Frank T.-C. Tsai

Non-negativity and stability analyses of lattice Boltzmann method for advection-diffusion equation

Stability is one of the main concerns in the lattice Boltzmann method (LBM). The objectives of this study are to investigate the linear stability of the lattice Boltzmann equation with the Bhatnagar-Gross-Krook collision operator (LBGK) for the advection-diffusion equation (ADE), and to understand the relationship between the stability of the LBGK and non-negativity of the equilibrium distribution functions (EDFs). This study conducted linear stability analysis on the LBGK, whose stability depends on the lattice Peclet number, the Courant number, the single relaxation time, and the flow direction. The von Neumann analysis was applied to delineate the stability domains by systematically varying these parameters. Moreover, the dimensionless EDFs were analyzed to identify the non-negative domains of the dimensionless EDFs. As a result, this study obtained linear stability and non-negativity domains for three different lattices with linear and second-order EDFs. It was found that the second-order EDFs have larger stability and non-negativity domains than the linear EDFs and outperform linear EDFs in terms of stability and numerical dispersion. Furthermore, the non-negativity of the EDFs is a sufficient condition for linear stability and becomes a necessary condition when the relaxation time is very close to 0.5. The stability and non-negativity domains provide useful information to guide the selection of dimensionless parameters to obtain stable LBM solutions. We use mass transport problems to demonstrate the consistency between the theoretical findings and LBM solutions.

Multiple Parameterization for Hydraulic Conductivity Identification

Hydraulic conductivity identification remains a challenging inverse problem in ground water modeling because of the inherent nonuniqueness and lack of flexibility in parameterization methods. This study introduces maximum weighted log-likelihood estimation (MWLLE) along with multiple generalized parameterization (GP) methods to identify hydraulic conductivity and to address nonuniqueness and inflexibility problems in parameterization. A scaling factor for information criteria is suggested to obtain reasonable weights of parameterization methods for the MWLLE and model averaging method. The scaling factor is a statistical parameter relating to a desired significance level in Occams window and the variance of the chi-squares distribution of the fitting error. Through model averaging with multiple GP methods, the conditional estimate of hydraulic conductivity and its total conditional covariances are calculated. A numerical example illustrates the issue arising from Occams window in estimating model weights and shows the usefulness of the scaling factor to obtain reasonable model weights. Moreover, the numerical example demonstrates the advantage of using multiple GP methods over the zonation and interpolation methods because GP provides better models in the model averaging method. The methodology is applied to the Alamitos Gap area, California, to identify the hydraulic conductivity field. The results show that the use of the scaling factor is necessary in order to incorporate good parameterization methods and to avoid a dominant parameterization method.

Salinity and Soluble Organic Matter on Virus Sorption in Sand and Soil Columns

The objective of this research was to study the sorption and transport of bacteriophage MS-2 (a bacterial virus) in saturated sediments under the effect of salinity and soluble organic matter (SOM). One-dimensional column experiments were conducted on washed high-purity silica sand and sandy soil. In sand column tests, increasing salinity showed distinct effect on enhancing MS-2 sorption. However, SOM decreased MS-2 sorption. Using a two-site reversible-irreversible sorption model and the double layer theory, we explained that pore-water salinity potentially compressed the theoretical thickness of double layers of MS-2 and sand, and thus increased sorption on reversible sorption sites. On irreversible sorption sites, increasing salinity reversed charges of some sand particles from negative to positive, and thus converted reversible sorption sites into irreversible sites and enhanced sorption of MS-2. SOM was able to expand the double layer thickness on reversible sites and competed with MS-2 for the same binding place on irreversible sites. In sandy soil column tests, the bonded and dissolved (natural) soil organic matters suppressed the effects of pore-water salinity and added SOM and significantly reduced MS-2 adsorption. This was explained that the bonded soil organic matter occupied a great portion of sorption sites and significantly reduced sorption sites for MS-2. In addition, the dissolved soil organic matter potentially expanded the double layer thickness of MS-2 and sandy soil on reversible sorption sites and competed with MS-2 for the same binding place.

Bayesian Artificial Intelligence Model Averaging for Hydraulic Conductivity Estimation

AbstractThis research presents a Bayesian artificial intelligence model averaging (BAIMA) method that incorporates multiple artificial intelligence (AI) models to estimate hydraulic conductivity and evaluate estimation uncertainties. Uncertainty in AI model outputs stems from errors in model input and nonuniqueness in selecting different AI methods. Using one single AI model tends to bias the estimation and underestimate uncertainty. The BAIMA employs a Bayesian model averaging (BMA) technique to address the issue of using one single AI model for estimation. The BAIMA estimates hydraulic conductivity by averaging the outputs of AI models according to their model weights. In this study, the model weights are determined using the Bayesian information criterion (BIC) that follows the parsimony principle. The BAIMA calculates the within-model variances to account for uncertainty propagation from input data to AI model output. Between-model variances are evaluated to account for uncertainty because of model no...

Parallel Inverse Modeling and Uncertainty Quantification for Computationally Demanding Groundwater-Flow Models Using Covariance Matrix Adaptation

AbstractThis study investigates the performance of the covariance matrix adaptation-evolution strategy (CMA-ES), a stochastic optimization method, in solving groundwater inverse problems. The objectives of the study are to evaluate the computational efficiency of the parallel CMA-ES and to investigate the use of the empirically estimated covariance matrix in quantifying model prediction uncertainty due to parameter estimation uncertainty. First, the parallel scaling with increasing number of processors up to a certain limit is discussed for synthetic and real-world groundwater inverse problems. Second, through the use of the empirically estimated covariance matrix of parameters from the CMA-ES, the study adopts the Monte Carlo simulation technique to quantify model prediction uncertainty. The study shows that the parallel CMA-ES is an efficient and powerful method for solving the groundwater inverse problem for computationally demanding groundwater flow models and for deriving covariances of estimated par...

GIS-Based Water Budget Framework for High-Resolution Groundwater Recharge Estimation of Large-Scale Humid Regions

AbstractGroundwater recharge plays a vital role in replenishing aquifers, which impacts on groundwater resources availability. This paper develops a geographic information system (GIS)-based water budget framework in conjunction with a hydrologic model to derive high-resolution spatial-temporal distribution of groundwater recharge for the Southern Hills aquifer system, southwestern Mississippi, and southeastern Louisiana, United States. The framework includes parallel programming to distribute the large amount of software runs to a cluster of supercomputers to expedite computation time. Under the parallel computation, the hydrologic models are calibrated by the USGS WaterWatch runoff dataset and verified by the moderate resolution imaging spectroradiometer (MODIS) evapotranspiration dataset. A map of recharge time lag is derived to understand travel time of infiltrated precipitation reaching the last soil layer. A recharge index map is derived to quantify the percentage of precipitation that becomes groun...

Indicator geostatistics for reconstructing Baton Rouge aquifer-fault hydrostratigraphy, Louisiana, USA

The complex siliciclastic aquifer system underneath the Baton Rouge area, Louisiana (USA), is fluvial in origin and is characterized by strongly binary heterogeneity of sand units and mudstones as pervious and impervious hydrofacies. The east–west trending Baton Rouge fault and Denham Springs-Scotlandville fault cut across East Baton Rouge Parish and play an important role in groundwater flow and aquifer salinization. This study reconstructs the Baton Rouge aquifer-fault system architecture for a Miocene-Pliocene depth interval that consists of the 1,200-foot sand to the 2,000-foot sand. The results show the spatial extent of sand units, their interconnections, and flow paths within each sand unit. The regional-scale formation dip, the sand unit offset on the faults, and the volumetric spatial extent of individual sand units are quantified. The study reveals the complexity of the Baton Rouge aquifer-fault system where the sand deposition is non-uniform, different sand units are interconnected, the sand unit displacement on the faults is significant, and the spatial distribution of flow pathways through the faults is sporadic. The identified locations of flow pathways through the Baton Rouge fault provide useful information on possible windows for saltwater intrusion from the south.RésuméLe système aquifère détritique siliceux complexe se trouvant sous Bâton Rouge, Louisiane (USA) a une origine alluviale et est caractérisé par deux hydro faciès hétérogènes, une unité de sable et une unité d’argilite. La faille Est-Ouest de Bâton Rouge, et la faille de Denham Springs- Scotlandville recoupent l’Est de la paroisse de Bâton Rouge et jouent un rôle important dans l’écoulement souterrain et la salinisation de l’aquifère. Cette étude reconstitue l’architecture du système aquifère faillé sur l’intervalle de temps Miocène-Pliocène représentant 1200 à 2000 pieds de sable. Les résultats montre l’extension spatiale des unités de sable, leurs interconnections, et chenaux d’écoulement à l’intérieur de chaque unité. Le pendage de la formation à l’échelle régionale, le rejet des failles de l’unité sableuse et l’extension volumétrique spatiale de chaque unité sableuse sont évalués. L’étude révèle la complexité du système aquifère faillé de Bâton Rouge où la disposition du sable n’est pas uniforme. Différentes unités de sable sont interconnectées, le rejet de l’unité de sable sur la faille est important, et la distribution des chenaux d’écoulement à travers la faille est discontinue. La localisation des chenaux d’écoulement identifiés à travers la faille de Bâton Rouge fournit une information utile sur les fenêtres d’intrusion possibles d’eau salée depuis le Sud.ResumenEl sistema acuífero silicoclástico complejo por debajo del área de Baton Rouge, Louisiana (EEUU), es de origen fluvial y está caracterizado por una fuerte heterogeneidad binaria de las unidades de arenas y fangolitas como hidrofacies permeables e impermeables. El rumbo este–oeste de la falla de Baton Rouge y la falla Denham Springs -Scotlandville atraviesa a la East Baton Rouge Parish y juega un rol importante en el flujo de agua subterránea y la salinización del acuífero. Este estudio reconstruye la arquitectura del sistema acuífero fallado de Baton Rouge para un intervalo de profundidad Mioceno-Plioceno que comprende 1,200-pies de arena a 2,000-pies de arena. Los resultados muestran la extensión espacial de las unidades de arenas, sus interconexiones, y las trayectorias de flujo dentro de cada unidad de arena. Se cuantificaron la inclinación de la formación en la escala regional, las unidades de arena sobrepuestas a las fallas, y la extensión volumétrica espacial de las unidades individuales de arena. El estudio revela la complejidad del sistema acuífero fallado de Baton Rouge donde la depositación de arena es no uniforme, distintas unidades de arenas están interconectadas, el desplazamiento de las unidades de arena sobre las fallas es significativo, y la distribución espacial de las trayectorias de flujo a través de las fallas es esporádica. Las ubicaciones identificadas de las trayectorias de flujo a través de la falla de Baton Rouge proporcionan información útil sobre posibles ventanas para la intrusión de agua salada desde el sur.摘要美国路易斯安那州Baton Rouge地区 之下的复杂硅质碎屑含水层系统是河流成因的,作为渗透的和非渗透的水相砂岩单元和泥岩具有强烈的二元不均匀性特征。东--西向的Baton Rouge断层和Denham Springs –Scotlandville断层穿过东Baton Rouge Parish,在地下水流和含水层盐化中发挥重要作用。本研究 重建了Baton Rouge 含水层-断层系统架构,中新世—上新世深度间隔由1200英尺到 2000英尺的沙组成。结果显示了每个沙单元之内的沙单元空间范围、相互连接及水流通道。区域尺度的地层下沉,沙单元偏移到断层 上,对各自沙单元的空间分布进行了量化。研究揭示了Baton Rouge含水层—断层系统的复杂性,在Baton Rouge含水层—断层系统中,沙沉积是非均一的,不同的沙单元相互连通,断层上的沙单元位移很小,通过断层的水流通道的空间分布是零星的。通过Baton Rouge断层确定的水流通道位置提供了来自南部的海水入侵的有用信息。ResumoO complexo sistema aquífero siliciclástico sobrejacente à área de Baton Rouge, no Louisiana (EUA), é de origem fluvial, e é caraterizado por fortes heterogeneidades binárias das unidades arenosas e de argilito que constituem respetivamente hidrofácies permeáveis e impermeáveis. A falha este–oeste de Baton Rouge e a falha de Denham Springs-Scotlandville, que intersetam a Paróquia de East Baton Rouge, têm um papel fundamental na circulação das águas subterrâneas e na salinização do aquífero. Este estudo reconstitui a arquitetura do sistema aquífero-falha de Baton Rouge para profundidades do Mio-Pliocénico que consistem no intervalo entre a areia à profundidade de 1,200-pés e a areia à profundidade de 2,000-pés. Para cada unidade de areia, os resultados mostram a sua extensão, as suas interconexões e os caminhos de escoamento. Quantificaram-se os declives das unidades regionais, a deslocação das camadas de areia pelas falhas e a volumetria e extensão de cada camada individual. O estudo revela o grau de complexidade do sistema aquífero-falha de Baton Rouge, onde a deposição de areia não é uniforme, onde há interconexões das diferentes camadas de areia, onde o deslocamento das camadas de areia nas falhas é importante e onde a distribuição espacial dos caminhos de escoamento através das falhas é casuístico. A identificação da localização dos caminhos de escoamento através da falha de Baton Rouge fornece informação útil sobre potenciais janelas para intrusão salina proveniente do sul.

Ensemble Subsurface Modeling Using Grid Computing Technology

Ensemble Kalman filter (EnKF) uses a randomized ensemble of subsurface models for error and uncertainty estimation. However, the complexity of geological models and the requirement of a large number of simulation runs make routine applications extremely difficult due to expensive computation cost. Grid computing technologies provide a cost-efficient way to combine geographically distributed computing resources to solve large-scale data and computation intensive problems. Hence, we design and implement a grid-enabled EnKF solution to ill-posed model inversion problems for subsurface modeling. It has been integrated into the ResGrid, a problem solving environment aimed at managing distributed computing resources and conducting subsurface-related modeling studies. Two synthetic cases in reservoir studies indicate that the enhanced ResGrid efficiently performs EnKF inversions to obtain accurate, uncertainty-ware predictions on reservoir production. This grid-enabled EnKF solution is also being applied for data assimilation of large-scale groundwater hydrology nonlinear models. The ResGrid with EnKF solution is open-source and available for downloading.

Modeling complex aquifer systems: a case study in Baton Rouge, Louisiana (USA)

This study targets two challenges in groundwater model development: grid generation and model calibration for aquifer systems that are fluvial in origin. Realistic hydrostratigraphy can be developed using a large quantity of well log data to capture the complexity of an aquifer system. However, generating valid groundwater model grids to be consistent with the complex hydrostratigraphy is non-trivial. Model calibration can also become intractable for groundwater models that intend to match the complex hydrostratigraphy. This study uses the Baton Rouge aquifer system, Louisiana (USA), to illustrate a technical need to cope with grid generation and model calibration issues. A grid generation technique is introduced based on indicator kriging to interpolate 583 wireline well logs in the Baton Rouge area to derive a hydrostratigraphic architecture with fine vertical discretization. Then, an upscaling procedure is developed to determine a groundwater model structure with 162 layers that captures facies geometry in the hydrostratigraphic architecture. To handle model calibration for such a large model, this study utilizes a derivative-free optimization method in parallel computing to complete parameter estimation in a few months. The constructed hydrostratigraphy indicates the Baton Rouge aquifer system is fluvial in origin. The calibration result indicates hydraulic conductivity for Miocene sands is higher than that for Pliocene to Holocene sands and indicates the Baton Rouge fault and the Denham Springs-Scotlandville fault to be low-permeability leaky aquifers. The modeling result shows significantly low groundwater level in the “2,000-foot” sand due to heavy pumping, indicating potential groundwater upward flow from the “2,400-foot” sand.RésuméCette étude tente de relever deux défis dans le développement de modélisation d’aquifères: la génération de grille et le calage du modèle pour des systèmes aquifères d’origine fluviale. Une hydrostratigraphie réaliste peut être développée en utilisant une grande quantité de données de logs de forages pour appréhender la complexité d’un système aquifère. Toutefois, générer des grilles valides de modèle d’aquifère qui soient cohérentes avec une hydrostratigraphie complexe n’est pas triviale. La calibration du modèle peut aussi devenir impossible pour les modèles d’aquifères destinés à correspondre à une hydrostratigraphie complexe. Cette étude utilise le système aquifère de Baton Rouge, en Louisiane (Etats-Unis d’Amérique), pour illustrer les besoins techniques à gérer en matière de génération de grille et de calage du modèle. Une technique de génération de grille est présentée, basée sur le krigeage d’un indicateur pour interpoler 583 logs de forages dans la zone de Baton Rouge, afin d’en déduire une architecture hydrostratigraphique avec une discrétisation verticale fine. Ensuite, une procédure de mise à l’échelle est développée pour déterminer une structure du modèle de l’aquifère avec 162 couches qui intègre la géométrie des faciès dans l’architecture hydrostratigraphique. Pour réaliser le calage d’un grand modèle comme celui-ci, cette étude utilise une méthode d’optimisation sans dérivée dans un calcul parallélisé afin d’achever l’estimation des paramètres en quelques mois. L’hydrostratigraphie élaborée indique que le système aquifère de Baton Rouge est d’origine fluviale. Le résultat du calage indique une conductivité hydraulique plus élevée des sables du Miocène par rapport aux sables du Pliocène à l’Holocène, et indique que la faille de Baton Rouge et les sources de Denham, au niveau de la faille de Scotlandville, sont des zones d’aquifères de faible perméabilité avec fuites. Le résultat de la modélisation montre un niveau significativement bas de la piézométrie dans les sables des « 2,000 pieds » en raison de pompages intensifs, indiquant un flux ascendant potentiel d’eaux souterraines depuis la formation des sables des “2,400 pieds”.ResumenEste estudio tiene como objetivo dos desafíos en el desarrollo de modelos de agua subterránea: la generación de la red y la calibración de modelos para sistemas acuíferos de origen fluvial. La hidroestratigrafía realista puede desarrollarse utilizando una gran cantidad de datos de registro de pozos para captar la complejidad de un sistema acuífero. Sin embargo, la generación de grillas válidas del modelo de agua subterránea para ser coherente con la compleja hidroestratigrafía no es trivial. La calibración del modelo también puede volverse intratable para los modelos de aguas subterráneas que pretenden igualar la compleja hidroestratigrafía. Este estudio utiliza el sistema acuífero de Baton Rouge, Luisiana (EEUU), para ilustrar la necesidad técnica para hacer frente a la generación de la red y los problemas de calibración del modelo. Se introduce una técnica de generación de cuadrícula basada en el indicador kriging para interpolar 583 registros de pozos en el área de Baton Rouge para derivar una arquitectura hidroestratigráfica con discretización vertical fina. Luego, se desarrolla un procedimiento de escalado para determinar una estructura de modelo de agua subterránea con 162 capas que captura la geometría de las facies en la arquitectura hidroestratigráfica. Para manejar la calibración en un modelo tan grande, este estudio utiliza un método de optimización sin derivado en computación paralela para completar la estimación de parámetros en pocos meses. La hidroestratigrafía construida indica que el sistema acuífero de Baton Rouge es de origen fluvial. El resultado de la calibración indica que la conductividad hidráulica para las arenas del Mioceno es mayor que la de las arenas del Plioceno a Holoceno e indica que la falla de Baton Rouge y la falla de Denham Springs-Scotlandville son de acuíferos permeables de baja permeabilidad. El resultado del modelado muestra un nivel de agua subterránea significativamente bajo en la arena de “2,000 pies” debido al bombeo intenso, indicando el flujo ascendente de agua subterránea desde la arena de “2,400 pies”.摘要本研究的目标就是地下水模型开发中的两个挑战:河流起源的含水层系统的网格生成和模型校准。可以利用大量的测井数据创建逼真的的水文地层,以获知含水层系统的复杂性。然而,生成与复杂的水文地层一致的有效地下水模型网格绝非简单易事。针对意欲匹配复杂的水文地层的地下水模型,模型的校准也是非常棘手。本研究采用(美国)路易斯安那州的Baton Rouge含水层系统来说明应付网格生成和模型校准问题的一个技术需要。基于指示克里格引入网格生成技术在Baton Rouge地区插入583个电缆井测井记录,根据精细垂直离散化获得水文地层结构。然后,建立一个粗化的程序,用水文地层结构中捕获相几何形状的162层确定地下水模型结构。为了处理这样一个大的模型的模型校准问题,本研究采用了平行计算中无导数的优化方法,在几个月内完成参数估算。构建的水文地层表明,Baton Rouge含水层系统起源于河流。校准结果表明,中新世砂层的水力传导系数高于上新世至全新世的砂层的水力传导系数,还表明Baton Rouge断层及Denham Springs-Scotlandville断层为低渗透性的漏水含水层。建模结果显示,由于强烈抽水,在“2000英尺”的砂层地下水水位很低,表明从“2400英尺”的砂层有潜在的地下水向上流动的水流。ResumoEste estudo mira dois desafios no desenvolvimento de modelos de águas subterrâneas: geração de grades e calibração de modelos para sistemas aquíferos de origem fluvial. A hidroestratigrafia realista pode ser desenvolvida usando uma grande quantidade de dados de registro de poços para capturar a complexidade de um sistema aquífero. No entanto, a geração de grades de modelos de águas subterrâneas válidas para serem consistentes com a hidroestratigrafia complexa não é trivial. A calibração do modelo também pode se tornar intratável para modelos de águas subterrâneas que visam corresponder à hidroestratigrafia complexa. Este estudo utiliza o sistema aquífero Baton Rouge, Luisiana (EUA), para ilustrar uma necessidade técnica de lidar com geração de grade e questões de calibração de modelos. Uma técnica de geração de grade é introduzida baseada na krigagem de indicadores para interpolar 583 registros de poços na área de Baton Rouge para derivar uma arquitetura hidroestratigráfica com discretização vertical fina. Em seguida, desenvolve-se um procedimento de escalonamento para determinar uma estrutura de modelo de águas subterrâneas com 162 camadas que captura a geometria de fácies na arquitetura hidroestratigráfica. Para tratar a calibração de modelo para um modelo tão grande, este estudo utiliza um método de otimização sem derivada na computação paralela para completar a estimativa de parâmetros em alguns poucos meses. A hidroestratigrafia construída indica que o sistema aquífero Baton Rouge é de origem fluvial. O resultado da calibração indica que a condutividade hidráulica para as areias do Mioceno é maior do que aquela para as areias do Plioceno ao Holoceno e indica a falha de Baton Rouge e a falha de Denham Springs-Scotlandville para serem aquíferos permeáveis de baixa permeabilidade. O resultado da modelagem mostra um nível das águas subterrâneas significativamente baixo na areia de “2,000 pés” devido ao bombeamento intenso, indicando um fluxo ascendente no potencial subterrâneo da areia de “2,400 pés”.

A comparison study of DRASTIC methods with various objective methods for groundwater vulnerability assessment

Groundwater vulnerability assessment is a measure of potential groundwater contamination for areas of interest. The main objective of this study is to modify original DRASTIC model using four objective methods, Weights-of-Evidence (WOE), Shannon Entropy (SE), Logistic Model Tree (LMT), and Bootstrap Aggregating (BA) to create a map of groundwater vulnerability for the Sari-Behshahr plain, Iran. The study also investigated impact of addition of eight additional factors (distance to fault, fault density, distance to river, river density, land-use, soil order, geological time scale, and altitude) to improve groundwater vulnerability assessment. A total of 109 nitrate concentration data points were used for modeling and validation purposes. The efficacy of the four methods was evaluated quantitatively using the Area Under the Receiver Operating Characteristic (ROC) Curve (AUC). AUC value for original DRASTIC model without any modification of weights and rates was 0.50. Modification of weights and rates resulted in better performance with AUC values of 0.64, 0.65, 0.75, and 0.81 for BA, SE, LMT, and WOE methods, respectively. This indicates that performance of WOE is the best in assessing groundwater vulnerability for DRASTIC model with 7 factors. The results also show more improvement in predictability of the WOE model by introducing 8 additional factors to the DRASTIC as AUC value increased to 0.91. The most effective contributing factor for ground water vulnerability in the study area is the net recharge. The least effective factors are the impact of vadose zone and hydraulic conductivity.