Averaging kernels for DOAS total-column satellite retrievals

International audienceThe Differential Optical Absorption Spectroscopy (DOAS) method is used extensively to retrieve total column amounts of trace gases based on UV-visible measurements of satellite spectrometers, such as ERS-2 GOME. In practice the sensitivity of the instrument to the tracer density is strongly height dependent, especially in the troposphere. The resulting tracer profile dependence may introduce large systematic errors in the retrieved columns that are difficult to quantify without proper additional information, as provided by the averaging kernel (AK). In this paper we discuss the DOAS retrieval method in the context of the general retrieval theory as developed by Rodgers. An expression is derived for the DOAS AK for optically thin absorbers. It is shown that the comparison with 3D chemistry-transport models and independent profile measurements, based on averaging kernels, is no longer influenced by errors resulting from a priori profile assumptions. The availability of averaging kernel information as part of the total column retrieval product is important for the interpretation of the observations, and for applications like chemical data assimilation and detailed satellite validation studies

Global ozone forecasting based on ERS-2 GOME observations

International audienceThe availability of near-real time ozone observations from satellite instruments has recently initiated the development of ozone data assimilation systems. In this paper we present the results of an ozone assimilation and forecasting system, in use since Autumn 2000. The forecasts are produced by an ozone transport and chemistry model, driven by the operational medium range forecasts of ECMWF. The forecasts are initialised with realistic ozone distributions, obtained by the assimilation of near-real time total column observations of the GOME spectrometer on ERS-2. The forecast error diagnostics demonstrate that the system produces meaningful total ozone forecasts for up to 6 days in the extratropics. In the tropics meaningful forecasts of the small anomalies are restricted to shorter periods of about two days with the present model setup. It is demonstrated that important events, such as the breakup of the South Pole ozone hole and mini-hole events above Europe can be successfully predicted 4--5 days in advance

Spectral function of the 1D Hubbard model in the U→+∞U\to +\infty limit

We show that the one-particle spectral functions of the one-dimensional Hubbard model diverge at the Fermi energy like $|\omega-\varepsilon_F|^{-3/8}$ in the $U\to +\infty$ limit. The Luttinger liquid behaviour $|\omega-\varepsilon_F|^\alpha$, where $\alpha \to 1/8$ as $U\to +\infty$, should be limited to $|\omega-\varepsilon_F| \sim t^2/U$ (for $U$ large but finite), which shrinks to a single point, $\omega=\varepsilon_F$,in that limit. The consequences for the observation of the Luttinger liquid behaviour in photoemission and inverse photoemission experiments are discussed.Comment: 4 pages, RevTeX, 2 figures on reques

Consistent low-energy reduction of the three-band model for copper oxides with O-O hopping to the effective t-J model

A full three-band model for the CuO$_{2}$ plane with inclusion of all essential interactions - Cu-O and O-O hopping, repulsion at the copper and oxygen and between them - is considered. A general procedure of the low-energy reduction of the primary Hamiltonian to the Hamiltonian of the generalized $t$-$t'$-$J$ model is developed. An important role of the direct O-O hopping is discussed. Parameters of the effective low-energy model (the hopping integral, the band position and the superexchange constant $J$ are calculated. An analysis of the obtained data shows that the experimental value of $J$ fixes the charge transfer energy $\Delta =(\epsilon_{p}-\epsilon_{d})$ in a narrow region of energies.Comment: 32 pp. (LATEX), two figures (PostScript) appende

Dynamical density-density correlations in one-dimensional Mott insulators

The dynamical density-density correlation function is calculated for the one-dimensional, half-filled Hubbard model extended with nearest neighbor repulsion using the Lanczos algorithm for finite size systems and analytically for large on site repulsion compared to hopping amplitudes. At the zone boundary an excitonic feature exists for any finite nearest neighbor repulsion and exhausts most of the spectral weight, even for parameters where no exciton is visible at zero momentum.Comment: 5 pages, REVTeX, epsf, 3 postscript figure

Anisotropic Spin Hamiltonians due to Spin-Orbit and Coulomb Exchange Interactions

This paper contains the details of Phys. Rev. Lett. 73, 2919 (1994) and, to a lesser extent, Phys. Rev. Lett. 72, 3710 (1994). We treat a Hubbard model which includes all the 3d states of the Cu ions and the 2p states of the O ions. We also include spin-orbit interactions, hopping between ground and excited crystal field states of the Cu ions, and rather general Coulomb interactions. Our analytic results for the spin Hamiltonian, H, are corroborated by numerical evaluations of the energy splitting of the ground manifold for two holes on either a pair of Cu ions or a Cu-O-Cu complex. In the tetragonal symmetry case and for the model considered, we prove that H is rotationally invariant in the absence of Coulomb exchange. When Coulomb exchange is present, each bond Hamiltonian has full biaxial anisotropy, as expected for this symmetry. For lower symmetry situations, the single bond spin Hamiltonian is anisotropic at order t**6 for constant U and at order t**2 for nonconstant U. (Constant U means that the Coulomb interaction between orbitals does not depend on which orbitals are involved.)Comment: 50 pages, ILATEX Version 2.09 <13 Jun 1989

Hubbard model versus t-J model: The one-particle spectrum

The origin of the apparent discrepancies between the one-particle spectra of the Hubbard and t-J models is revealed: Wavefunction corrections, in addition to the three-site terms, should supplement the bare t-J. In this way a quantitative agreement between the two models is obtained, even for the intermediate-$U$ values appropriate for the high-Tc cuprate superconductors. Numerical results for clusters of up to 20 sites are presented. The momentum dependence of the observed intensities in the photoemission spectra of Sr2CuO2Cl2 are well described by this complete strong-coupling approach.Comment: 4 two-column RevTeX pages, including 4 Postscript figures. Uses epsf. Accepted for publication in Physical Review B, Rapid Communicatio

Averaging kernels for DOAS total-column satellite retrievals

The Differential Optical Absorption Spectroscopy (DOAS) method is used extensively to retrieve total column amounts of trace gases based on UV-visible measurements of satellite spectrometers, such as ERS-2 GOME. In practice the sensitivity of the instrument to the tracer density is strongly height dependent, especially in the troposphere. The resulting tracer profile dependence may introduce large systematic errors in the retrieved columns that are difficult to quantify without proper additional information, as provided by the averaging kernel (AK). In this paper we discuss the DOAS retrieval method in the context of the general retrieval theory as developed by Rodgers. An expression is derived for the DOAS AK for optically thin absorbers. It is shown that the comparison with 3D chemistry-transport models and independent profile measurements, based on averaging kernels, is no longer influenced by errors resulting from a priori profile assumptions. The availability of averaging kernel information as part of the total column retrieval product is important for the interpretation of the observations, and for applications like chemical data assimilation and detailed satellite validation studies

Dynamics of lattice pinned charge stripes

We study the transversal dynamics of a charged stripe (quantum string) and show that zero temperature quantum fluctuations are able to depin it from the lattice. If the hopping amplitude t is much smaller than the string tension J, the string is pinned by the underlying lattice. At t>>J, the string is depinned and allowed to move freely, if we neglect the effect of impurities. By mapping the system onto a 1D array of Josephson junctions, we show that the quantum depinning occurs at t/J = 2 / pi^2. Besides, we exploit the relation of the stripe Hamiltonian to the sine-Gordon theory and calculate the infrared excitation spectrum of the quantum string for arbitrary t/J values.Comment: 4 pages, 2 figure

Phonon Assisted Multimagnon Optical Absorption and Long Lived Two-Magnon States in Undoped Lamellar Copper Oxides

We calculate the effective charge for multimagnon infrared (IR) absorption assisted by phonons in the parent insulating compounds of cuprate superconductors and the spectra for two-magnon absorption using interacting spin-wave theory. Recent measured bands in the mid IR [Perkins et al. Phys. Rev. Lett. {\bf 71} 1621 (1993)] are interpreted as involving one phonon plus a two-magnon virtual bound state, and one phonon plus higher multimagnon absorption processes. The virtual bound state consists of a narrow resonance occurring when the magnon pair has total momentum close to $(\pi,0)$.Comment: 4 page