Characterization of non-Gaussian conductivities and porosities with hydraulic heads, solute concentrations, and water temperatures

Reliable characterization of hydraulic parameters is important for the understanding of groundwater flow and solute transport. The normal-score ensemble Kalman filter (NS-EnKF) has proven to be an effective inverse method for the characterization of non-Gaussian hydraulic conductivities by assimilating transient piezometric head data, or solute concentration data. Groundwater temperature, an easily captured state variable, has not drawn much attention as an additional state variable useful for the characterization of aquifer parameters. In this work, we jointly estimate non-Gaussian aquifer parameters (hydraulic conductivities and porosities) by assimilating three kinds of state variables (piezometric head, solute concentration, and groundwater temperature) using the NS-EnKF. A synthetic example including seven tests is designed, and used to evaluate the ability to characterize hydraulic conductivity and porosity in a non-Gaussian setting by assimilating different numbers and types of state variables. The results show that characterization of aquifer parameters can be improved by assimilating groundwater temperature data and that the main patters of the non-Gaussian reference fields can be retrieved with more accuracy and higher precision if multiple state variables are assimilated.Financial support to carry out this work was provided by the Spanish Ministry of Economy and Competitiveness through project CGL2014-59841-P. All data used in this analysis are available from the authors.Xu, T.; Gómez-Hernández, JJ. (2016). Characterization of non-Gaussian conductivities and porosities with hydraulic heads, solute concentrations, and water temperatures. 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Inverse sequential simulation: Performance and implementation details

For good groundwater flow and solute transport numerical modeling, it is important to characterize the formation properties. In this paper, we analyze the performance and important implementation details of a new approach for stochastic inverse modeling called inverse sequential simulation (iSS). This approach is capable of characterizing conductivity fields with heterogeneity patterns difficult to capture by standard multiGaussian-based inverse approaches. The method is based on the multivariate sequential simulation principle, but the covariances and cross-covariances used to compute the local conditional probability distributions are computed by simple co-kriging which are derived from an ensemble of conductivity and piezometric head fields, in a similar manner as the experimental covariances are computed in an ensemble Kalman filtering. A sensitivity analysis is performed on a synthetic aquifer regarding the number of members of the ensemble of realizations, the number of conditioning data, the number of piezometers at which piezometric heads are observed, and the number of nodes retained within the search neighborhood at the moment of computing the local conditional probabilities. The results show the importance of having a sufficiently large number of all of the mentioned parameters for the algorithm to characterize properly hydraulic conductivity fields with clear non-multiGaussian features. © 2015 Elsevier Ltd. All rights reserved.The first author acknowledgs the financial support from the China Scholarship Council (CSC [2010]3010). Financial support to carry out this work was also received from the Spanish Ministry of Economy and Competitiveness through Project CGL2014-59841-P. We thank the three reviewers for their thorough review and their insightful comments, which have helped to improve the final manuscript.Xu, T.; Gómez-Hernández, JJ. (2015). Inverse sequential simulation: Performance and implementation details. Advances in Water Resources. 86B:311-326. https://doi.org/10.1016/j.advwatres.2015.04.015S31132686

The Power of Transient Piezometric Head Data in Inverse Modeling: An Application of the Localized Normal-score EnKF with Covariance Inflation in a Heterogenous Bimodal Hydraulic Conductivity Field

The localized normal-score ensemble Kalman filter (NS-EnKF) coupled with covariance inflation is used to characterize the spatial variability of a channelized bimodal hydraulic conductivity field, for which the only existing prior information about conductivity is its univariate marginal distribution. We demonstrate that we can retrieve the main patterns of the reference field by assimilating a sufficient number of piezometric observations using the NS-EnKF. The possibility of characterizing the conductivity spatial variability using only piezometric head data shows the importance of accounting for these data in inverse modeling.The first author acknowledges the financial support from the China Scholarship Council (CSC). Financial support to carry out this work was also received from the Spanish Ministry of Science and Innovation through project CGL2011-23295.Xu, T.; Gómez-Hernández, JJ.; Zhou, H.; Li, L. (2013). The Power of Transient Piezometric Head Data in Inverse Modeling: An Application of the Localized Normal-score EnKF with Covariance Inflation in a Heterogenous Bimodal Hydraulic Conductivity Field. Advances in Water Resources. 54:100-118. https://doi.org/10.1016/j.advwatres.2013.01.006S1001185

Color vision deficiencies and camouflage: a comparative study between normal and CVD observers

Ministerio de Economia, Industria y Competitividad, Gobierno de Espana (FIS2017-89258-P).There is a belief that observers with color vision deficiencies (CVD) perform better in detecting camouflaged objects than normal observers. Some studies have concluded contradictory findings when studying the performance of normal and CVD observers in the camouflage detection tasks in different conditions. This work presents a literature review on this topic, dividing it into three different and contradictory types of results: better performance for CVD, for normal observers, or same performance. Besides, two psychophysical experiments have been designed and carried out in a calibrated computer monitor on both normal and CVD human observers to measure the searching times of the different types of observers needed to find camouflaged stimuli in two different types of stimuli. Results show the trend that, in our experimental conditions, normal observers need shorter searching times than CVD observers in finding camouflaged stimuli both in images of natural scenes and in images with synthetic stimuli.Spanish Government FIS2017-89258-

Preconditioned Crank‐Nicolson Markov Chain Monte Carlo Coupled With Parallel Tempering: An Efficient Method for Bayesian Inversion of Multi‐Gaussian Log‐Hydraulic Conductivity Fields

Geostatistical inversion with quantified uncertainty for nonlinear problems requires techniques for providing conditional realizations of the random field of interest. Many first‐order second‐moment methods are being developed in this field, yet almost impossible to critically test them against high‐accuracy reference solutions in high‐dimensional and nonlinear problems. Our goal is to provide a high‐accuracy reference solution algorithm. Preconditioned Crank‐Nicolson Markov chain Monte Carlo (pCN‐MCMC) has been proven to be more efficient in the inversion of multi‐Gaussian random fields than traditional MCMC methods; however, it still has to take a long chain to converge to the stationary target distribution. Parallel tempering aims to sample by communicating between multiple parallel Markov chains at different temperatures. In this paper, we develop a new algorithm called pCN‐PT. It combines the parallel tempering technique with pCN‐MCMC to make the sampling more efficient, and hence converge to a stationary distribution faster. To demonstrate the high‐accuracy reference character, we test the accuracy and efficiency of pCN‐PT for estimating a multi‐Gaussian log‐hydraulic conductivity field with a relative high variance in three different problems: (1) in a high‐dimensional, linear problem; (2) in a high‐dimensional, nonlinear problem and with only few measurements; and (3) in a high‐dimensional, nonlinear problem with sufficient measurements. This allows testing against (1) analytical solutions (kriging), (2) rejection sampling, and (3) pCN‐MCMC in multiple, independent runs, respectively. The results demonstrate that pCN‐PT is an asymptotically exact conditional sampler and is more efficient than pCN‐MCMC in geostatistical inversion problems

Comparing Seven Variants of the Ensemble Kalman Filter: How Many Synthetic Experiments Are Needed?

The ensemble Kalman filter (EnKF) is a popular estimation technique in the geosciences. It is used as a numerical tool for state vector prognosis and parameter estimation. The EnKF can, for example, help to evaluate the geothermal potential of an aquifer. In such applications, the EnKF is often used with small or medium ensemble sizes. It is therefore of interest to characterize the EnKF behavior for these ensemble sizes. For seven ensemble sizes (50, 70, 100, 250, 500, 1,000, and 2,000) and seven EnKF variants (damped, iterative, local, hybrid, dual, normal score, and classical EnKF), we computed 1,000 synthetic parameter estimation experiments for two setups: a 2‐D tracer transport problem and a 2‐D flow problem with one injection well. For each model, the only difference among synthetic experiments was the generated set of random permeability fields. The 1,000 synthetic experiments allow to calculate the probability density function of the root‐mean‐square error (RMSE) of the characterization of the permeability field. Comparing mean RMSEs for different EnKF variants, ensemble sizes and flow/transport setups suggests that multiple synthetic experiments are needed for a solid performance comparison. In this work, 10 synthetic experiments were needed to correctly distinguish RMSE differences between EnKF variants smaller than 10%. For detecting RMSE differences smaller than 2%, 100 synthetic experiments were needed for ensemble sizes 50, 70, 100, and 250. The overall ranking of the EnKF variants is strongly dependent on the physical model setup and the ensemble size