W. R. Peltier

Simulating the impact of glaciations on continental groundwater flow systems: 1. Relevant processes and model formulation

[1]xa0In the recent literature, it has been shown that Pleistocene glaciations had a large impact on North American regional groundwater flow systems. Because of the myriad of complex processes and large spatial scales involved during periods of glaciation, numerical models have become powerful tools to examine how ice sheets control subsurface flow systems. In this paper, the key processes that must be represented in a continental-scale 3-D numerical model of groundwater flow during a glaciation are reviewed, including subglacial infiltration, density-dependent (i.e., high-salinity) groundwater flow, permafrost evolution, isostasy, sea level changes, and ice sheet loading. One-dimensional hydromechanical coupling associated with ice loading and brine generation were included in the numerical model HydroGeoSphere and tested against newly developed exact analytical solutions to verify their implementation. Other processes such as subglacial infiltration, permafrost evolution, and isostasy were explicitly added to HydroGeoSphere. A specified flux constrained by the ice sheet thickness was found to be the most appropriate boundary condition in the subglacial environment. For the permafrost, frozen and unfrozen elements can be selected at every time step with specified hydraulic conductivities. For the isostatic adjustment, the elevations of all the grid nodes in each vertical grid column below the ice sheet are adjusted uniformly to account for the Earths crust depression and rebound. In a companion paper, the model is applied to the Wisconsinian glaciation over the Canadian landscape in order to illustrate the concepts developed in this paper and to better understand the impact of glaciation on 3-D continental groundwater flow systems.

Simulating the impact of glaciations on continental groundwater flow systems: 2. Model application to the Wisconsinian glaciation over the Canadian landscape

[1]xa0A 3-D groundwater flow and brine transport numerical model of the entire Canadian landscape up to a depth of 10 km is constructed in order to capture the impacts of the Wisconsinian glaciation on the continental groundwater flow system. The numerical development of the model is presented in the companion paper of Lemieux et al. (2008b). Although the scale of the model prevents the use of a detailed geological model, commonly occurring geological materials that exhibit relatively consistent hydrogeological properties over the continent justify the simplifications while still allowing the capture of large-scale flow system trends. The model includes key processes pertaining to coupled groundwater flow and glaciation modeling, such a density-dependent (i.e., brine) flow, hydromechanical loading, subglacial infiltration, isostasy, and permafrost development. The surface boundary conditions are specified with the results of a glacial system model. The significant impact of the ice sheet on groundwater flow is evident by increases in the hydraulic head values below the ice sheet by as much as 3000 m down to a depth of 1.5 km into the subsurface. Results also indicate that the groundwater flow system after glaciation did not fully revert to its initial condition and that it is still recovering from the glaciation perturbation. This suggests that the current groundwater flow system cannot be interpreted solely on the basis of present-day boundary conditions and it is likely that several thousands of years of additional equilibration time will be necessary for the system to reach a new quasi-steady state. Finally, we find permafrost to have a large impact on the rate of dissipation of high hydraulic heads that build at depth and capturing its accurate distribution is important to explain the current hydraulic head distribution across the Canadian landscape.

High‐resolution numerical modeling of tides in the western Atlantic, Gulf of Mexico, and Caribbean Sea during the Holocene

[1]xa0Tidal constituents and datums are computed on a high resolution grid of the northwestern Atlantic Ocean, including the Gulf of Mexico and the Caribbean Sea. A global model is used to determine tidal parameters on a grid with a nominal resolution of 800 × 800. The global model includes self-attraction and loading, drag in shallow marginal seas, and internal tide drag in the deep ocean. Simulations are performed at 1000 year intervals during the Holocene (10,000 calibrated years before present (10 ka)) in combination with changes in bathymetry and coastline location derived from a glacial isostatic adjustment model. The global model results are then used to force a regional barotropic tidal model. The regional model uses an unstructured finite element grid, with very high resolution at the coastline. The model results reveal significant variations in tidal constituent amplitudes throughout the Holocene. In the northwestern Atlantic, semi-diurnal components show a strong amplification at around 9 ka while in the Gulf of Mexico, the response is much more muted. Variations in diurnal tidal parameters are found to be less significant than semi-diurnal parameters throughout the model domain. Changes in tidal range, of great relevance to changes in relative sea level (RSL), are also investigated throughout the Holocene. The overall structure is similar to the patterns observed in the M2 tide, with peak increases of 200–300%, relative to present-day, being observed along the east coast of the United States from 9 to 8 ka. Finally, the high spatial resolution of the regional model allows for the investigation of tidal changes at spatial scales (e.g., individual bays) much smaller than in previous studies.

Thermal evolution of Earth: Models with time‐dependent layering of mantle convection which satisfy the Urey ratio constraint

[1]xa0We present a new set of Earth thermal history calculations in which the effect of increasing mantle layering with convection Rayleigh number is included in a parameterized mantle convection model. We demonstrate that the inclusion of this effect results in strong buffering of the upper mantle temperature and surface heat flow. Models of this type deliver the observed surface heat flow when geochemically constrained internal heating rates (Urey ratios) are assumed with reasonable initial core temperatures. The surface heat flow is also relatively unchanged for the last 3 Gyr of Earth history in models of this kind, in accord with geological inferences concerning ancient geotherms derived from the study of Archean continental materials. In contrast, models with constant degrees of layering spanning the range from whole mantle to fully layered convection are shown to require unreasonably high initial core temperatures in order to meet the surface heat flow constraint. All successful models require that the coupling of heat flow between reservoirs be smaller than would be expected if mantle viscosities are those inferred on the basis of postglacial rebound (PGR) observations. This may indicate that viscosity for convection is significantly greater than that for rebound and hence that mantle rheology is non-Newtonian and that the PGR process is governed by transient rather than steady state creep.

A multibasin reduced model of the global thermohaline circulation: Paleoceanographic analyses of the origins of ice-age climate variability

A new, multibasin reduced model of the global thermohaline circulation has been developed that builds upon the single-basin Atlantic model recently described in Sakai and Peltier [1995]. The model comprises individual, two-dimensional, Atlantic, Indian, and Pacific components which are linked via a circumpolar basin representative of the Southern Ocean. It also includes a complete seasonal cycle for sea surface temperature, a sea ice component, and an acceptably accurate representation of the influence of both wind stress and bottom topography. The circulation in the individual basins is described using a stretched coordinate system in order to allow the use of reduced vertical resolution where high resolution is unnecessary. Values for the control parameters of the new multibasin model are established in the same manner as was employed in analysis of the single-basin model, and the basic conclusion of that study, that there exists a natural oscillatory mode of behavior of the deep circulation on a timescale ranging from a century to several millennia, is confirmed. The precise timescale of the internal variability is determined by the detailed nature of the hydrological cycle which is herein constrained far more realistically than was possible for the single basin model. The simulations performed with the model deliver a rather realistic facsimile of the millennium timescale Dansgaard-Oeschger oscillations [Dansgaard et al., 1984] that were such a prominent feature of North Atlantic glacial climate according to climate proxy data from the Greenland Ice Core Project and Greenland Ice Sheet Project ice cores from Summit, Greenland, when boundary conditions are fixed to those appropriate to full glacial conditions. We also describe a sequence of paleoceanographic experiments that have been designed to explore the sensitivity of the deep circulation to the impact of the specific surface freshwater anomalies that are known to have developed during the last deglaciation event of the current ice age. The simulation of the response of the thermohaline circulation to such anomalies provides strong additional support for the notion that modulation of the strength of the overturning flow in the Atlantic basin played a very important role in the Younger-Dryas climate reversal.

On scaling relations in time-dependent mantle convection and the heat transfer constraint on layering

We present a series of simulations of the mantle convection process based upon an axisymmetric numerical model and highlight a wide range of results in which scaling emerges. For the more challenging simulations it was found necessary to employ a finite difference mesh with uneven grid spacing in the radial coordinate, and we present the appropriate transformed field equations that are required to implement a model of this kind. The statistics of mass flux events transiting the 660-km phase transition are calculated for a large number of high-resolution calculations, and some of these are shown to display scale invariance properties in the high Rayleigh number regime. We also present a new parameterized model of convection and demonstrate its success in predicting the manner in which many of the bulk properties of the convection process scale with convection control parameters. Results are also presented which demonstrate that quantities such as heat flow, characteristic velocity, and thermal boundary layer thickness scale with the mean viscosity even in time-dependent simulations in which the effects of phase transitions, depth-varying viscosity, and internal heating are active. The heat flow scaling exponent is seen to decrease in magnitude with increasing internal heating rate and Clapeyron slope of the 660-km phase transition, but it is shown to be insensitive to depth variation of viscosity. Heat flow is seen to be reduced only modestly as the degree of layering increases unless layering is extreme. These calculations clearly demonstrate that in order for the surface heat flow predicted by the model to equal that characteristic of Earth, the mean viscosity of the mantle that controls the convection process must be considerably higher than the viscosity inferred on the basis of postglacial rebound and/or the flow must be significantly layered by the endothermic phase transition at 660 km depth. If mantle viscosity may be assumed to be Newtonian, in which case the creep resistance that controls rebound and convection must be the same, this constitutes a strong argument for the importance of layering. The force of this argument depends upon the existence of an accurate estimate of the temperature at the core-mantle boundary which has only recently become available.

The high-pressure electronic spin transition in iron: Potential impacts upon mantle mixing

[1]xa0At the Rayleigh number appropriate to Earths mantle, radial heat transport is dominated by solid state thermal convection. Because of the large number of physical properties required to determine the Rayleigh number, and because these properties are expected to be (perhaps strong) functions of pressure and temperature (P-T), laboratory measurements of them under the high pressure and temperature conditions that occur in the deep Earth are of fundamental importance. Recent experimental data demonstrate that an electronic spin transition in iron that occurs at midmantle depths results in significant changes in the physical properties of the ferropericlase component of mantle mineralogy. Additional recent results suggest that it may also exist in the dominant perovskite component. Using control volume based numerical models we investigate the impacts on mantle mixing of this spin transition through its influence on the most important subset of these physical properties, namely density, thermal expansivity, bulk modulus and heat capacity. Our numerical model results demonstrate that this electronic transition enhances mixing in the lower regions of the lower mantle by enhancing the vigor of rising plumes. The lowermost region of the mantle is slightly warmed and the upper mantle slightly cooled by spin-induced effects. However, the spin crossover in the lower mantle appears not to significantly influence mantle layering. Due to the competition that could exist between the strength of the spin-induced thermodynamic properties of ferropericlase and perovskite, cold descending thermal anomalies could stagnate at middle-to-lower mantle depths and lead to the occurrence of “mid mantle avalanches.”

Comment on “Ocean mass from GRACE and glacial isostatic adjustment” by D. P. Chambers et al.

[1]xa0The modern global theory of the glacial isostatic adjustment (GIA) process is a theory that directly addresses the extent to which the geoid of classical geodesy is impacted by this phenomenon. Because the geoid is, by conventional definition, the surface of constant potential that overlaps the surface of the sea in the absence of currents and tides, we may determine the impact of the GIA process upon it only by explicit analysis of the manner in which mass is redistributed among the ocean basins and the level of the sea is thereby influenced. Although the dominant contribution to GIA is that associated with the transfer of mass between the oceans and the continents, there is an additional influence due to the variations in Earths rotational state. This influence “feeds-back” onto the geoid. In the recent paper by Chambers et al. (2010), several arguments were presented that question earlier attempts to discuss the consequences of this feedback. These arguments are interesting and we address them in what follows.

Climate Dynamics in Deep Time: Modeling the “Snowball Bifurcation” and Assessing the Plausibility of its Occurrence

The apparently global scale glaciation events that occurred during the Neoproterozoic era, in the interval from 750 Ma to 550 Ma, represent a significant challenge to our understanding of climate system behavior. If these episodes of glaciation were truly of snowball type, with the continents covered by thick ice-sheets and the oceans entirely capped by sea ice, then special pleading is required to understand the Cambrian explosion of life that occurred subsequently. Detailed models of Neoproterozoic climate, however, suggest the plausibility of preference for equatorial refugium or oasis solutions in which significant regions of open water are able to persist at the equator. We describe further analyses of such solutions in this paper, using both simple EBM coupled ice sheet models and fully articulated atmosphere-ocean-sea ice coupled models of climate evolution. Recently published analyses of the dynamics of the Neoproterozoic carbon cycle, taken together with the predictions of the models discussed herein, are strongly supportive of the equatorial refugium solutions as the most plausible form of the Neoproterozoic cooling events.

Internal thermal boundary layer stability in phase transition modulated convection

The stability of a horizontal thermal boundary layer embedded within a very viscous fluid is investigated using the formalism of linear stability analysis. Thin thermal boundary layers in deep fluid regions and in the absence of phase transition and dynamical effects are thereby shown to be unstable at extremely long wavelengths. The stability of the internal thermal boundary layer which may exist at 660 km depth in the Earths mantle as a consequence of the dynamical influence of the endothermic phase transition from γ spinel to a mixture of perovskite and magnesiowustite, recently discussed in some detail by Solheim and Peltier [1994a], is investigated in order to better understand the “avalanche effect” observed in this and similar nonlinear, time dependent simulations of the mantle convection process. It is demonstrated that if the stability problem is treated as purely thermal, then the boundary layer is predicted to be extremely unstable and the presence of the 660-km endothermic phase transition at middepth within the boundary layer is further destabilizing. When the kinematic effect of flow convergence onto the boundary layer and phase transition region is active, however, it is shown that the layer may be strongly stabilized. In the regime of physically realistic velocity convergence, the critical Rayleigh number is predicted to lie in the range suggested by the numerical simulations of Solheim and Peltier [1994a]. A threshold value of the magnitude of the Clapeyron slope of the endothermic phase transition for a given velocity convergence is also shown to exist, beyond which the fastest-growing mode of instability changes from avalanche type to layered type.