The equilibrium structure of HCN

The equilibrium structure of HCN has been determined from the previously published ground state rotational constants of eight isotopomers by using (B0‐Be) values obtained from a variational calculation of the vibration–rotation spectrum. The results are re(CH)=1.065 01(8) Å, and re(CN)=1.153 24(2) Å.

A stochastic parameterization for deep convection based on equilibrium statistics

A stochastic parameterization scheme for deep convection is described, suitable for use in both climate and NWP models. Theoretical arguments and the results of cloud-resolving models, are discussed in order to motivate the form of the scheme. In the deterministic limit, it tends to a spectrum of entraining/detraining plumes and is similar to other current parameterizations. The stochastic variability describes the local fluctuations about a large-scale equilibrium state. Plumes are drawn at random from a probability distribution function (pdf) that defines the chance of finding a plume of given cloud-base mass flux within each model grid box. The normalization of the pdf is given by the ensemble-mean mass flux, and this is computed with a CAPE closure method. The characteristics of each plume produced are determined using an adaptation of the plume model from the Kain-Fritsch parameterization. Initial tests in the single column version of the Unified Model verify that the scheme is effective in producing the desired distributions of convective variability without adversely affecting the mean state.

Does reactive surface area depend on grain size? Results from pH 3, 25 circle C far-from-equilibrium flow-through dissolution experiments on anorthite and biotite

Laboratory determined mineral weathering rates need to be normalised to allow their extrapolation to natural systems. The principle normalisation terms used in the literature are mass, and geometric- and BET specific surface area (SSA). The purpose of this study was to determine how dissolution rates normalised to these terms vary with grain size. Different size fractions of anorthite and biotite ranging from 180-150 to 20-10 mu m were dissolved in pH 3, HCl at 25 degrees C in flow through reactors under far from equilibrium conditions. Steady state dissolution rates after 5376 h (anorthite) and 4992 h (biotite) were calculated from Si concentrations and were normalised to initial- and final- mass and geometric-, geometric edge- (biotite), and BET SSA. For anorthite, rates normalised to initial- and final-BET SSA ranged from 0.33 to 2.77 X 10(-10) mol(feldspar) m(-2) s(-1), rates normalised to initial- and final-geometric SSA ranged from 5.74 to 8.88 X 10(-10) mol(feldspar) m(-2) s(-1) and rates normalised to initial- and final-mass ranged from 0.11 to 1.65 mol(feldspar) g(-1) s(-1). For biotite, rates normalised to initial- and final-BET SSA ranged from 1.02 to 2.03 X 10(-12) mol(biotite) m(-2) s(-1), rates normalised to initial- and final-geometric SSA ranged from 3.26 to 16.21 X 10(-12) mol(biotite) m(-2) s(-1), rates normalised to initial- and final-geometric edge SSA ranged from 59.46 to 111.32 x 10(-12) mol(biotite) m(-2) s(-1) and rates normalised to initial- and final-mass ranged from 0.81 to 6.93 X 10(-12) mol(biotite) g(-1) s(-1). For all normalising terms rates varied significantly (p <= 0.05) with grain size. The normalising terms which gave least variation in dissolution rate between grain sizes for anorthite were initial BET SSA and initial- and final-geometric SSA. This is consistent with: (1) dissolution being dominated by the slower dissolving but area dominant non-etched surfaces of the grains and, (2) the walls of etch pits and other dissolution features being relatively unreactive. These steady state normalised dissolution rates are likely to be constant with time. Normalisation to final BET SSA did not give constant ratios across grain size due to a non-uniform distribution of dissolution features. After dissolution coarser grains had a greater density of dissolution features with BET-measurable but unreactive wall surface area than the finer grains. The normalising term which gave the least variation in dissolution rates between grain sizes for biotite was initial BET SSA. Initial- and final-geometric edge SSA and final BET SSA gave the next least varied rates. The basal surfaces dissolved sufficiently rapidly to influence bulk dissolution rate and prevent geometric edge SSA normalised dissolution rates showing the least variation. Simple modelling indicated that biotite grain edges dissolved 71-132 times faster than basal surfaces. In this experiment, initial BET SSA best integrated the different areas and reactivities of the edge and basal surfaces of biotite. Steady state dissolution rates are likely to vary with time as dissolution alters the ratio of edge to basal surface area. Therefore they would be more properly termed pseudo-steady state rates, only appearing constant because the time period over which they were measured (1512 h) was less than the time period over wich they would change significantly. (c) 2006 Elsevier Inc. All rights reserved.

Salt marsh morphodynamics: An investigation of tidal flows and marsh channel equilibrium

Although numerous field studies have evaluated flow and transport processes in salt marsh channels, the overall role of channels in delivering and removing material from salt marsh platforms is still poorly characterised. In this paper, we consider this issue based on a numerical hydrodynamic model for a prototype marsh system and on a field survey of the cross-sectional geometry of a marsh channel network. Results of the numerical simulations indicate that the channel transfers approximately three times the volume of water that would be estimated from mass balance considerations alone. Marsh platform roughness exerts a significant influence on the partitioning of discharge between the channel and the marsh platform edge, alters flow patterns on the marsh platform due to its effects on channel-to-platform transfer and also controls the timing of peak discharge relative to marsh-edge overtopping. Although peak channel discharges and velocities are associated with the flood tide and marsh inundation, a larger volume of water is transferred by the channel during ebb flows, a portion of which transfer takes place after the tidal height is below the marsh platform. Detailed surveys of the marsh channels crossing a series of transects at Upper Stiffkey Marsh, north Norfolk, England, show that the total channel cross-sectional area increases linearly with catchment area in the inner part of the marsh, which is consistent with the increase in shoreward tidal prism removed by the channels. Toward the marsh edge, however, a deficit in the total cross-sectional area develops, suggesting that discharge partitioning between the marsh channels and the marsh platform edge may also be expressed in the morphology of marsh channel systems.

Fast approximate calculation of multiply scattered lidar returns

An efficient method is described for the approximate calculation of the intensity of multiply scattered lidar returns. It divides the outgoing photons into three populations, representing those that have experienced zero, one, and more than one forward-scattering event. Each population is parameterized at each range gate by its total energy, its spatial variance, the variance of photon direction, and the covariance, of photon direction and position. The result is that for an N-point profile the calculation is O(N-2) efficient and implicitly includes up to N-order scattering, making it ideal for use in iterative retrieval algorithms for which speed is crucial. In contrast, models that explicitly consider each scattering order separately are at best O(N-m/m!) efficient for m-order scattering and often cannot be performed to more than the third or fourth order in retrieval algorithms. For typical cloud profiles and a wide range of lidar fields of view, the new algorithm is as accurate as an explicit calculation truncated at the fifth or sixth order but faster by several orders of magnitude. (C) 2006 Optical Society of America.

Mesoscale simulations of organized convection: importance of convective equilibrium

The validity of convective parametrization breaks down at the resolution of mesoscale models, and the success of parametrized versus explicit treatments of convection is likely to depend on the large-scale environment. In this paper we examine the hypothesis that a key feature determining the sensitivity to the environment is whether the forcing of convection is sufficiently homogeneous and slowly varying that the convection can be considered to be in equilibrium. Two case studies of mesoscale convective systems over the UK, one where equilibrium conditions are expected and one where equilibrium is unlikely, are simulated using a mesoscale forecasting model. The time evolution of area-average convective available potential energy and the time evolution and magnitude of the timescale of convective adjustment are consistent with the hypothesis of equilibrium for case 1 and non-equilibrium for case 2. For each case, three experiments are performed with different partitionings between parametrized and explicit convection: fully parametrized convection, fully explicit convection and a simulation with significant amounts of both. In the equilibrium case, bulk properties of the convection such as area-integrated rain rates are insensitive to the treatment of convection. However, the detailed structure of the precipitation field changes; the simulation with parametrized convection behaves well and produces a smooth field that follows the forcing region, and the simulation with explicit convection has a small number of localized intense regions of precipitation that track with the mid-levelflow. For the non-equilibrium case, bulk properties of the convection such as area-integrated rain rates are sensitive to the treatment of convection. The simulation with explicit convection behaves similarly to the equilibrium case with a few localized precipitation regions. In contrast, the cumulus parametrization fails dramatically and develops intense propagating bows of precipitation that were not observed. The simulations with both parametrized and explicit convection follow the pattern seen in the other experiments, with a transition over the duration of the run from parametrized to explicit precipitation. The impact of convection on the large-scaleflow, as measured by upper-level wind and potential-vorticity perturbations, is very sensitive to the partitioning of convection for both cases. © Royal Meteorological Society, 2006. Contributions by P. A. Clark and M. E. B. Gray are Crown Copyright.

The calculation of force constants and normal coordinates IV: XH4 and XH3 molecules

Normal coordinate calculations of XH4 and XH3 molecules are reviewed and discussed. It is shown that for most of these molecules the true values of the force constants in the most General Harmonic Force Field can be uniquely determined only by making use of vibration-rotation interaction constants. It is emphasized that without these extra data the GFF is not determined. The results are compared with various model force fields for these molecules.

The calculation of accurate normal coordinates I: general theory, and application to methane

The calculation of accurate and reliable vibrational potential functions and normal co-ordinates is discussed, for such simple polyatomic molecules as it may be possible. Such calculations should be corrected for the effects of anharmonicity and of resonance interactions between the vibrational states, and should be fitted to all the available information on all isotopic species: particularly the vibrational frequencies, Coriolis zeta constants and centrifugal distortion constants. The difficulties of making these corrections, and of making use of the observed data are reviewed. A programme for the Ferranti Mercury Computer is described by means of which harmonic vibration frequencies and normal co-ordinate vectors, zeta factors and centrifugal distortion constants can be calculated, from a given force field and from given G-matrix elements, etc. The programme has been used on up to 5 × 5 secular equations for which a single calculation and output of results takes approximately l min; it can readily be extended to larger determinants. The best methods of using such a programme and the possibility of reversing the direction of calculation are discussed. The methods are applied to calculating the best possible vibrational potential function for the methane molecule, making use of all the observed data.

A refined quartic forcefield for acetylene: accurate calculation of the vibrational spectrum

It is now possible to calculate the nine-dimensional rovibrational wavefunctions of sequentially bonded four-atom molecules variationally without dynamical approximation. In the case of HCCH, the simplest such molecule, many hundreds of rovibrational (J = 0, 1, 2) levels can be converged to better than 1.5 cm −1. Variational calculations of this kind are used here systematically to refine the well-known quartic valence-coordinate forcefleld of Strey and Mills [J.Mol. Spectrosc.59, 103-115 (1976)] against experimental term values up to three C-H stretch quanta for the principal and two deuterated isotopomers, yielding a new surface that reproduces the energies of all the known Σ, Π, and Δ states of these species up to the energy of two C-H stretch quanta with an rms error of 3 cm−1 . The refined forcefield is used to study the resonances associated with the accidental degeneracies (ν2 + ν4 + ν5, ν3) and (ν2 + 2ν5, ν1) in the principal isotopomer, leading to a clarification of the assignment of she experimentally detected states in the 2ν3 and 3ν3, polyads, and to the finding that vibrational Coriolis (kinetic energy) terms, rather than quartic anharmonicities in the potential, are the primary cause of the resonant interactions. Using a new cubic ab initio electric dipole field to calculate IR absorption coefficients, 24 undetected Σ and Π states of 1H12C12C1H and 5 undetected Σ states of D12C12CD are identified as candidates for experimental study, and their calculated energies and assignments are given.

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 calculation of force constants and normal coordinates III: constrained force fields for the methyl halides

A method is discussed for imposing any desired constraint on the force field obtained in a force constant refinement calculation. The application of this method to force constant refinement calculations for the methyl halide molecules is reported. All available data on the vibration frequencies, Coriolis interaction constants and centrifugal stretching constants of CH3X and CD3X molecules were used in the refinements, but despite this apparent abundance of data it was found that constraints were necessary in order to obtain a unique solution to the force field. The results of unconstrained calculations, and of three different constrained calculations, are reported in this paper. The constrained models reported are a Urey—Bradley force field, a modified valence force field, and a constraint based on orbital-following bond-hybridization arguments developed in the following paper. The results are discussed, and compared with previous results for these molecules. The third of the above models is found to reproduce the observed data better than either of the first two, and additional reasons are given for preferring this solution to the force field for the methyl halide molecules.