scholarly journals Sensitivity and identifiability of hydraulic and geophysical parameters from streaming potential signals in unsaturated porous media

2018 ◽  
Vol 22 (7) ◽  
pp. 3561-3574 ◽  
Author(s):  
Anis Younes ◽  
Jabran Zaouali ◽  
François Lehmann ◽  
Marwan Fahs
Keyword(s):  
Parameter Estimation ◽  
Order Approximation ◽  
Streaming Potential ◽  
Residual Water ◽  
Data Set ◽  
Sparse Polynomial ◽  
Marquardt Algorithm ◽  
Highly Nonlinear ◽  
Time Periods ◽  
Parameter Values

Abstract. Fluid flow in a charged porous medium generates electric potentials called streaming potential (SP). The SP signal is related to both hydraulic and electrical properties of the soil. In this work, global sensitivity analysis (GSA) and parameter estimation procedures are performed to assess the influence of hydraulic and geophysical parameters on the SP signals and to investigate the identifiability of these parameters from SP measurements. Both procedures are applied to a synthetic column experiment involving a falling head infiltration phase followed by a drainage phase. GSA is used through variance-based sensitivity indices, calculated using sparse polynomial chaos expansion (PCE). To allow high PCE orders, we use an efficient sparse PCE algorithm which selects the best sparse PCE from a given data set using the Kashyap information criterion (KIC). Parameter identifiability is performed using two approaches: the Bayesian approach based on the Markov chain Monte Carlo (MCMC) method and the first-order approximation (FOA) approach based on the Levenberg–Marquardt algorithm. The comparison between both approaches allows us to check whether FOA can provide a reliable estimation of parameters and associated uncertainties for the highly nonlinear hydrogeophysical problem investigated. GSA results show that in short time periods, the saturated hydraulic conductivity (Ks) and the voltage coupling coefficient at saturation (Csat) are the most influential parameters, whereas in long time periods, the residual water content (θs), the Mualem–van Genuchten parameter (n) and the Archie saturation exponent (na) become influential, with strong interactions between them. The Mualem–van Genuchten parameter (α) has a very weak influence on the SP signals during the whole experiment. Results of parameter estimation show that although the studied problem is highly nonlinear, when several SP data collected at different altitudes inside the column are used to calibrate the model, all hydraulic (Ks,θs,α,n) and geophysical parameters (na,Csat) can be reasonably estimated from the SP measurements. Further, in this case, the FOA approach provides accurate estimations of both mean parameter values and uncertainty regions. Conversely, when the number of SP measurements used for the calibration is strongly reduced, the FOA approach yields accurate mean parameter values (in agreement with MCMC results) but inaccurate and even unphysical confidence intervals for parameters with large uncertainty regions.

scholarly journals Sensitivity and identifiability of hydraulic and geophysical parameters from streaming potential signals in unsaturated porous media

2018 ◽  
Author(s):  
Anis Younes ◽  
Jabran Zaouali ◽  
Francois Lehmann ◽  
Marwan Fahs
Keyword(s):  
Parameter Estimation ◽  
Order Approximation ◽  
Streaming Potential ◽  
Strong Interactions ◽  
Residual Water ◽  
Data Set ◽  
Sparse Polynomial ◽  
Marquardt Algorithm ◽  
Highly Nonlinear ◽  
Parameter Values

Abstract. Fluid flow in a charged porous medium generates electric potentials called Streaming potential (SP). The SP signal is related to both hydraulic and electrical properties of the soil. In this work, Global Sensitivity Analysis (GSA) and parameter estimation procedures are performed to assess the influence of hydraulic and geophysical parameters on the SP signals and to investigate the identifiability of these parameters from SP measurements. Both procedures are applied to a synthetic column experiment involving a falling head infiltration phase followed by a drainage phase. GSA is used through variance-based sensitivity indices, calculated using sparse Polynomial Chaos Expansion (PCE). To allow high PCE orders, we use an efficient sparse PCE algorithm which selects the best sparse PCE from a given data set using the Kashyap Information Criterion (KIC). Parameter identifiability is performed using two approaches: the Bayesian approach based on the Markov Chain Monte Carlo (MCMC) method and the First-Order Approximation (FOA) approach based on the Levenberg Marquardt algorithm. GSA results show that at short times, the saturated hydraulic conductivity (KS) and the voltage coupling coefficient at saturation (Csat) are the most influential parameters, whereas, at long times, the residual water content (σr), the Mualem-van Genuchten parameter (n) and the Archies’s saturation exponent (na) become influential with strong interactions between them. The Mualem-van Genuchten parameter (α) has a very weak influence on the SP signals during the whole experiment. Results of parameter estimation show that, although the studied problem is highly nonlinear, when several SP data collected at different altitudes inside the column are used to calibrate the model, all hydraulic (KS, σr, and n) and geophysical (na and Csat) parameters can be reasonably estimated from the SP measurements. Further, in this case, the FOA approach provides accurate estimations of both mean parameter values and uncertainty regions. Conversely, when the number of SP measurements used for the calibration is strongly reduced, the FOA approach yields accurate mean parameter values (in agreement with MCMC results) but inaccurate and even unphysical confidence intervals for parameters with large uncertainty regions.

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.

scholarly journals MLE-Based Parameter Estimation for Four-Parameter Exponential Gamma Distribution and Asymptotic Variance of Its Quantiles

Water ◽  
2021 ◽  
Vol 13 (15) ◽  
pp. 2092
Author(s):  
Songbai Song ◽  
Yan Kang ◽  
Xiaoyan Song ◽  
Vijay P. Singh
Keyword(s):  
Parameter Estimation ◽  
Confidence Intervals ◽  
Asymptotic Variance ◽  
Information Matrix ◽  
Estimation Method ◽  
Flood Frequency Analysis ◽  
Annual Precipitation ◽  
Precipitation Data ◽  
Marquardt Algorithm ◽  
Design Values

The choice of a probability distribution function and confidence interval of estimated design values have long been of interest in flood frequency analysis. Although the four-parameter exponential gamma (FPEG) distribution has been developed for application in hydrology, its maximum likelihood estimation (MLE)-based parameter estimation method and asymptotic variance of its quantiles have not been well documented. In this study, the MLE method was used to estimate the parameters and confidence intervals of quantiles of the FPEG distribution. This method entails parameter estimation and asymptotic variances of quantile estimators. The parameter estimation consisted of a set of four equations which, after algebraic simplification, were solved using a three dimensional Levenberg-Marquardt algorithm. Based on sample information matrix and Fisher’s expected information matrix, derivatives of the design quantile with respect to the parameters were derived. The method of estimation was applied to annual precipitation data from the Weihe watershed, China and confidence intervals for quantiles were determined. Results showed that the FPEG was a good candidate to model annual precipitation data and can provide guidance for estimating design values

scholarly journals Selecting single cell clustering parameter values using subsampling-based robustness metrics

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Ryan B. Patterson-Cross ◽  
Ariel J. Levine ◽  
Vilas Menon
Keyword(s):  
Single Cell ◽  
Optimal Parameter ◽  
Clustering Algorithms ◽  
Cell Types ◽  
Parameter Selection ◽  
Data Set ◽  
Biologically Relevant ◽  
Cell Clustering ◽  
Parameter Values ◽  
Robustness Metrics

Abstract Background Generating and analysing single-cell data has become a widespread approach to examine tissue heterogeneity, and numerous algorithms exist for clustering these datasets to identify putative cell types with shared transcriptomic signatures. However, many of these clustering workflows rely on user-tuned parameter values, tailored to each dataset, to identify a set of biologically relevant clusters. Whereas users often develop their own intuition as to the optimal range of parameters for clustering on each data set, the lack of systematic approaches to identify this range can be daunting to new users of any given workflow. In addition, an optimal parameter set does not guarantee that all clusters are equally well-resolved, given the heterogeneity in transcriptomic signatures in most biological systems. Results Here, we illustrate a subsampling-based approach (chooseR) that simultaneously guides parameter selection and characterizes cluster robustness. Through bootstrapped iterative clustering across a range of parameters, chooseR was used to select parameter values for two distinct clustering workflows (Seurat and scVI). In each case, chooseR identified parameters that produced biologically relevant clusters from both well-characterized (human PBMC) and complex (mouse spinal cord) datasets. Moreover, it provided a simple “robustness score” for each of these clusters, facilitating the assessment of cluster quality. Conclusion chooseR is a simple, conceptually understandable tool that can be used flexibly across clustering algorithms, workflows, and datasets to guide clustering parameter selection and characterize cluster robustness.

scholarly journals Diurnal variations in middle-atmospheric water vapor by ground-based microwave radiometry

2013 ◽  
Vol 13 (14) ◽  
pp. 6877-6886 ◽  
Author(s):  
D. Scheiben ◽  
A. Schanz ◽  
B. Tschanz ◽  
N. Kämpfer
Keyword(s):  
Water Vapor ◽  
Observational Data ◽  
Climate Model ◽  
Correlation Coefficients ◽  
Diurnal Variations ◽  
Atmospheric Water Vapor ◽  
Atmospheric Water ◽  
Data Set ◽  
Diurnal Variability ◽  
Time Periods

Abstract. In this paper, we compare the diurnal variations in middle-atmospheric water vapor as measured by two ground-based microwave radiometers in the Alpine region near Bern, Switzerland. The observational data set is also compared to data from the chemistry–climate model WACCM. Due to the small diurnal variations of usually less than 1%, averages over extended time periods are required. Therefore, two time periods of five months each, December to April and June to October, were taken for the comparison. The diurnal variations from the observational data agree well with each other in amplitude and phase. The linear correlation coefficients range from 0.8 in the upper stratosphere to 0.5 in the upper mesosphere. The observed diurnal variability is significant at all pressure levels within the sensitivity of the instruments. Comparing our observations with WACCM, we find that the agreement of the phase of the diurnal cycle between observations and model is better from December to April than from June to October. The amplitudes of the diurnal variations for both time periods increase with altitude in WACCM, but remain approximately constant at 0.05 ppm in the observations. The WACCM data are used to separate the processes that lead to diurnal variations in middle-atmospheric water vapor above Bern. The dominating processes were found to be meridional advection below 0.1 hPa, vertical advection between 0.1 and 0.02 hPa and (photo-)chemistry above 0.02 hPa. The contribution of zonal advection is small. The highest diurnal variations in water vapor as seen in the WACCM data are found in the mesopause region during the time period from June to October with diurnal amplitudes of 0.2 ppm (approximately 5% in relative units).

Spatial scale effects on model parameter estimation and predictive uncertainty in ungauged basins

2012 ◽  
Vol 44 (3) ◽  
pp. 441-453 ◽  
Author(s):  
Denis A. Hughes ◽  
Evison Kapangaziwiri ◽  
Jane Tanner
Keyword(s):  
Parameter Estimation ◽  
Spatial Scale ◽  
Scale Effects ◽  
Physical Property ◽  
Hydrological Modelling ◽  
Ungauged Basins ◽  
Estimation Equations ◽  
Property Data ◽  
Physical Property Data ◽  
Parameter Values

The most appropriate scale to use for hydrological modelling depends on the model structure, the purpose of the results and the resolution of available data used to quantify parameter values and provide the climatic forcing. There is little consensus amongst the community of model users on the appropriate model complexity and number of model parameters that are needed for satisfactory simulations. These issues are not independent of modelling scale, the methods used to quantify parameter values, nor the purpose of use of the simulations. This paper reports on an investigation of spatial scale effects on the application of an approach to quantify the parameter values (with uncertainty) of a rainfall-runoff model with a relatively large number of parameters. The quantification approach uses estimation equations based on physical property data and is applicable to gauged and ungauged basins. Within South Africa the physical property data are available at a finer spatial resolution than is typically used for hydrological modelling. The results suggest that reducing the model spatial scale offers some advantages. Potential disadvantages are related to the need for some subjective interpretation of the available physical property data, as well as inconsistencies in some of the parameter estimation equations.

scholarly journals Robust estimation of vertical symmetry axis models via joint migration inversion: Including multiples in anisotropic parameter estimation

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. C57-C74 ◽  
Author(s):  
Abdulrahman A. Alshuhail ◽  
Dirk J. Verschuur
Keyword(s):  
Symmetry Axis ◽  
Transverse Isotropy ◽  
Half Cycle ◽  
Anisotropic Parameter ◽  
Data Set ◽  
Trade Off ◽  
Trade Offs ◽  
Highly Nonlinear ◽  
Wide Range ◽  
Internal Multiples

Because the earth is predominately anisotropic, the anisotropy of the medium needs to be included in seismic imaging to avoid mispositioning of reflectors and unfocused images. Deriving accurate anisotropic velocities from the seismic reflection measurements is a highly nonlinear and ambiguous process. To mitigate the nonlinearity and trade-offs between parameters, we have included anisotropy in the so-called joint migration inversion (JMI) method, in which we limit ourselves to the case of transverse isotropy with a vertical symmetry axis. The JMI method is based on strictly separating the scattering effects in the data from the propagation effects. The scattering information is encoded in the reflectivity operators, whereas the phase information is encoded in the propagation operators. This strict separation enables the method to be more robust, in that it can appropriately handle a wide range of starting models, even when the differences in traveltimes are more than a half cycle away. The method also uses internal multiples in estimating reflectivities and anisotropic velocities. Including internal multiples in inversion not only reduces the crosstalk in the final image, but it can also reduce the trade-off between the anisotropic parameters because internal multiples usually have more of an imprint of the subsurface parameters compared with primaries. The inverse problem is parameterized in terms of a reflectivity, vertical velocity, horizontal velocity, and a fixed [Formula: see text] value. The method is demonstrated on several synthetic models and a marine data set from the North Sea. Our results indicate that using JMI for anisotropic inversion makes the inversion robust in terms of using highly erroneous initial models. Moreover, internal multiples can contain valuable information on the subsurface parameters, which can help to reduce the trade-off between anisotropic parameters in inversion.

scholarly journals Diurnal variations in middle atmospheric water vapor by ground-based microwave radiometry

2013 ◽  
Vol 13 (2) ◽  
pp. 3859-3880 ◽  
Author(s):  
D. Scheiben ◽  
A. Schanz ◽  
B. Tschanz ◽  
N. Kämpfer
Keyword(s):  
Water Vapor ◽  
Observational Data ◽  
Climate Model ◽  
Correlation Coefficients ◽  
Diurnal Variations ◽  
Atmospheric Water Vapor ◽  
Atmospheric Water ◽  
Data Set ◽  
Diurnal Variability ◽  
Time Periods

Abstract. In this paper, we compare the diurnal variations in middle atmospheric water vapor as measured by two ground-based microwave radiometers in the Alpine region near Bern, Switzerland. The observational data set is also compared to data from the chemistry-climate model WACCM. Due to the small diurnal variations of usually less than 1%, averages over extended time periods are required. Therefore, two time periods of five months each, December to April and June to October, were taken for the comparison. The diurnal variations from the observational data agree well with each other in amplitude and phase. The linear correlation coefficients range from 0.8 in the upper stratosphere to 0.5 in the upper mesosphere. The observed diurnal variability is significant at all pressure levels within the sensitivity of the instruments. Comparing our observations with WACCM, we find that the agreement of the phase of the diurnal cycle between observations and model is better from December to April than from June to October. The amplitudes of the diurnal variations for both time periods increase with altitude in WACCM, but remain approximately constant at 0.05 parts per million in the observations. The WACCM data is used to separate the processes that lead to diurnal variations in middle atmospheric water vapor above Bern. The dominating processes were found to be meridional advection below 0.1 hPa, vertical advection between 0.1 and 0.02 hPa and (photo-)chemistry above 0.02 hPa. The contribution of zonal advection is small. The highest diurnal variations in water vapor are found in the mesopause region during the time period from June to October with diurnal amplitudes of 0.2 ppm (approximately 5% in relative units).

scholarly journals Parameter Selection in the Parameter Estimation of Grade Transitions in a Polyethylene Plant

2015 ◽  
Vol 3 (1) ◽  
pp. 1
Author(s):  
Niklas Andersson ◽  
Per-Ola Larsson ◽  
Johan Åkesson ◽  
Niclas Carlsson ◽  
Staffan Skålén ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Steady State ◽  
State Parameter ◽  
Parameter Selection ◽  
Selection Algorithm ◽  
Parameter Estimations ◽  
Dynamic Case ◽  
Nominal Parameter ◽  
Best Parameter ◽  
Parameter Values

A polyethylene plant at Borealis AB is modelled in the Modelica language and considered for parameter estimations at grade transitions. Parameters have been estimated for both the steady-state and the dynamic case using the JModelica.org platform, which offers tools for steady-state parameter estimation and supports simulation with parameter sensitivies. The model contains 31 candidate parameters, giving a huge amount of possible parameter combinations. The best parameter sets have been chosen using a parameter-selection algorithm that identified parameter sets with poor numerical properties. The parameter-selection algorithm reduces the number of parameter sets that is necessary to explore. The steady-state differs from the dynamic case with respect to parameter selection. Validations of the parameter estimations in the dynamic case show a significant reduction in an objective value used to evaluate the quality of the solution from that of the nominal reference, where the nominal parameter values are used.

Sign in / Sign up

Export Citation Format

Share Document