Algorithmic Randomness and Capacity of Closed Sets

We investigate the connection between measure, capacity and algorithmic randomness for the space of closed sets. For any computable measure m, a computable capacity T may be defined by letting T(Q) be the measure of the family of closed sets K which have nonempty intersection with Q. We prove an effective version of Choquet's capacity theorem by showing that every computable capacity may be obtained from a computable measure in this way. We establish conditions on the measure m that characterize when the capacity of an m-random closed set equals zero. This includes new results in classical probability theory as well as results for algorithmic randomness. For certain computable measures, we construct effectively closed sets with positive capacity and with Lebesgue measure zero. We show that for computable measures, a real q is upper semi-computable if and only if there is an effectively closed set with capacity q

A Global Ozone Climatology from Ozone Soundings via Trajectory Mapping: A Stratospheric Perspective

This study explores a domain-filling trajectory approach to generate a global ozone climatology from sparse ozonesonde data. Global ozone soundings of 51,898 profiles at 116 stations over 44 years (1965-2008) are used, from which forward and backward trajectories are performed for 4 days, driven by a set of meteorological reanalysis data. Ozone mixing ratios of each sounding from the surface to 26 km altitude are assigned to the entire path along the trajectory. The resulting global ozone climatology is archived monthly for five decades from the 1960s to the 2000s with grids of 5 degree 5 degree 1 km (latitude, longitude, and altitude). It is also archived yearly from 1965 to 2008. This climatology is validated at 20 ozonesonde stations by comparing the actual ozone sounding profile with that found through the trajectories, using the ozone soundings at all the stations except one being tested. The two sets of profiles are in good agreement, both individually with correlation coefficients between 0.975 and 0.998 and root mean square (RMS) differences of 87 to 482 ppbv, and overall with a correlation coefficient of 0.991 and an RMS of 224 ppbv. The ozone climatology is also compared with two sets of satellite data, from the Satellite Aerosol and Gas Experiment (SAGE) and the Optical Spectrography and InfraRed Imager System (OSIRIS). Overall, the ozone climatology compares well with SAGE and OSIRIS data by both seasonal and zonal means. The mean difference is generally under 20 above 15 km. The comparison is better in the northern hemisphere, where there are more ozonesonde stations, than in the southern hemisphere; it is also better in the middle and high latitudes than in the tropics, where assimilated winds are imperfect in some regions. This ozone climatology can capture known features in the stratosphere, as well as seasonal and decadal variations of these features. Furthermore, it provides a wealth of detail about longitudinal variations in the stratosphere such as the spring ozone maximum over the Canadian Arctic. It also covers higher latitudes than current satellite data. The climatology shows clearly the depletion of ozone from the 1970s to the mid 1990s and ozone recovery in the 2000s. When this climatology is used as the upper boundary condition in an Environment Canada operational chemical forecast model, the forecast is improved in the vicinity of the upper tropospherelower stratosphere region. As this ozone climatology is neither dependent on a priori data or photochemical modeling, it provides independent information and insight that can supplement satellite data and model simulations and enhance our understanding of stratospheric ozone

Trend and variability in ozone in the tropical lower stratosphere over 2.5 solar cycles observed by SAGE II and OSIRIS

We have extended the satellite-based ozone anomaly time series to the present (December 2012) by merging SAGE II (Stratospheric Aerosol and Gas Experiment II) with OSIRIS (Optical Spectrograph and Infrared Imager System) and correcting for the small bias (~0.5%) between them, determined using their temporal overlap of 4 years. Analysis of the merged data set (1984–2012) shows a statistically significant negative trend at all altitudes in the 18–25 km range, including a trend of (−4.6 ± 2.6)% decade⁻¹ at 19.5 km where the relative standard error is a minimum. We are also able to replicate previously reported decadal trends in the tropical lower-stratospheric ozone anomaly based on SAGE II observations. Uncertainties are smaller on the merged trend than the SAGE II trend at all altitudes. Underlying strong fluctuations in ozone anomaly due to El Niño–Southern Oscillation (ENSO), the altitude-dependent quasi-biennial oscillation, and tropopause pressure need to be taken into account to reduce trend uncertainties and, in the case of ENSO, to accurately determine the linear trend just above the tropopause. We also compare the observed ozone trend with a calculated trend that uses information on tropical upwelling and its temporal trend from model simulations, tropopause pressure trend information derived from reanalysis data, and vertical profiles from SAGE II and OSIRIS to determine the vertical gradient of ozone and its trend. We show that the observed trend agrees with the calculated trend and that the magnitude of the calculated trend is dominated by increased tropical upwelling, with minor but increasing contribution from the vertical ozone gradient trend as the tropical tropopause is approached. Improvements are suggested for future regression modelling efforts which could reduce trend uncertainties and biases in trend magnitudes, thereby allowing accurate trend detection to extend below 18 km

Constraining the Lyα escape fraction with far-infrared observations of Lyα emitters

We study the far-infrared properties of 498 Lyα emitters (LAEs) at z = 2.8, 3.1, and 4.5 in the Extended Chandra Deep Field-South, using 250, 350, and 500μm data from the Herschel Multi-tiered Extragalactic Survey and 870μm data from the LABOCA ECDFS Submillimeter Survey. None of the 126, 280, or 92 LAEs at z = 2.8, 3.1, and 4.5, respectively, are individually detected in the far-infrared data. We use stacking to probe the average emission to deeper flux limits, reaching 1σ depths of ∼0.1 to 0.4 mJy. The LAEs are also undetected at ?3σ in the stacks, although a 2.5σ signal is observed at 870μm for the z = 2.8 sources. We consider a wide range of far-infrared spectral energy distributions (SEDs), including an M82 and an Sd galaxy template, to determine upper limits on the far-infrared luminosities and far-infrared-derived star formation rates of the LAEs. These star formation rates are then combined with those inferred from the Lyα and UV emission to determine lower limits on the LAEs’ Lyα escape fraction (f esc (Lyα)). For the Sd SED template, the inferred LAEs f esc (Lyα) are ?30% (1σ) at z = 2.8, 3.1, and 4.5, which are all significantly higher than the global f esc (Lyα) at these redshifts. Thus, if the LAEs f esc (Lyα) follows the global evolution, then they have warmer far-infrared SEDs than the Sd galaxy template. The average and M82 SEDs produce lower limits on the LAE f esc (Lyα) of ∼10%–20% (1σ), all of which are slightly higher than the global evolution of f esc (Lyα), but consistent with it at the 2σ–3σ level

Hubble Space Telescope Imaging of Lyman Alpha Emission at z=4.4

We present the highest redshift detections of resolved Lyman alpha emission, using Hubble Space Telescope/ACS F658N narrowband-imaging data taken in parallel with the Wide Field Camera 3 Early Release Science program in the GOODS CDF-S. We detect Lyman alpha emission from three spectroscopically confirmed z = 4.4 Lyman alpha emitting galaxies (LAEs), more than doubling the sample of LAEs with resolved Lyman alpha emission. Comparing the light distribution between the rest-frame ultraviolet continuum and narrowband images, we investigate the escape of Lyman alpha photons at high redshift. While our data do not support a positional offset between the Lyman alpha and rest-frame ultraviolet (UV) continuum emission, the half-light radii in two out of the three galaxies are significantly larger in Lyman alpha than in the rest-frame UV continuum. This result is confirmed when comparing object sizes in a stack of all objects in both bands. Additionally, the narrowband flux detected with HST is significantly less than observed in similar filters from the ground. These results together imply that the Lyman alpha emission is not strictly confined to its indigenous star-forming regions. Rather, the Lyman alpha emission is more extended, with the missing HST flux likely existing in a diffuse outer halo. This suggests that the radiative transfer of Lyman alpha photons in high-redshift LAEs is complicated, with the interstellar-medium geometry and/or outflows playing a significant role in galaxies at these redshifts.Comment: Submitted to the Astrophysical Journal. 11 pages, 10 figure

Attribution of observed changes in stratospheric ozone and temperature

Three recently-completed sets of simulations of multiple chemistry-climate models with greenhouse gases only, with all anthropogenic forcings, and with anthropogenic and natural forcings, allow the causes of observed stratospheric changes to be quantitatively assessed using detection and attribution techniques. The total column ozone response to halogenated ozone depleting substances and to natural forcings is detectable in observations, but the total column ozone response to greenhouse gas changes is not separately detectable. In the middle and upper stratosphere, simulated and observed SBUV/SAGE ozone changes are broadly consistent, and separate anthropogenic and natural responses are detectable in observations. The influence of ozone depleting substances and natural forcings can also be detected separately in observed lower stratospheric temperature, and the magnitudes of the simulated and observed responses to these forcings and to greenhouse gas changes are found to be consistent. In the mid and upper stratosphere the simulated natural and combined anthropogenic responses are detectable and consistent with observations, but the influences of greenhouse gases and ozone-depleting substances could not be separately detected in our analysis

OSIRIS: A Decade of Scattered Light

Into year 11 of a 2-yr mission, OSIRIS is redefining how limb-scattered sunlight can be used to probe the atmosphere, even into the upper troposphere

Modelling high redshift Lyman-alpha Emitters

We present a new model for high redshift Lyman-Alpha Emitters (LAEs) in the cosmological context which takes into account the resonant scattering of Ly-a photons through expanding gas. The GALICS semi-analytic model provides us with the physical properties of a large sample of high redshift galaxies. We implement a gas outflow model for each galaxy based on simple scaling arguments. The coupling with a library of numerical experiments of Ly-a transfer through expanding or static dusty shells of gas allows us to derive the Ly-a escape fractions and profiles. The predicted distribution of Ly-a photons escape fraction shows that galaxies with a low star formation rate have a f_esc of the order of unity, suggesting that, for those objects, Ly-a may be used to trace the star formation rate assuming a given conversion law. In galaxies forming stars intensely, the escape fraction spans the whole range from 0 to 1. The model is able to get a good match to the UV and Ly-a luminosity function (LF) data at 3 < z < 5. We find that we are in good agreement with both the bright Ly-a data and the faint population observed by Rauch et al. (2008) at z=3. Most of the Ly-a profiles of our LAEs are redshifted by the diffusion in the outflow which suppresses IGM absorption. The bulk of the observed Ly-a equivalent width (EW) distribution is recovered by our model, but we fail to obtain the very large values sometimes detected. Predictions for stellar masses and UV LFs of LAEs show a satisfactory agreement with observational estimates. The UV-brightest galaxies are found to show only low Ly-a EWs in our model, as it is reported by many observations of high redshift LAEs. We interpret this effect as the joint consequence of old stellar populations hosted by UV-bright galaxies, and high HI column densities that we predict for these objects, which quench preferentially resonant Ly-a photons via dust extinction.Comment: 17 pages, 12 figures, 3 tables, accepted for publication in MNRA