Extension of spherical nonparametric estimators to nonisotropic kernels: An oceanographic application

In a recently published paper. spherical nonparametric estimators were applied to feature-track ensembles to determine a range of statistics for the atmospheric features considered. This approach obviates the types of bias normally introduced with traditional estimators. New spherical isotropic kernels with local support were introduced. Ln this paper the extension to spherical nonisotropic kernels with local support is introduced, together with a means of obtaining the shape and smoothing parameters in an objective way. The usefulness of spherical nonparametric estimators based on nonisotropic kernels is demonstrated with an application to an oceanographic feature-track ensemble.

Spherical nonparametric estimators applied to the UGAMP model integration for AMIP

The aim of this paper is essentially twofold: first, to describe the use of spherical nonparametric estimators for determining statistical diagnostic fields from ensembles of feature tracks on a global domain, and second, to report the application of these techniques to data derived from a modern general circulation model. New spherical kernel functions are introduced that are more efficiently computed than the traditional exponential kernels. The data-driven techniques of cross-validation to determine the amount elf smoothing objectively, and adaptive smoothing to vary the smoothing locally, are also considered. Also introduced are techniques for combining seasonal statistical distributions to produce longer-term statistical distributions. Although all calculations are performed globally, only the results for the Northern Hemisphere winter (December, January, February) and Southern Hemisphere winter (June, July, August) cyclonic activity are presented, discussed, and compared with previous studies. Overall, results for the two hemispheric winters are in good agreement with previous studies, both for model-based studies and observational studies.

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.

A review of the theoretical basis for bulk mass flux convective parameterization

Most parameterizations for precipitating convection in use today are bulk schemes, in which an ensemble of cumulus elements with different properties is modelled as a single, representative entraining-detraining plume. We review the underpinning mathematical model for such parameterizations, in particular by comparing it with spectral models in which elements are not combined into the representative plume. The chief merit of a bulk model is that the representative plume can be described by an equation set with the same structure as that which describes each element in a spectral model. The equivalence relies on an ansatz for detrained condensate introduced by Yanai et al. (1973) and on a simplified microphysics. There are also conceptual differences in the closure of bulk and spectral parameterizations. In particular, we show that the convective quasi-equilibrium closure of Arakawa and Schubert (1974) for spectral parameterizations cannot be carried over to a bulk parameterization in a straightforward way. Quasi-equilibrium of the cloud work function assumes a timescale separation between a slow forcing process and a rapid convective response. But, for the natural bulk analogue to the cloud-work function (the dilute CAPE), the relevant forcing is characterised by a different timescale, and so its quasi-equilibrium entails a different physical constraint. Closures of bulk parameterization that use the non-entraining parcel value of CAPE do not suffer from this timescale issue. However, the Yanai et al. (1973) ansatz must be invoked as a necessary ingredient of those closures.

Stochastic resonance in a nonlinear model of a rotating, stratified shear flow, with a simple stochastic inertia-gravity wave parameterization

We report on a numerical study of the impact of short, fast inertia-gravity waves on the large-scale, slowly-evolving flow with which they co-exist. A nonlinear quasi-geostrophic numerical model of a stratified shear flow is used to simulate, at reasonably high resolution, the evolution of a large-scale mode which grows due to baroclinic instability and equilibrates at finite amplitude. Ageostrophic inertia-gravity modes are filtered out of the model by construction, but their effects on the balanced flow are incorporated using a simple stochastic parameterization of the potential vorticity anomalies which they induce. The model simulates a rotating, two-layer annulus laboratory experiment, in which we recently observed systematic inertia-gravity wave generation by an evolving, large-scale flow. We find that the impact of the small-amplitude stochastic contribution to the potential vorticity tendency, on the model balanced flow, is generally small, as expected. In certain circumstances, however, the parameterized fast waves can exert a dominant influence. In a flow which is baroclinically-unstable to a range of zonal wavenumbers, and in which there is a close match between the growth rates of the multiple modes, the stochastic waves can strongly affect wavenumber selection. This is illustrated by a flow in which the parameterized fast modes dramatically re-partition the probability-density function for equilibrated large-scale zonal wavenumber. In a second case study, the stochastic perturbations are shown to force spontaneous wavenumber transitions in the large-scale flow, which do not occur in their absence. These phenomena are due to a stochastic resonance effect. They add to the evidence that deterministic parameterizations in general circulation models, of subgrid-scale processes such as gravity wave drag, cannot always adequately capture the full details of the nonlinear interaction.

Ruthenium complexes of C,C '-bis(ethynyl)carboranes: an investigation of electronic interactions mediated by spherical pseudo-aromatic spacers

The complexes [Ru(1-C=C-1,10-C2B8H9)(dppe)Cp*] (3a), [Ru(1-C C-1,12-C2B10H11)(dppe)-Cp*] (3b), [{Ru(dppe)Cp*}(2){mu-1,10-(C C)(2)-1,10-C2B8H8}] (4a) and [{Ru(dppe)Cp*}(2){mu-1,12-(C C)2- 1,12-C2B10-H-10}] (4b), which form a representative series of mono- and bimetallic acetylide complexes featuring 10- and 12-vertex carboranes embedded within the dethynyl bridging ligand, have been prepared and structurally characterized. In addition, these compounds have been examined spectroscopically (UV-is-NIR, IR) in all accessible redox states. The significant separation of the two, one-electron anodic waves observed in the cyclic voltammograms of the bimetallic complexes 4a and 4b is largely independent of the nature of the electrolyte and is attributed to stabilization of the intermediate redox products [4a](+) and [4b](+) through interactions between the metal centers across a distance of ca. 12.5 angstrom. The mono-oxidized bimetallic complexes (4a](+) and [4b](+) exhibit spectroscopic properties consistent with a description of these species in terms of valence-localized (class II) mixed-valence compounds, including a unique low-energy electronic absorption band, attributed to an, IVCT-type transition that tails into the IR region. DFT calculations with model systems [4a-H](+) and [4b-H](+) featuring simplified ligand sets reproduce the observed spectroscopic data and localized electronic structures for the mixed-valence cations [4a](+) and [4b](+).

pH-mediated interactions between poly(acrylic acid) and methylcellulose in the formation of ultrathin multilayered hydrogels and spherical nanoparticles

Poly(acrylic acid) forms insoluble hydrogen-bonded interpolymer complexes with methylcellulose in aqueous solutions under acidic conditions. In this work the reaction heats and binding constants were determined for the complexation between poly(acrylic acid) and methylcellulose by isothermal titration calorimetry at different pH and findings are correlated with the aggregation processes occurring in this system. The principal contribution to the complexation heat results from primary polycomplex particle aggregation. Transmission electron microscopy of nanoparticles produced at pH 1.4 and 2.4 demonstrated that they are spherical and dense structures. The nanoparticles ranged from 80 to 200 nm, whereas particles formed at pH 3.2 were 20-30 nm and were stabilized against aggregation by a network of uncomplexed macromolecules. For the first time, multilayered materials were developed on the basis of hydrogen-bonded complexes of poly(acrylic acid) and methylcellulose using layer-by-layer deposition on a glass surface. The thickness of these films was a linear function of the number of deposition cycles. The materials were subsequently cross-linked by thermal treatment, resulting in ultrathin hydrogels which detached from the glass substrate upon swelling. The swelling capacity of ultrathin hydrogels differed from the swelling of the thicker films of a similar chemical composition.

Oriented vehicles travelling in spherical space

This paper tackles the path planning problem for oriented vehicles travelling in the non-Euclidean 3-Dimensional space; spherical space S3. For such problem, the orientation of the vehicle is naturally represented by orthonormal frame bundle; the rotation group SO(4). Orthonormal frame bundles of space forms coincide with their isometry groups and therefore the focus shifts to control systems defined on Lie groups. The oriented vehicles, in this case, are constrained to travel at constant speed in a forward direction and their angular velocities directly controlled. In this paper we identify controls that induce steady motions of these oriented vehicles and yield closed form parametric expressions for these motions. The paths these vehicles trace are defined explicitly in terms of the controls and therefore invariant with respect to the coordinate system used to describe the motion.

An Efficient Parameterization of Dynamic Neural Networks for Nonlinear System Identification

Dynamic neural networks (DNNs), which are also known as recurrent neural networks, are often used for nonlinear system identification. The main contribution of this letter is the introduction of an efficient parameterization of a class of DNNs. Having to adjust less parameters simplifies the training problem and leads to more parsimonious models. The parameterization is based on approximation theory dealing with the ability of a class of DNNs to approximate finite trajectories of nonautonomous systems. The use of the proposed parameterization is illustrated through a numerical example, using data from a nonlinear model of a magnetic levitation system.