A contour-advective semi-lagrangian numerical algorithm for simulating fine-scale conservative dynamical fields

This paper describes a novel numerical algorithm for simulating the evolution of fine-scale conservative fields in layer-wise two-dimensional flows, the most important examples of which are the earth's atmosphere and oceans. the algorithm combines two radically different algorithms, one Lagrangian and the other Eulerian, to achieve an unexpected gain in computational efficiency. The algorithm is demonstrated for multi-layer quasi-geostrophic flow, and results are presented for a simulation of a tilted stratospheric polar vortex and of nearly-inviscid quasi-geostrophic turbulence. the turbulence results contradict previous arguments and simulation results that have suggested an ultimate two-dimensional, vertically-coherent character of the flow. Ongoing extensions of the algorithm to the generally ageostrophic flows characteristic of planetary fluid dynamics are outlined.

Viewing the body modulates tactile receptive fields

Tactile discrimination performance depends on the receptive field (RF) size of somatosensory cortical (SI) neurons. Psychophysical masking effects can reveal the RF of an idealized "virtual" somatosensory neuron. Previous studies show that top-down factors strongly affect tactile discrimination performance. Here, we show that non-informative vision of the touched body part influences tactile discrimination by modulating tactile RFs. Ten subjects performed spatial discrimination between touch locations on the forearm. Performance was improved when subjects saw their forearm compared to viewing a neutral object in the same location. The extent of visual information was relevant, since restricted view of the forearm did not have this enhancing effect. Vibrotactile maskers were placed symmetrically on either side of the tactile target locations, at two different distances. Overall, masking significantly impaired discrimination performance, but the spatial gradient of masking depended on what subjects viewed. Viewing the body reduced the effect of distant maskers, but enhanced the effect of close maskers, as compared to viewing a neutral object. We propose that viewing the body improves functional touch by sharpening tactile RFs in an early somatosensory map. Top-down modulation of lateral inhibition could underlie these effects.

Assessing the uncertainty associated with intermittent rainfall fields

[1] In many practical situations where spatial rainfall estimates are needed, rainfall occurs as a spatially intermittent phenomenon. An efficient geostatistical method for rainfall estimation in the case of intermittency has previously been published and comprises the estimation of two independent components: a binary random function for modeling the intermittency and a continuous random function that models the rainfall inside the rainy areas. The final rainfall estimates are obtained as the product of the estimates of these two random functions. However the published approach does not contain a method for estimation of uncertainties. The contribution of this paper is the presentation of the indicator maximum likelihood estimator from which the local conditional distribution of the rainfall value at any location may be derived using an ensemble approach. From the conditional distribution, representations of uncertainty such as the estimation variance and confidence intervals can be obtained. An approximation to the variance can be calculated more simply by assuming rainfall intensity is independent of location within the rainy area. The methodology has been validated using simulated and real rainfall data sets. The results of these case studies show good agreement between predicted uncertainties and measured errors obtained from the validation data.

Evaluation of ozone and water vapor fields from the ECMWF reanalysis ERA-40 during 1991-1999 in comparison with UARS satellite and MOZAIC aircraft observations

[ 1] The European Centre for Medium-Range Weather Forecasts (ECMWF) 40-year Reanalysis (ERA-40) ozone and water vapor reanalysis fields during the 1990s have been compared with independent satellite data from the Halogen Occultation Experiment (HALOE) and Microwave Limb Sounder (MLS) instruments on board the Upper Atmosphere Research Satellite (UARS). In addition, ERA-40 has been compared with aircraft data from the Measurements of Ozone and Water Vapour by Airbus In-Service Aircraft (MOZAIC) program. Overall, in comparison with the values derived from the independent observations, the upper stratosphere in ERA-40 has about 5 - 10% more ozone and 15 - 20% less water vapor. This dry bias in the reanalysis appears to be global and extends into the middle stratosphere down to 40 hPa. Most of the discrepancies and seasonal variations between ERA-40 and the independent observations occur within the upper troposphere over the tropics and the lower stratosphere over the high latitudes. ERA-40 reproduces a weaker Antarctic ozone hole, and of less vertical extent, than the independent observations; values in the ozone maximum in the tropical stratosphere are lower for the reanalysis. ERA-40 mixing ratios of water vapor are considerably larger than those for MOZAIC, typically by 20% in the tropical upper troposphere, and they may exceed 60% in the lower stratosphere over high latitudes. The results imply that the Brewer-Dobson circulation in the ECMWF reanalysis system is too fast, as is also evidenced by deficiencies in the way ERA-40 reproduces the water vapor "tape recorder'' signal in the tropical stratosphere. Finally, the paper examines the biases and their temporal variation during the 1990s in the way ERA-40 compares to the independent observations. We also discuss how the evaluation results depend on the instrument used, as well as on the version of the data.

Anharmonic force constant calculations

The relationship of the anharmonic force constants in curvilinear internal coordinates to the observed vibration-rotation spectrum of a molecule is reviewed. A simplified method of setting up the required non-linear coordinate transformations is described: this makes use of an / tensor, which is a straightforward generalization of the / matrix used in the customary description of harmonic force constant calculations. General formulae for the / tensor elements, in terms of the familiar L matrix elements, are presented. The use of non-linear symmetry coordinates and redundancies are described. Sample calculations on the water and ammonia molecules are reported.

Force constants and dipole‐moment derivatives of molecules from perturbed Hartree–Fock calculations

General expressions for the force constants and dipole‐moment derivatives of molecules are derived, and the problems arising in their practical application are reviewed. Great emphasis is placed on the use of the Hartree–Fock function as an approximate wavefunction, and a number of its properties are discussed and re‐emphasised. The main content of this paper is the development of a perturbed Hartree–Fock theory that makes possible the direct calculation of force constants and dipole‐moment derivatives from SCF–MO wavefunctions. Essentially the theory yields ∂ϕi / ∂RJα, the derivative of an MO with respect to a nuclear coordinate.

Anharmonic force field of acetylene

The harmonic and anharmonic force field of acetylene has been determined in a least-squares calculation from recently determined data on the spectroscopic constants of various isotopic species (including the vibrational l-doubling constant). A general quadratic and cubic force field was used, but a constrained quartic force field containing only 8 of the 23 possible quartic constants. The results are discussed and compared with earlier work.

Microwave spectrum of CHD2CN and CHD2NC, and the harmonic force field and rz structure of methyl cyanide and isocyanide

The microwave spectra of CHD2CN and CHD2NC have been measured from 18 to 40 GHz; about 20 type A and 30 type C transitions have been observed for each molecule. These have been fitted to a Hamiltonian using 3 rotational constants, and 5 quartic and 4 sextic distortion constants, in the IrS reduction of Watson [in “Vibrational spectra and structure” Vol. 6 (1977)]; the standard error of the fit is 26 kHz. For methyl cyanide the 5 quartic distortion constants have been used to further refine the recent harmonic force field of Duncan et al. [J. Mol. Spectrosc. 69, 123 (1978)], but the changes are small. Finally, for both molecules, the harmonic force field has been used to determine zero point average moments of inertia Iz from the ground state rotational constants for many isotopic species, and these have been used to determine an rz structure. The results are compared with rs structure calculations.

Force constants and dipole moment derivatives of molecules from perturbed Hartree-Fock calculations II. Applications to limited basis set SCF-MO wavefunctions

The perturbed Hartree–Fock theory developed in the preceding paper is applied to LiH, BH, and HF, using limited basis‐set SCF–MO wavefunctions derived by previous workers. The calculated values for the force constant ke and the dipole‐moment derivative μ(1) are (experimental values in parentheses): LiH, ke  =  1.618(1.026)mdyn/Å,μ(1)  =  −18.77(−2.0±0.3)D/ÅBH,ke  =  5.199(3.032)mdyn/Å,μ(1)  =  −1.03(−)D/Å;HF,ke  =  12.90(9.651)mdyn/Å,μ(1)  =  −2.15(+1.50)D/Å. The values of the force on the proton were calculated exactly and according to the Hellmann–Feynman theorem in each case, and the discrepancies show that none of the wavefunctions used are close to the Hartree–Fock limit, so that the large errors in ke and μ(1) are not surprising. However no difficulties arose in the perturbed Hartree–Fock calculation, so that the application of the theory to more accurate wavefunctions appears quite feasible.

Excited vibrational state microwave spectra, structure, and force-field of trifluorosilane

The J = 2−1 microwave spectrum of six isotopic species of HSiF3 has been observed and assigned in excited states of five of the six fundamental vibrations. The assignment is based on relative intensities, double resonance experiments, and trial anharmonic force constant calculations. Analysis of the spectra leads to experimental values for five of the constants, all three l-doubling constants qt, one Fermi resonance constant φ233, and one zeta constant. The harmonic force field has been refined to all the available data on vibration wavenumbers, centrifugal distortion constants, and zeta constants. The cubic anharmonic force field has been refined to the data on and qt constants, using two models: a valence force model with two cubic force constants for SiH and SiF stretching, and a more sophisticated model. With the help of these calculations, the following equilibrium structure has been determined: re(SiH) = 1.4468(±5) Å, re(SiF) = 1.5624(±1) Å, HSiF = 110.64(±3)°,

The calculation of force constants and normal co-ordinates II: methyl fluoride

The mathematical difficulties which can arise in the force constant refinement procedure for calculating force constants and normal co-ordinates are described and discussed. The method has been applied to the methyl fluoride molecule, using an electronic computer. The best values of the twelve force constants in the most general harmonic potential field were obtained to fit twenty-two independently observed experimental data, these being the six vibration frequencies, three Coriolis zeta constants and two centrifugal stretching constants DJ and DJK, for both CH3F and CD3F. The calculations have been repeated both with and without anharmonicity corrections to the vibration frequencies. All the experimental data were weighted according to the reliability of the observations, and the corresponding standard errors and correlation coefficients of the force constants have been deduced. The final force constants are discussed briefly, and compared with previous treatments, particularly with a recent Urey-Bradley treatment for this molecule.

The anharmonic force field of HCN and HCP

The quadratic, cubic, and quartic force field of HCN has been calculated by a least squares refinement to fit the most recent observed data on the vibration-rotation constants of HCN, DCN and H13CN. All of the observed parameters are fitted within their standard errors of observation. The corresponding parameters for other isotopic species are calculated. For HCP and DCP the more limited data available have been fitted to an anharmonic force field using constraints based on comparison with HCN. Using this force field the zero-point rotational constants B0 have been corrected to obtain the equilibrium constants Be, and hence the equilibrium structure has been determined to be re(CH) = 1•0692(7)A, and re(CP) = 1•5398(2)A.