Variational data assimilation using targetted random walks

The variational approach to data assimilation is a widely used methodology for both online prediction and for reanalysis (offline hindcasting). In either of these scenarios it can be important to assess uncertainties in the assimilated state. Ideally it would be desirable to have complete information concerning the Bayesian posterior distribution for unknown state, given data. The purpose of this paper is to show that complete computational probing of this posterior distribution is now within reach in the offline situation. In this paper we will introduce an MCMC method which enables us to directly sample from the Bayesian\ud posterior distribution on the unknown functions of interest, given observations. Since we are aware that these\ud methods are currently too computationally expensive to consider using in an online filtering scenario, we frame this in the context of offline reanalysis. Using a simple random walk-type MCMC method, we are able to characterize the posterior distribution using only evaluations of the forward model of the problem, and of the model and data mismatch. No adjoint model is required for the method we use; however more sophisticated MCMC methods are available\ud which do exploit derivative information. For simplicity of exposition we consider the problem of assimilating data, either Eulerian or Lagrangian, into a low Reynolds number (Stokes flow) scenario in a two dimensional periodic geometry. We will show that in many cases it is possible to recover the initial condition and model error (which we describe as unknown forcing to the model) from data, and that with increasing amounts of informative data, the uncertainty in our estimations reduces

Comparative analysis of techniques for evaluating the effectiveness of aircraft computing systems

Performability analysis is a technique developed for evaluating the effectiveness of fault-tolerant computing systems in multiphase missions. Performability was evaluated for its accuracy, practical usefulness, and relative cost. The evaluation was performed by applying performability and the fault tree method to a set of sample problems ranging from simple to moderately complex. The problems involved as many as five outcomes, two to five mission phases, permanent faults, and some functional dependencies. Transient faults and software errors were not considered. A different analyst was responsible for each technique. Significantly more time and effort were required to learn performability analysis than the fault tree method. Performability is inherently as accurate as fault tree analysis. For the sample problems, fault trees were more practical and less time consuming to apply, while performability required less ingenuity and was more checkable. Performability offers some advantages for evaluating very complex problems

The Global Star Formation Rate from the 1.4 GHz Luminosity Function

The decimetric luminosity of many galaxies appears to be dominated by synchrotron emission excited by supernova explosions. Simple models suggest that the luminosity is directly proportional to the rate of supernova explosions of massive stars averaged over the past 30 Myr. The proportionality may be used together with models of the evolving 1.4 GHz luminosity function to estimate the global star formation rate density in the era z < 1. The local value is estimated to be 0.026 solar masses per year per cubic megaparsec, some 50% larger than the value inferred from the Halpha luminosity density. The value at z ~ 1 is found to be 0.30 solar masses per year per cubic megaparsec. The 10-fold increase in star formation rate density is consistent with the increase inferred from mm-wave, far-infrared, ultra-violet and Halpha observations.Comment: 10 pages, 2 figures, Astrophysical Journal Letters (in press); new PS version has improved figure placemen

The star-formation history of the universe - an infrared perspective

A simple and versatile parameterized approach to the star formation history allows a quantitative investigation of the constraints from far infrared and submillimetre counts and background intensity measurements. The models include four spectral components: infrared cirrus (emission from interstellar dust), an M82-like starburst, an Arp220-like starburst and an AGN dust torus. The 60 $\mu$m luminosity function is determined for each chosen rate of evolution using the PSCz redshift data for 15000 galaxies. The proportions of each spectral type as a function of 60 $\mu$m luminosity are chosen for consistency with IRAS and SCUBA colour-luminosity relations, and with the fraction of AGN as a function of luminosity found in 12 $\mu$m samples. The luminosity function for each component at any wavelength can then be calculated from the assumed spectral energy distributions. With assumptions about the optical seds corresponding to each component and, for the AGN component, the optical and near infrared counts can be accurately modelled. A good fit to the observed counts at 0.44, 2.2, 15, 60, 90, 175 and 850 $\mu$m can be found with pure luminosity evolution in all 3 cosmological models investigated: $\Omega_o$ = 1, $\Omega_o$ = 0.3 ($\Lambda$ = 0), and $\Omega_o$ = 0.3, $\Lambda$ = 0.7. All 3 models also give an acceptable fit to the integrated background spectrum. Selected predictions of the models, for example redshift distributions for each component at selected wavelengths and fluxes, are shown. The total mass-density of stars generated is consistent with that observed, in all 3 cosmological models.Comment: 20 pages, 25 figures. Accepted for publication in ApJ. Full details of models can be found at http://astro.ic.ac.uk/~mrr/countmodel

The European Large Area ISO Survey - ISOPHOT results using the MPIA-pipeline

The European Large Area ISO Survey (ELAIS) will provide Infrared observations of 4 regions in the sky with ISO. Around 2000 Infrared sources have been detected at 7 and 15 microns (with ISOCAM), 90 and 175 microns (with ISOPHOT)) over 13 square degrees of the sky. We present the source extraction pipeline of the 90 microns ISOPHOT observations, describe and discuss the results obtained and derive the limits of the ELAIS observational strategy.Comment: 4 pages, 5 figures, to appear in the ISO conference "The Universe as seen by ISO", 1998, UNESCO, Pari

On the nature of the ISO-selected sources in the ELAIS S2 region

We have studied the optical, near-IR and radio properties of a complete sample of 43 sources detected at 15-micron in one of the deeper ELAIS repeatedly observed region. The extragalactic objects in this sample have 15-micron flux densities in the range 0.4-10 mJy, where the source counts start diverging from no evolution models. About 90% of the sources (39 out of 43) have optical counterparts brighter than I=21 mag. Eight of these 39 sources have been identified with stars on the basis of imaging data, while for another 22 sources we have obtained optical spectroscopy, reaching a high identification percentage (30/43, ~70%). All but one of the 28 sources with flux density > 0.7 mJy are identified. Most of the extragalactic objects are normal spiral or starburst galaxies at moderate redshift (z_med~0.2); four objects are Active Galactic Nuclei. We have used the 15-micron, H_alpha and 1.4-GHz luminosities as indicators of star-formation rate and we have compared the results obtained in these three bands. While 1.4-GHz and 15-micron estimates are in good agreement, showing that our galaxies are forming stars at a median rate of ~40 Mo/yr, the raw H_alpha-based estimates are a factor ~5-10 lower and need a mean correction of ~2 mag to be brought on the same scale as the other two indicators. A correction of ~2 mag is consistent with what suggested by the Balmer decrements H_alpha/H_beta and by the optical colours. Moreover, it is intermediate between the correction found locally for normal spirals and the correction needed for high-luminosity 15-micron objects, suggesting that the average extinction suffered by galaxies increases with infrared luminosity.Comment: 19 pages, 11 figures (3 in JPEG format), MNRAS, accepte

A local potential for the Weyl tensor in all dimensions

In all dimensions and arbitrary signature, we demonstrate the existence of a new local potential -- a double (2,3)-form -- for the Weyl curvature tensor, and more generally for all tensors with the symmetry properties of the Weyl curvature tensor. The classical four-dimensional Lanczos potential for a Weyl tensor -- a double (2,1)-form -- is proven to be a particular case of the new potential: its double dual.Comment: 7 pages; Late

Identifying Very Metal-Rich Stars with Low-Resolution Spectra: Finding Planet-Search Targets

We present empirical calibrations that estimate stellar metallicity, effective temperature and surface gravity as a function of Lick/IDS indices. These calibrations have been derived from a training set of 261 stars for which (1) high-precision measurements of [Fe/H], T_eff and log g have been made using spectral-synthesis analysis of HIRES spectra, and (2) Lick indices have also been measured. Our [Fe/H] calibration, which has precision 0.07 dex, has identified a number of bright (V < 9) metal-rich stars which are now being screened for hot Jupiter-type planets. Using the Yonsei-Yale stellar models, we show that the calibrations provide distance estimates accurate to 20% for nearby stars. This paper outlines the second tier of the screening of planet-search targets by the N2K Consortium, a project designed to identify the stars most likely to harbor extrasolar planets. Discoveries by the N2K Consortium include the transiting hot Saturn HD 149026 b (Sato et al. 2005, astro-ph/0507009) and HD 88133 b (Fischer et al. 2005). See Ammons et al. (2005, In Press) for a description of the first tier of N2K metallicity screening, calibrations using broadband photometry.Comment: Accepted for publication in the Astrophysical Journa