Approximate factorization constraint preconditioners for saddle-point matrices

We consider the application of the conjugate gradient method to the solution of large, symmetric indefinite linear systems. Special emphasis is put on the use of constraint preconditioners and a new factorization that can reduce the number of flops required by the preconditioning step. Results concerning the eigenvalues of the preconditioned matrix and its minimum polynomial are given. Numerical experiments validate these conclusions.

Implicit-factorization preconditioning and iterative solvers for regularized saddle-point systems

We consider conjugate-gradient like methods for solving block symmetric indefinite linear systems that arise from saddle-point problems or, in particular, regularizations thereof. Such methods require preconditioners that preserve certain sub-blocks from the original systems but allow considerable flexibility for the remaining blocks. We construct a number of families of implicit factorizations that are capable of reproducing the required sub-blocks and (some) of the remainder. These generalize known implicit factorizations for the unregularized case. Improved eigenvalue clustering is possible if additionally some of the noncrucial blocks are reproduced. Numerical experiments confirm that these implicit-factorization preconditioners can be very effective in practice.

The zonal asymmetry of the Southern Hemisphere storm-track

Atmospheric general circulation model experiments have been performed to investigate how the significant zonal asymmetry in the Southern Hemisphere (SH) winter storm track is forced by sea surface temperature (SST) and orography. An experiment with zonally symmetric tropical SSTs expands the SH upper-tropospheric storm track poleward and eastward and destroys its spiral structure. Diagnosis suggests that these aspects of the observed storm track result from Rossby wave propagation from a wave source in the Indian Ocean region associated with the monsoon there. The lower-tropospheric storm track is not sensitive to this forcing. However, an experiment with zonally symmetric midlatitude SSTs exhibits a marked reduction in the magnitude of the maximum intensity of the lower-tropospheric storm track associated with reduced SST gradients in the western Indian Ocean. Experiments without the elevation of the South African Plateau or the Andes show reductions in the intensity of the major storm track downstream of them due to reduced cyclogenesis associated with the topography. These results suggest that the zonal asymmetry of the SH winter storm track is mainly established by stationary waves excited by zonal asymmetry in tropical SST in the upper troposphere and by local SST gradients in the lower troposphere, and that it is modified through cyclogenesis associated with the topography of South Africa and South America.

Influence of the seasonal cycle on the termination of El Nino events in a coupled general circulation model

In this study, the mechanisms leading to the El Nino peak and demise are explored through a coupled general circulation model ensemble approach evaluated against observations. The results here suggest that the timing of the peak and demise for intense El Nino events is highly predictable as the evolution of the coupled system is strongly driven by a southward shift of the intense equatorial Pacific westerly anomalies during boreal winter. In fact, this systematic late-year shift drives an intense eastern Pacific thermocline shallowing, constraining a rapid El Nino demise in the following months. This wind shift results from a southward displacement in winter of the central Pacific warmest SSTs in response to the seasonal evolution of solar insolation. In contrast, the intensity of this seasonal feedback mechanism and its impact on the coupled system are significantly weaker in moderate El Nino events, resulting in a less pronounced thermocline shallowing. This shallowing transfers the coupled system into an unstable state in spring but is not sufficient to systematically constrain the equatorial Pacific evolution toward a rapid El Nino termination. However, for some moderate events, the occurrence of intense easterly wind anomalies in the eastern Pacific during that period initiate a rapid surge of cold SSTs leading to La Nina conditions. In other cases, weaker trade winds combined with a slightly deeper thermocline allow the coupled system to maintain a broad warm phase evolving through the entire spring and summer and a delayed El Nino demise, an evolution that is similar to the prolonged 1986/87 El Nino event. La Nina events also show a similar tendency to peak in boreal winter, with characteristics and mechanisms mainly symmetric to those described for moderate El Nino cases.

Ocean circulation and climate in an idealised Pangean OAGCM

An idealised Pangean configuration is integrated in a coupled ocean atmosphere general circulation model to investigate the form of the ocean circulation and its impacts on the large scale climate system. A vigorous, hemispherically symmetric overturning is found, driven by deep water formation at high latitudes. Whilst the peak mass transport is around 100Sv, a low vertical temperature gradient in the ocean means that the maximum heat transport is only 1.2PW. The geographical change in the coupled model is found to produce a global average warming of 2°C, despite an increase in global surface albedo. This occurs through changes in the atmospheric water vapour and cloud distributions. There is also reduction in the equator-pole temperature gradient, largely attributable to the same causes, avoiding the paradox of low meridional temperature gradients without increased polar heat transport.

Performance of the OPA/ARPEGE-T21 global ocean-atmosphere coupled model

The climatology of the OPA/ARPEGE-T21 coupled general circulation model (GCM) is presented. The atmosphere GCM has a T21 spectral truncation and the ocean GCM has a 2°×1.5° average resolution. A 50-year climatic simulation is performed using the OASIS coupler, without flux correction techniques. The mean state and seasonal cycle for the last 10 years of the experiment are described and compared to the corresponding uncoupled experiments and to climatology when available. The model reasonably simulates most of the basic features of the observed climate. Energy budgets and transports in the coupled system, of importance for climate studies, are assessed and prove to be within available estimates. After an adjustment phase of a few years, the model stabilizes around a mean state where the tropics are warm and resemble a permanent ENSO, the Southern Ocean warms and almost no sea-ice is left in the Southern Hemisphere. The atmospheric circulation becomes more zonal and symmetric with respect to the equator. Once those systematic errors are established, the model shows little secular drift, the small remaining trends being mainly associated to horizontal physics in the ocean GCM. The stability of the model is shown to be related to qualities already present in the uncoupled GCMs used, namely a balanced radiation budget at the top-of-the-atmosphere and a tight ocean thermocline.

Coriolis perturbations in the infrared spectrum of ethylene

Rotational structure has been resolved and analyzed in two of the infrared‐active perpendicular bands of C2H4 vapor: the Type b fundamental band, ν10, at 826 cm—1, and the Type c fundamental band, ν7, at 949 cm—1. Many of the individual PP and RR branch lines have been observed. The analysis has been confined to values of the quantum number K≥3, for which energy levels ethylene shows no detectable deviations from a symmetric‐top rotational structure. The analysis reveals a Coriolis interaction between ν7 and ν10, and between ν4 and ν10, and values of the Coriolis constants ζ7,10z and ζ4,10y are obtained; these are related to normal coordinate calculations for the appropriate symmetry species, and force constants are derived to fit the observed zeta constants. The band center of ν10 has been revised from the original figure of 810 cm—1 to the new value, 826 cm—1, and the inactive frequency ν4 is estimated to lie at 1023±3 cm—1, in good agreement with the previous estimate of 1027 cm—1. The change in the value of ν10 leads to a suggested change in the value of the Raman‐active fundamental ν6 from 1236 to 1222 cm—1. New combination bands have been observed at 2174 cm—1, assigned as ν3+ν10; and at 2252 cm—1, assigned as ν4+ν6; also rotational structure has been resolved and analyzed in the ν6+ν10 band at 2048 cm—1. The new data obtained for the C2H4 molecule are summarized in Table XII, with all of the other data presently available on the vibrational and rotational constants.

Rotational spectra induced by vibrations

Mizushima and Venkateswarlu showed in 1953 that certain molecules have the property that excited vibrational states may possess rotational spectra even when the rotational spectrum of the ground vibrational state is forbidden by symmetry. We call such a spectrum a vibrationally induced rotational spectrum, and have made a systematic examination of the point groups which permit such behaviour. We also give formulae for the approximate line frequencies and intensities in these spectra, and discuss some of the problems involved in observing them. The spectra can only arise from degenerate vibrational states, and are of three possible types: i) symmetric top perpendicular spectra, shown by molecules belonging to the point groups Dnh, Dn and Cnh, where n is odd; (ii) symmetric top parallel spectra, shown by molecules belonging to Dnd and S2n, where n is even; and (iii) spherical top spectra, shown by molecules belonging to T or Td. Excited vibrational states of polar molecules of point groups Cnv or Cn, where n is odd, may also possess vibrationally induced perpendicular components of type (i), in addition to their ordinary parallel spectra. In addition to the above limitations on the point groups there are, in general, limitations on the symmetry species of the degenerate vibrational states.

Wave functions for the methane molecule

If the potential field due to the nuclei in the methane molecule is expanded in terms of a set of spherical harmonics about the carbon nucleus, only the terms involving s, f, and higher harmonic functions differ from zero in the equilibrium configuration. Wave functions have been calculated for the equilibrium configuration, first including only the spherically symmetric s term in the potential, and secondly including both the s and the f terms. In the first calculation the complete Hartree-Fock S.C.F. wave functions were determined; in the second calculation a variation method was used to determine the best form of the wave function involving f harmonics. The resulting wave functions and electron density functions are presented and discussed

l-resonance perturbations in infrared perpendicular bands

The effects of ℓ-type resonance on rovibrational bands in infrared spectra are reviewed. Observed spectra are compared with computer-simulated spectra obtained by solving the Hamiltonian matrix numerically and calculating the true (perturbed) wavenumber and intensity of each line in the band. The most obvious effects in the spectra are shown to result from intensity perturbations rather than line-shifts; in oblate symmetric tops the Q branch structure near the band center may show anomalies due to ℓ-resonance even at quite low resolution and even when the accidental resonance is not very exact. Numerical values of ℓ-doubling constants are obtained for several cyclopropane bands by comparing observed band contours at about 0.2-cm−1 resolution with computed contours. Although the constants are not determined with great precision, the sign of the ℓ-doubling constants is determined unambiguously.

Simultaneous analysis of v1, v4, 2v2, v2+v5, and 2v5 bands of 12CH3F

The Fourier-transform spectrum of CH3F from 2800 to 3100 cm−1, obtained by Guelachvili in Orsay at a resolution of about 0.003 cm−1, was analyzed. The effective Hamiltonian used contained all symmetry allowed interactions up to second order in the Amat-Nielsen classification, together with selected third-order terms, amongst the set of nine vibrational basis functions represented by the states ν1(A1), ν4(E), 2ν2(A1), ν2 + ν5(E), 2ν50(A1), and 2ν5±2(E). A number of strong Fermi and Coriolis resonances are involved. The vibrational Hamiltonian matrix was not factorized beyond the requirements of symmetry. A total of 59 molecular parameters were refined in a simultaneous least-squares analysis to over 1500 upper-state energy levels for J ≤ 20 with a standard deviation of 0.013 cm−1. Although the standard deviation remains an order of magnitude greater than the precision of the measurements, this work breaks new ground in the simultaneous analysis of interacting symmetric top vibrational levels, in terms of the number of interacting vibrational states and the number of parameters in the Hamiltonian.

Parcel theory in three dimensions and the calculation of SCAPE

Slantwise convective available potential energy (SCAPE) is a measure of the degree to which the atmosphere is unstable to conditional symmetric instability (CSI). It has, until now, been defined by parcel theory in which the atmosphere is assumed to be nonevolving and balanced, that is, two-dimensional. When applying this two-dimensional theory to three-dimensional evolving flows, these assumptions can be interpreted as an implicit assumption that a timescale separation exists between a relatively rapid timescale for slantwise ascent and a slower timescale for the development of the system. An approximate extension of parcel theory to three dimensions is derived and it is shown that calculations of SCAPE based on the assumption of relatively rapid slantwise ascent can be qualitatively in error. For a case study example of a developing extratropical cyclone, SCAPE calculated along trajectories determined without assuming the existence of the timescale separation show large SCAPE values for parcels ascending from the warm sector and along the warm front. These parcels ascend into the cloud head within which there is some evidence consistent with the release of CSI from observational and model cross sections. This region of high SCAPE was not found for calculations along the relatively rapidly ascending trajectories determined by assuming the existence of the timescale separation.

Arctic oscillation or North Atlantic oscillation?

The definition and interpretation of the Arctic oscillation (AO) are examined and compared with those of the North Atlantic oscillation (NAO). It is shown that the NAO reflects the correlations between the surface pressure variability at its centers of action, whereas this is not the case for the AO. The NAO pattern can be identified in a physically consistent way in principal component analysis applied to various fields in the Euro-Atlantic region. A similar identification is found in the Pacific region for the Pacific–North American (PNA) pattern, but no such identification is found here for the AO. The AO does reflect the tendency for the zonal winds at 35° and 55°N to anticorrelate in both the Atlantic and Pacific regions associated with the NAO and PNA. Because climatological features in the two ocean basins are at different latitudes, the zonally symmetric nature of the AO does not mean that it represents a simple modulation of the circumpolar flow. An increase in the AO or NAO implies strong, separated tropospheric jets in the Atlantic but a weakened Pacific jet. The PNA has strong related variability in the Pacific jet exit, but elsewhere the zonal wind is similar to that related to the NAO. The NAO-related zonal winds link strongly through to the stratosphere in the Atlantic sector. The PNA-related winds do so in the Pacific, but to a lesser extent. The results suggest that the NAO paradigm may be more physically relevant and robust for Northern Hemisphere variability than is the AO paradigm. However, this does not disqualify many of the physical mechanisms associated with annular modes for explaining the existence of the NAO.

Threshold effects in price transmission: The case of Brazilian wheat, maize, and soya prices

Recent studies into price transmission have recognized the important role played by transport and transaction costs. Threshold models are one approach to accommodate such costs. We develop a generalized Threshold Error Correction Model to test for the presence and form of threshold behavior in price transmission that is symmetric around equilibrium. We use monthly wheat, maize, and soya prices from the United States, Argentina, and Brazil to demonstrate this model. Classical estimation of these generalized models can present challenges but Bayesian techniques avoid many of these problems. Evidence for thresholds is found in three of the five commodity price pairs investigated.

Buddenbrockia is a Cnidarian worm

A major evolutionary divide occurs in the animal kingdom between the so-called radially symmetric animals, which includes the cnidarians, and the bilaterally symmetric animals, which includes all worm phyla. Buddenbrockia plumatellae is an active, muscular, parasitic worm that belongs to the phylum Myxozoa, a group of morphologically simplified microscopic endoparasites that has proved difficult to place phylogenetically. Phylogenetic analyses of multiple protein-coding genes demonstrate that Buddenbrockia is a cnidarian. This active muscular worm increases the known diversity in cnidarian body plans and demonstrates that a muscular, wormlike form can evolve in the absence of overt bilateral symmetry.