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

2011 ◽  
Vol 8 (5) ◽  
pp. 9587-9635
Author(s):  
R. T. Bailey ◽  
D. Baù
Keyword(s):  
Parameter Estimation ◽  
Spatial Distribution ◽  
Hydraulic Conductivity ◽  
Water Table ◽  
Subsurface Flow ◽  
Estimation Methods ◽  
Future Research ◽  
Ensemble Smoother ◽  
Streamflow Data ◽  
Parameter Values

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 fully-coupled, 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.

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

2012 ◽  
Vol 16 (2) ◽  
pp. 287-304 ◽  
Author(s):  
R. T. Bailey ◽  
D. Baù
Keyword(s):  
Parameter Estimation ◽  
Spatial Distribution ◽  
Hydraulic Conductivity ◽  
Water Table ◽  
Subsurface Flow ◽  
Estimation Methods ◽  
Future Research ◽  
Ensemble Smoother ◽  
Streamflow Data ◽  
Parameter Values

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 fully-coupled, 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.

scholarly journals Large-scale lateral saturated soil hydraulic conductivity as metric for the connectivity of the subsurface flow paths at hillslope scale

2021 ◽  
Author(s):  
Mario Pirastru ◽  
Massimo Iovino ◽  
Hassan Awada ◽  
Roberto Marrosu ◽  
Simone Di Prima ◽  
...  
Keyword(s):  
Soil Moisture ◽  
Hydraulic Conductivity ◽  
Spatial Scale ◽  
Water Table ◽  
Subsurface Flow ◽  
Lateral Flow ◽  
Saturated Soil ◽  
Flow Paths ◽  
Soil Hydraulic Conductivity ◽  
Hillslope Scale

Lateral saturated soil hydraulic conductivity, Ks,l, is the soil property governing subsurface water transfer in hillslopes, and the key parameter in many numerical models simulating hydrological processes both at the hillslope and catchment scales. Likewise, the hydrological connectivity of lateral flow paths plays a significant role in determining the intensity of the subsurface flow at various spatial scales. The objective of the study is to investigate the relationship between Ks,l and hydraulic connectivity at the hillslope spatial scale. Ks,l was determined by the subsurface flow rates intercepted by drains, and by water table depths observed in a well network. Hydraulic connectivity of the lateral flow paths was evaluated by the synchronicity among piezometric peaks, and between the latter and the peaks of drained flow. Soil moisture and precipitation data were used to investigate the influence of the transient hydrological soil condition on connectivity and Ks,l. It was found that the higher was the synchronicity of the water table response between wells, the lower was the time lag between the peaks of water levels and those of the drained subsurface flow. Moreover, the most synchronic water table rises determined the highest drainage rates. The relationships between Ks,l and water table depths were highly non-linear, with a sharp increase of the values for water table levels close to the soil surface. Estimated Ks,l values for the full saturated soil were in the order of thousands of mm h-1, suggesting the activation of macropores in the root zone. The Ks,l values determined at the peak of the drainage events were correlated with the indicators of synchronicity. The sum of the antecedent soil moisture and of the precipitation was correlated with the indicators of connectivity and with Ks,l. We suggest that, for simulating realistic processes at the hillslope scale, the hydraulic connectivity could be implicitly considered in hydrological modelling through an evaluation of Ks,l at the same spatial scale.

scholarly journals Reviews and syntheses: parameter identification in marine planktonic ecosystem modelling

2017 ◽  
Vol 14 (6) ◽  
pp. 1647-1701 ◽  
Author(s):  
Markus Schartau ◽  
Philip Wallhead ◽  
John Hemmings ◽  
Ulrike Löptien ◽  
Iris Kriest ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Data Assimilation ◽  
Parameter Identification ◽  
Estimation Methods ◽  
Model Parameters ◽  
Ecosystem Modelling ◽  
Ecosystem Models ◽  
Element Cycling ◽  
Biogeochemical Models ◽  
Parameter Values

Abstract. To describe the underlying processes involved in oceanic plankton dynamics is crucial for the determination of energy and mass flux through an ecosystem and for the estimation of biogeochemical element cycling. Many planktonic ecosystem models were developed to resolve major processes so that flux estimates can be derived from numerical simulations. These results depend on the type and number of parameterizations incorporated as model equations. Furthermore, the values assigned to respective parameters specify a model's solution. Representative model results are those that can explain data; therefore, data assimilation methods are utilized to yield optimal estimates of parameter values while fitting model results to match data. Central difficulties are (1) planktonic ecosystem models are imperfect and (2) data are often too sparse to constrain all model parameters. In this review we explore how problems in parameter identification are approached in marine planktonic ecosystem modelling. We provide background information about model uncertainties and estimation methods, and how these are considered for assessing misfits between observations and model results. We explain differences in evaluating uncertainties in parameter estimation, thereby also discussing issues of parameter identifiability. Aspects of model complexity are addressed and we describe how results from cross-validation studies provide much insight in this respect. Moreover, approaches are discussed that consider time- and space-dependent parameter values. We further discuss the use of dynamical/statistical emulator approaches, and we elucidate issues of parameter identification in global biogeochemical models. Our review discloses many facets of parameter identification, as we found many commonalities between the objectives of different approaches, but scientific insight differed between studies. To learn more from results of planktonic ecosystem models we recommend finding a good balance in the level of sophistication between mechanistic modelling and statistical data assimilation treatment for parameter estimation.

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.

scholarly journals Reviews and syntheses: Parameter identification in marine planktonic ecosystem modelling

2016 ◽  
Author(s):  
Markus Schartau ◽  
Philip Wallhead ◽  
John Hemmings ◽  
Ulrike Löptien ◽  
Iris Kriest ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Data Assimilation ◽  
Parameter Identification ◽  
Estimation Methods ◽  
Model Parameters ◽  
Ecosystem Modelling ◽  
Ecosystem Models ◽  
Element Cycling ◽  
Biogeochemical Models ◽  
Parameter Values

Abstract. To describe the underlying processes involved in oceanic plankton dynamics is crucial for the determination of energy and mass flux through an ecosystem and for the estimation of biogeochemical element cycling. Many planktonic ecosystem models were developed to resolve major processes so that flux estimates can be derived from numerical simulations. These results depend on the type and number of parameterisations incorporated as model equations. Furthermore, the values assigned to respective parameters specify a model's solution. Representative model results are those that can explain data, therefore data assimilation methods are utilised to yield optimal estimates of parameter values while fitting model results to match data. Central difficulties are 1) planktonic ecosystem models are imperfect and 2) data are often too sparse to constrain all model parameters. In this review we explore how problems in parameter identification are approached in marine planktonic ecosystem modelling. We provide background information about model uncertainties and estimation methods, and how these are considered for assessing misfits between observations and model results. We explain differences in evaluating uncertainties in parameter estimation, thereby also addressing issues of parameter identifiability. Aspects of model complexity will be covered and we describe how results from cross-validation studies provide much insight in this respect. Moreover, we elucidate inferences made in studies that allowed for variations in space and time of parameter values. The usage of dynamical and statistical emulator approaches will be briefly explained, discussing their advantage for parameter optimisations of large-scale biogeochemical models. Our survey extends to studies that approached parameter identification in global biogeochemical modelling. Parameter estimation results will exemplify some of the advantages and remaining problems in optimising global biogeochemical models. Our review discloses many facets of parameter identification, as we found many commonalities between the objectives of different approaches, but scientific insight differed between studies. To learn more from results of planktonic ecosystem models we recommend finding a good balance in the level of sophistication between mechanistic modelling and statistical data assimilation treatment for parameter estimation.

Identification of Biodegradation models under model and data uncertainty

1996 ◽  
Vol 33 (2) ◽  
pp. 91-105 ◽  
Author(s):  
Peter A. Vanrolleghem ◽  
Karel J. Keesman
Keyword(s):  
Parameter Estimation ◽  
Real World ◽  
Data Uncertainty ◽  
Estimation Methods ◽  
Parameter Estimates ◽  
Local Minima ◽  
Real World Data ◽  
Correlation Matrices ◽  
Parameter Estimation Methods ◽  
Parameter Values

In this paper a number of nonlinear parameter estimation methods are evaluated with respect to their ability to identify biodegradation models from “real-world” data. Important aspects are then the sensitivity to local minima, rate of convergence, required prior knowledge and direct or indirect availability of parameter estimates uncertainty. Furthermore, it is important whether a method is robust against invalid assumptions. In addition to the final parameter values, covariance and correlation matrices, confidence intervals and residual sequences are presented to obtain information about the validity of the models and noise assumptions. Finally, recommendations on the method's applicability range are provided.

Heterotrophic Kinetic Parameter Estimation for Enhanced Biological Phosphorus Removal Processes Operated in Conventional and Membrane-Assisted Modes

2006 ◽  
Vol 41 (1) ◽  
pp. 72-83 ◽  
Author(s):  
Zhe Zhang ◽  
Eric R. Hall
Keyword(s):  
Parameter Estimation ◽  
Phosphorus Removal ◽  
Growth Yield ◽  
Pilot Scale ◽  
Enhanced Biological Phosphorus Removal ◽  
Biological Phosphorus Removal ◽  
Nitrogen And Phosphorus ◽  
Parameter Values ◽  
The Impact ◽  
Biological Phosphorus

Abstract Parameter estimation and wastewater characterization are crucial for modelling of the membrane enhanced biological phosphorus removal (MEBPR) process. Prior to determining the values of a subset of kinetic and stoichiometric parameters used in ASM No. 2 (ASM2), the carbon, nitrogen and phosphorus fractions of influent wastewater at the University of British Columbia (UBC) pilot plant were characterized. It was found that the UBC wastewater contained fractions of volatile acids (SA), readily fermentable biodegradable COD (SF) and slowly biodegradable COD (XS) that fell within the ASM2 default value ranges. The contents of soluble inert COD (SI) and particulate inert COD (XI) were somewhat higher than ASM2 default values. Mixed liquor samples from pilot-scale MEBPR and conventional enhanced biological phosphorus removal (CEBPR) processes operated under parallel conditions, were then analyzed experimentally to assess the impact of operation in a membrane-assisted mode on the growth yield (YH), decay coefficient (bH) and maximum specific growth rate of heterotrophic biomass (µH). The resulting values for YH, bH and µH were slightly lower for the MEBPR train than for the CEBPR train, but the differences were not statistically significant. It is suggested that MEBPR simulation using ASM2 could be accomplished satisfactorily using parameter values determined for a conventional biological phosphorus removal process, if MEBPR parameter values are not available.

EFFECT OF SPATIAL VARIABILITY IN HYDRAULIC CONDUCTIVITY ON WATER TABLE DRAWDOWN

1997 ◽  
Vol 40 (2) ◽  
pp. 371-375
Author(s):  
S. O. Prasher ◽  
M. Singh ◽  
A. K. Maheshwari ◽  
R. S. Clemente
Keyword(s):  
Hydraulic Conductivity ◽  
Spatial Variability ◽  
Water Table
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