The Inhomogeneous Hall's Ray

We show that the inhomogenous approximation spectrum, associated to an irrational number \alpha\ always has a Hall's Ray; that is, there is an \epsilon>0 such that [0,\epsilon) is a subset of the spectrum. In the case when \alpha\ has unbounded partial quotients we show that the spectrum is just a ray.Comment: Fixed typos in bibliograph

Near-infrared oxygen airglow from the Venus nightside

Groundbased imaging and spectroscopic observations of Venus reveal intense near-infrared oxygen airglow emission from the upper atmosphere and provide new constraints on the oxygen photochemistry and dynamics near the mesopause (approximately 100 km). Atomic oxygen is produced by the Photolysis of CO2 on the dayside of Venus. These atoms are transported by the general circulation, and eventually recombine to form molecular oxygen. Because this recombination reaction is exothermic, many of these molecules are created in an excited state known as O2(delta-1). The airglow is produced as these molecules emit a photon and return to their ground state. New imaging and spectroscopic observations acquired during the summer and fall of 1991 show unexpected spatial and temporal variations in the O2(delta-1) airglow. The implications of these observations for the composition and general circulation of the upper venusian atmosphere are not yet understood but they provide important new constraints on comprehensive dynamical and chemical models of the upper mesosphere and lower thermosphere of Venus

Deuterium on Venus: Observations from Earth

In view of the importance of the deuterium-to-hydrogen ratio in understanding the evolutionary scenario of planetary atmospheres and its relationship to understanding the evolution of our own Earth, we undertook a series of observations designed to resolve previous observational conflicts. We observed the dark side of Venus in the 2.3 micron spectral region in search of both H2O and HDO, which would provide us with the D/H ratio in Venus' atmosphere. We identified a large number of molecular lines in the region, belonging to both molecules, and, using synthetic spectral techniques, obtained mixing ratios of 34 plus or minus 10 ppm and 1.3 plus or minus 0.2 ppm for H2O and HDO, respectively. These mixing ratios yield a D/H ratio for Venus of D/H equals 1.9 plus or minus 0.6 times 10 (exp 12) and 120 plus or minus 40 times the telluric ratio. Although the detailed interpretation is difficult, our observations confirm that the Pioneer Venus Orbiter results and establish that indeed Venus had a period in its early history in which it was very wet, perhaps not unlike the early wet period that seems to have been present on Mars, and that, in contrast to Earth, lost much of its water over geologic time

The ACOS CO_2 retrieval algorithm – Part II: Global X_(CO_2) data characterization

Here, we report preliminary estimates of the column averaged carbon dioxide (CO_2) dry air mole fraction, X_(CO_2), retrieved from spectra recorded over land by the Greenhouse gases Observing Satellite, GOSAT (nicknamed "Ibuki"), using retrieval methods originally developed for the NASA Orbiting Carbon Observatory (OCO) mission. After screening for clouds and other known error sources, these retrievals reproduce much of the expected structure in the global X_(CO_2) field, including its variation with latitude and season. However, low yields of retrieved X_(CO_2) over persistently cloudy areas and ice covered surfaces at high latitudes limit the coverage of some geographic regions, even on seasonal time scales. Comparisons of early GOSAT X_(CO_2) retrievals with X_(CO_2) estimates from the Total Carbon Column Observing Network (TCCON) revealed a global, −2% (7–8 parts per million, ppm, with respect to dry air) X_(CO_2) bias and 2 to 3 times more variance in the GOSAT retrievals. About half of the global X_(CO_2) bias is associated with a systematic, 1% overestimate in the retrieved air mass, first identified as a global +10 hPa bias in the retrieved surface pressure. This error has been attributed to errors in the O_2 A-band absorption cross sections. Much of the remaining bias and spurious variance in the GOSAT X_(CO_2) retrievals has been traced to uncertainties in the instrument's calibration, oversimplified methods for generating O_2 and CO_2 absorption cross sections, and other subtle errors in the implementation of the retrieval algorithm. Many of these deficiencies have been addressed in the most recent version (Build 2.9) of the retrieval algorithm, which produces negligible bias in X_(CO_2) on global scales as well as a ~30% reduction in variance. Comparisons with TCCON measurements indicate that regional scale biases remain, but these could be reduced by applying empirical corrections like those described by Wunch et al. (2011b). We recommend that such corrections be applied before these data are used in source sink inversion studies to minimize spurious fluxes associated with known biases. These and other lessons learned from the analysis of GOSAT data are expected to accelerate the delivery of high quality data products from the Orbiting Carbon Observatory-2 (OCO-2), once that satellite is successfully launched and inserted into orbit

Low Simulated Radiation Limit for Runaway Greenhouse Climates

Terrestrial planet atmospheres must be in long-term radiation balance, with solar radiation absorbed matched by thermal radiation emitted. For hot moist atmospheres, however, there is an upper limit on the thermal emission which is decoupled from the surface temperature. If net absorbed solar radiation exceeds this limit the planet will heat uncontrollably, the so-called \runaway greenhouse". Here we show that a runaway greenhouse induced steam atmosphere may be a stable state for a planet with the same amount of incident solar radiation as Earth has today, contrary to previous results. We have calculated the clear-sky radiation limits at line-by-line spectral resolution for the first time. The thermal radiation limit is lower than previously reported (282 W/sq m rather than 310W/sq m) and much more solar radiation would be absorbed (294W/sq m rather than 222W/sq m). Avoiding a runaway greenhouse under the present solar constant requires that the atmosphere is subsaturated with water, and that cloud albedo forcing exceeds cloud greenhouse forcing. Greenhouse warming could in theory trigger a runaway greenhouse but palaeoclimate comparisons suggest that foreseeable increases in greenhouse gases will be insufficient to do this