Stochastic Transport Model Research Articles

Stochastic Modeling of Two-Phase Transport in Fractured Porous Media Under Geological Uncertainty Using an Improved Probabilistic Collocation Method

Stochastic Modeling of Two-Phase Transport in Fractured Porous Media Under Geological Uncertainty Using an Improved Probabilistic Collocation Method

Designing additional CO2 in-situ surface observation networks over South Korea using bayesian inversion coupled with Lagrangian modelling

Efforts to enhance greenhouse gas (GHG) emission reduction in East Asia play a pivotal role on both global and regional scales in advancing climate mitigation strategies. This study aimed to better constrain anthropogenic CO2 emission estimates by expanding the network of near-surface in-situ stations for CO2 observations across South Korea. To achieve an optimal CO2 network design, we conducted an Observing System Simulation Experiment (OSSE) coupled with the Stochastic Lagrangian Transport model (STILT), utilizing meteorological data from the Korean Integrated Model (KIM). Our inversion setup incorporated two CO2 emission datasets with a 0.1o resolution: EDGAR v6 for prior emissions and GRACED for truth emissions. A uniform model-mismatch error of 3 ppm was introduced across sites. The effectiveness of the existing five in-situ stations, termed the base network, in South Korea was evaluated to gauge their ability to constrain CO2 surface flux estimates. However, the findings revealed a reduction in flux uncertainty of only 29.2%, which fell short of the desired uncertainty reduction goal. In this base network, the Lotte World Tower (LWT: 37.5126°E, 127.1025°E) in Seoul and the Anmyeondo (AMY: 36.538576° N, 126.330071° E) site in Taean county stood as major contributors, with estimated reductions of 17.48% and 6.35%, respectively. Consequently, we proposed and developed an extended network, identifying seven candidate sites based on consideration of logistical factors, existing infrastructures, and proximity to the emission source regions. An incremental optimization scheme ranked their contributions, resulting in an additional 25% reduction, bringing the total to 54.13%. However, it is noteworthy that diminishing returns (ranging from 13% to less than 0.1%) were observed with an increase in station count mainly due to the possibility that adding a station earlier in the sequence might render subsequent stations redundant. Despite this, the proposed CO2 network successfully reduced uncertainty in emissions, narrowing the gap with the objectives of the Global Greenhouse Gas Watch (G3W).

How Fast or How Many? Sources of Intermittent Sediment Transport

AbstractNear the threshold of grain motion, sediment transport is “on‐off” intermittent, characterized by large but rare bursts separated by long periods of low transport. Without models that can account for the effects of intermittency, measurements of average sediment flux can be in error by up to an order of magnitude. Despite its known presence and impact, it is not clear whether on‐off intermittency arises from the grain activity (the number of moving grains) or grain velocities, which together determine the sediment flux. We use laboratory flume experiments to show that the on‐off intermittency has its origins in the velocity distributions of grains that move by rolling along the bed, whereas grain activity is not on‐off intermittent. Incorporating the types of intermittency we identify into stochastic models of sediment transport could yield improved predictions of sediment flux, including physically based estimates of the uncertainty in time‐averaged sediment flux.

A newly developed Lagrangian chemical transport scheme: Part 1. Simulation of a boreal forest fire plume

Forest fire research over the last several decades has improved the understanding of fire emissions and impacts. Nevertheless, the evolution of forest fire plumes remains poorly quantified and understood. Here, a Lagrangian chemical transport model, the Forward Atmospheric Stochastic Transport model coupled with the Master Chemical Mechanism (FAST-MCM), has been developed to simulate the transport and chemical transformations of plumes from a boreal forest fire over several hours since their emission. The model results for NOx (NO and NO2), O3, HONO, HNO3, pNO3 and 70 VOC species are compared with airborne in-situ measurements within plume centers and their surrounding portions during the transport. Comparisons between simulation results and measurements show that the FAST-MCM model can properly reproduce the physical and chemical evolution of forest fire plumes. The results indicate that the model can be an important tool used to aid the understanding of the downwind impacts of forest fire plumes.

Developing a Lagrangian sediment transport model for open channel flows

A three-dimensional stochastic Lagrangian particle tracking sediment transport model is developed to solve the discrete advection–dispersion equation using a combination of empirical dispersion equations. The performance of three widely-used longitudinal dispersion coefficient equations was examined to select one of them as the primary dispersion equation term in the developed model. Also, a conditional empirical equation was used to consider the effect of vertical dispersion term in top layers near the water surface. The performance of particle tracking model (PTM) to calculate the sediment concentration was evaluated for various sediment classes (very fine sand, fine sand, and medium sand) using available laboratory dataset. Multiple statistical measures were calculated using the Taylor diagram for each dispersion equation. Based on the result, the developed particle tracking model estimated the suspended sediment concentration in a rectangular open channel with a correlation coefficient (R) of 0.96, standard deviation (STD) of 0.262, and root mean square deviation (RMSD) of 0.06 for three different sediment classes proving the acceptable accuracy of the developed model for different range of sediment gradations. In addition, the accuracy of PTM was compared to recently developed models. Comparison between the particle tracking model and the analytical solution of the advection–dispersion equation showed that the developed model predicted the maximum concentration of suspended sediment 6% and 9.4% lower than the analytical solution result for 30 and 50 s simulation time in the straight channel, respectively. However, there was a good agreement between the longitudinal and transverse sediment concentration distribution from the model and the analytical solution approach. The result of the sensitivity analysis and validation process showed that the model could be used to simulate sediment transport in open channel flows.

A Stochastic Transport Model for the Cumulative Number of Fissions and Deposited Fission Energy

The stochastic theory of neutron transport is extended to describe the cumulative distribution of fission numbers and deposited fission energy in a subvolume of a multiplying assembly. Solutions for the probability distributions are obtained using analytical approximations and Monte Carlo simulation in lumped geometry and in symmetric homogeneous and heterogeneous spheres. The results show the development of a power-law tail in the steady-state fission number and deposited energy distributions when the medium is critical, independent of the fission neutron multiplicity distribution and domain heterogeneity. In contrast, the asymptotic decay is faster than exponential in subcritical media due to rapid chain extinction and in supercritical media due to the increasing probability of chain divergence. A formal asymptotic analysis of the problem in lumped geometry with an arbitrary fission neutron multiplicity confirms the existence of power-law tails at critical.

Untangling the controls on bedload transport in a wood‐loaded river with RFID tracers and linear mixed modelling

AbstractBedload transport is a fundamental process by which coarse sediment is transferred through landscapes by river networks and may be well described stochastically by distributions of grain step length and rest time obtained through tracer studies. To date, none of these published tracer studies have specifically investigated the influence of large wood in the river channel on sediment transport dynamics, limiting the applicability of stochastic sediment transport models in these settings. Large wood is a major component of many forested rivers and is increasing due to anthropogenic ‘Natural Flood Management’ (NFM) practices. This study aims to investigate and model the influence of large wood on grain‐scale bedload transport.We tagged 957 cobble to pebble sized particles (D50 = 73 mm) and 28 pieces of large wood (> 1 m in length) with radio frequency identification (RFID) tracers in an alpine mountain stream. We monitored the transport distance of tracers annually over 3 years, building distributions of tracer transport distances with which to compare with published distributions from wood free settings. We also applied linear mixed modelling (LMM), to tease out the influence of wood from other controls on likelihood of entrainment, deposition, and the transport distances of sediments.Tracer sediments accumulated both upstream and downstream of large wood pieces, with LMM analysis confirming a reduction in the probability of entrainment of tracers closer to wood in all 3 years. Upon remobilization, tracers entrained from positions closer to large wood had shorter subsequent transport distances in each year. In 2019, large wood also had a trapping effect, significantly reducing the transport distances of tracer particles entrained from upstream, that is forcing premature deposition of tracers. This study demonstrates the role of large wood in influencing bedload transport in alpine stream environments, with implications for both natural and anthropogenic addition of wood debris in fluvial environments.

A Dual Heterogeneous Domain Model for Upscaling Anomalous Transport With Multi‐Peaks in Heterogeneous Aquifers

AbstractNatural aquifers are often characterized by multiscale heterogeneity and complex flow networks, challenging the reliable simulation and prediction of contaminant transport. Classic stochastic transport models usually assume independent, identically distributed probability density functions when upscaling solute dynamics, but this assumption is not valid for media with multiscale heterogeneity. To address this issue, a dual heterogeneous domain model (DHDM) was proposed to quantify solute transport in heterogeneous aquifers where solute breakthrough curves (BTCs) exhibit multiple peaks and transient tailing behaviors. To efficiently solve the resultant DHDM, a Lagrangian solver was developed by combining the renewal‐reward process (to capture solute dynamics in each domain) and the state transition probability (to capture solute particle transfer between the two heterogeneous domains). The DHDM and its Lagrangian solver were then applied to simulate solute transport in three different aquifer settings (alluvial, fractured, and karst). Analyses showed that in the alluvial aquifer, early arrivals and bi‐peaks of the observed solute BTC might be caused by interconnected preferential flow paths consisting of high conductivity sediments, while the front edge or long tails of local peaks might be a result of small‐scale heterogeneity. Fracture networks and karst conduits also resulted in anomalous transport with multiple peaks, and mass transfer between the preferential flow channels and matrix led to solute retention. All these complex, coexisting anomalous transport characteristics can be simultaneously and accurately captured by the unifying DHDM approach, significantly expanding the capability of nonlocal transport models.

Stochastic Modeling of Particle Transport in Confined Geometries: Problems and Peculiarities

The equivalence between parabolic transport equations for solute concentrations and stochastic dynamics for solute particle motion represents one of the most fertile correspondences in statistical physics originating from the work by Einstein on Brownian motion. In this article, we analyze the problems and the peculiarities of the stochastic equations of motion in microfluidic confined systems. The presence of solid boundaries leads to tensorial hydrodynamic coefficients (hydrodynamic resistance matrix) that depend also on the particle position. Singularity issues, originating from the non-integrable divergence of the entries of the resistance matrix near a solid no-slip boundary, determine some mass-transport paradoxes whenever surface phenomena, such as surface chemical reactions at the walls, are considered. These problems can be overcome by considering the occurrence of non vanishing slippage. Added-mass effects and the influence of fluid inertia in confined geometries are also briefly addressed.

Empirical Lagrangian parametrization for wind-driven mixing of buoyant particles at the ocean surface

Abstract. Turbulent mixing is a vital component of vertical particulate transport, but ocean global circulation models (OGCMs) generally have low-resolution representations of near-surface mixing. Furthermore, turbulence data are often not provided in OGCM model output. We present 1D parametrizations of wind-driven turbulent mixing in the ocean surface mixed layer that are designed to be easily included in 3D Lagrangian model experiments. Stochastic transport is computed by Markov-0 or Markov-1 models, and we discuss the advantages and disadvantages of two vertical profiles for the vertical diffusion coefficient Kz. All vertical diffusion profiles and stochastic transport models lead to stable concentration profiles for buoyant particles, which for particles with rise velocities of 0.03 and 0.003 m s−1 agree relatively well with concentration profiles from field measurements of microplastics when Langmuir-circulation-driven turbulence is accounted for. Markov-0 models provide good model performance for integration time steps of Δt≈30 s and can be readily applied when studying the behavior of buoyant particulates in the ocean. Markov-1 models do not consistently improve model performance relative to Markov-0 models and require an additional parameter that is poorly constrained.

Performance trade-offs for collective motor-driven transport

Motor-driven intracellular transport of organelles, vesicles, and other molecular cargo is a highly collective process. An individual cargo is often pulled by a team of transport motors, with numbers ranging from only a few to several hundred. We investigate the behaviour of these systems using an analytically tractable stochastic model for transport of molecular cargo by an arbitrary number N of motors which allows us to explore the N-dependence performance metrics such as velocity, precision, and efficiency.

Stochastic radiative transfer in random media. II. Coupling of radiation to material.

We study the mechanism of the impact of random media on the stochastic radiation transport based on a one-dimensional (1D) planar model. To this end, we use a random sampling of mixtures combined with a deterministic solution of the time-dependent radiation transport equationcoupled to a material temperature equation. Compared to purely absorbing cases [C.-Z. Gao etal., Phys. Rev. E 102, 022111 (2020)10.1103/PhysRevE.102.022111], we find that material temperatures can significantly suppress the impact of mixing distribution and size, which is understood from the analysis of energy transport channels. By developing a steady-state stochastic transport model, it is found that the mechanism of transmission of radiation is distance dependent, which is closely related to the mean free path of photons l_{p}. Furthermore, we suggest that it is the relationship between l_{p} and L (the width of random medium) that determines the impact of random media on the stochastic radiation transport, which is further corroborated by additional simulations. Most importantly, combining the proposed simple relationship and 1D simulations, we resolve the existing disputable issue of the impact of random media in previous multidimensional works, showing that multidimensional results are essentially consistent and the observed weak or remarkable impact of random media is mainly due to the distinctly different relationship between l_{p} and L. Our results may have practical implications in relevant experiments of stochastic radiative transfer.

Performance scaling and trade-offs for collective motor-driven transport

Motor-driven intracellular transport of organelles, vesicles, and other molecular cargo is a highly collective process. An individual cargo is often pulled by a team of transport motors, with numbers ranging from only a few to several hundred. We explore the behavior of these systems using a stochastic model for transport of molecular cargo by an arbitrary number N of motors obeying linear Langevin dynamics, finding analytic solutions for the N-dependence of the velocity, precision of forward progress, energy flows between different system components, and efficiency. In two opposing regimes, we show that these properties obey simple scaling laws with N. Finally, we explore trade-offs between performance metrics as N is varied, providing insight into how different numbers of motors might be well-matched to distinct contexts where different performance metrics are prioritized.

Solidarity measures: Assessment of strategic gas storage on EU regional risk groups natural gas supply resilience

This paper focuses on strategic storage as a solidarity measure in response to short-term “high-impact, low-probability” (HILP) disruptions in the European Union (EU) gas supply from major suppliers (i.e., Ukraine, Russia, Norway, and North Africa), assuming its implementation in selected Member States. A two-stage stochastic cost minimization gas transport model is used to evaluate the impact of HILP events on the level of demand curtailment, survival time, and the natural gas supply mix of EU regional risk group. Results show that geographic proximity alone, without solidarity measures, is inadequate in providing system resilience. In contrast, solidarity measures lead to a longer survival time for regional risk groups (14 days) and to a reduction in system (15%) and LNG (70%) costs relative to a base scenario with no strategic storage. The analysis stresses the value of the coordinated use of strategic storage in balancing the natural gas network during emergencies, and provides further evidence supporting the EU legislative path towards an Energy Union.

Probability of Non-Exceedance of Arsenic Concentration in Groundwater Estimated Using Stochastic Multicomponent Reactive Transport Modeling

Stochastic multicomponent reactive transport modeling is a powerful approach to quantify the probability of non-exceedance (PNE) of arsenic (As) critical concentration thresholds in groundwater. The approach is applied to a well-characterized shallow alluvial aquifer near Venice, Italy. Here, As mobility depends primarily on rainfall-controlled redox-dependent precipitation-dissolution of iron hydroxides. A Monte-Carlo analysis based on a calibrated three-dimensional flow and transport model targeted the geochemical initial conditions as the main source of uncertainty of As concentrations in the studied aquifer. It was found that, during 115 simulated days, the fraction of the entire aquifer volume with As > 10 μgL−1 decreased on average from ~43% to ~39% and the average As concentration from ~32 μgL−1 to ~27 μgL−1. Meanwhile, PNE increased from 55% to 60% when 10 μgL−1 was set as target threshold, and from 71% to 78% for 50 μgL−1. The time dependence of As attenuation can be ascribed to the increase of oxidizing conditions during rainfall-dependent aquifer recharge, which causes As sorption on precipitating iron hydroxides. When computing the same statistics for the shallowest 6 m, As attenuation was even more evident. The volume fraction of aquifer with As > 10μgL−1 dropped from 40% to 28% and the average As concentration from 31 μgL−1 to 20 μgL−1, whereas PNE increased from 58% to 70% for As < 10 μgL−1 and from 71% to 86% for As < 50 μgL−1. Thus, the wells screen depth in the aquifer can be a critical aspect when estimating As risk, owing to the depth-dependent relative change in redox conditions during rainfall events.

Stochastic parametric skeletal dosimetry model for humans: General approach and application to active marrow exposure from bone-seeking beta-particle emitters.

The objective of this study is to develop a skeleton model for assessing active marrow dose from bone-seeking beta-emitting radionuclides. This article explains the modeling methodology which accounts for individual variability of the macro- and microstructure of bone tissue. Bone sites with active hematopoiesis are assessed by dividing them into small segments described by simple geometric shapes. Spongiosa, which fills the segments, is modeled as an isotropic three-dimensional grid (framework) of rod-like trabeculae that "run through" the bone marrow. Randomized multiple framework deformations are simulated by changing the positions of the grid nodes and the thickness of the rods. Model grid parameters are selected in accordance with the parameters of spongiosa microstructures taken from the published papers. Stochastic modeling of radiation transport in heterogeneous media simulating the distribution of bone tissue and marrow in each of the segments is performed by Monte Carlo methods. Model output for the human femur at different ages is provided as an example. The uncertainty of dosimetric characteristics associated with individual variability of bone structure was evaluated. An advantage of this methodology for the calculation of doses absorbed in the marrow from bone-seeking radionuclides is that it does not require additional studies of autopsy material. The biokinetic model results will be used in the future to calculate individual doses to members of a cohort exposed to 89,90Sr from liquid radioactive waste discharged to the Techa River by the Mayak Production Association in 1949-1956. Further study of these unique cohorts provides an opportunity to gain more in-depth knowledge about the effects of chronic radiation on the hematopoietic system. In addition, the proposed model can be used to assess the doses to active marrow under any other scenarios of 90Sr and 89Sr intake to humans.

Comparison of the Dynamic Thermal Gradient to Temperature-Programmed Conditions in Gas Chromatography Using a Stochastic Transport Model.

This paper compares dynamic (i.e., temporally changing) thermal gradient gas chromatography (GC) to temperature-programmed GC using a previously published stochastic transport model to simulate peak characteristics for the separation of C12-C40 hydrocarbons. All comparisons are made using chromatographic conditions that give approximately equal analyte retention times (tR). As shown previously, a static thermal gradient does not improve resolution (Rs) equally for all analytes, which highlights the need for a dynamic thermal gradient. An optimal dynamic thermal gradient should result in constant analyte velocities at any instant in time for those analytes that are actively being separated (i.e., analytes that have low retention factors). The average separation temperature for each analyte is used to determine the thermal gradient profile at different times in the temperature ramp. Because many of the analytes require a similar thermal gradient profile when actively being separated, the thermal gradient profile in this study was held fixed; however, the temperature of the entire thermal gradient was raised over time. From the simulations performed in this study, optimized dynamic thermal gradient conditions are shown to improve Rs by up to 13% over comparative temperature-programmed conditions, even with a perfect injection (i.e., zero injection bandwidth). In the dynamic thermal gradient simulations, all analytes showed improvements in Rs along with slightly shorter tR values compared to simulations for traditional temperature-programmed conditions.

Strategic natural gas storage coordination among EU member states in response to disruption in the trans Austria gas pipeline: A stochastic approach to solidarity

The 2019 EU energy security agenda has led to the concept of solidarity: a coordinated response of Member States to “high-impact, low-probability” events jeopardizing the EU energy supply. At the core of this paper is a modeling analysis of storage as a non-market-based solidarity measure (the so-called strategic storage) considering whether it could be economically desirable to secure gas supply in case of disruption to the EU network. A two-stage stochastic cost minimization gas transport model was developed to study the short-term resilience of the network to supply shocks, such as a natural gas pipeline rupture, and the cost effective system response, in terms of transmission of gas flows, capacity use, and storage utilization in an interconnected gas system, taken the EU as a reference. Relative to a base scenario with no strategic storage, results show that gas import loss up to 80% on multiple different pipelines could lead to a +76% in total costs when no coordinated strategic storage is in place, compared with a −30% in total cost and a −60% in liquefied natural gas cost, when in use, emphasizing the cost-effectiveness achieved with strategic storage in securing energy to the system in emergency.

Hydrogeological Uncertainty Estimation With the Analytic Element Method

AbstractUncertainty estimation plays an important part in practical hydrogeology. With most of the subsurface unobservable, attempts at system characterization will invariably be incomplete. Uncertainty estimation, then, must quantify the influence of unknown parameters, forcings, and structural deficiencies. In this endeavor, numerical modeling frameworks can resolve a high degree of subsurface complexity and its associated uncertainty. Where boundary uncertainty is concerned, however, numerical frameworks can be restrictive. The interdependence of grid discretization and its enclosing boundaries render exploration of uncertainties in their extent or nature challenging. The analytic element method (AEM) may be an interesting complement, as it is computationally efficient, economic with its parameter count, and does not require enclosure through finite boundaries. These properties make AEM well suited for uncertainty estimation, particularly in data‐scarce settings or exploratory studies. In this study, we explore the use of AEM for flow field uncertainty estimation, with a particular focus on boundary uncertainty. To induce diverse, uncertain regional flow more easily, we propose a new element based on a Möbius transformation. We include this element in a simple Python‐based AEM toolbox and benchmark it against MODFLOW. Coupling AEM with a Markov Chain Monte Carlo routine using adaptive proposals, we explore its use in a synthetic case study. We find that AEM permits efficient uncertainty estimation for groundwater flow fields, which may form a basis for stochastic Lagrangian transport modeling or can support advanced model design by informing the placement of numerical model boundaries.

A Stochastic Microstructure Reconstruction-Based Mechanical and Transport Modeling Approach for Learning the Microstructure-Property Relationship of Li-Ion Battery Graphite Anodes

Understanding the relationships between microstructural characteristics and multiphysics properties is key to designing battery electrode materials for desired properties. Significant efforts have been made to achieve a quantitative understanding of the relationship between mass transport properties and Li-ion microstructure characteristics [1-3] in literature, but it is still challenging to predict the coupled mechanical and electrochemical behaviors based on microstructure characteristics.We seek to further this understanding through an investigation of how deformation affects the transport properties of the Li-ion battery graphite anode microstructure, which features packed particles and irregular pore networks. We propose a statistical Microstructure Characterization and Reconstruction (MCR) approach to characterize statistical microstructure features from 2D microscopic images and then reconstruct 3D stochastic microstructures. MCR is an effective tool for material property prediction [4] and microstructure-mediated material design [5]. The proposed MCR approach generates microstructure designs that are beyond the scope of empirical data.By exploring the input microstructure feature space, 3D microstructure samples are reconstructed and simulated to investigate relationships between the microstructural characteristics and properties of Li-ion battery graphite anodes. The selection of microstructure characteristics is informed by an external open access battery microstructures library. For each microstructure reconstruction, compression and transport simulations are conducted to determine the Young’s modulus and to understand the transport properties (e.g. diffusivity) of the undeformed and deformed microstructures. Convergence studies are conducted to establish a Representative Volume Element (RVE) size. With the simulation dataset, the microstructure-property relationship is examined. A feature selection algorithm is used to examine the size of the effects of microstructural characteristics on multiphysics properties. Machine learning models are established to predict the microstructure-property relationship.