Local Mass Balance Research Articles

Glacier Surges Controlled by the Close Interplay Between Subglacial Friction and Drainage

AbstractThe flow of glaciers and ice sheets is largely influenced by friction at the ice‐bed interface that can trigger rapid changes in glacier motion ranging from seasonal velocity variations to cyclic surge instabilities or even devastating glacier collapse. This wide range of transient glacier dynamics is currently not captured by models, and its implications for long‐term glacier evolution are uncertain. This highlights the need of developing improved descriptions for processes that occur at the glacier bed. Here, we present a model that describes the evolution of basal friction inspired by a “rate and state” approach, coupled to models of subglacial drainage and glacier flow, and investigate how these couplings affect the dynamics of glaciers. We show that a wide range of sliding behavior results from a feedback loop between subglacial drainage efficiency and friction which depends on the evolution of a frictional state that can be interpreted as the degree of cavitation or till porosity for hard and soft beds, respectively. In our simulations, we find that glaciers are susceptible to surging if they exhibit a transition to velocity weakening friction associated with a poor sensitivity of the drainage capacity to the frictional state. This potential materializes if the local topography and mass balance create the conditions for high water pressure to build up in an area sufficiently large to exceed a critical length. We advocate accounting for feedback loops between friction and drainage as a promising avenue for better understanding dynamical instabilities of glaciers and ice sheets.

First results of the polar regional climate model RACMO2.4

Abstract. The next version of the polar Regional Atmospheric Climate Model (referred to as RACMO2.4p1) is presented in this study. The principal update includes embedding of the package of physical parameterizations of the Integrated Forecast System (IFS) cycle 47r1. This constitutes changes in the precipitation, convection, turbulence, aerosol and surface schemes and includes a new cloud scheme with more prognostic variables and a dedicated lake model. Furthermore, the standalone IFS radiation physics module ecRad is incorporated into RACMO, and a multilayer snow module for non-glaciated regions is introduced. Other updates involve the introduction of a fractional land–ice mask, new and updated climatological data sets (such as aerosol concentrations and leaf area index), and the revision of several parameterizations specific to glaciated regions. As a proof of concept, we show first results for Greenland, Antarctica and a region encompassing the Arctic. By comparing the results with observations and the output from the previous model version (RACMO2.3p3), we show that the model performs well regarding the surface mass balance, surface energy balance, temperature, wind speed, cloud content and snow depth. The advection of snow hydrometeors strongly impacts the ice sheet's local surface mass balance, particularly in high-accumulation regions such as southeast Greenland and the Antarctic Peninsula. We critically assess the model output and identify some processes that would benefit from further model development.

Quantifying local and global mass balance errors in physics-informed neural networks

Physics-informed neural networks (PINN) have recently become attractive for solving partial differential equations (PDEs) that describe physics laws. By including PDE-based loss functions, physics laws such as mass balance are enforced softly in PINN. This paper investigates how mass balance constraints are satisfied when PINN is used to solve the resulting PDEs. We investigate PINN’s ability to solve the 1D saturated groundwater flow equations (diffusion equations) for homogeneous and heterogeneous media and evaluate the local and global mass balance errors. We compare the obtained PINN’s solution and associated mass balance errors against a two-point finite volume numerical method and the corresponding analytical solution. We also evaluate the accuracy of PINN in solving the 1D saturated groundwater flow equation with and without incorporating hydraulic heads as training data. We demonstrate that PINN’s local and global mass balance errors are significant compared to the finite volume approach. Tuning the PINN’s hyperparameters, such as the number of collocation points, training data, hidden layers, nodes, epochs, and learning rate, did not improve the solution accuracy or the mass balance errors compared to the finite volume solution. Mass balance errors could considerably challenge the utility of PINN in applications where ensuring compliance with physical and mathematical properties is crucial.

Geothermal heat source estimations through ice flow modelling at Mýrdalsjökull, Iceland

Abstract. Geothermal heat sources beneath glaciers and ice caps influence local ice-dynamics and mass balance but also control ice surface depression evolution as well as subglacial water reservoir dynamics. Resulting jökulhlaups (i.e., glacier lake outburst floods) impose danger to people and infrastructure, especially in Iceland, where they are closely monitored. Due to hundreds of meters of ice, direct measurements of heat source strength and extent are not possible. We present an indirect measurement method which utilizes ice flow simulations and glacier surface data, such as surface mass balance and surface depression evolution. Heat source locations can be inferred accurately to simulation grid scales; heat source strength and spatial distributions are also well quantified. Our methods are applied to the Mýrdalsjökull ice cap in Iceland, where we are able to refine previous heat source estimates.

Local Ice Mass Balance Rates via Bayesian Analysis of Mars Polar Trough Migration

AbstractWith the aim of better understanding the past depositional environment of the north polar region of Mars, we infer local ice accumulation and retreat rates in the area between 86° and 87°N and 16°–20°E. We follow a novel approach utilizing a Bayesian framework with observations of bounding surfaces associated with the migration of two polar spiral troughs. Over time, spiral troughs have migrated toward the north pole due to ice accumulation, sublimation, and wind transport. We relate the record of trough migration with local ice accumulation and retreat rates using a phenomenological migration model and explore the climate parameters that affect these rates using a Markov chain Monte Carlo algorithm. Using this data‐driven approach, we find best fit mean accumulation rates of 0.11–0.18 mm/yr in the upper 500 m of the stratigraphy of our study region. These mean accumulation rates correspond to trough ages of over 4 Myr, which implies that the north polar cap is older than most current assumptions. We also find that the relationship between accumulation rates and the obliquity of Mars is complex, with periods of positive correlation occurring in the last several Myr. Future work extending this analysis to all troughs in the cap will further constrain these relationships and ages.

Estimating local surface glacier mass balance from migration of the 1918 Katla eruption tephra layer on Sléttjökull, southern Iceland

Abstract We use the apparent horizontal shift of an englacial tephra layer outcrop to calculate local glacier mass balance on Sléttjökull, a lobe of Mýrdalsjökull in Southern Iceland. For this approach, the dipping angle of the englacial tephra layer in the glacier upstream of the outcrop and the flow velocity of the ice need to be known. An earlier investigation was expanded by the application of ground-penetrating radar, detecting the depth of the tephra along tracks with a total length of 10 km. Interpolation between the tracks enables us to derive the dipping angle of the layer along several flow lines. Together with glacier surface velocities, determined from feature tracking, we are able to estimate the local surface mass balance from the horizontal displacement of the tephra outcrop using freely available satellite imagery without additional fieldwork. The earlier local balance series was extended to the period 2014/15 to 2019/20. Although the results for the individual profiles differ slightly from each other, they show the same temporal pattern and clear variations from year to year. The results are compared to traditional mass-balance data from Hofsjökull. The two series show a good agreement in their interannual variability.

Changes in climate extremes in a typical glacierized region in central Eastern Tianshan Mountains and their relationship with observed glacier mass balance

As an icon of anthropogenic climate change, alpine glaciers are highly sensitive to climate change. However, there remain research gaps regarding trends in climate extremes in glacierized regions and their relationship with local glacier mass balance. In this study, these relationships and their underlying links were explored in a typical glacierized region in the Eastern Tianshan Mountains, China, from 1959 to 2018. All warm extremes exhibited increasing trends that intensified dramatically from the 1990s. Meanwhile, decreasing trends were found for all cold extremes except for the temperatures of the coldest days and coldest nights. All of the precipitation extremes demonstrated increasing trends, except for consecutive dry days and consecutive wet days. Statistically significant positive/negative correlations were detected between glacier mass balance and six warm extremes (TN90p, TX90p, SU99p, TR95p, TXx, and TNx)/four cold extremes (TN10p, TX10p, FD0, and ID0). Simulation results showed that the impact of the intensity/frequency of the warm extremes (TN90p, TX90p, SU99p, and TR95p) on glacier ablation was remarkable and the effect of the cold extremes (FD0 and ID0) on accumulation was also significant. Additionally, the increases in the intensity and frequency of most climate extremes seemed more remarkable in glacierized regions than in non-glacierized regions. Hence, studies on glacier-climate interactions should focus greater attention on the impacts of climate extremes on glacier evolution.

Scale-up of membrane distillation systems using bench-scale data

A procedure to design full-scale air gap membrane distillation (AGMD) processes is presented. A mathematical model was then developed for both direct contact membrane distillation (DCMD) and AGMD. The model is centered on solving local mass and energy balances using a finite difference approach. The full-scale model was calibrated by utilizing the membrane distillation coefficient (MDC) determined by DCMD bench-scale experiments, as the sole adjustable parameter. The MDC was then used to model the water production and energy efficiency of a spiral-wound AGMD full-scale element. The model yields accurate representation of full-scale AGMD elements using polytetrafluoroethylene (PTFE) and polyethylene (PE) membranes. Full-scale experimental results obtained over a wide range of feed flow rates (2 to 4.5 L/min), temperatures (40 to 80 °C), and salinities (0 to 200 g/L NaCl) confirmed that the developed procedure can be applied to model and design large-scale AGMD elements. Furthermore, the model guides the selection of specific temperature and flow conditions at a given salinity and element geometry to maximize water production and energy efficiency. This methodology is suitable for rapid evaluation of novel MD membranes performance in field AGMD applications.

Thermophysical Characterization of Paraffin Wax Based on Mass-Accommodation Methods Applied to a Cylindrical Thermal Energy-Storage Unit.

Two mass-accommodation methods are proposed to describe the melting of paraffin wax used as a phase-change material in a centrally heated annular region. The two methods are presented as models where volume changes produced during the phase transition are incorporated through total mass conservation. The mass of the phase-change material is imposed as a constant, which brings an additional equation of motion. Volume changes in a cylindrical unit are pictured in two different ways. On the one hand, volume changes in the radial direction are proposed through an equation of motion where the outer radius of the cylindrical unit is promoted as a dynamical variable of motion. On the other hand, volume changes along the axial symmetry axis of the cylindrical unit are proposed through an equation of motion, where the excess volume of liquid constitutes the dynamical variable. The energy–mass balance at the liquid–solid interface is obtained according to each method of conceiving volume changes. The resulting energy–mass balance at the interface constitutes an equation of motion for the radius of the region delimited by the liquid–solid interface. Subtle differences are found between the equations of motion for the interface. The differences are consistent with mass conservation and local mass balance at the interface. Stationary states for volume changes and the radius of the region delimited by the liquid–solid interface are obtained for each mass-accommodation method. We show that the relationship between these steady states is proportional to the relationship between liquid and solid densities when the system is close to the high melting regime. Experimental tests are performed in a vertical annular region occupied by a paraffin wax. The boundary conditions used in the experimental tests produce a thin liquid layer during a melting process. The experimental results are used to characterize the phase-change material through the proposed models in this work. Finally, the thermodynamic properties of the paraffin wax are estimated by minimizing the quadratic error between the temperature readings within the phase-change material and the temperature field predicted by the proposed model.

Extended isogeometric analysis of a progressively fracturing fluid‐saturated porous medium

AbstractAn extended isogeometric analysis (XIGA) approach is proposed for modeling fracturing in a fluid‐saturated porous material. XIGA provides a definition of the discontinuity independent of the underlying mesh layout, which obviates the need of knowing the crack extension direction a priori. Unlike Lagrange shape functions used in the standard finite element approach, non‐uniform rational B‐splines (NURBS) provide a higher‐order interelement continuity which leads to a continuous fluid flow also at element boundaries, thereby satisfying the local mass balance. It also leads to an improved estimate of the crack path due to a smoother stress distribution. The NURBS basis functions are cast in finite element data structure using Bézier extraction. To model the discontinuity, the Heaviside sign function is utilized within the displacement and the pressure fields, complemented by the shifting and the blending techniques to enforce compatibility perpendicular and parallel to the crack path, respectively. Different aspects of the approach are assessed through examples comprising straight and curved crack paths for stationary and propagating discontinuities.

Impact of Slopes on ICESat-2 Elevation Accuracy Along the CHINARE Route in East Antarctica

As the follow-on study to the assessment of ICESat-2 ice surface elevations, we assessed how they are influenced by the surface slopes, which are derived from the ICESat-2 elevations of the received photons and available in the land-ice surface heights product (ATL06), by using coordinated GNSS observations along a 520 km long traverse of the 36th CHINese Antarctic Research Expedition (CHINARE) route in East Antarctica. We further analyzed the impact of the slopes on the ICESat-2 elevation accuracy, which is important for the studies of the local ice flow dynamics, mass balance, and Antarctic contribution to sea level rise. We found that the along-track surface slopes in the ICESat-2 ATL06 data have a high overall agreement of 0.18° ± 0.16° (1σ) and a correlation of 0.66 (R²) with the GNSS slopes. Furthermore, two waveform related corrections, first-photon and transmit-pulse shape bias corrections, were able to adjust on average a combined elevation bias of ∼1.0 cm. Finally, we found a high linear dependency of elevation errors on slopes, i.e., ∼6.2 cm per 1° slope (R² = 0.57, slope <0.7°). Although significantly smaller than those in ICESat elevation data, these slope-induced elevation errors in ICESat-2 ATL06 data should be carefully considered for studies using high precision elevations, such as the mass balance estimation in sloped areas in Antarctica.

Multi-scale model of a top-fired steam methane reforming reactor and validation with industrial experimental data

A multi-scale model is presented for a steam methane reforming reactor. The reactor is a typical top-fired, packed-bed multi-tubular reactor. The model embeds, at the microscopic scale, a 1-dimensional simulation of mass transport and reaction inside the catalyst particles. At the intermediate (mesoscopic) scale, the tubular reactor model is based on local mass, energy, and momentum balances, coupled to appropriate steam methane reforming reaction kinetics; the equations are written and solved in 2-dimensional cylindrical symmetry. At the macroscopic level, the tube simulation is then coupled to the furnace simulation. For the latter, a 1-dimensional model is proposed, based on local mass and energy balances, coupled to linear combustion kinetics. Overall, the model contains only one adjustable parameter i.e., Lf, the length of the flame in the furnace. The model equations are integrated through a finite element method. The predictive capability of the model is assessed through validation against previous literature results, as well as three sets of experimental data obtained from a full-scale industrial SMR reactor, operating from middle to high capacity. The model makes it possible to account for the effects of the catalyst features, on the one hand, and the operating conditions of the furnace, on the other. The model provides a detailed study of the phenomena occurring inside the steam methane reforming reactor, with an acceptable computational burden and time. This lays the foundations for in-depth fault detection and identification studies and online deployment of the model for control purposes.

A Detailed, Multi‐Scale Assessment of an Atmospheric River Event and Its Impact on Extreme Glacier Melt in the Southern Alps of New Zealand

AbstractNorth‐westerly airflow and associated atmospheric rivers (ARs) have been found to profoundly influence New Zealand’s west coasts, by causing flooding, landslides and extreme ablation and accumulation on glaciers in the Southern Alps. However, the response of local glacier mass balance to synoptic‐scale circulation, including events with ARs, has typically not been investigated by considering mesoscale processes explicitly. In this study, high‐resolution atmospheric simulations from the Weather Research and Forecasting model are used to investigate the mesoscale drivers of an extreme ablation event on Brewster Glacier (Southern Alps), which occurred on February 6, 2011 during the landfall of an AR on the South Island. The following processes were found to be crucial for transferring the high temperature and water vapor contained in the AR into energy available for melt on Brewster Glacier: First, the moist‐neutral character of the air mass enabled the flow to pass over the ridge, leading to the development of orographic clouds and precipitation on the windward side of the orography, and foehn winds on the leeside. These processes fueled melt through longwave radiation and strong turbulent and rain heat fluxes within the high‐condensation environment of the orographic cloud. Second, orographic enhancement occurred due to both cellular convection within the cloud and the combined effect of multiple precipitating systems by the seeder‐feeder‐mechanism. These results indicate the potential importance of AR dynamics for New Zealand’s glaciers. They also illustrate the benefit of mesoscale atmospheric modeling for advancing process understanding of the glacier‐climate relationship in New Zealand.

An isogeometric approach to Biot-Cosserat continuum for simulating dynamic strain localization in saturated soils

The Biot-Cosserat continuum theory is combined with isogeometric analysis (Biot-CIGA) to simulate dynamic strain localization in saturated soils. The results demonstrate that Biot-CIGA can solve the ill-posed problem of saturated soils caused by strain-softening properties and non-associated flow rules, thereby obtaining a convergent, mesh-independent numerical solution. Compared with the finite element analysis of Biot-Cosserat continuum (Biot-CFEA), the high-order continuity of Biot-CIGA provides a smooth pore pressure gradient field and thus ensures the local mass balance of pore fluids. Additionally, the Biot-CIGA describes the inflow and outflow of pore fluids in the element, which means it is able to accurately simulate the volumetric strain of the element. Simulation results also show that the Biot-CIGA method can also effectively alleviate the mesh distortion in shear bands when materials experience large deformation. Last but not least, because Biot-CIGA adopts NURBS as its shape functions, it can conduct simulations directly on CAD models, which not only maintains the precise geometry, but also avoids an expensive intermediate meshing step.

Achieving local mass conservation when using continuous Galerkin finite element methods to solve solute transport equations with spatially variable coefficients in a transient state

Mass balance checks are often used to evaluate the abilities of numerical simulators and assess the accuracy of the solutions but are often insufficient. In addition, there is a need to calculate the difference in mass fluxes, through downstream subdomain analysis, to determine whether remediation technologies are suitable for upstream contaminated sites. The Galerkin finite element method (GFEM) has been commonly considered locally nonconservative, whereas the finite difference method (FDM) is a local mass conservation method. In this study, we proved that the GFEM has local mass balance equations on “mass conserved elements” (constructed by connecting lines that perpendicularly cross element faces at midpoints) in solute transport problems with spatially variable velocities and dispersion coefficients, identical to discretized balance equations in the FDM. Furthermore, we found that locally conservative GFEMs with two types of approaches involving spatially variable coefficients (i.e., a linear combination approach and an average approach) give rise to two types of postprocessing techniques for calculating local mass fluxes. These are equivalent to an area-weighted method and first-order Taylor series method, respectively. Finally, to illustrate the practical applicability of these GFEMs, we used the proposed postprocessing approaches to resolve practical problems involving computation of local mass fluxes, based on information directly obtainable from finite element solutions of concentration distribution. Our findings revealed that the local mass balance errors were negligibly small, regardless of numerical concentration accuracy.

A combined hybrid mixed element method for incompressible miscible displacement problem with local discontinuous Galerkin procedure

AbstractIn this article, we propose a combined hybrid discontinuous mixed finite element method for miscible displacement problem with local discontinuous Galerkin method. Here, to obtain more accurate approximation and deal with the discontinuous case, we use the hybrid mixed element method to approximate the pressure and velocity, and use the local discontinuous Galerkin finite element method for the concentration. Compared with other combined methods, this method can improve the efficiency of computation, deal with the discontinuous problem well and keep local mass balance. We study the convergence of this method and give the corresponding optimal error estimates in L∞(L2) for velocity and concentration and the super convergence in L∞(H1) for pressure. Finally, we also present some numerical examples to confirm our theoretical analysis.

Numerical evaluation of a combined chemical enhanced oil recovery process with polymer and nanoparticles based on experimental observations

Polymer flooding is the most widely implemented chemical enhanced oil recovery (CEOR) process. However, polymer degradation, caused by chemical, thermal, and mechanical stresses, is still the most notable limitation on the implementation of the technology at the field scale. Recent studies have shown that the addition of nanoparticles in a traditional polymer flooding can improve operating conditions and hydrocarbon production. Thus, a comprehensive numerical simulation study is presented to model the performance of the co-injection of polymers with nanoparticles in oil reservoirs. An articulated process was followed to take into account most of the physical and chemical mechanisms of the technique. Initially, a conceptual model was developed by identifying relevant mass transport and surface mechanisms, and their dynamics. The following phases are accounted in the model: oleic, volatile, and aqueous. Then, local mass balance equations were written for the following components: oil, gas, water, solid nanoparticles and polymers. An extended black-oil model for the hydrocarbon and aqueous phases was used. Constitutive equations were specified for polymer adsorption, rheology, degradation, and nanoparticles retention and remobilization, as well. The numerical strategy was described for numerically solving the Jacobian matrix. The model was subsequently validated in two steps: initially, the simulation results of a polymer flooding are compared to the ones obtained using a commercial software. Then, the nanoparticles transport and retention on the solid matrix was validated with experimental core-flooding tests reported in specialized literature. A set of numerical experiments of the co-injection of polymer-nanoparticles were done, showing that the synergy between both chemical species allowed to retain the viscoelastic network, which considerably improves operational and production parameters. This investigation provides a powerful tool for Oil & Gas industry and can be used to design novel CEOR deployment strategies in sandstone reservoirs.

Modeling the release of curcumin from microparticles of poly(hydroxybutyrate) [PHB

Polyhydroxybutyrate (PHB) is biodegradable and biocompatible polyester that has been recently used for developing different drug delivery systems (DDS). Microspheres as DDS, consist of a polymeric matrix with a diameter of 1–125 μm which contains a substance entrapped, and then released mainly through diffusion. In order to make DDS viable for commercial applications, it is essential to develop models that describe and predict the substance release kinetic. In this study, microspheres of PHB with curcumin entrapped were synthesized; the release of curcumin was studied and modeled. As a first approach, a physical model was introduced, in which mass transference was considered analogous to heat transference. The proposed model was based on local mass balance through the classical diffusion equation and total mass balance imposed through an integro-differential equation. The total mass balance introduced nonlinearities in the dynamics of the drug within the fluid; therefore, a semi-analytical approach based on the heat balance integral method was applied to solve the proposed model. Finally, by using the experimental rate of release of curcumin, the semi-analytical solutions to the proposed model were compared with the experimental release data, showing the importance of adding mass balance in the nonlinear mathematical model in order to describe more accurately the release kinetics.

The evolution of the seasonal ice mass balance buoy

Arctic sea ice plays a crucial role in the global climate system, acting as both an indicator and an amplifier of climate change. Sea ice mass balance, which is simply the net difference between ice grown and ice melted, is an important parameter that can connect changes in ice thickness to environmental forcings. Opportunities for long-term observations of sea ice mass balance have been greatly expanded by the use of autonomous ice mass balance buoys, which are able to resolve changes to local ice mass balance by measuring time series of snow depth and ice surface and bottom position. This paper presents the design for a newly improved Seasonal Ice Mass Balance buoy (referred to as SIMB-3) that was created to enhance the ability to monitor mass balance with design features that maximize reliability and survivability, reduce installation difficultly, and reduce cost. Operational advancements were also made to make the buoy easy to manufacture, ship worldwide, and assemble in the cold. A custom low-cost datalogger-controller was developed to operate the mass balance sensor package while allowing future expandability for use with non-standard instruments. Several test deployments were conducted in 2018, and the instrument demonstrated ability to successfully collect mass balance data in seasonal sea ice. Results from one of these test deployments in the Beaufort Sea during April 2018, are presented and discussed.

Effects of correlated morphological and topological heterogeneity of pore network on effective transport and reaction parameters

The effective diffusivity and the effective Thiele modulus of reactive porous matrices are determined by using a hybrid discrete and continuum model. The model describes static heterogeneity with weak noise on both morphology and topology of the matrix. Variations in diffusivity with respect to pore size (radius and length) and network connectivity up to second order are analyzed to assess the effect of stochastic media on catalytic reaction and transition of a single species. The porous medium is simulated by several building blocks (BB) which are regular in topology and morphology. A methodology is presented to construct a BB such that it fits the true matrix. Permutation of several regular pore networks in series constructs the porous media. Local mass balances over each BB yields model equations for reaction and transport in the matrix. Correlated random walk theory is used in each BB in order to relate the diffusivity to the coordination number.The Gaussian correlation function is assumed to model the autocorrelation of independent variables which are used to characterize the correlated porous media. The contribution of the fluctuating parameters in the mass conservation of the matrix yields a new closure equation in which ensemble average concentration of the reactant depends on different cross-correlations. The model is stable as long as the Thiele modulus at the correlation length scale is small. It predicts that geometrical heterogeneities lead to correction in effective diffusivity while the reaction rate is unaffected due to small Thiele modulus at correlation length scale. The model is verified by assessing the Thiele modulus of a pore network under Knudsen regime during a first order catalytic reaction; a good agreement was found especially for moderate Thiele modulus of correlated network. However, it fails to simulate random networks. Our systematic study revealed that the pore radius statistics impact significantly the diffusivity and the Thiele modulus while the topological parameters are important in weakly connected networks. The model predictions show that the diffusion constant decreases sharply as pore radius variance increases but increases smoothly with Thiele modulus.