Very large inverse problems in atmosphere and ocean modelling

For the very large nonlinear dynamical systems that arise in a wide range of physical, biological and environmental problems, the data needed to initialize a numerical forecasting model are seldom available. To generate accurate estimates of the expected states of the system, both current and future, the technique of ‘data assimilation’ is used to combine the numerical model predictions with observations of the system measured over time. Assimilation of data is an inverse problem that for very large-scale systems is generally ill-posed. In four-dimensional variational assimilation schemes, the dynamical model equations provide constraints that act to spread information into data sparse regions, enabling the state of the system to be reconstructed accurately. The mechanism for this is not well understood. Singular value decomposition techniques are applied here to the observability matrix of the system in order to analyse the critical features in this process. Simplified models are used to demonstrate how information is propagated from observed regions into unobserved areas. The impact of the size of the observational noise and the temporal position of the observations is examined. The best signal-to-noise ratio needed to extract the most information from the observations is estimated using Tikhonov regularization theory. Copyright © 2005 John Wiley & Sons, Ltd.

Sonogashira coupling on an extended gold surface in vacuo: reaction of phenylacetylene with iodobenzene on Au(111)

Temperature-programmed reaction measurements supported by scanning tunneling microscopy have shown that phenylacetylene and iodobenzene react on smooth Au(111) under vacuum conditions to yield biphenyl and diphenyldiacetylene, the result of homocoupling of the reactant molecules. They also produce diphenylacetylene, the result of Sonogashira cross-coupling, prototypical of a class of reactions that are of paramount importance in synthetic organic chemistry and whose mechanism remains controversial. Roughened Au(111) is completely inert toward all three reactions, indicating that the availability of crystallographically well-defined adsorption sites is crucially important. High-resolution X-ray photoelectron spectroscopy and near-edge X-ray absorption fine structure spectroscopy show that the reactants are initially present as intact, essentially flat-lying molecules and that the temperature threshold for Sonogashira coupling coincides with that for C−I bond scission in the iodobenzene reactant. The fractional-order kinetics and low temperature associated with desorption of the Sonogashira product suggest that the reaction occurs at the boundaries of islands of adsorbed reactants and that its appearance in the gas phase is rate-limited by the surface reaction. These findings demonstrate unambiguously and for the first time that this heterogeneous cross-coupling chemistry is an intrinsic property of extended, metallic pure gold surfaces: no other species, including solvent molecules, basic or charged (ionic) species are necessary to mediate the process.

Time-resolved gas-phase kinetic and quantum chemical studies of the reaction of silylene with oxygen

Time-resolved kinetic studies of the reaction of silylene, SiH2, generated by laser flash photolysis of phenylsilane, have been carried out to obtain rate constants for its bimolecular reaction with O-2. The reaction was studied in the gas phase over the pressure range 1-100 Torr in SF6 bath gas, at five temperatures in the range 297-600 K. The second order rate constants at 10 Torr were fitted to the Arrhenius equation: log(k/cm(3) molecule(-1) s(-1)) = (-11.08 +/- 0.04) + (1.57 +/- 0.32 kJ mol(-1))/RT ln10 The decrease in rate constant values with increasing temperature, although systematic is very small. The rate constants showed slight increases in value with pressure at each temperature, but this was scarcely beyond experimental uncertainty. From estimates of Lennard-Jones collision rates, this reaction is occurring at ca. 1 in 20 collisions, almost independent of pressure and temperature. Ab initio calculations at the G3 level backed further by multi-configurational (MC) SCF calculations, augmented by second order perturbation theory (MRMP2), support a mechanism in which the initial adduct, H2SiOO, formed in the triplet state (T), undergoes intersystem crossing to the more stable singlet state (S) prior to further low energy isomerisation processes leading, via a sequence of steps, ultimately to dissociation products of which the lowest energy pair are H2O + SiO. The decomposition of the intermediate cyclo-siladioxirane, via O-O bond fission, plays an important role in the overall process. The bottleneck for the overall process appears to be the T -> S process in H2SiOO. This process has a small spin orbit coupling matrix element, consistent with an estimate of its rate constant of 1 x 10(9) s(-1) obtained with the aid of RRKM theory. This interpretation preserves the idea that, as in its reactions in general, SiH2 initially reacts at the encounter rate with O-2. The low values for the secondary reaction barriers on the potential energy surface account for the lack of an observed pressure dependence. Some comparisons are drawn with the reactions of CH2 + O-2 and SiCl2 + O-2.

The addition reaction between silylene and ethyne: further isotope studies, pressure dependence studies, and quantum chemical calculations

Time-resolved kinetic studies of the reaction of dideutero-silylene, SiD2, generated by laser flash photolysis of phenylsilane-d(3), have been carried out to obtain rate constants for its bimolecular reaction with C2H2. The reaction was studied in the gas phase over the pressure range 1-100 Torr in SF6 bath gas, at five temperatures in the range 297-600 K. The second-order rate constants obtained by extrapolation to the high-pressure limits at each temperature fitted the Arrhenius equation log(k(infinity)/cm(3) molecule(-1) s(-1)) = (-10.05 +/- 0.05) + (3.43 +/- 0.36 kJ mol(-1))/RT ln 10. The rate constants were used to obtain a comprehensive set of isotope effects by comparison with earlier obtained rate constants for the reactions of SiH2 with C2H2 and C2D2. Additionally, pressure-dependent rate constants for the reaction of SiH2 with C2H2 in the presence of He (1-100 Tort) were obtained at 300, 399, and 613 K. Quantum chemical (ab initio) calculations of the SiC2H4 reaction system at the G3 level support the initial formation of silirene, which rapidly isomerizes to ethynylsilane as the major pathway. Reversible formation of vinylsilylene is also an important process. The calculations also indicate the involvement of several other intermediates, not previously suggested in the mechanism. RRKM calculations are in semiquantitative agreement with the pressure dependences and isotope effects suggested by the ab initio calculations, but residual discrepancies suggest the possible involvement of the minor reaction channel, SiH2 + C2H2 - SWPO + C2H4. The results are compared and contrasted with previous studies of this reaction system.

Investigation of the prototype silylene reaction, SiH2+H2O(and D2O): time-resolved gas-phase kinetic studies, isotope effects, RRKM calculations, and quantum chemical calculations of the reaction energy surface

Time-resolved kinetic studies of the reaction of silylene, SiH2, with H2O and with D2O have been carried out in the gas phase at 296 and at 339 K, using laser flash photolysis to generate and monitor SiH2. The reaction was studied over the pressure range 10-200 Torr with SF6 as bath gas. The second-order rate constants obtained were pressure dependent, indicating that the reaction is a third-body assisted association process. Rate constants at 339 K were about half those at 296 K. Isotope effects, k(H)/k(D), were small averaging 1.076 0.080, suggesting no involvement of H- (or D-) atom transfer in the rate determining step. RRKM modeling was undertaken based on a transition state appropriate to formation of the expected zwitterionic donoracceptor complex, H2Si...OH2. Because the reaction is close to the low pressure (third order) region, it is difficult to be definitive about the activated complex structure. Various structures were tried, both with and without the incorporation of rotational modes, leading to values for the high-pressure limiting (i.e., true secondorder) rate constant in the range 9.5 x 10(-11) to 5 x 10(-10) cm(3) molecule' s(-1). The RRKM modeling and mechanistic interpretation is supported by ab initio quantum calculations carried out at the G2 and G3 levels. The results are compared and contrasted with the previous studies.

Development of a process for the production and purification of alpha- and beta-galactooligosaccharides from Bifobacterium bifidum NCIMB 41171

Synthesis of prebiotic alpha- and beta-galactooligosaccharides (GOS) using the whole cells of Bifidobacterium bifidum NCIMB 41171 was investigated. Determination of alpha- and beta-galactosidase activities showed them to be at 3 and 205 g(-1) of freeze dried biomass, respectively, and they increased to 5 and 344 U g(-1), respectively, when cells were treated with toluene. Starting with 450-500 mg mL(-1) lactose, maximum GOS concentrations were observed at 80-85% lactose conversions and the mixtures contained oligosaccharides (with a degree of polymerisation >= 3) at 77-109 mg mL(-1) and trans-galactosylated disaccharides between 85-115 mg mL(-1). The GOS yield values varied between 36% and 43%. An alpha-linked disaccharide was detected and its presence was confirmed by gas chromatography mass spectroscopy. Cells were re-used up to 8 times without changes in reaction times or the substrate conversions to GOS. Oligosaccharide synthesis was not inhibited by the presence of glucose or galactose. The mixtures were successfully purified from glucose (92% of glucose removed) by fermentation with Saccharomyces cerevisiae with no losses in the oligosaccharide content and only a small decrease on the galactose. (c) 2006 Elsevier Ltd. All rights reserved.

Time-resolved gas-phase kinetic study of the germylene addition reaction, GeH2 + C2D2

Time-resolved studies of germylene, GeH2, generated by laser. ash photolysis of 3,4-dimethyl-1-germacyclopent-3-ene, have been carried out to obtain rate coefficients for its bimolecular reaction with C2D2. The reaction was studied in the gas phase, mainly at a total pressure of 1.3 kPa (in SF6 bath gas) at five temperatures in the range 298-558 K. Pressure variation measurements over the range 0.13-13 kPa ( SF6) at 298, 397 and 558 K revealed a small pressure dependence but only at 558 K. After correction for this, the second-order rate coefficients gave the Arrhenius equation: log(k(infinity)/cm(3) molecule(-1) s(-1)) = (-10.96 +/- 0.05) + ( 6.16 +/- 0.37 kJ mol(-1))/RT ln 10 Comparison with the reaction of GeH2 + C2H2 (studied earlier) showed a similar behaviour with almost identical rate coefficients. The lack of a significant isotope effect is consistent with a rate-determining addition process and is explained by irreversible decomposition of the reaction intermediate to give Ge(P-3) + C2H4. This result contrasts with that for GeH2 + C2H4/C2D4 and those for the analogous silylene reactions. The underlying reasons for this are discussed.

The gas-phase reaction between silylene and 2-butyne: kinetics, isotope studies, pressure dependence studies and quantum chemical calculations

Time-resolved kinetic studies of the reactions of silylene, SiH2, and dideutero-silylene, SiD2, generated by laser. ash photolysis of phenylsilane and phenylsilane-d(3), respectively, have been carried out to obtain rate coefficients for their bimolecular reactions with 2-butyne, CH3C CCH3. The reactions were studied in the gas phase over the pressure range 1-100 Torr in SF6 bath gas at five temperatures in the range 294-612 K. The second-order rate coefficients, obtained by extrapolation to the high pressure limits at each temperature, fitted the Arrhenius equations where the error limits are single standard deviations: log(k(H)(infinity)/cm(3) molecule(-1) s(-1)) = (-9.67 +/- 0.04) + (1.71 +/- 0.33) kJ mol(-1)/RTln10 log(k(D)(infinity)/cm(3) molecule(-1) s(-1)) = (-9.65 +/- 0.01) + (1.92 +/- 0.13) kJ mol(-1)/RTln10 Additionally, pressure-dependent rate coefficients for the reaction of SiH2 with 2-butyne in the presence of He (1-100 Torr) were obtained at 301, 429 and 613 K. Quantum chemical (ab initio) calculations of the SiC4H8 reaction system at the G3 level support the formation of 2,3-dimethylsilirene [cyclo-SiH2C(CH3)=C(CH3)-] as the sole end product. However, reversible formation of 2,3-dimethylvinylsilylene [CH3CH=C(CH3)SiH] is also an important process. The calculations also indicate the probable involvement of several other intermediates, and possible products. RRKM calculations are in reasonable agreement with the pressure dependences at an enthalpy value for 2,3-dimethylsilirene fairly close to that suggested by the ab initio calculations. The experimental isotope effects deviate significantly from those predicted by RRKM theory. The differences can be explained by an isotopic scrambling mechanism, involving H - D exchange between the hydrogens of the methyl groups and the D-atoms in the ring in 2,3-dimethylsilirene-1,1-d(2). A detailed mechanism involving several intermediate species, which is consistent with the G3 energy surface, is proposed to account for this.

A study of the ethene-ozone reaction with photoelectron spectroscopy: measurement of product branching ratios and atmospheric implications

The ozone-ethene reaction has been investigated at low pressure in a flow-tube interfaced to a u.v. photoelectron spectrometer. Photoelectron spectra recorded as a function of reaction time have been used to estimate partial pressures of the reagents and products, using photoionization cross-sections for selected photoelectron bands of the reagents and products, which have been measured separately. Product yields compare favourably with results of other studies, and the production of oxygen and acetaldehyde have been measured as a function of time for the first time. A reaction scheme developed for the ozone-ethene reaction has been used to simulate the reagents and products as a function of time. The results obtained are in good agreement with the experimental measurements. For each of the observed products, the simulations allow the main reaction (or reactions) for production of that product to be established. The product yields have been used in a global model to estimate their global annual emissions in the atmosphere. Of particular interest are the calculated global annual emissions of formaldehyde (0.96 ± 0.10 Tg) and formic acid, (0.05 ± 0.01 Tg) which are estimated as 0.04% and 0.7% of the total annual emission respectively.

Kinetics of the reaction between OH radicals and monochlorodimethylsulphide (CH3SCH2Cl)

The gas-phase rate coefficient for the reaction between OH radicals and CH3SCH2Cl (MCDMS) was determined to be (2.5±1.3)×10−12 cm3 molecule−1 s−1 using the discharge–flow kinetic technique. An estimate of ≈10−10 cm3 molecule−1 s−1 was obtained for the rate coefficient for reaction of Cl with MCDMS. It would appear that the reaction with OH is not the main loss process for CH3SCH2Cl in the marine boundary layer. The possible implications for the MBL of halogen-promoted oxidation of dimethylsulphide are considered.

A novel study of the polymerisation process involved in the formation of the network component of polymer-stabilised liquid crystals within electro-optic cells using high performance liquid chromatography

Polymer-stabilised liquid crystals are systems in which a small amount of monomer is dissolved within a liquid crystalline host, and then polymerised in situ to produce a network. The progress of the polymerisation, performed within electro-optic cells, was studied by establishing an analytical method novel to these systems. Samples were prepared by photopolymerisation of the monomer under well-defined reaction conditions; subsequent immersion in acetone caused the host and any unreacted monomer to dissolve. High performance liquid chromatography was used to separate and detect the various solutes in the resulting solutions, enabling the amount of unreacted monomer for a given set of conditions to be quantified. Longer irradiations cause a decrease in the proportion of unreacted monomer since more network is formed, while a more uniform LC director alignment (achieved by decreasing the sample thickness) or a higher level of order (achieved by decreasing the polymerisation temperature) promotes faster reactions.

The role of atmosphere feedbacks during ENSO in the CMIP3 models. Part III: the shortwave flux feedback

Previous studies using coupled general circulation models (GCMs) suggest that the atmosphere model plays a dominant role in the modeled El Nin ̃ o–Southern Oscillation (ENSO), and that intermodel differences in the thermodynamical damping of sea surface temperatures (SSTs) are a dominant contributor to the ENSO amplitude diversity. This study presents a detailed analysis of the shortwave flux feedback (aSW) in 12 Coupled Model Intercomparison Project phase 3 (CMIP3) simulations, motivated by findings that aSW is the primary contributor to model thermodynamical damping errors. A ‘‘feedback decomposition method,’’ developed to elucidate the aSW biases, shows that all models un- derestimate the dynamical atmospheric response to SSTs in the eastern equatorial Pacific, leading to un- derestimated aSW values. Biases in the cloud response to dynamics and the shortwave interception by clouds also contribute to errors in aSW. Changes in the aSW feedback between the coupled and corresponding atmosphere-only simulations are related to changes in the mean dynamics. A large nonlinearity is found in the observed and modeled SW flux feedback, hidden when linearly cal- culating aSW. In the observations, two physical mechanisms are proposed to explain this nonlinearity: 1) a weaker subsidence response to cold SST anomalies than the ascent response to warm SST anomalies and 2) a nonlinear high-level cloud cover response to SST. The shortwave flux feedback nonlinearity tends to be underestimated by the models, linked to an underestimated nonlinearity in the dynamical response to SST. The process-based methodology presented in this study may help to correct model ENSO atmospheric biases, ultimately leading to an improved simulation of ENSO in GCMs.

Unusual isotope effect in the reaction of chlorosilylene with trimethylsilane-1-d: Absolute rate studies and quantum chemical and Rice–Ramsperger–Kassel–Marcus calculations provide strong evidence for the involvement of an intermediate complex

Time-resolved studies of chlorosilylene, ClSiH, generated by the 193 nm laser flash photolysis of 1-chloro-1- silacyclopent-3-ene, have been carried out to obtain rate constants for its bimolecular reaction with trimethylsilane-1-d, Me3SiD, in the gas phase. The reaction was studied at total pressures up to 100 Torr (with and without added SF6) over the temperature range of 295−407 K. The rate constants were found to be pressure independent and gave the following Arrhenius equation: log[(k/(cm3 molecule−1 s−1)] = (−13.22 ± 0.15) + [(13.20 ± 1.00) kJ mol−1]/(RT ln 10). When compared with previously published kinetic data for the reaction of ClSiH with Me3SiH, kinetic isotope effects, kD/kH, in the range from 7.4 (297 K) to 6.4 (407 K) were obtained. These far exceed values of 0.4−0.5 estimated for a single-step insertion process. Quantum chemical calculations (G3MP2B3 level) confirm not only the involvement of an intermediate complex, but also the existence of a low-energy internal isomerization pathway which can scramble the D and H atom labels. By means of Rice−Ramsperger−Kassel−Marcus modeling and a necessary (but small) refinement of the energy surface, we have shown that this mechanism can reproduce closely the experimental isotope effects. These findings provide the first experimental evidence for the isomerization pathway and thereby offer the most concrete evidence to date for the existence of intermediate complexes in the insertion reactions of silylenes.