Flowline Model Research Articles

Two-dimensional prognostic experiments for fast-flowing ice streams from the Academy of Sciences Ice Cap

Abstract. Prognostic experiments for fast-flowing ice streams on the southern side of the Academy of Sciences Ice Cap on Komsomolets Island, Severnaya Zemlya archipelago, were undertaken in this study. The experiments were based on inversions of basal friction coefficients using a two-dimensional flow-line thermocoupled model and Tikhonov's regularization method. The modeled ice temperature distributions in the cross sections were obtained using ice surface temperature histories that were inverted previously from borehole temperature profiles derived at the summit of the Academy of Sciences Ice Cap and the elevational gradient of ice surface temperature changes (about 6.5 °C km−1). Input data included interferometric synthetic aperture radar (InSAR) ice surface velocities, ice surface elevations, and ice thicknesses obtained from airborne measurements, while the surface mass balance was adopted from previous investigations for the implementation of both the forward and inverse problems. The prognostic experiments revealed that both ice mass and ice stream extent declined for the reference time-independent surface mass balance. Specifically, the grounding line retreated: (a) along the B–B′ flow line from ∼ 40 to ∼ 30 km (the distance from the summit), (b) along the C–C′ flow line from ∼ 43 to ∼ 37 km, and (c) along the D–D′ flow line from ∼ 41 to ∼ 32 km, when considering a time period of 500 years and assuming a time-independent surface mass balance. Ice flow velocities in the ice streams decreased with time and this trend resulted in the overall decline of the outgoing ice flux. Generally, the modeled glacial evolution was in agreement with observations of deglaciation of the Severnaya Zemlya archipelago.

A Plastic Network Approach to Model Calving Glacier Advance and Retreat

Calving glaciers contribute substantially to sea level rise, but they are challenging to represent in models. Fine resolution is required for continental-scale models to accurately resolve calving dynamics and in many cases glacier geometry is too complicated to be adequately reflected by more simplified models. Flowline models are able to resolve flow along the main branch of a glacier, but many of those in current use either ignore tributaries entirely or parameterize their effect using a measure of “equivalent width”. Here we present a simple method to simulate terminus advance and retreat for an interacting network of glacier branches, based on a model extending Nye’s 1953 perfect plastic flow approximation to calving glaciers. We apply the method to case studies of four marine-terminating glaciers: Jakobshavn Isbrae and Helheim Glacier of Greenland, and Columbia and Hubbard Glaciers of Alaska. Given bed topography and upstream elevation history, our method reproduces observed patterns of terminus advance and retreat in all cases, as well as centerline profiles for all branches.

Exit Recursion Models of Clustered Photolithography Tools for Fab Level Simulation

In semiconductor wafer fabricators (fabs), clustered photolithography tools (CPTs) are often the bottleneck. With a focus on fab-level simulation, we propose a new class of equipment models for CPTs called exit recursion models (ERMs). These models are inspired by concepts from flow line theory. We describe the intuition behind ERMs and provide the parameterization and simulation equations. These ERMs are data-driven empirical models and we develop three types based on different data perspectives: 1) tool log; 2) wafer log; and 3) lot log. To assess the quality of the proposed models, we conduct three classes of simulation experiments. A detailed CPT model, an affine model, and an empirical flow line model are used as the baselines. We consider mean cycle time, lot residency time, throughput time, and computation time as our primary performance metrics. The results suggest that ERMs are more accurate and robust than the affine models for all metrics and sometimes rival the performance of the empirical flow line models considered. ERMs require about 1.9 times as much computation as an affine model and about 250 times less computation than an empirical flow line model. ERMs may be helpful to increase the accuracy of fab-level simulation results without significant additional computation.

Marine ice sheet model performance depends on basal sliding physics and sub-shelf melting

Abstract. Computer models are necessary for understanding and predicting marine ice sheet behaviour. However, there is uncertainty over implementation of physical processes at the ice base, both for grounded and floating glacial ice. Here we implement several sliding relations in a marine ice sheet flow-line model accounting for all stress components and demonstrate that model resolution requirements are strongly dependent on both the choice of basal sliding relation and the spatial distribution of ice shelf basal melting.Sliding relations that reduce the magnitude of the step change in basal drag from grounded ice to floating ice (where basal drag is set to zero) show reduced dependence on resolution compared to a commonly used relation, in which basal drag is purely a power law function of basal ice velocity. Sliding relations in which basal drag goes smoothly to zero as the grounding line is approached from inland (due to a physically motivated incorporation of effective pressure at the bed) provide further reduction in resolution dependence.A similar issue is found with the imposition of basal melt under the floating part of the ice shelf: melt parameterisations that reduce the abruptness of change in basal melting from grounded ice (where basal melt is set to zero) to floating ice provide improved convergence with resolution compared to parameterisations in which high melt occurs adjacent to the grounding line.Thus physical processes, such as sub-glacial outflow (which could cause high melt near the grounding line), impact on capability to simulate marine ice sheets. If there exists an abrupt change across the grounding line in either basal drag or basal melting, then high resolution will be required to solve the problem. However, the plausible combination of a physical dependency of basal drag on effective pressure, and the possibility of low ice shelf basal melt rates next to the grounding line, may mean that some marine ice sheet systems can be reliably simulated at a coarser resolution than currently thought necessary.

Brief communication: Thinning of debris-covered and debris-free glaciers in a warming climate

Abstract. Recent geodetic mass-balance measurements reveal similar thinning rates on glaciers with or without debris cover in the Himalaya–Karakoram region. This comes as a surprise as a thick debris cover reduces the surface melting significantly due to its insulating effects. Here we present arguments, supported by results from numerical flowline model simulations of idealised glaciers, that a competition between the changes in the surface mass-balance forcing and that of the emergence/submergence velocities can lead to similar thinning rates on these two types of glaciers. As the climate starts warming, the thinning rate on a debris-covered glacier is initially smaller than that on a similar debris-free glacier. Subsequently, the rate on the debris-covered glacier becomes comparable to and then larger than that on the debris-free one. The time evolution of glacier-averaged thinning rates after an initial warming is strongly controlled by the time variation of the corresponding emergence velocity profile.

The experimental verification of the known flow line models describing local flow during ECAE (ECAP)

In spite of the existence of a number of studies suggesting various models of flow-lines during ECAE, there are few studies dedicated to the experimental visualization of the empirically observable flow-lines. The present research is focused on an experimental verification of the known previously published research results by Han et al (2008), Hasani et al (2008) — Hosseini et al (2009), and Tóth et al (2004) for material flow lines through a die of classical Segal geometry. The experimental research used physical simulation techniques to visualize moving marker trajectories in the vicinity of the channel intersection zone during ECAE of plasticine models. The successive positions of moving markers were recorded with a digital camera with further recognition and digitalization of experimental marker trajectories. This research has shown that experimental flow-lines do not fully fit Toth et al’s and Han et al’s flow models. It was found that the best fit of experimental flow-lines is achieved by using of Hasani et al’s — Hosseini et al’s model. Experimental / theoretical results which were obtained in the current study are of interest to the interdisciplinary SPD mechanics sphere. The experimental verification of the earlier published models quoted in the paper provides the succession, sustainability and academic integrity of the experimental / theoretical results from the SPD mechanics of the various schools of sciences. New results of the study relate to the experimental visualization of the moving markers positions during ECAE physical modeling and the experimental / theoretical determination of corresponding empirical flow-lines.

Controls on Last Glacial Maximum ice extent in the Weddell Sea embayment, Antarctica

AbstractThe Weddell Sea sector of the Antarctic Ice Sheet is hypothesized to have made a significant contribution to sea‐level rise since the Last Glacial Maximum. Using a numerical flowline model we investigate the controls on grounding line motion across the eastern Weddell Sea and compare our results with field data relating to past ice extent. Specifically, we investigate the influence of changes in ice temperature, accumulation, sea level, ice shelf basal melt, and ice shelf buttressing on the dynamics of the Foundation Ice Stream. We find that ice shelf basal melt plays an important role in controlling grounding line advance, while a reduction in ice shelf buttressing is found to be necessary for grounding line retreat. There are two stable positions for the grounding line under glacial conditions: at the northern margin of Berkner Island and at the continental shelf break. Global mean sea‐level contributions associated with these two scenarios are ~50 mm and ~130 mm, respectively. Comparing model results with field evidence from the Pensacola Mountains and the Shackleton Range, we find it unlikely that ice was grounded at the continental shelf break for a prolonged period during the last glacial cycle. However, we cannot rule out a brief advance to this position or a scenario in which the grounding line retreated behind present during deglaciation and has since re‐advanced. Better constraints on past ice sheet and ice shelf geometry, ocean temperature, and ocean circulation are needed to reconstruct more robustly past behavior of the Foundation Ice Stream.

Research of Modeling and Simulation for Operation Scheduling Process of Block Stockyard Based on Petri Net

As for the problem of low efficiency and difficulty of the operation of block, a method of modeling and simulation of the operation scheduling process of block stockyard based on Petri net is proposed. Firstly, based on the analysis of the operation scheduling process of block yard, the operation scheduling mode of virtual flow line is presented; Secondly, a virtual flow line model according to the operation scheduling model of block stockyard based on hierarchical-timed Petri net is established and the feasibility of the virtual flow line is proved with the method of invariant; Finally, a block stockyard operation scheduling simulation model based on the digital factory strategy is established and the digital simulation analysis of block yard operation scheduling is carried out. The results show that the mode of virtual flow line operation and the Petri net contribute to improving efficiency of the block stockyard operation scheduling and resources using, the virtual flow line can also avoid the blocking. The effective method and theoretical support are provided in this paper for the block stockyard scheduling.

Controls on the early Holocene collapse of the Bothnian Sea Ice Stream

AbstractNew high‐resolution multibeam data in the Gulf of Bothnia reveal for the first time the subglacial environment of a Bothnian Sea Ice Stream. The geomorphological record suggests that increased meltwater production may have been important in driving rapid retreat of Bothnian Sea Ice during deglaciation. Here we apply a well‐established, one‐dimensional flow line model to simulate ice flow through the Gulf of Bothnia and investigate controls on retreat of the ice stream during the post‐Younger Dryas deglaciation of the Fennoscandian Ice Sheet. The relative influence of atmospheric and marine forcings are investigated, with the modeled ice stream exhibiting much greater sensitivity to surface melting, implemented through surface mass balance and hydrofracture‐induced calving, than to submarine melting or relative sea level change. Such sensitivity is supported by the presence of extensive meltwater features in the geomorphological record. The modeled ice stream does not demonstrate significant sensitivity to changes in prescribed ice stream width or overall bed slope, but local variations in basal topography and ice stream width result in nonlinear retreat of the grounding line, notably demonstrating points of short‐lived retreat slowdown on reverse bed slopes. Retreat of the ice stream was most likely governed by increased ice surface meltwater production, with the modeled retreat rate less sensitive to marine forcings despite the marine setting.

Persistence and variability of ice-stream grounding lines on retrograde bed slopes

Abstract. In many ice streams, basal resistance varies in space and time due to the dynamically evolving properties of subglacial till. These variations can cause internally generated oscillations in ice-stream flow. However, the potential for such variations in basal properties is not considered by conventional theories of grounding-line stability on retrograde bed slopes, which assume that bed properties are static in time. Using a flow-line model, we show how internally generated, transient variations in ice-stream state interact with retrograde bed slopes. In contrast to predictions from the theory of the marine ice-sheet instability, our simulated grounding line is able to persist and reverse direction of migration on a retrograde bed when undergoing oscillations in the grounding-line position. In turn, the presence of a retrograde bed may also suppress or reduce the amplitude of internal oscillations in ice-stream state. We explore the physical mechanisms responsible for these behaviors and discuss the implications for observed grounding-line migration in West Antarctica.

Bi-objective scheduling of flexible flow lines: a gradual transition tabu search approach

This paper deals with flexible flow line scheduling problem. Studied researches of the literature assumed that either no setup has to be performed or that setup times are sequence-independent, chiefly. Besides, they are mostly conducted in single objective environment. Therefore, in this study, these two real world concepts are mimicked in the flow line model. The considered objectives of the proposed model are minimizing makespan and total tardiness. Due to the hard solvability of the problem, this research proposes a new multi-objective algorithm based on the single objective tabu search, called gradual transition tabu search (GTTS). GTTS is implemented in two phases and in each phase it tries to gradually modify one objective to the other objective. The neighborhood search efficiency is also improved by defining new candidate list strategies and implementing new dynamic tabu tenure. In addition, the results of the proposed algorithm are compared with two popular existing algorithms, called fast non-dominated sort genetic algorithm (NSGA-II) and multi-objective genetic algorithm, on a number of randomly generated test problems. The suitability of GTTS is demonstrated through different multi-objective evaluation metrics.

Modelling calving front dynamics using a level-set method: application to Jakobshavn Isbræ, West Greenland

Abstract. Calving is a major mechanism of ice discharge of the Antarctic and Greenland ice sheets, and a change in calving front position affects the entire stress regime of marine terminating glaciers. The representation of calving front dynamics in a 2-D or 3-D ice sheet model remains non-trivial. Here, we present the theoretical and technical framework for a level-set method, an implicit boundary tracking scheme, which we implement into the Ice Sheet System Model (ISSM). This scheme allows us to study the dynamic response of a drainage basin to user-defined calving rates. We apply the method to Jakobshavn Isbræ, a major marine terminating outlet glacier of the West Greenland Ice Sheet. The model robustly reproduces the high sensitivity of the glacier to calving, and we find that enhanced calving triggers significant acceleration of the ice stream. Upstream acceleration is sustained through a combination of mechanisms. However, both lateral stress and ice influx stabilize the ice stream. This study provides new insights into the ongoing changes occurring at Jakobshavn Isbræ and emphasizes that the incorporation of moving boundaries and dynamic lateral effects, not captured in flow-line models, is key for realistic model projections of sea level rise on centennial timescales.

Temperature reconstruction from glacier length fluctuations in the Himalaya

AbstractA temperature reconstruction in the glacierized Himalaya over the past centuries using glacial length fluctuation records is challenging due to the abundance of debris-covered glaciers and a scarcity of glacial length fluctuation data. Using idealized flowline model simulations, we show that supraglacial debris cover significantly alters the length fluctuations only when the debris cover is very thick. An expanded database of length fluctuation records for 43 glaciers in the Himalaya and Karakoram is compiled and a standard linear inversion procedure is applied to a subset of 34 glaciers in this database. The reconstructed temperature anomaly during 1860-2010 indicates a continued warming of the region with a total temperature change of ~1.6 K. A close resemblance of the regional temperature anomaly to global trends is seen.

Controlled Wafer Release in Clustered Photolithography Tools: Flexible Flow Line Job Release Scheduling and an LMOLP Heuristic

As a clustered photolithography tool (CPT) in semiconductor wafer manufacturing can cost as much as US$100 million, it must be operated efficiently. To maximize throughput, wafers are generally admitted to a CPT opportunistically, that is, as soon as they are available and the tool can accept them. Here, our goal is to develop release methods that retain throughput but increase manufacturing agility. As Petri net methods prove intractable, we develop a heuristic based on the use of flexible flow line models for the CPT. Such models are appropriate when the tool throughput for each class of wafers is dictated by the bottleneck process time plus unavoidable robot handling overhead. The heart of the heuristic is a lexicographic multiple objective linear program (LMOLP). It first ensures that wafers exit the tool as early as possible and subsequently delays the wafer admission to minimize the mean residency time.

Thermomechanically coupled modelling for land-terminating glaciers: a comparison of two-dimensional, first-order and three-dimensional, full-Stokes approaches

AbstractFor many regions, glacier inaccessibility results in sparse geometric datasets for use as model initial conditions (e.g. along the central flowline only). In these cases, two-dimensional (2-D) flowline models are often used to study glacier dynamics. Here we systematically investigate the applicability of a 2-D, first-order Stokes approximation flowline model (FLM), modified by shape factors, for the simulation of land-terminating glaciers by comparing it with a 3-D, ‘full’-Stokes ice-flow model (FSM). Based on steady-state and transient, thermomechanically uncoupled and coupled computational experiments, we explore the sensitivities of the FLM and FSM to ice geometry, temperature and forward model integration time. We find that, compared to the FSM, the FLM generally produces slower horizontal velocities, due to simplifications inherent to the FLM and to the underestimation of the shape factor. For polythermal glaciers, those with temperate ice zones, or when basal sliding is important, we find significant differences between simulation results when using the FLM versus the FSM. Over time, initially small differences between the FLM and FSM become much larger, particularly near cold/temperate ice transition surfaces. Long time integrations further increase small initial differences between the two models. We conclude that the FLM should be applied with caution when modelling glacier changes under a warming climate or over long periods of time.

On Equilibrium Probabilities for the Delays in Deterministic Flow Lines With Random Arrivals

While flow line models have been studied for decades, excepting some cases with three servers or less, their equilibrium probabilities remain elusive. As such, approximations based on aggregation or decomposition methods are generally employed. In this paper, by focusing on flow lines with deterministic service durations and a renewal arrival process, we develop exact methods for steady-state analysis. Our starting point is the investigation of recursions for customer delay based on exact decomposition methods. We demonstrate that the delay a customer faces in each server possesses a Markovian property. For discrete-time flow lines, we obtain a multidimensional discrete-time time-homogeneous Markov chain for the delays; there are an infinite number of balance equations for the equilibrium probabilities. Exploiting a similarity between our system and the GI/D/1 queue allows us to reduce these to a finite number of balance equations that can be solved numerically. We also investigate the implications for continuous-time flow lines and consider an example inspired by production time windows in semiconductor manufacturing. To our knowledge, these are the first results that allow one to exactly obtain the equilibrium probabilities in flow lines consisting of more than three servers.

Tidally driven ice speed variation at Helheim Glacier, Greenland, observed with terrestrial radar interferometry

AbstractWe used a terrestrial radar interferometer (TRI) at Helheim Glacier, Greenland, in August 2013, to study the effects of tidal forcing on the terminal zone of this tidewater glacier. During our study period, the glacier velocity was up to 25 m d–1. Our measurements show that the glacier moves out of phase with the semi-diurnal tides and the densely packed melange in the fjord. Here detrended glacier displacement lags behind the forecasted tidal height by ∼8 hours. The transition in phase lag between the glacier and the melange happens within a narrow (∼500 m) zone in the fjord in front of the ice cliff. The TRI data also suggest that the impact of tidal forcing decreases rapidly up-glacier of the terminus. A flowline model suggests this pattern of velocity perturbation is consistent with weak ice flowing over a weakly nonlinear bed.

Insights into ice stream dynamics through modelling their response to tidal forcing

Abstract. The tidal forcing of ice streams at their ocean boundary can serve as a natural experiment to gain an insight into their dynamics and constrain the basal sliding law. A nonlinear 3-D viscoelastic full Stokes model of coupled ice stream ice shelf flow is used to investigate the response of ice streams to ocean tides. In agreement with previous results based on flow-line modelling and with a fixed grounding line position, we find that a nonlinear basal sliding law can qualitatively reproduce long-period modulation of tidal forcing found in field observations. In addition, we show that the inclusion of lateral drag, or allowing the grounding line to migrate over the tidal cycle, does not affect these conclusions. Further analysis of modelled ice stream flow shows a varying stress-coupling length scale of boundary effects upstream of the grounding line. We derive a viscoelastic stress-coupling length scale from ice stream equations that depends on the forcing period and closely agrees with model output.

Effect of back pressure on material flow and texture in ECAP of aluminum

Large billets (5 x 5 x 30) cm3 of technically pure aluminum (AA 1050) taken from thick rolled sheets were deformed at room temperature by single pass equal-channel angular pressing (ECAP). ECAP was done at different back pressures (0 – 60 MPa) using a square die with channels intersecting at 90° in sharp corners. The normal direction of rolling was taken parallel to the transverse direction of ECAP. The flow pattern was visualized by marker lines on split billets. The initial texture of the coarse-grained rolled sheet was measured by neutron diffraction. After ECAP, X-ray diffraction was used to measure the texture gradient from top to bottom of the billets. The results show, that with increasing back pressure the corner gap is closed and the flow line pattern becomes more symmetric. The flow line exponent increases strongly from top to bottom of the billets. Moreover, the inhomogeneous deformed zone at the bottom of the billets becomes smaller. The texture changes from a typical rolling texture to a typical shear texture with the intensity of the different shear texture components changing with back pressure. For the ACcomponent splitting is observed. The texture changes are discussed considering Toth's flow line model and grain refinement.

An ETKF approach for initial state and parameter estimation in ice sheet modelling

Abstract. Estimating the contribution of Antarctica and Greenland to sea-level rise is a hot topic in glaciology. Good estimates rely on our ability to run a precisely calibrated ice sheet evolution model starting from a reliable initial state. Data assimilation aims to provide an answer to this problem by combining the model equations with observations. In this paper we aim to study a state-of-the-art ensemble Kalman filter (ETKF) to address this problem. This method is implemented and validated in the twin experiments framework for a shallow ice flowline model of ice dynamics. The results are very encouraging, as they show a good convergence of the ETKF (with localisation and inflation), even for small-sized ensembles.