Can wavelets improve the representation of forecast error covariances in variational data assimilation?

Two wavelet-based control variable transform schemes are described and are used to model some important features of forecast error statistics for use in variational data assimilation. The first is a conventional wavelet scheme and the other is an approximation of it. Their ability to capture the position and scale-dependent aspects of covariance structures is tested in a two-dimensional latitude-height context. This is done by comparing the covariance structures implied by the wavelet schemes with those found from the explicit forecast error covariance matrix, and with a non-wavelet- based covariance scheme used currently in an operational assimilation scheme. Qualitatively, the wavelet-based schemes show potential at modeling forecast error statistics well without giving preference to either position or scale-dependent aspects. The degree of spectral representation can be controlled by changing the number of spectral bands in the schemes, and the least number of bands that achieves adequate results is found for the model domain used. Evidence is found of a trade-off between the localization of features in positional and spectral spaces when the number of bands is changed. By examining implied covariance diagnostics, the wavelet-based schemes are found, on the whole, to give results that are closer to diagnostics found from the explicit matrix than from the nonwavelet scheme. Even though the nature of the covariances has the right qualities in spectral space, variances are found to be too low at some wavenumbers and vertical correlation length scales are found to be too long at most scales. The wavelet schemes are found to be good at resolving variations in position and scale-dependent horizontal length scales, although the length scales reproduced are usually too short. The second of the wavelet-based schemes is often found to be better than the first in some important respects, but, unlike the first, it has no exact inverse transform.

The representation of conditional expectations of non-Gaussian noise

For Wiener spaces conditional expectations and $L^{2}$-martingales w.r.t. the natural filtration have a natural representation in terms of chaos expansion. In this note an extension to larger classes of processes is discussed. In particular, it is pointed out that orthogonality of the chaos expansion is not required.

Devolution and the political representation of business interests in the UK

The devolution of political power in Scotland, Wales and Northern Ireland and the developing regional agenda in England are widely read as a significant reconfiguration of the institutions and scales of economic governance. The process is furthest developed in Scotland while Wales and Northern Ireland, in their own distinct ways, provide intermediate cases. Devolution is least developed in England where regional political identities are generally weak and the historical legacy of regional institutions is limited. Within the overall context of devolution government policy has continued to emphasize partnership forms of. governance. Accordingly, the political representation of business interests has a particular salience in the new arrangements. This paper reports on findings from a study designed to examine the relationship between devolution and changes in the political representation of business interests in the territories and regions of the UK. It highlights a number of changes in the nature and extent of business representation. While some of these are significant the evidence suggests that they fail to mark a fundamental shift in the institutional foundation for sub-national business interest representation in the UK. Indeed the political geography of business representation remains dominated by an overarching centralism that is likely to provide a significant check on the further devolution of political power and democratic authority. (c) 2004 Elsevier Ltd. All rights reserved.

Devolution and the political representation of business interests in the UK

The devolution of political power in Scotland, Wales and Northern Ireland and the developing regional agenda in England are widely read as a significant reconfiguration of the institutions and scales of economic governance. The process is furthest developed in Scotland while Wales and Northern Ireland, in their own distinct ways, provide intermediate cases. Devolution is least developed in England where regional political identities are generally weak and the historical legacy of regional institutions is limited. Within the overall context of devolution government policy has continued to emphasize partnership forms of. governance. Accordingly, the political representation of business interests has a particular salience in the new arrangements. This paper reports on findings from a study designed to examine the relationship between devolution and changes in the political representation of business interests in the territories and regions of the UK. It highlights a number of changes in the nature and extent of business representation. While some of these are significant the evidence suggests that they fail to mark a fundamental shift in the institutional foundation for sub-national business interest representation in the UK. Indeed the political geography of business representation remains dominated by an overarching centralism that is likely to provide a significant check on the further devolution of political power and democratic authority. (c) 2004 Elsevier Ltd. All rights reserved.

Spin spaces and positive decomposition of linear maps on ordered Banach spaces

Spin factors and generalizations are used to revisit positive generation of B(E, F), where E and F are ordered Banach spaces. Interior points of B(E, F)+ are discussed and in many cases it is seen that positive generation of B(E, F) is controlled by spin structure in F when F is a JBW-algebra.

Evaluation of the model representation of the evolution of convective systems using satellite observations of outgoing longwave radiation

We introduce a technique for assessing the diurnal development of convective storm systems based on outgoing longwave radiation fields. Using the size distribution of the storms measured from a series of images, we generate an array in the lengthscale-time domain based on the standard score statistic. It demonstrates succinctly the size evolution of storms as well as the dissipation kinematics. It also provides evidence related to the temperature evolution of the cloud tops. We apply this approach to a test case comparing observations made by the Geostationary Earth Radiation Budget instrument to output from the Met Office Unified Model run at two resolutions. The 12km resolution model produces peak convective activity on all lengthscales significantly earlier in the day than shown by the observations and no evidence for storms growing in size. The 4km resolution model shows realistic timing and growth evolution although the dissipation mechanism still differs from the observed data.

A mechanistic study of the low pressure pyrolysis of linear siloxanes

Matrix isolation IR spectroscopy has been used to study the vacuum pyrolysis of 1,1,3,3-tetramethyldisiloxane (L1), 1,1,3,3,5,5-hexamethyltrisiloxane (L2) and 3H,5H-octamethyltetrasiloxane (L3) at ca. 1000 K in a flow reactor at low pressures. The hydrocarbons CH3, CH4, C2H2, C2H4, and C2H6 were observed as prominent pyrolysis products in all three systems, and amongst the weaker features are bands arising from the methylsilanes Me2SiH2 (for L1 and L2) and Me3SiH (for L3). The fundamental of SiO was also observed very weakly. By use of quantum chemical calculations combined with earlier kinetic models, mechanisms have been proposed involving the intermediacy of silanones Me2Si = O and MeSiH = O. Model calculations on the decomposition pathways of H3SiOSiH3 and H3SiOSiH2OSiH3 show that silanone elimination is favoured over silylene extrusion.

Alternative syntheses of linear polyurethanes using masked isocyanate monomers

A range of linear polyurethanes featuring aliphatic, aromatic and ether residues have been prepared by co-polymerisation of novel 'masked' isocyanate A(2)-type monomers and diols. The reactive isocyanate monomers were generated in situ via the triphenylphosphine mediated decomposition of the heterocyclic disulfide, 1,2,4-dithiazolidine-3,5-dione. Two different synthetic approaches were examined and assessed for the construction of the novel A(2)-type monomers, which involved either coupling two 1,2,4-dithiazolidine-3,5-diones together through a spacer group or construction of 1,2,4-dithiazolidine-3,5-diones directly from diamines. The resulting polyurethanes were purified via solvent extraction and analysed using GPC, NMR and IR spectroscopic analyses. Molecular weight data were obtained and compared from both GPC and H-1 NMR (via end-group analysis) spectroscopic analysis. The thermal properties of the polyurethanes were determined using DSC and their solubility in common aprotic organic solvents was also assessed and related to their structural composition. (c) 2006 Elsevier B.V. All rights reserved.

Facile strategies for the synthesis and crystallization of linear trinuclear nickel(II)-Schiff base, complexes with carboxylate bridges: Tuning of coordination geometry and magnetic properties

Three new linear trinuclear nickel(II) complexes, [Ni-3(salpen)(2)(OAc)(2)(H2O)(2)]center dot 4H(2)O (1) (OAc = acetate, CH3COO-), [Ni-3(salpen)(2)(OBz)(2)] (2) (OBz=benzoate, PhCOO-) and [Ni-3(salpen)(2)(OCn)(2)(CH3CN)(2)] (4) (OCn = cinnamate, PhCH=CHCOO-), H(2)salpen = tetradentate ligand, N,N'-bis(salicylidene)-1,3-pentanediamine have been synthesized and characterized structurally and magnetically. The choice of solvent for growing single crystal was made by inspecting the morphology of the initially obtained solids with the help of SEM study. The magnetic properties of a closely related complex, [Ni-3(salpen)(2)(OPh)(2)(EtOH)] (3) (OPh = phenyl acetate, PhCH2COO-) whose structure and solution properties have been reported recently, has also been studied here. The structural analyses reveal that both phenoxo and carboxylate bridging are present in all the complexes and the three Ni(II) atoms remain in linear disposition. Although the Schiff base ligand and the syn-syn bridging bidentate mode of the carboxylate group remain the same in complexes 1-4, the change of alkyl/aryl group of the carboxylates brings about systematic variations between six- and five-coordination in the geometry of the terminal Ni(II) centres of the trinuclear units. The steric demand as well as hydrophobic nature of the alkyl/aryl group of the carboxylate is found to play a crucial role in the tuning of the geometry. Variable-temperature (2-300 K) magnetic susceptibility measurements show that complexes 1-4 are antiferromagnetically coupled (J = -3.2(1), -4.6(1). -3.2(1) and -2.8(1) cm(-1) in 1-4, respectively). Calculations of the zero-field splitting parameter indicate that the values of D for complexes 1-4 are in the high range (D = +9.1(2), +14.2(2), +9.8(2) and +8.6(1) cm(-1) for 1-4, respectively). The highest D value of +14.2(2) and +9.8(2) cm(-1) for complexes 2 and 3, respectively, are consistent with the pentacoordinated geometry of the two terminal nickel(II) ions in 2 and one terminal nickel(II) ion in 3. (C) 2009 Elsevier Ltd. All rights reserved.