Ozone is present in low concentrations throughout the Earth's atmosphere. In the troposphere ozone is a pollutant which largely results from human activity. However, ozone is harmful to humans, animals and plants at even trace concentrations. Conversely stratospheric ozone, the ``ozone layer'', provides an extremely important shield of solar ultraviolet radiation. Human activity has resulted in a significant reduction in stratospheric ozone and this loss has lead to increased holes at the poles. Studies of atmospheric ozone concentrations rely heavily on the use of spectroscopic remote sensing from a mixture of ground-based, airborne and satellite instruments. These instruments observe the characteristic absorption features of ozone either in the infrared or the ultraviolet. Retrievals based on these observations require accurate laboratory data to make them useful. In particular the many studies of atmospheric currently being conducted require intensity / cross section data for both ultraviolet (UV) and infrared (IR) which is accurate to 1% or better. Unfortunately, as has been extensively documented in the scientific literature, the situation with the laboratory intensity determinations is far from satisfactory. Firstly, there are many measurements showing systematic differences between atmospheric studies performed at infrared and ultraviolet wavelengths at the 4 to 5 % level. Secondly, while laboratory measurements of the ultraviolet cross sections show a measure of agreement, those for the infrared do not. A recent (2012) analysis concluded that for the key 10 micron region agreement between measurements was only at best 4% with intensity discrepancies much higher than this. There are other discrepancies within the infrared region. There is an urgent need for a solution to this problem for missions such as TES+OMI on Aura satellite mission (NASA), IASI+GOME-2 on Metop satellite (ESA) AIRS on the Auqa satellite (NASA). The proposal will use high accuracy, first principles quantum mechanical methods to compute the transition intensities for both the IR and UV portions of the spectrum. For the IR region, methods of computing high accuracy dipole moment surfaces already used successful for water and CO2, will be employed. These will be combined with measured transition frequencies to complete line lists with intensities accurate to about 0.5%. New methodologies will be developed to transfer the experience gained computing IR vibration-rotation intensities (which require electronically diagonal dipole moments) to electronic transitions in the UV. Initial work will focus on the Huggins band and will also require further development of the methods used for treating nuclear motion. These calculations will provide complete independent assessment of the absolute line intensities / cross sections removed from experimental issues such as the ozone concentration. Results will be made widely available via the web, databases and submitted for inclusion in standard compilations used for atmospheric studies such as HITRAN. HITRAN will be a project partner on the proposal and undertake independent evaluation of the results.

Statistical theory and methods play a fundamental role in scientific discovery and advancement, including in modern astronomy, where data are collected on increasingly massive scales and with more varieties and complexity. New technology and instrumentation are spawning a diverse array of emerging data types and data analytic challenges, which in turn require and inspire ever more innovative statistical methods and theories. This proposal is guided by the dual aims of advancing statistical foundations and frontiers, motivated by astronomical problems and providing principled data analytic solutions to challenges in astronomy. The CHASC International Center for Astrostatistics has an extensive track record in accomplishing both tasks. This NSF-EPSRC project leverages CHASC's track record to make progress in several new projects. Fitting sophisticated astrophysical models to complex data that were collected with high-tech instruments, for example, often involves a sequence of statistical analyses. Several UK-led projects center on developing new statistical methods that properly account for errors and carry uncertainty forward within such sequences of analyses. Additional US-led work will focus on developing theoretical properties of novel statistical estimation procedures to address data-analytic challenges associated with solar flares and X-ray observations. Other US-led projects involve fast and automatic detection of astronomical objects such as galaxies from 2D or even 4D data. The PIs will develop statistical theory and methods in the context of these projects, building statistical foundations and pushing the frontiers of statistics forward for broad impact that will extend well beyond astrostatistics. The PIs plan to offer effective methods and algorithms for tackling emerging challenges in astronomy, with the aspiration of promoting such principled data-analytic methods among researchers in astronomy. Its provision of free software via the CHASC GitHub Software Library will enable the distribution and impact of the proposed methods and algorithms.

It is widely recognised that the development of a mature chip spectrometer technology, where each pixel in a focal-plane array is intrinsically capable of yielding detailed spectroscopic information, would revolutionise far-infrared and submm-wave(4 mm to 300 um) astronomy. Low spectral-resolution channels (R = 5-20) could be used for CMB and SZ astronomy, and for determining dust temperatures through simultaneous multicolour observations of continuum sources; medium spectral-resolution channels (R = 500-1000) could be used for wide-field blind surveys of high-redshift spectral-lines; and high spectral-resolution channels (R = 2000-4000) could be used for multiline mapping of molecular gas in star-forming regions and extended nearby galaxies. Once the core technology is available, a large number of pixels could be packed into arrays for mapping and surveys, or a small number of pixels could be positioned sparsely over a wide field of view to enable multi-object spectroscopy. Although a number of organisations are working on chip spectrometers, the international community is falling short of demonstrating science-grade observations. To some extent this situation has occurred because a significant amount time is needed on a submm-wave telescope to understand behaviour and refine designs. To address this situation, we propose to demonstrate a high-resolution (R = 3000) superconducting filter-bank spectrometer for the 70-115 GHz (4.3-2.6 mm) atmospheric window. The Cambridge Emission Line Surveyor (CAMELS) is a collaborative project between the Cavendish Laboratory and the Harvard Smithsonian Center for Astrophysics (CFA). CAMELS will be installed on the Greenland Telescope (GLT) and used to map isotopic abundances in low-z galaxies by measuring 12CO (vr = 115.271 GHz) and 13CO (vr =110.201 GHz) line strengths simultaneously. We will assess two slightly different designs: One will map bright lines from extended galaxies (z = 0.005 - 0.05) against high backgrounds (NEP = 2 x 10-17 WHz-1/2), and the other will detect faint lines from point sources (z = 0.05 - 0.12) against low backgrounds (NEP = 4 x 10-18 WHz-1/2). As well as being scientifically important, operation in the 70-115 GHz window will allow us to explore performance, without worrying about scheduling limitations imposed by the atmosphere. The elements of a chip spectrometer are easy to understand in principle, but the realisation of a complete instrument that is capable of making science-grade observations requires detailed knowledge. Our pixels will comprise a single-mode antenna, a bank of superconducting RF filters, coupling terminations to an array of Kinetic Inductance Detectors (KIDs), and a single superconducting readout line. All of these will be realised on a single wafer using multi-layer superconducting microcircuit technology. The chip will be read out using fast digital electronics and Software Defined Radio (SDR) techniques. The Cambridge Group runs a state of the art facility for manufacturing superconducting quantum sensors, and has considerable expertise in fabricating multi-layer microcircuits using bcc-Ta, beta-Ta, NbN, Nb, Al, Mo, Hf, Ir, Au, Cu, SiO, SiO2 films on Si substrates and SiN membranes. This facility will be used to realize the spectrometer modules. The outlook for the technology is considerable, and our programme contributes strongly to STFC's vision. All existing and planned ground-based and space-borne far-infrared observatories are completely reliant on superconducting imaging arrays and receivers. Superconducting device processing technology is now well established, and the next step is to produce microcircuits having complex on-chip functionality. For example, the ability to realise hyperspectral imaging where each pixel is capable of measuring the temperature of the continuum background and the strengths of certain widely space lines simultaneously would have a major impact on the design of future space telescopes.

The two dominant radiative transport processes in our atmosphere are absorption of incoming sunlight, and the absorption of outgoing radiation in what is commonly called the greenhouse effect. Despite occurring at significantly different wavelengths, the rotation-vibration spectrum of water is both the dominant absorber of sunlight and the major greenhouse gas. Thus the rotation-vibration spectrum of water is, by some distance, the single most important spectrum for atmospheric processes. Accurate knowledge of water spectra is required for models of global radiative transport and the earth's energy budget and for more detailed studies such as retrievals of column densities and profiles of other species by remote sensing. The spectrum of water is of course very well studied but remains a challenge: it is very extended, complicated (with no regular structure at high resolution) and the intensities of individual atmospherically important transitions have a huge dynamic range. The demands of modern remote sensing satellites require water line intensities with high accuracy for both monitoring water columns and, because water absorption is so ubiquitous that its lines interferes other retrievals, for detection of a long list of trace species. Failure to model water absorptions accurately at best introduces a major source of error into retrievals and at worst can mean they fail altogether thus severely degrading the usefulness of remote observations. Many species, such as HONO, OClO, NO2, SO2, O3, BrO, HCHO, O4, IO and Glyoxal are monitored using their ultraviolet (UV) spectrum. It has become apparent from recent atmospheric studies that accurate representation of water absorption in the near UV is essential for their accurate retrieval. Retrieval of water columns is a major and important activity. Retrieval of water columns in the near UV has significant advantages since the Earth reflects sunlight in a much more uniform fashion at these wavelengths and the weaker absorption means that optical thickness effects which prevent the determination of reliable water columns in humid atmospheres are largely eliminated. However, precise retrievals rely on the availability of accurate laboratory data which are largely lacking. Satellites flying or planned such as NASA's first Earth Venture Instrument Class mission TEMPO (Tropospheric Emissions: Monitoring Pollution) mission, ESA's Sentinal series and Korea's GEMS (geostationary environmental monetaring satellite) mission will analyse the chemical composition of air with high spatial resolution at near UV wavelengths. All these missions will require high quality laboratory data for water over an extended wavelength range stretching into the near-UV. At present these data are simply not available: there are no direct, high-resolution laboratory or atmospheric measurements of water vapour spectra in the region, and atmospheric database such as HITRAN, contain no relevant information on it. The aim of this proposal is to provide comprehensive and accurate data on water absorption at short wavelengths. These data will be generated using techniques of first principle quantum mechanics that have been successfully applied to both absorption by water vapour at longer wavelengths and other key atmospheric species. Where possible the positions of absorption features will be adjusted using laboratory measurements. The resulting line lists will be made available to key groups involved monitoring the Earth's atmosphere in the near UV, placed in data depositories and made available to databases such as HITRAN.

The dynamics of quantum many-body systems is a fundamental yet notoriously difficult subject due to the nature of strong interactions between macroscopic number of constituents in the systems. Consider setting up a many-body system in a "simple" quantum state, one that does not have much non-local correlation between different subsystems. What are the fates of the system as it evolves in time? Does the system thermalize and exhibit chaotic behaviour, or does it localize and retain information of its initial state? A simple and elegant way of tackling these questions is to investigate the spectral statistics of the quantum many-body systems. A physical system can often be represented by a Hamiltonian - a matrix with a spectrum of energy levels which the system can occupy. The study of spectral statistics asks, what generic features does the correlation among the energy levels in the spectrum capture? Spectral statistics is a fundamental subject in physics due to its role as a robust diagnostic of quantum chaos, and due to universality - generic systems exhibit identical spectral statistics depending only on symmetry classes and dimensionality. In the last five years, spectral statistics has been utilized in multiple frontiers of modern physics, including the demonstration that black holes behave like random matrices in sufficiently late time; a debate concerning the existence of an important dynamical phase called the many-body localization; and the discovery of universal spectral signatures in quantum many-body chaotic systems, as described below. A recent discovery shows that the spectrum of generic quantum many-body chaotic systems has an extended region in which the spectral correlation deviates from known behaviour derived from random matrices. This region grows as the system size increases, and therefore presents a significant gap in our understanding of spectral statistics in the presence of many-body interaction. How does the existence of anomalous spectral correlation affect the scrambling of quantum information? This proposal aims to address such a question, and analytically extract novel signatures of spectral statistics and dynamics in isolated and open quantum many-body systems. Furthermore, despite its importance, spectral statistics in quantum many-body systems has not been experimentally measured, owing to the difficulties of resolving the tight spacing in the spectrum. The second aim of this fellowship is to experimentally measure, in collaboration with experimentalist partners, key signatures of spectral statistics in quantum many-body simulators in the lab for the first time. This project is especially timely, as it deepens and sharpens the understanding of the roles of many-body interaction in the information scrambling and processing in quantum systems, responding to the recent revival in quantum chaos, and to the rapid developments in quantum simulations of quantum many-body systems. Achieving these goals will deliver significant impacts in the constructions of broadly applicable analytical frameworks; in the first experimental measurement of spectral statistics in quantum many-body simulators; and in establishing new connections between communities in condensed matter, quantum information, and high energy physics.