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. Water Resources Research. 52(8):6111-6136. https://doi.org/10.1002/2016WR019011S61116136528Alcolea, A., Carrera, J., & Medina, A. (2006). Pilot points method incorporating prior information for solving the groundwater flow inverse problem. Advances in Water Resources, 29(11), 1678-1689. doi:10.1016/j.advwatres.2005.12.009Anderson, M. P. (2005). Heat as a Ground Water Tracer. Ground Water, 43(6), 951-968. doi:10.1111/j.1745-6584.2005.00052.xBravo, H. R., Jiang, F., & Hunt, R. J. (2002). Using groundwater temperature data to constrain parameter estimation in a groundwater flow model of a wetland system. Water Resources Research, 38(8), 28-1-28-14. doi:10.1029/2000wr000172Capilla, J. E., & Llopis-Albert, C. (2009). Gradual conditioning of non-Gaussian transmissivity fields to flow and mass transport data: 1. Theory. Journal of Hydrology, 371(1-4), 66-74. doi:10.1016/j.jhydrol.2009.03.015Chang, H., Zhang, D., & Lu, Z. (2010). History matching of facies distribution with the EnKF and level set parameterization. Journal of Computational Physics, 229(20), 8011-8030. doi:10.1016/j.jcp.2010.07.005Chen , Y. D. S. Oliver 2010Chen, Y., Oliver, D. S., & Zhang, D. (2009). Data assimilation for nonlinear problems by ensemble Kalman filter with reparameterization. Journal of Petroleum Science and Engineering, 66(1-2), 1-14. doi:10.1016/j.petrol.2008.12.002Doussan, C., Toma, A., Paris, B., Poitevin, G., Ledoux, E., & Detay, M. (1994). Coupled use of thermal and hydraulic head data to characterize river-groundwater exchanges. Journal of Hydrology, 153(1-4), 215-229. doi:10.1016/0022-1694(94)90192-9Dovera, L., & Della Rossa, E. (2010). Multimodal ensemble Kalman filtering using Gaussian mixture models. Computational Geosciences, 15(2), 307-323. doi:10.1007/s10596-010-9205-3Evensen, G. (2003). The Ensemble Kalman Filter: theoretical formulation and practical implementation. Ocean Dynamics, 53(4), 343-367. doi:10.1007/s10236-003-0036-9Franssen, H.-J. H., Gómez-Hernández, J., & Sahuquillo, A. (2003). Coupled inverse modelling of groundwater flow and mass transport and the worth of concentration data. Journal of Hydrology, 281(4), 281-295. doi:10.1016/s0022-1694(03)00191-4Fu, J., & Jaime Gómez-Hernández, J. (2009). Uncertainty assessment and data worth in groundwater flow and mass transport modeling using a blocking Markov chain Monte Carlo method. Journal of Hydrology, 364(3-4), 328-341. doi:10.1016/j.jhydrol.2008.11.014Gómez-Hernández, J. J., & Journel, A. G. (1993). Joint Sequential Simulation of MultiGaussian Fields. Geostatistics Tróia ’92, 85-94. doi:10.1007/978-94-011-1739-5_8Gómez-Hernández, J. J., & Wen, X.-H. (1994). Probabilistic assessment of travel times in groundwater modeling. Stochastic Hydrology and Hydraulics, 8(1), 19-55. doi:10.1007/bf01581389G�mez-Hern�ndez, J. J., Franssen, H.-J. W. M. H., & Sahuquillo, A. (2003). Stochastic conditional inverse modeling of subsurface mass transport: A brief review and the self-calibrating method. Stochastic Environmental Research and Risk Assessment (SERRA), 17(5), 319-328. doi:10.1007/s00477-003-0153-5Gordon , N. D. Salmond A. Smith 1993 Novel approach to nonlinear/non-Gaussian Bayesian state estimation Proc. Inst. Electr. Eng. 140 107 113Gu, Y., & Oliver, D. S. (2005). The Ensemble Kalman Filter for Continuous Updating of Reservoir Simulation Models. Journal of Energy Resources Technology, 128(1), 79-87. doi:10.1115/1.2134735Gu, Y., & Oliver, D. S. (2007). An Iterative Ensemble Kalman Filter for Multiphase Fluid Flow Data Assimilation. SPE Journal, 12(04), 438-446. doi:10.2118/108438-paHu, L. Y. (2000). Mathematical Geology, 32(1), 87-108. doi:10.1023/a:1007506918588Kalman, R. E. (1960). A New Approach to Linear Filtering and Prediction Problems. Journal of Basic Engineering, 82(1), 35-45. doi:10.1115/1.3662552Kurtz, W., Hendricks Franssen, H.-J., Kaiser, H.-P., & Vereecken, H. (2014). Joint assimilation of piezometric heads and groundwater temperatures for improved modeling of river-aquifer interactions. Water Resources Research, 50(2), 1665-1688. doi:10.1002/2013wr014823Li, L., Zhou, H., Gómez-Hernández, J. J., & Hendricks Franssen, H.-J. (2012). Jointly mapping hydraulic conductivity and porosity by assimilating concentration data via ensemble Kalman filter. Journal of Hydrology, 428-429, 152-169. doi:10.1016/j.jhydrol.2012.01.037Li, L., Zhou, H., Hendricks Franssen, H. J., & Gómez-Hernández, J. J. (2011). Groundwater flow inverse modeling in non-MultiGaussian media: performance assessment of the normal-score Ensemble Kalman Filter. Hydrology and Earth System Sciences Discussions, 8(4), 6749-6788. doi:10.5194/hessd-8-6749-2011Liu , N. D. Oliver 2005 Critical evaluation of the ensemble Kalman filter on history matching of geologic facies SPE Reservoir Eval. Eng. 8 6 470 477Losa, S. N., Kivman, G. A., Schröter, J., & Wenzel, M. (2003). Sequential weak constraint parameter estimation in an ecosystem model. Journal of Marine Systems, 43(1-2), 31-49. doi:10.1016/j.jmarsys.2003.06.001Ma , R. C. Zheng 2010 Effects of density and viscosity in modeling heat as a groundwater tracer, Groundwater 48 3 380 389Ma, R., Zheng, C., Zachara, J. M., & Tonkin, M. (2012). Utility of bromide and heat tracers for aquifer characterization affected by highly transient flow conditions. Water Resources Research, 48(8). doi:10.1029/2011wr011281McDonald , M. A. Harbaugh 1988Oliver, D. S., Cunha, L. B., & Reynolds, A. C. (1997). Markov chain Monte Carlo methods for conditioning a permeability field to pressure data. Mathematical Geology, 29(1), 61-91. doi:10.1007/bf02769620RamaRao, B. S., LaVenue, A. M., De Marsily, G., & Marietta, M. G. (1995). Pilot Point Methodology for Automated Calibration of an Ensemble of conditionally Simulated Transmissivity Fields: 1. Theory and Computational Experiments. Water Resources Research, 31(3), 475-493. doi:10.1029/94wr02258Reich, S. (2011). A Gaussian-mixture ensemble transform filter. Quarterly Journal of the Royal Meteorological Society, 138(662), 222-233. doi:10.1002/qj.898Simon, E., & Bertino, L. (2009). Application of the Gaussian anamorphosis to assimilation in a 3-D coupled physical-ecosystem model of the North Atlantic with the EnKF: a twin experiment. Ocean Science, 5(4), 495-510. doi:10.5194/os-5-495-2009Strebelle, S. (2002). Mathematical Geology, 34(1), 1-21. doi:10.1023/a:1014009426274Sun, A. Y., Morris, A. P., & Mohanty, S. (2009). Sequential updating of multimodal hydrogeologic parameter fields using localization and clustering techniques. Water Resources Research, 45(7). doi:10.1029/2008wr007443Van Leeuwen, P. J. (2009). Particle Filtering in Geophysical Systems. Monthly Weather Review, 137(12), 4089-4114. doi:10.1175/2009mwr2835.1Wang, Y., Li, G., & Reynolds, A. C. (2010). Estimation of Depths of Fluid Contacts by History Matching Using Iterative Ensemble-Kalman Smoothers. SPE Journal, 15(02), 509-525. doi:10.2118/119056-paWen, X.-H., & Chen, W. H. (2006). Real-Time Reservoir Model Updating Using Ensemble Kalman Filter With Confirming Option. SPE Journal, 11(04), 431-442. doi:10.2118/92991-paWen, X.-H., Deutsch, C. V., & Cullick, A. S. (2002). Construction of geostatistical aquifer models integrating dynamic flow and tracer data using inverse technique. Journal of Hydrology, 255(1-4), 151-168. doi:10.1016/s0022-1694(01)00512-1Wen, X. H., Capilla, J. E., Deutsch, C. V., Gómez-Hernández, J. J., & Cullick, A. S. (1999). A program to create permeability fields that honor single-phase flow rate and pressure data. Computers & Geosciences, 25(3), 217-230. doi:10.1016/s0098-3004(98)00126-5Xu, T., & Gómez‐Hernández, J. J. (2015). Inverse sequential simulation: A new approach for the characterization of hydraulic conductivities demonstrated on a non‐ G aussian field. Water Resources Research, 51(4), 2227-2242. doi:10.1002/2014wr016320Xu, T., & Gómez-Hernández, J. J. (2015). Inverse sequential simulation: Performance and implementation details. Advances in Water Resources, 86, 311-326. doi:10.1016/j.advwatres.2015.04.015Xu, T., Jaime Gómez-Hernández, J., 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. doi:10.1016/j.advwatres.2013.01.006Zheng , C. 2010Zhou, H., Gómez-Hernández, J. J., Hendricks Franssen, H.-J., & Li, L. (2011). An approach to handling non-Gaussianity of parameters and state variables in ensemble Kalman filtering. Advances in Water Resources, 34(7), 844-864. doi:10.1016/j.advwatres.2011.04.014Zhou, H., Li, L., Hendricks Franssen, H.-J., & Gómez-Hernández, J. J. (2011). Pattern Recognition in a Bimodal Aquifer Using the Normal-Score Ensemble Kalman Filter. Mathematical Geosciences, 44(2), 169-185. doi:10.1007/s11004-011-9372-3Zhou, H., Gómez-Hernández, J. J., & Li, L. (2014). Inverse methods in hydrogeology: Evolution and recent trends. Advances in Water Resources, 63, 22-37. doi:10.1016/j.advwatres.2013.10.01

Recent advances in modeling and simulation of the exposure and response of tungsten to fusion energy conditions

Under the anticipated operating conditions for demonstration magnetic fusion reactors beyond ITER, structural and plasma-facing materials will be exposed to unprecedented conditions of irradiation, heat flux, and temperature. While such extreme environments remain inaccessible experimentally, computational modeling and simulation can provide qualitative and quantitative insights into materials response and complement the available experimental measurements with carefully validated predictions. For plasma-facing components such as the first wall and the divertor, tungsten (W) has been selected as the leading candidate material due to its superior high-temperature and irradiation properties, as well as for its low retention of implanted tritium. In this paper we provide a review of recent efforts in computational modeling of W both as a plasma-facing material exposed to He deposition as well as a bulk material subjected to fast neutron irradiation. We use a multiscale modeling approach-commonly used as the materials modeling paradigm-to define the outline of the paper and highlight recent advances using several classes of techniques and their interconnection. We highlight several of the most salient findings obtained via computational modeling and point out a number of remaining challenges and future research directions.Peer reviewe

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

Investigating variation in replicability

Although replication is a central tenet of science, direct replications are rare in psychology. This research tested variation in the replicability of 13 classic and contemporary effects across 36 independent samples totaling 6,344 participants. In the aggregate, 10 effects replicated consistently. One effect – imagined contact reducing prejudice – showed weak support for replicability. And two effects – flag priming influencing conservatism and currency priming influencing system justification – did not replicate. We compared whether the conditions such as lab versus online or US versus international sample predicted effect magnitudes. By and large they did not. The results of this small sample of effects suggest that replicability is more dependent on the effect itself than on the sample and setting used to investigate the effect

Canagliflozin and Renal Outcomes in Type 2 Diabetes and Nephropathy

BACKGROUND Type 2 diabetes mellitus is the leading cause of kidney failure worldwide, but few effective long-term treatments are available. In cardiovascular trials of inhibitors of sodium–glucose cotransporter 2 (SGLT2), exploratory results have suggested that such drugs may improve renal outcomes in patients with type 2 diabetes. METHODS In this double-blind, randomized trial, we assigned patients with type 2 diabetes and albuminuric chronic kidney disease to receive canagliflozin, an oral SGLT2 inhibitor, at a dose of 100 mg daily or placebo. All the patients had an estimated glomerular filtration rate (GFR) of 30 to 300 to 5000) and were treated with renin–angiotensin system blockade. The primary outcome was a composite of end-stage kidney disease (dialysis, transplantation, or a sustained estimated GFR of <15 ml per minute per 1.73 m 2), a doubling of the serum creatinine level, or death from renal or cardiovascular causes. Prespecified secondary outcomes were tested hierarchically. RESULTS The trial was stopped early after a planned interim analysis on the recommendation of the data and safety monitoring committee. At that time, 4401 patients had undergone randomization, with a median follow-up of 2.62 years. The relative risk of the primary outcome was 30% lower in the canagliflozin group than in the placebo group, with event rates of 43.2 and 61.2 per 1000 patient-years, respectively (hazard ratio, 0.70; 95% confidence interval [CI], 0.59 to 0.82; P=0.00001). The relative risk of the renal-specific composite of end-stage kidney disease, a doubling of the creatinine level, or death from renal causes was lower by 34% (hazard ratio, 0.66; 95% CI, 0.53 to 0.81; P<0.001), and the relative risk of end-stage kidney disease was lower by 32% (hazard ratio, 0.68; 95% CI, 0.54 to 0.86; P=0.002). The canagliflozin group also had a lower risk of cardiovascular death, myocardial infarction, or stroke (hazard ratio, 0.80; 95% CI, 0.67 to 0.95; P=0.01) and hospitalization for heart failure (hazard ratio, 0.61; 95% CI, 0.47 to 0.80; P<0.001). There were no significant differences in rates of amputation or fracture. CONCLUSIONS In patients with type 2 diabetes and kidney disease, the risk of kidney failure and cardiovascular events was lower in the canagliflozin group than in the placebo group at a median follow-up of 2.62 years

Canagliflozin and renal outcomes in type 2 diabetes and nephropathy

BACKGROUND Type 2 diabetes mellitus is the leading cause of kidney failure worldwide, but few effective long-term treatments are available. In cardiovascular trials of inhibitors of sodium–glucose cotransporter 2 (SGLT2), exploratory results have suggested that such drugs may improve renal outcomes in patients with type 2 diabetes. METHODS In this double-blind, randomized trial, we assigned patients with type 2 diabetes and albuminuric chronic kidney disease to receive canagliflozin, an oral SGLT2 inhibitor, at a dose of 100 mg daily or placebo. All the patients had an estimated glomerular filtration rate (GFR) of 30 to &lt;90 ml per minute per 1.73 m2 of body-surface area and albuminuria (ratio of albumin [mg] to creatinine [g], &gt;300 to 5000) and were treated with renin–angiotensin system blockade. The primary outcome was a composite of end-stage kidney disease (dialysis, transplantation, or a sustained estimated GFR of &lt;15 ml per minute per 1.73 m2), a doubling of the serum creatinine level, or death from renal or cardiovascular causes. Prespecified secondary outcomes were tested hierarchically. RESULTS The trial was stopped early after a planned interim analysis on the recommendation of the data and safety monitoring committee. At that time, 4401 patients had undergone randomization, with a median follow-up of 2.62 years. The relative risk of the primary outcome was 30% lower in the canagliflozin group than in the placebo group, with event rates of 43.2 and 61.2 per 1000 patient-years, respectively (hazard ratio, 0.70; 95% confidence interval [CI], 0.59 to 0.82; P=0.00001). The relative risk of the renal-specific composite of end-stage kidney disease, a doubling of the creatinine level, or death from renal causes was lower by 34% (hazard ratio, 0.66; 95% CI, 0.53 to 0.81; P&lt;0.001), and the relative risk of end-stage kidney disease was lower by 32% (hazard ratio, 0.68; 95% CI, 0.54 to 0.86; P=0.002). The canagliflozin group also had a lower risk of cardiovascular death, myocardial infarction, or stroke (hazard ratio, 0.80; 95% CI, 0.67 to 0.95; P=0.01) and hospitalization for heart failure (hazard ratio, 0.61; 95% CI, 0.47 to 0.80; P&lt;0.001). There were no significant differences in rates of amputation or fracture. CONCLUSIONS In patients with type 2 diabetes and kidney disease, the risk of kidney failure and cardiovascular events was lower in the canagliflozin group than in the placebo group at a median follow-up of 2.62 years

Inverse Methods in Hydrogeology: Evolution and Recent Trends

[EN] Parameter identification is an essential step in constructing a groundwater model. The process of recognizing model parameter values by conditioning on observed data of the state variable is referred to as the inverse problem. A series of inverse methods has been proposed to solve the inverse problem, ranging from trial-and-error manual calibration to the current complex automatic data assimilation algorithms. This paper does not attempt to be another overview paper on inverse models, but rather to analyze and track the evolution of the inverse methods over the last decades, mostly within the realm of hydrogeology, revealing their transformation, motivation and recent trends. Issues confronted by the inverse problem, such as dealing with multiGaussianity and whether or not to preserve the prior statistics are discussed. (C) 2013 Elsevier Ltd. All rights reserved.The authors gratefully acknowledge the financial support by the Spanish Ministry of Science and Innovation through project CGL2011-23295. We would like to thank Dr. Alberto Guadagnini (Politecnico di Milano, Italy) for his comments during the reviewing process, which helped improving the final paper.Zhou, H.; Gómez-Hernández, JJ.; Li, L. (2014). Inverse Methods in Hydrogeology: Evolution and Recent Trends. Advances in Water Resources. 63:22-37. https://doi.org/10.1016/j.advwatres.2013.10.014S22376