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Efforts to include more detailed representations of biogeochemical processes in basin-scale water quality simulation tools face the challenge of how to tractably represent mass exchange between the flowing channels of streams and rivers and biogeochemical hotspots in the hyporheic zones. Multiscale models that use relatively coarse representations of the channel network with subgrid models for mass exchange and reactions in the hyporheic zone have started to emerge to address that challenge. Two such multiscale models are considered here, one based on a stochastic Lagrangian travel time representation of advective pumping and one on multirate diffusive exchange. The two models are formally equivalent to well-established integrodifferential representations for transport of non-reacting tracers in steady stream flow, which have been very successful in reproducing stream tracer tests. Despite that equivalence, the two models are based on very different model structures and produce significantly different results in reactive transport. In a simple denitrification example, denitrification is two to three times greater for the advection-based model because the multirate diffusive model has direct connections between the stream channel and transient storage zones and an assumption of mixing in the transient storage zones that prevent oxygen levels from dropping to the point where denitrification can progress uninhibited. By contrast, the advection-based model produces distinct redox zonation, allowing for denitrification to proceed uninhibited on part of the hyporheic flowpaths. These results demonstrate that conservative tracer tests alone are inadequate for constraining representation of mass transfer in models for reactive transport in streams and rivers.

Integrated surface/subsurface models for simulating the thermal hydrology of permafrost-affected regions in a warming climate have recently become available, but computational demands of those new process-rich simu- lation tools have thus far limited their applications to one-dimensional or small two-dimensional simulations. We present a mixed-dimensional model structure for efficiently simulating surface/subsurface thermal hydrology in low-relief permafrost regions at watershed scales. The approach replaces a full three-dimensional system with a two-dimensional overland thermal hydrology system and a family of one-dimensional vertical columns, where each column represents a fully coupled surface/subsurface thermal hydrology system without lateral flow. The system is then operator split, sequentially updating the overland flow system without sources and the one-dimensional columns without lateral flows. We show that the app- roach is highly scalable, supports subcycling of different processes, and compares well with the corresponding fully three-dimensional representation at significantly less computational cost. Those advances enable recently developed representations of freezing soil physics to be coupled with thermal overland flow and surface energy balance at scales of 100s of meters. Although developed and demonstrated for permafrost thermal hydrology, the mixed-dimensional model structure is applicable to integrated surface/subsurface thermal hydrology in general.

The need to understand potential climate impacts and feedbacks in Arctic regions has prompted recent interest in modeling of permafrost dynamics in a warming climate. A new fine-scale integrated surface/subsurface thermal hydrology modeling capability is described and demonstrated in proof-of-concept simulations. The new modeling capability combines a surface energy balance model with recently developed three-dimensional subsurface thermal hydrology models and new models for nonisothermal surface water flows and snow distribution in the microtopography. Surface water flows are modeled using the diffusion wave equation extended to include energy transport and phase change of ponded water. Variation of snow depth in the microtopography, physically the result of wind scour, is also modeled heuristically with a diffusion wave equation. The multiple surface and subsurface processes are implemented by leveraging highly parallel community software. Fully integrated thermal hydrology simulations on the tilted open book catchment, an important test case for integrated surface/subsurface flow modeling, are presented. Fine-scale 100-year projections of the integrated permafrost thermal hydrological system on an ice wedge polygon at Barrow Alaska in a warming climate are also presented. Finally, these simulations demonstrate the feasibility of microtopography-resolving, process-rich simulations as a tool to help understand possible future evolution of the carbon-rich Arcticmore » tundra in a warming climate.« less

The apertures of natural fractures in fractured rock are highly heterogeneous. However, in-fracture aperture variability is often neglected in flow and transport modeling and individual fractures are assumed to have uniform aperture distribution. The relative importance of in-fracture variability in flow and transport modeling within kilometer-scale field–scale fracture networks has been under a matter of debate for a long time because the flow in each single fracture is controlled not only by in-fracture variability but also by boundary conditions. Computational limitations have previously prohibited researchers from investigating the relative importance of in-fracture variability in flow and transport modeling within large-scale fracture networks. We address this question by incorporating internal heterogeneity of individual fractures into flow simulations within kilometer scale three-dimensional fracture networks, where fracture intensity, P32 (ratio between total fracture area and domain volume) is between 0.027 and 0.031 [1/m]. A recently developed discrete fracture network (DFN) simulation capability, dfnWorks, is used to generate DFNs that include in-fracture aperture variability represented by a stationary log-normal stochastic field with various correlation lengths and variances. The Lagrangian transport parameters, non-reacting travel time and cumulative retention, are calculated along particles streamlines. It is observed that due to local flow channeling early particle travel times are more sensitive to in-fracture variability than the tails of travel time distributions, where no significant effect of the in-fracture transmissivity variations and spatial correlation length is observed.

The effect of three environmental conditions: 1) thickness of organic soil, 2) snow depth, and 3) soil moisture content or water table height above and below the soil surface, on active layer thickness (ALT) are investigated using an ensemble of 1D thermal hydrology models. Sensitivity analyses of the ensemble exposed the isolated influence of each environmental condition on ALT and their multivariate interactions. The primary and interactive influences are illustrated in the form of color maps of ALT change. Results show that organic layer acts as a strong insulator, and its thickness is the dominant control of ALT, but the strength of the effect of organic layer thickness is dependent on the saturation state. Snow depth, subsurface saturation, and ponded water depth are strongly codependent and positively correlated to ALT.

Increasing computing power and the growing role of simulation in Earth systems science have led to an increase in the number and complexity of processes in modern simulators. We present a multiphysics framework that specifies interfaces for coupled processes and automates weak and strong coupling strategies to manage this complexity. Process management is enabled by viewing the system of equations as a tree, where individual equations are associated with leaf nodes and coupling strategies with internal nodes. A dynamically generated dependency graph connects a variable to its dependencies, streamlining and automating model evaluation, easing model development, and ensuring models are modular and flexible. Additionally, the dependency graph is used to ensure that data requirements are consistent between all processes in a given simulation. Here we discuss the design and implementation of these concepts within the Arcos framework, and demonstrate their use for verification testing and hypothesis evaluation in numerical experiments. We describe a conceptual model for managing complexity in multiphysics software.A process tree describes how individual equations are coupled.A dependency graph describes how variables are dependent upon each other.The model is implemented within the Arcos software framework.Examples of code and model runs are shown to demonstrate the idea.

Modeling and observation of ground temperature dynamics are the main tools for understanding current permafrost thermal regimes and projecting future thaw. Until recently, most studies on permafrost have focused on vertical ground heat fluxes. Groundwater can transport heat in both lateral and vertical directions but its influence on ground temperatures at local scales in permafrost environments is not well understood. In this study we combine field observations from a subarctic fen in the sporadic permafrost zone with numerical simulations of coupled water and thermal fluxes. At the Tavvavuoma study site in northern Sweden, ground temperature profiles and groundwater levels were observed in boreholes. These observations were used to set up one- and two-dimensional simulations down to 2 m depth across a gradient of permafrost conditions within and surrounding the fen. Two-dimensional scenarios representing the fen under various hydraulic gradients were developed to quantify the influence of groundwater flow on ground temperature. Our observations suggest that lateral groundwater flow significantly affects ground temperatures. This is corroborated by modeling results that show seasonal ground ice melts 1 month earlier when a lateral groundwater flux is present. Further, although the thermal regime may be dominated by vertically conducted heat fluxes during most of the year, isolated high groundwater flow rate events such as the spring freshet are potentially important for ground temperatures. As sporadic permafrost environments often contain substantial portions of unfrozen ground with active groundwater flow paths, knowledge of this heat transport mechanism is important for understanding permafrost dynamics in these environments.

The effects of soil property uncertainties on permafrost thaw projections are studied using a three-phase subsurface thermal hydrology model and calibration-constrained uncertainty analysis. The null-space Monte Carlo method is used to identify soil hydrothermal parameter combinations that are consistent with borehole temperature measurements at the study site, the Barrow Environmental Observatory. Each parameter combination is then used in a forward projection of permafrost conditions for the 21st century (from calendar year 2006 to 2100) using atmospheric forcings from the Community Earth System Model (CESM) in the Representative Concentration Pathway (RCP) 8.5 greenhouse gas concentration trajectory. A 100-year projection allows for the evaluation of predictive uncertainty (due to soil property (parametric) uncertainty) and the inter-annual climate variability due to year to year differences in CESM climate forcings. After calibrating to measured borehole temperature data at this well-characterized site, soil property uncertainties are still significant and result in significant predictive uncertainties in projected active layer thickness and annual thaw depth-duration even with a specified future climate. Inter-annual climate variability in projected soil moisture content and Stefan number are small. A volume- and time-integrated Stefan number decreases significantly, indicating a shift in subsurface energy utilization in the future climate (latent heat of phase change becomes more important than heat conduction). Out of 10 soil parameters, ALT, annual thaw depth-duration, and Stefan number are highly dependent on mineral soil porosity, while annual mean liquid saturation of the active layer is highly dependent on the mineral soil residual saturation and moderately dependent on peat residual saturation. By comparing the ensemble statistics to the spread of projected permafrost metrics using different climate models, we quantify the relative magnitude of soil property uncertainty to another source of permafrost uncertainty, structural climate model uncertainty. We show that the effect of calibration-constrained uncertainty in soil properties, although significant, is less than that produced by structural climate model uncertainty for this location.

Radionuclide transport in fractured crystalline rocks is a process of interest in evaluating long term safety of potential disposal systems for radioactive wastes. Given their numerical efficiency and the absence of numerical dispersion, Lagrangian methods (e.g. particle tracking algorithms) are appealing approaches that are often used in safety assessment (SA) analyses. In these approaches, many complex geochemical retention processes are typically lumped into a single parameter: the distribution coefficient (Kd). Usually, the distribution coefficient is assumed to be constant over the time frame of interest. However, this assumption could be critical under long-term geochemical changes as it is demonstrated that the distribution coefficient depends on the background chemical conditions (e.g. pH, Eh, and major chemistry). In this work, we provide a computational framework that combines the efficiency of Lagrangian methods with a sound and explicit description of the geochemical changes of the site and their influence on the radionuclide retention properties. HighlightsA methodology for the dynamic update of Kd values is proposed.The update of Kd values is related to the evolution of the background chemistry.A particle tracking code uses the updated Kds to compute radionuclide breakthrough curves.The proposed methodology is numerically efficient and free of numerical dispersion.The framework is tested against synthetic problems.

Time-domain random-walk (TDRW) algorithms are efficient methods for simulating solute transport along one-dimensional pathways. New extensions of the TDRW algorithm accommodate decay and ingrowth of radionuclides in a decay chain and time-dependent transport velocities. Tests using equilibrium sorption and matrix diffusion retention models demonstrate that the extended TDRW algorithm is accurate and computationally efficient. When combined with stochastic simulation of transport properties, the resulting algorithm, Particle on Random Streamline Segment (PORSS), also captures the effects of random spatial variations in transport velocities, including the effects of very broad velocity distributions. When used in combination with discrete fracture network simulations, the PORSS algorithm provides an accurate and practical method for simulating radionuclide transport at the geosphere scale without invoking the advection-dispersion equation.

A probabilistic model for assessing the capacity of a fractured crystalline rock volume to contain radionuclides is developed The rock volume is viewed as a network of discrete fractures through wh ...

Novel and efficient methods for evaluating fusion reactor plasma performance are discussed. The approach, which is based on spectral collocation techniques for solving the particle and power balanc...

This paper studies confinement properties of 1 = 2 torsatron/heliotron configurations with number of toroidal field periods, M, in the range of 10 to 14. This involves the calculation of zero-current and flux-conserving equilibria; stability against Mercier modes and low-n ideal modes, with n denoting the toroidal mode number; and orbit confinement of deeply trapped energetic particles. Optimization of both magnetohydrodynamic (MHD) and transport properties is pursued under the condition of plasma aspect ratio A = R/a {ge} 7, with R denoting the major radius and a the average plasma radius. For configurations with M, {le} 12, an average MHD beta limit of 4 to 5% is possible. The addition of a quadrupole field improves the confinement of trapped particles at zero pressure, but particle losses increase with increasing beta. This loss is less severe if the vacuum magnetic axis is shifted slightly inward. A configuration with M = 10, a coil pitch parameter p{sub c} in the range 1.25 to 1.30, and an added quadrupole field satisfies the beta and energetic particle confinement requirements for the next generation of large torsatron/heliotron devices.

Design studies for a low-aspect-ratio, large next-generation stellarator, Advanced Toroidal Facility II (ATF-II), with high-current-density, high-field, stable NbTi/Cu helical windings are described. The design parameters are an average plasma radius of 0.52 m, a major radius of 2 m, and a field on axis of 4 to 5 T, with 10 to 15 MW of heating power. Such a device would be comparable in cope to other next-generation stellarators but would have roughly the same aspect ratio as the tokamaks without, however, the need for current drive to sustain steady-state operation. A number of low-aspect-ratio physics issues need to be addressed in the design of ATF-II, primarily compromises between high-beta capability and good confinement properties. A six-field-period compact torsatron is chosen as a reference design for ATF-II, and its main features and performance predictions are discussed. An integrated (beta capability and confinement) optimization approach and optimization of superconducting windings are also discussed.

Loss of alpha particles in compact torsatron reactors is studied. For 6, 9, and 12 field period reactors, the direct loss is a relatively weak function of radius and energy and varies from approx. =33% for M = 6 to approx. =18% for M = 12. Loss of alpha particles through scattering into the loss region is calculated using the Fokker-Plank equation for fast ions and found to contribute an additional alpha-particle energy loss of approx. =15%. The consequences of these relatively large losses for torsatron reactor design are discussed. The relationship between the direct particle losses and the magnetic field structure is also studied. Orbit losses from a variety of stellarator configurations are calculated and a figure-of-merit that characterizes the orbit confinement of a magnetic configuration is deduced from these calculations. This figure-of-merit is used to show how the direct losses might be reduced at low aspect-ratio. Effects of finite beta on the direct particle losses are also addressed, and are shown to significantly increase the direct losses in some configurations. 15 refs., 8 figs.