Geometric Covariograms,Indicator Variograms and Boundaries of Planar Closed Sets

In the plane, consider a compact set with nonempty interior and piecewise C ¹ boundary such that any line segment crosses this boundary at only finitely many points. Then the second derivatives of the geometric covariogram of the compact set at the origin are related to geometrical characteristics of the set boundary. Specifically, the mean second derivative is zero when the boundary has no singular point, it is positive when the boundary has finitely many vertices but no cusp, and it is infinite when the boundary has at least one cusp.     

Eigenanalysis of recent United States sea levels

Spatial and temporal patterns of recent sea-level rise along the United States coastline have been examined to ascertain rates of rise, and possible causes for high-frequency fluctuations in sea level. Eigenanalysis identified several distinct coastal compartments within each of which sea-level behavior is consistent. The United States east coast has three of these compartments: one north of Cape Cod, where sea-level rise increases with distance to the north; one between Cape Cod and Cape Hatteras where sea-level rise increases to the south; and the third from Cape Hatteras south to Pensacola, where sea-level rise decreases to the south. The western gulf coast represents another compartment (poorly sampled in this study), where subsidence is partly due to compaction. The final compartment is along the United States west coast, where poor spatial sampling produces a highly spatially variable sea-level record that has some temporal uniformity. Spectral analysis shows a dominant time scale of six years for sea-level variability, with different coastal compartments responding relatively in or out of phase. No evidence for increased rates of sea-level rise over the past 10 years was found. This objective statistical technique is a valuable tool for identifying spatial and temporal sea-level trends in the United States. It may later prove useful for identifying elusive world-wide trends of sea level, related to glacial melting, glacial rebound, tectonism, and volcanic activity.     

The high latitude circulation and temperature structure of the thermosphere near solstice

The neutral gas temperature and circulation of the thermosphere are calculated for December solstice conditions near solar cycle maximum using NCAR's thermospheric general circulation model (TGCM). High-latitude heat and momentum sources significantly alter the basic solar-driven circulation during solstice. At F-region heights, the increased ion density in the summer hemisphere results in a larger ion drag momentum source for the neutral gas than in the winter hemisphere. As a result there are larger wind velocities and a greater tendency for the neutral gas to follow the magnetospheric convection pattern in the summer hemisphere than in the winter hemisphere. There is about three times more Joule heating in the summer than the winter hemisphere for moderate levels of geomagnetic activity due to the greater electrical conductivity in the summer E-region ionosphere.

The results of several TGCM runs are used to show that at F-region heights it is possible to linearly combine the solar-driven and high-latitude driven solutions to obtain the total temperature structure and circulation to within 10–20%. In the lower thermosphere, however, non-linear terms cause significant departures and a linear superposition of fields is not valid.

The F-region winds at high latitudes calculated by the TGCM are also compared to the meridional wind derived from measurements by the Fabry-Perot Interferometer (FPI) and the zonal wind derived from measurements by the Wind and Temperature Spectrometer (WATS) instruments onboard the Dynamics Explorer (DE−2) satellite for a summer and a winter day. For both examples, the observed and modeled wind patterns are in qualitative agreement, indicating a dominant control of high latitude winds by ion drag. The magnitude of the calculated winds (400–500 m s⁻¹) for the assumed 60 kV cross-tail potential, however, is smaller than that of the measured winds (500–800 m s⁻¹). This suggests the need for an increased ion drag momentum source in the model calculations due to enhanced electron densities, higher ion drift velocities, or some combination that needs to be further denned from the DE−2 satellite measurements.     

On the global mean temperature of the thermosphere

The solar extreme ultraviolet (e.u.v.) flux and solar ultraviolet (u.v.) flux in the Schumann-Runge continuum region have been measured by spectrometers on board the Atmosphere Explorer satellites from about 1974 to 1981. The solar flux spectra measured on 23 April 1974 (a day the Atmosphere Explorer satellite reference spectrum was obtained), 13–28 July 1976 (a period of spotless conditions near solar cycle minimum), and 19 February 1979 (a day near solar cycle maximum) are used to examine the global mean temperature structure of the thermosphere above 120 km. The results show that for solar cycle minimum the calculated global mean exospheric temperature is in agreement with empirical model predictions, indicating that the energy absorbed by the thermosphere is balanced by downward molecular thermal conduction. For solar cycle maximum the energy absorbed by the thermosphere is not balanced by downward thermal conduction but agreement between the calculated and observed temperature is obtained with the inclusion of 5.3μm radiational cooling by nitric oxide. Model calculations of the minor neutral constituents in the thermosphere show that about three times more nitric oxide is produced during solar cycle maximum than solar cycle minimum conditions. The results suggest that nitric oxide cooling is small during solar cycle minimum, because of low nitric oxide densities and low thermospheric temperatures, but it becomes significantly larger during solar cycle maximum, when nitric oxide densities and thermospheric temperatures are larger.23 April 1974 was a moderately disturbed day and the results of the global mean temperature calculation indicate that it is necessary to consider a high latitude heat source associated with the geomagnetic activity to obtain agreement between the calculated and observed global mean temperature structure.     

A compositional interpretation of trans-neptunian objects taxonomies

Trans-neptunian objects (TNOs) are a population of small objects orbiting the Sun beyond Neptune. Because of their distance they are difficult to observe spectroscopically, but a large body of photometric observations is available and growing. TNOs are important tracers of the evolution of the outer Solar System and key when testing current dynamical evolution theories. Previous statistical studies of the colors of TNOs have yielded useful but limited results regarding the chemical history and evolution of these bodies.With the aim at obtaining compositional information on the small and distant TNOs we introduce a statistical cluster analysis (labelled albedo) based on colors and published albedos of TNOs. We compare it to a previous taxonomy, to illustrate the significance of including the albedo information when determining the composition of the objects. When the albedo contribution is removed from the data, the new taxonomy (now labelled classical) is in general agreement with the published ones, supporting the applicability of our approach. Making use of modeled reflectance spectra of a variety of plausible mixtures found on the surface of TNOs, we extract the average surface composition of each taxon, for both the classical and the albedo taxonomy, in a statistically consistent fashion.Differently from previous and classical, the albedo taxonomy establishes a direct link between the colors and albedos of the objects and their surface composition, allowing, for the first time, a quick assessment of the chemical history of TNOs. In fact, under closer examination the taxa show trends in composition that might be evolutionary in nature. If a simple ‘snow lines’ model is adopted, we can infer that albedo taxa relate the current objects’ locations to their original ones, prior to the migration of the outer planets. We regard the large population that characterizes the darkest classes spread at a variety of semi-major axis distances as one of the intriguing results of this work.     

Solar Rotational Periodicities and the Semiannual Variation in the Solar Wind, Radiation Belt, and Aurora

The behavior of a number of solar wind, radiation belt, auroral and geomagnetic parameters is examined during the recent extended solar minimum and previous solar cycles, covering the period from January 1972 to July 2010. This period includes most of the solar minimum between Cycles 23 and 24, which was more extended than recent solar minima, with historically low values of most of these parameters in 2009. Solar rotational periodicities from 5 to 27 days were found from daily averages over 81 days for the parameters. There were very strong 9-day periodicities in many variables in 2005?–?2008, triggered by recurring corotating high-speed streams (HSS). All rotational amplitudes were relatively large in the descending and early minimum phases of the solar cycle, when HSS are the predominant solar wind structures. There were minima in the amplitudes of all solar rotational periodicities near the end of each solar minimum, as well as at the start of the reversal of the solar magnetic field polarity at solar maximum (～?1980, ～?1990, and ～?2001) when the occurrence frequency of HSS is relatively low. Semiannual equinoctial periodicities, which were relatively strong in the 1995?–?1997 solar minimum, were found to be primarily the result of the changing amplitudes of the 13.5- and 27-day periodicities, where 13.5-day amplitudes were better correlated with heliospheric daily observations and 27-day amplitudes correlated better with Earth-based daily observations. The equinoctial rotational amplitudes of the Earth-based parameters were probably enhanced by a combination of the Russell-McPherron effect and a reduction in the solar wind-magnetosphere coupling efficiency during solstices. The rotational amplitudes were cross-correlated with each other, where the 27-day amplitudes showed some of the weakest cross-correlations. The rotational amplitudes of the >?2 MeV radiation belt electron number fluxes were progressively weaker from 27- to 5-day periods, showing that processes in the magnetosphere act as a low-pass filter between the solar wind and the radiation belt. The A _p/K _p magnetic currents observed at subauroral latitudes are sensitive to proton auroral precipitation, especially for 9-day and shorter periods, while the A _p/K _p currents are governed by electron auroral precipitation for 13.5- and 27-day periodicities.     

Asteroids (65) Cybele, (107) Camilla and (121) Hermione: Infrared spectral diversity among the Cybeles

We find a clear diversity in the 3 μm and 10 μm features of three Cybele asteroids: (107) Camilla, (121) Hermione, and (65) Cybele. (121) Hermione exhibits a “check-like” 3 μm feature, which may be attributed to OH-dominated minerals and (107) Camilla shows a rounded “bowl” like feature closer to that of (65) Cybele, which may be attributed to H₂O-dominated minerals. The 10 μm features of these three asteroids are also different from each other.