied cokriging to estimate the saturated conductivity of geological media using tracer concentration measurements.…”

Section: Introductionmentioning

confidence: 99%

Cokriging estimation of the conductivity field under variably saturated flow conditions

Yeh²

1999

Water Resources Research

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Abstract. A linear estimator, cokriging, was applied to estimate hydraulic conductivity, using pressure head, solute concentration, and solute arrival time measurements in a hypothetical, heterogeneous vadose zone under steady state infiltrations at different degrees of saturation. Covariances and cross-covariances required by the estimator were determined by a first-order approximation in which sensitivity matrices were calculated using an adjoint state method, The effectiveness of the pressure, concentration, and arrival time measurements for the estimator were then evaluated using two statistical criteria, L • and L 2 norms, i.e., the average absolute error and the mean square error of the estimated conductivity field. Results of our analysis showed that pressure head measurements at steady state flow provided the best estimation of hydraulic conductivity among the three types of measurements. In addition, head measurements of flow near saturation were found more useful for estimating conductivity than those at low saturations. The arrival time measurements do not have any significant advantage over concentration. Factors such as variability, linearity, and ergodicity were discussed to explain advantage and limitation of each type of data set. Finally, to take advantage of different types of data set (e.g., head and concentration), a computationally efficient estimation approach was developed to combine them sequentially to estimate the hydraulic conductivity field. The conductivity field estimated by using this sequential approach proves to be better than all the previous estimates, using one type of data set alone. IntroductionDuring the past decades, the cokriging technique has been applied extensively to many studies of subsurface hydrology. timates of the heterogeneous conductivity field. On the other hand, Yeh et al. [1995, 1996] proposed iterative cokriging techniques for nonlinear systems in which the requirement of unbiasedness and minimum variance were imposed during each iteration. By incorporating the nonlinear relationship between head and conductivity in groundwater flow systems, the estimated conductivity field revealed more detailed heterogeneity than using the linear model and more closely resembled the true field. This iterative approach was further extended to unsaturated flow by Zhang and Yeh [1997] to estimate parameters for unsaturated hydraulic conductivity in the vadose zone. Similarly, a quasi-linear geostatistical approach was presented by Kitanidis [1995] in an attempt to incorporate the nonlinear relationship between the parameter and secondary information of the subsurface flow system.In spite of the advance in parameter estimation techniques, a practical question remains regarding what kind of measurements (e.g., head, concentration, or other variables) are most useful for estimating the hydrological parameters. Several attempts to address this issue were carried out in the past. For example, Yeh and Zhang [1996] found that pressure head measurements can improve estimates of s...

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“…Yeh and Zhang [1996] applied a geostatistical method to estimating saturated hydraulic conductivity K s and the pore size distribution parameter a of the Gardner-Russo unsaturated hydraulic conductivity model [Russo, 1988] using limited data of pressure and moisture content in two-dimensional steady state unsaturated flow. These methods essentially involve a cokriged estimate of parameters using a first-order approximation of the cross covariances between parameters and the secondary information and covariances of the seco, ndary information.…”

Section: Introductionmentioning

confidence: 99%

An inverse model for three‐dimensional flow in variably saturated porous media

Hughson

Yeh²

2000

Water Resources Research

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Abstract. Geostatistical theory has shown promise in dealing with issues of stability, uniqueness, and identity of estimates inherent in inverse problems of subsurface flow. Here the geostatistical method is extended to three-dimensional, unsteady flow in variably saturated porous geological media (the vadose zone) that are modeled using the Richards equation and the van Genuchten-Mualem constitutive equations. The saturated hydraulic conductivity, c•, and n parameters of this relationship are treated as spatially correlated, statistically independent, stochastic processes for representing heterogeneity of porous media. For given covariance functions of the parameters the adjoint-state sensitivity method is used to calculate first-order approximations for covariances of capillary pressure and moisture content and cross covariances between capillary pressure, moisture content, and the hydraulic properties. These covariances and cross covariances are then used in a successive linear estimator (SLE) to estimate the conditional means of the heterogeneous hydraulic property fields based on measurements of pressure and moisture content data. A sequential conditioning approach for our SLE was also applied to data sets collected at different sampling times during a transient infiltration event. This approach has the benefit of reducing the size of the matrices and so helps avoid numerical stability problems. On the basis of our study, pressure and moisture content data sets collected at later times of an infiltration event or during steady state flow were found to provide better estimates (smaller mean-square error compared to the true field) of the hydrological parameters of the vadose zone than data from very early times.

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A Geostatistical Inverse Method for Variably Saturated Flow in the Vadose Zone

Cited by 88 publications

References 32 publications

Estimating geostatistical parameters and spatially-variable hydraulic conductivity within a catchment system using an ensemble smoother

Estimating geostatistical parameters and spatially-variable hydraulic conductivity within a catchment system using an ensemble smoother

Cokriging estimation of the conductivity field under variably saturated flow conditions

An inverse model for three‐dimensional flow in variably saturated porous media

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