scholarly journals Geothermal heat flux at the COST B-2 and B-3 Wells, U. S. Atlantic continental margin

1987 ◽  
Author(s):  
Bruno Della Vedova ◽  
Richard P. Von Herzen
Keyword(s):  
Heat Flux ◽  
Continental Margin ◽  
Geothermal Heat ◽  
The Cost

scholarly journals Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

2016 ◽  
Author(s):  
Hongyu Zhu ◽  
Noemi Petra ◽  
Georg Stadler ◽  
Tobin Isaac ◽  
Thomas J. R. Hughes ◽  
...  
Keyword(s):  
Heat Flux ◽  
Inverse Problem ◽  
Optimization Problem ◽  
Premature Termination ◽  
Adjoint Equations ◽  
Surface Velocity ◽  
Geothermal Heat ◽  
Ice Flow ◽  
Cost Functional ◽  
The Cost

Abstract. We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using an instantaneous thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection-diffusion equation, which couples to the nonlinear Stokes ice flow equations, which then determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to render the problem well-posed. We derive adjoint-based gradient and Hessian expressions for the resulting PDE-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov-Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases, and that small wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems — i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian — we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. We show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.

scholarly journals Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

2016 ◽  
Vol 10 (4) ◽  
pp. 1477-1494 ◽  
Author(s):  
Hongyu Zhu ◽  
Noemi Petra ◽  
Georg Stadler ◽  
Tobin Isaac ◽  
Thomas J. R. Hughes ◽  
...  
Keyword(s):  
Heat Flux ◽  
Inverse Problem ◽  
Optimization Problem ◽  
Premature Termination ◽  
Adjoint Equations ◽  
Surface Velocity ◽  
Geothermal Heat ◽  
Ice Flow ◽  
Cost Functional ◽  
The Cost

Abstract. We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection–diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov–Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems – i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian – we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. We show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.

The effect of geothermal heat flux on the deglacial evolution of the Greenland ice sheet

2021 ◽  
Author(s):  
Parviz Ajourlou ◽  
François PH Lapointe ◽  
Glenn A Milne ◽  
Yasmina Martos
Keyword(s):  
Boundary Condition ◽  
Heat Flux ◽  
Thermal State ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Sampling Procedure ◽  
Geophysical Research ◽  
Geothermal Heat ◽  
Input Field ◽  
Uncertainty Estimates

<p>Geothermal heat flux (GHF) is known to be an important control on the basal thermal state of an ice sheet which, in turn, is a key factor in governing how the ice sheet will evolve in response to a given climate forcing. In recent years, several studies have estimated GHF beneath the Greenland ice sheet using different approaches (e.g. Rezvanbehbahani et al., Geophysical Research Letters, 2017; Martos et al., Geophysical Research Letters, 2018; Greve, Polar Data Journal, 2019). Comparing these different estimates indicates poor agreement and thus large uncertainty in our knowledge of this important boundary condition for modelling the ice sheet. The primary aim of this study is to quantify the influence of this uncertainty on modelling the past evolution of the ice sheet with a focus on the most recent deglaciation. We build on past work that considered three GHF models (Rogozhina et al., 2011) by considering over 100 different realizations of this input field. We use the uncertainty estimates from Martos et al. (Geophysical Research Letters, 2018) to generate GHF realisations via a statistical sampling procedure. A sensitivity analysis using these realisations and the Parallel Ice Sheet Model (PISM, Bueler and Brown, Journal of Geophysical Research, 2009) indicates that uncertainty in GHF has a dramatic impact on both the volume and spatial distribution of ice since the last glacial maximum, indicating that more precise constraints on this boundary condition are required to improve our understanding of past ice sheet evolution and, consequently, reduce uncertainty in future projections.</p>

scholarly journals Evaluation of six geothermal heat flux maps for the Antarctic Lambert-Amery glacial system

2021 ◽  
Author(s):  
Haoran Kang ◽  
Liyun Zhao ◽  
Michael Wolovick ◽  
John C. Moore
Keyword(s):  
Heat Flux ◽  
Frictional Heating ◽  
Thermal Conditions ◽  
Ice Shelf ◽  
Geothermal Heat ◽  
Glacier System ◽  
Amery Ice Shelf ◽  
Ice Sheet Dynamics ◽  
Subglacial Lakes ◽  
The Antarctic

Abstract. Basal thermal conditions play an important role in ice sheet dynamics, and they are sensitive to geothermal heat flux (GHF). Here we estimate the basal thermal conditions, including basal temperature, basal melt rate, and friction heat underneath the Lambert-Amery glacier system in east Antarctica, using a combination of a forward model and an inversion from a 3D ice flow model. We assess the sensitivity and uncertainty of basal thermal conditions using six different GHFs. We evaluate the modelled results using all available observed subglacial lakes. There are very large differences in modelled spatial pattern of temperate basal conditions using the different GHFs. The two most-recent GHF fields inverted from aerial geomagnetic observations have higher values of GHF in the region, produce a larger warm-based area, and match the observed subglacial lakes better than the other GHFs. The fast flowing glacier region has a lower modelled basal friction coefficient, faster basal velocity, with higher basal frictional heating in the range of 50–2000 mW m−2 than the base under slower flowing glaciated areas. The modelled basal melt rate reaches ten to hundreds of mm per year locally in Lambert, Lepekhin and Kronshtadtskiy glaciers feeding the Amery ice shelf, and ranges from 0–5 mm yr−1 on the temperate base of the vast inland region.

scholarly journals A Review of Geothermal Technologies and Their Role in Reducing Greenhouse Gas Emissions in the USA

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Philip J. Ball
Keyword(s):  
Greenhouse Gas ◽  
Power Plants ◽  
Carbon Tax ◽  
Ghg Emissions ◽  
Abatement Cost ◽  
Combined Cycle ◽  
Low Carbon ◽  
Geothermal Heat ◽  
The Cost

Abstract A review of conventional, unconventional, and advanced geothermal technologies highlights just how diverse and multi-faceted the geothermal industry has become, harnessing temperatures from 7 °C to greater than 350 °C. The cost of reducing greenhouse emissions is examined in scenarios where conventional coal or combined-cycle gas turbine (CCGT) power plants are abated. In the absence of a US policy on a carbon tax, the marginal abatement cost potential of these technologies is examined within the context of the social cost of carbon (SCC). The analysis highlights that existing geothermal heat and power technologies and emerging advanced closed-loop applications could deliver substantial cost-efficient baseload energy, leading to the long-term decarbonization. When considering an SCC of $25, in a 2025 development scenario, geothermal technologies ideally need to operate with full life cycle assessment (FLCA) emissions, lower than 50 kg(CO2)/MWh, and aim to be within the cost range of $30−60/MWh. At these costs and emissions, geothermal can provide a cost-competitive low-carbon, flexible, baseload energy that could replace existing coal and CCGT providing a significant long-term reduction in greenhouse gas (GHG) emissions. This study confirms that geothermally derived heat and power would be well positioned within a diverse low-carbon energy portfolio. The analysis presented here suggests that policy and regulatory bodies should, if serious about lowering carbon emissions from the current energy infrastructure, consider increasing incentives for geothermal energy development.

scholarly journals Forty-seven new subglacial lakes in the 0–110° E sector of East Antarctica

2007 ◽  
Vol 53 (181) ◽  
pp. 289-297 ◽  
Author(s):  
Sergey V. Popov ◽  
Valery N. Masolov
Keyword(s):  
Heat Flux ◽  
Scientific Work ◽  
East Antarctica ◽  
Lake Area ◽  
Geothermal Heat ◽  
Subglacial Lake ◽  
Deep Faults ◽  
Radio Echo Sounding ◽  
Subglacial Lakes ◽  
Echo Sounding

AbstractDuring the summer field seasons of 1987–91, studies of central East Antarctica by airborne radio-echo sounding commenced. This scientific work continued in the 1990s in the Vostok Subglacial Lake area and along the traverse route from Mirny, and led to the discovery of 16 new subglacial water cavities in the areas of Domes Fuji and Argus and the Prince Charles Mountains. Twenty-nine subglacial water cavities were revealed in the area near Vostok, along with a feature we believe to be a subglacial river. Two subglacial lakes were discovered along the Mirny–Vostok traverse route. These are located 50 km north of Komsomolskaya station and under Pionerskaya station. We find high geothermal heat flux in the vicinity of the largest of the subglacial lakes, and suggest this may be due to their location over deep faults where additional mantle heat is available.

scholarly journals Coupled Northern Hemisphere permafrost–ice-sheet evolution over the last glacial cycle

2015 ◽  
Vol 11 (9) ◽  
pp. 1165-1180 ◽  
Author(s):  
M. Willeit ◽  
A. Ganopolski
Keyword(s):  
Heat Flux ◽  
Northern Hemisphere ◽  
Ice Sheet ◽  
The Arctic ◽  
Sediment Layer ◽  
Glacial Cycle ◽  
Geothermal Heat ◽  
Climate History ◽  
Last Glacial ◽  
The Last Glacial

Abstract. Permafrost influences a number of processes which are relevant for local and global climate. For example, it is well known that permafrost plays an important role in global carbon and methane cycles. Less is known about the interaction between permafrost and ice sheets. In this study a permafrost module is included in the Earth system model CLIMBER-2, and the coupled Northern Hemisphere (NH) permafrost–ice-sheet evolution over the last glacial cycle is explored. The model performs generally well at reproducing present-day permafrost extent and thickness. Modeled permafrost thickness is sensitive to the values of ground porosity, thermal conductivity and geothermal heat flux. Permafrost extent at the Last Glacial Maximum (LGM) agrees well with reconstructions and previous modeling estimates. Present-day permafrost thickness is far from equilibrium over deep permafrost regions. Over central Siberia and the Arctic Archipelago permafrost is presently up to 200–500 m thicker than it would be at equilibrium. In these areas, present-day permafrost depth strongly depends on the past climate history and simulations indicate that deep permafrost has a memory of surface temperature variations going back to at least 800 ka. Over the last glacial cycle permafrost has a relatively modest impact on simulated NH ice sheet volume except at LGM, when including permafrost increases ice volume by about 15 m sea level equivalent in our model. This is explained by a delayed melting of the ice base from below by the geothermal heat flux when the ice sheet sits on a porous sediment layer and permafrost has to be melted first. Permafrost affects ice sheet dynamics only when ice extends over areas covered by thick sediments, which is the case at LGM.

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