On electromagnetics of an isotropic chiral medium moving at constant velocity

A medium which is an isotropic chiral medium from the perspective of a co-moving observer is a Faraday chiral medium (FCM) from the perspective of a non-co-moving observer. The Tellegen constitutive relations for this FCM are established. By an extension of the Beltrami field concept, these constitutive relations are exploited to show that planewave propagation is characterized by four generally independent wavenumbers. This FCM can support negative phase velocity at certain translational velocities and with certain wavevectors, even though the corresponding isotropic chiral medium does not. The constitutive relations and Beltrami--like fields are also used to develop a convenient spectral representation of the dyadic Green functions for the FCM

Metric connections in projective differential geometry

We search for Riemannian metrics whose Levi-Civita connection belongs to a given projective class. Following Sinjukov and Mikes, we show that such metrics correspond precisely to suitably positive solutions of a certain projectively invariant finite-type linear system of partial differential equations. Prolonging this system, we may reformulate these equations as defining covariant constant sections of a certain vector bundle with connection. This vector bundle and its connection are derived from the Cartan connection of the underlying projective structure.Comment: 10 page

Continental heat gain in the global climate system

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95084/1/grl15494.pd

On Beltrami Model of de Sitter Spacetime

Based on some important properties of $dS$ space, we present a Beltrami model ${\cal B}_\Lambda$ that may shed light on the observable puzzle of $dS$ space and the paradox between the special relativity principle and cosmological principle. In ${\cal B}_\Lambda$, there are inertial-type coordinates and inertial-type observers. Thus, the classical observables can be defined for test particles and light signals. In addition, by choosing the definition of simultaneity the Beltrami metric is transformed to the Robertson-Walker-like metric. It is of positive spatial curvature of order $\Lambda$. This is more or less indicated already by the CMB power spectrum from WMAP and should be further confirmed by its data in large scale.Comment: 4 page

Impacts of the Last Glacial Cycle on ground surface temperature reconstructions over the last millennium

Borehole temperature profiles provide robust estimates of past ground surface temperature changes, in agreement with meteorological data. Nevertheless, past climatic changes such as the Last Glacial Cycle (LGC) generated thermal effects in the subsurface that affect estimates of recent climatic change from geothermal data. We use an ensemble of ice sheet simulations spanning the last 120 ka to assess the impact of the Laurentide Ice Sheet on recent ground surface temperature histories reconstructed from borehole temperature profiles over North America. When the thermal remnants of the LGC are removed, we find larger amounts of subsurface heat storage (2.8 times) and an increased warming of the ground surface over North America by 0.75 K, both relative to uncorrected borehole estimates

Propagation of linear surface air temperature trends into the terrestrial subsurface

Previous studies have tested the long-term coupling between air and terrestrial subsurface temperatures working under the assumption that linear trends in surface air temperature should be equal to those measured at depth within the subsurface. A one-dimensional model of heat conduction is used to show that surface trends are attenuated as a function of depth within conductive media on time scales of decades to centuries, therefore invalidating the above assumption given practical observational constraints. The model is forced with synthetic linear temperature trends as the time-varying upper boundary condition; synthetic trends are either noise free or include additions of Gaussian noise at the annual time scale. It is shown that over a 1000 year period, propagating surface trends are progressively damped with depth in both noise-free and noise-added scenarios. Over shorter intervals, the relationship between surface and subsurface trends is more variable and is strongly impacted by annual variability (i.e., noise). Using output from the FOR1 millennial simulation of the GKSS ECHO-G General Circulation Model as a more realistic surface forcing function for the conductive model, it is again demonstrated that surface trends are damped as a function of depth within the subsurface. Observational air and subsurface temperature data collected over 100 years in Armagh, Ireland, and 29 years in Fargo, North Dakota, are also analyzed and shown to have subsurface temperature trends that are not equal to the surface trend. While these conductive effects are correctly accounted for in inversions of borehole temperature profiles in paleoclimatic studies, they have not been considered in studies seeking to evaluate the long-term coupling between air and subsurface temperatures by comparing trends in their measured time series. The presented results suggest that these effects must be considered and that a demonstrated trend equivalency in air and subsurface temperatures is inconclusive regarding their long-term tracking

Ground surface temperature and continental heat gain: uncertainties from underground

Temperature changes at the Earthʼs surface propagate and are recorded underground as perturbations to the equilibrium thermal regime associated with the heat flow from the Earthʼs interior. Borehole climatology is concerned with the analysis and interpretation of these downward propagating subsurface temperature anomalies in terms of surface climate. Proper determination of the steady-state geothermal regime is therefore crucial because it is the reference against which climate-induced subsurface temperature anomalies are estimated. Here, we examine the effects of data noise on the determination of the steady-state geothermal regime of the subsurface and the subsequent impact on estimates of ground surface temperature (GST) history and heat gain. We carry out a series of Monte Carlo experiments using 1000 Gaussian noise realizations and depth sections of 100 and 200 m as for steady-state estimates depth intervals, as well as a range of data sampling intervals from 10 m to 0.02 m. Results indicate that typical uncertainties for 50 year averages are on the order of ±0.02 K for the most recent 100 year period. These uncertainties grow with decreasing sampling intervals, reaching about ±0.1 K for a 10 m sampling interval under identical conditions and target period. Uncertainties increase for progressively older periods, reaching ±0.3 K at 500 years before present for a 10 m sampling interval. The uncertainties in reconstructed GST histories for the Northern Hemisphere for the most recent 50 year period can reach a maximum of ±0.5 K in some areas. We suggest that continuous logging should be the preferred approach when measuring geothermal data for climate reconstructions, and that for those using the International Heat Flow Commission database for borehole climatology, the steady-state thermal conditions should be estimated from boreholes as deep as possible and using a large fitting depth range (~100 m)

Impact of borehole depths on reconstructed estimates of ground surface temperature histories and energy storage

Estimates of ground surface temperature changes and continental energy storage from geothermal data have become well-accepted indicators of climatic changes. These estimates are independent contributions to the ensemble of paleoclimatic reconstructions and have been used for the validation of general circulation models, and as a component of the energy budget accounting of the global climate system. Recent global and hemispheric analyses of geothermal data were based on data available in the borehole paleoclimatology database, which contains subsurface temperature profiles from a minimum depth of 200 m to about 600 m. Because of the nature of heat conduction, different depth ranges contain the record of past and persistent changes in the energy balance between the lower atmosphere and the ground for different time periods. Here we examine the dependency of estimated ground surface temperature histories and the magnitude of the subsurface heat content on the depth of borehole temperature profiles. Our results show that uncertainties in the estimates of the long-term surface temperature are in the range of ±0.5K. We conclude that previous estimates of ground surface temperature change remain valid for the period since industrialization, but longer-term estimates are subject to considerable uncertainties. The subsurface heat content shows a larger range of variability arising from differences in depth of the borehole temperature profiles, as well as from differences in the time of data acquisition, spanning four decades. These results indicate that estimates of subsurface heat should be carried out with caution to decrease cumulative errors in any spatial analysis

Characterizing land surface processes: A quantitative analysis using air-ground thermal orbits

A quantitative analysis of thermal orbits is developed and applied to modeled air and ground temperatures. Thermal orbits are phase-space representations of air and ground temperature relationships that are generated by plotting daily or monthly ground temperatures against air temperatures. Thermal orbits are useful descriptive tools that provide straightforward illustrations of air and ground temperature relationships in the presence of land surface processes related to snow cover, soil freezing, and vegetation effects. The utility of thermal orbits has been limited, however, by the lack of quantitative analyses that describe changes in orbits across different environments or in time. This shortcoming is overcome in the present study by developing a linear regression analysis of thermal orbits that allows changes to be tracked in time and space and as a function of depth within the subsurface. The theory that underlies the thermal orbit regression analysis is developed herein, and the utility of the application is demonstrated using controlled model experiments

Impact of maximum borehole depths on inverted temperature histories in borehole paleoclimatology

A quantitative assessment is presented for the impact of the maximum depth of a temperature-depth profile on the estimate of the climatic transient and the resultant ground surface temperature (GST) reconstruction used in borehole paleoclimatology. The depth of the profile is important because the downwelling climatic signal must be separated from the quasi-steady state thermal regime established by the energy in the Earth's interior. This component of the signal is estimated as a linear increase in temperature with depth from the lower section of a borehole temperature profile, which is assumed to be unperturbed by recent changes in climate at the surface. The validity of this assumption is dependent on both the subsurface thermophysical properties and the character of the downwelling climatic signal. Such uncertainties can significantly impact the determination of the quasi-steady state thermal regime, and consequently the magnitude of the temperature anomaly interpreted as a climatic signal. The quantitative effects and uncertainties that arise from the analysis of temperature-depth profiles of different depths are presented. Results demonstrate that widely different GST histories can be derived from a single temperature profile truncated at different depths. Borehole temperature measurements approaching 500-600 m depths are shown to provide the most robust GST reconstructions spanning 500 to 1000 yr BP. It is further shown that the bias introduced by a temperature profile of depths shallower than 500-600 m remains even if the time span of the reconstruction target is shortened