Gaussian anamorphosis in the analysis step of the EnKF: a joint state-variable/observation approach

The analysis step of the (ensemble) Kalman filter is optimal when (1) the distribution of the background is Gaussian, (2) state variables and observations are related via a linear operator, and (3) the observational error is of additive nature and has Gaussian distribution. When these conditions are largely violated, a pre-processing step known as Gaussian anamorphosis (GA) can be applied. The objective of this procedure is to obtain state variables and observations that better fulfil the Gaussianity conditions in some sense. In this work we analyse GA from a joint perspective, paying attention to the effects of transformations in the joint state variable/observation space. First, we study transformations for state variables and observations that are independent from each other. Then, we introduce a targeted joint transformation with the objective to obtain joint Gaussianity in the transformed space. We focus primarily in the univariate case, and briefly comment on the multivariate one. A key point of this paper is that, when (1)-(3) are violated, using the analysis step of the EnKF will not recover the exact posterior density in spite of any transformations one may perform. These transformations, however, provide approximations of different quality to the Bayesian solution of the problem. Using an example in which the Bayesian posterior can be analytically computed, we assess the quality of the analysis distributions generated after applying the EnKF analysis step in conjunction with different GA options. The value of the targeted joint transformation is particularly clear for the case when the prior is Gaussian, the marginal density for the observations is close to Gaussian, and the likelihood is a Gaussian mixture.

The slowly evolving background state of the atmosphere

The theory of wave–mean flow interaction requires a partition of the atmospheric flow into a notional background state and perturbations to it. Here, a background state, known as the Modified Lagrangian Mean (MLM), is defined as the zonally symmetric state obtained by requiring that every potential vorticity (PV) contour lying within an isentropic layer encloses the same mass and circulation as in the full flow. For adiabatic and frictionless flow, these two integral properties are time-invariant and the MLM state is a steady solution of the primitive equations. The time dependence in the adiabatic flow is put into the perturbations, which can be described by a wave-activity conservation law that is exact even at large amplitude. Furthermore, the effects of non-conservative processes on wave activity can be calculated from the conservation law. A new method to calculate the MLM state is introduced, where the position of the lower boundary is obtained as part of the solution. The results are illustrated using Northern Hemisphere ERA-Interim data. The MLM state evolves slowly, implying that the net non-conservative effects are weak. Although ‘adiabatic eddy fluxes’ cannot affect the MLM state, the effects of Rossby-wave breaking, PV filamentation and subsequent dissipation result in sharpening of the polar vortex edge and meridional shifts in the MLM zonal flow, both at tropopause level and on the winter stratospheric vortex. The rate of downward migration of wave activity during stratospheric sudden warmings is shown to be given by the vertical scale associated with polar vortex tilt divided by the time-scale for wave dissipation estimated from the wave-activity conservation law. Aspects of troposphere–stratosphere interaction are discussed. The new framework is suitable to examine the climate and its interactions with disturbances, such as midlatitude storm tracks, and makes a clean partition between adiabatic and non-conservative processes.

Conditioning and preconditioning of the optimal state estimation problem

Optimal state estimation is a method that requires minimising a weighted, nonlinear, least-squares objective function in order to obtain the best estimate of the current state of a dynamical system. Often the minimisation is non-trivial due to the large scale of the problem, the relative sparsity of the observations and the nonlinearity of the objective function. To simplify the problem the solution is often found via a sequence of linearised objective functions. The condition number of the Hessian of the linearised problem is an important indicator of the convergence rate of the minimisation and the expected accuracy of the solution. In the standard formulation the convergence is slow, indicating an ill-conditioned objective function. A transformation to different variables is often used to ameliorate the conditioning of the Hessian by changing, or preconditioning, the Hessian. There is only sparse information in the literature for describing the causes of ill-conditioning of the optimal state estimation problem and explaining the effect of preconditioning on the condition number. This paper derives descriptive theoretical bounds on the condition number of both the unpreconditioned and preconditioned system in order to better understand the conditioning of the problem. We use these bounds to explain why the standard objective function is often ill-conditioned and why a standard preconditioning reduces the condition number. We also use the bounds on the preconditioned Hessian to understand the main factors that affect the conditioning of the system. We illustrate the results with simple numerical experiments.

Direct observation by time-resolved infrared spectroscopy of the bright and the dark excited states of the [Ru(phen)2(dppz)]2+ light-switch compound in solution and when bound to DNA

The [Ru(phen)2(dppz)]2+ complex (1) is non-emissive in water but is highly luminescent in organic solvents or when bound to DNA, making it a useful probe for DNA binding. To date, a complete mechanistic explanation for this “light-switch” effect is still lacking. With this in mind we have undertaken an ultrafast time resolved infrared (TRIR) study of 1 and directly observe marker bands between 1280–1450 cm-1, which characterise both the emissive “bright” and the non-emissive “dark” excited states of the complex, in CD3CN and D2O respectively. These characteristic spectral features are present in the [Ru(dppz)3]2+ solvent light-switch complex but absent in [Ru(phen)3]2+, which is luminescent in both solvents. DFT calculations show that the vibrational modes responsible for these characteristic bands are predominantly localised on the dppz ligand. Moreover, they reveal that certain vibrational modes of the “dark” excited state couple with vibrational modes of two coordinating water molecules, and through these to the bulk solvent, thus providing a new insight into the mechanism of the light-switch effect. We also demonstrate that the marker bands for the “bright” state are observed for both L- and D enantiomers of 1 when bound to DNA and that photo-excitation of the complex induces perturbation of the guanine and cytosine carbonyl bands. This perturbation is shown to be stronger for the L enantiomer, demonstrating the different binding site properties of the two enantiomers and the ability of this technique to determine the identity and nature of the binding site of such intercalators.

Seasonal variation of Lutzomyia longipalpis (Lutz & neiva, 1912) (Diptera : Psychodidae : Phlebotominae) in endemic area of visceral leishmaniasis, Campo Grande, state of Mato Grosso do Sul, Brazil

The seasonal distribution of Lutzomyia longipalpis was studied in two forested and five domiciliary areas of the urban area of Campo Grande; MS, from December 2003 to November 2005. Weekly captures were carried out with CDC light traps positioned on ground and in the canopy inside a residual forest and on the edge (ground) of a woodland and in at least one of the following ecotopes in peridomiciles-a cultivated area, a chicken coop, a pigsty, a kennel, a goat and sheep shelter and an intradomicile. A total of 9519 sand flies were collected, 2666 during the first year and 6853 during the second. L. longipalpis was found throughout the 2-year period, presenting smaller peaks at intervals of 2-3 months and two greater peaks, the first in February and the second in April 2005, soon after periods of heavy rain. Only In one of the woodlands was a significant negative correlation (p < 0.05) between the number of insects and temperature during the first year and the climatic factors (temperature, RHA and rain) was observed. In the domiciliary areas in four domiciles some positive correlations (p < 0.05) occurred in relation to one or more climatic factors; however, the species shows a clear tendency to greater frequency (72%) in the rainy season than in the dry (28%). Thus, we recommend an intensification of the VL control measures applied in Campo Grande, MS, during the rainy season with a view to reducing the risk of the transmission of the disease. (C) 2007 Elsevier B.V. All fights reserved.

The intracratonic Caraibas-Itacarambi earthquake of December 09, 2007 (4.9 m(b)), Minas Gerais State, Brazil

On December 9, 2007, a 4.9 m(b) earthquake occurred in the middle of the Sao Francisco Craton, in a region with no known previous activity larger than 4 m(b). This event reached intensity VII MM (Modified Mercalli) causing the first fatal victim in Brazil. The activity had started in May 25, 2007 with a 3.5 magnitude event and continued for several months, motivating the deployment of a local 6-station network. A three week seismic quiescence was observed before the mainshock. Initial absolute hypocenters were calculated with best fitting velocity models and then relative locations were determined with hypoDD. The aftershock distribution indicates a 3 km long rupture for the mainshock. The fault plane solution, based on P-wave polarities and hypocentral trend, indicates a reverse faulting mechanism on a N30 degrees E striking plane dipping about 40 degrees to the SE. The rupture depth extends from about 0.3 to 1.2 km only. Despite the shallow depth of the mainshock, no surface feature could be correlated with the fault plane. Aeromagnetic data in the epicentral area show short-wavelength lineaments trending NNE-SSW to NE-SW which we interpret as faults and fractures in the craton basement beneath the surface limestone layer. We propose that the Caraibas-Itacarambi seismicity is probably associated with reactivation of these basement fractures and faults under the present E-W compressional stress field in this region of the South American Plate. (c) 2009 Elsevier B.V. All rights reserved.

Uranium series disequilibria in ground waters from a fractured bedrock aquifer (Morungaba Granitoids-Southern Brazil): Implications to the hydrochemical behavior of dissolved U and Ra

Activity concentrations of dissolved U-234, U-238, Ra-226 and Ra-228 were determined in ground waters fromtwo deep wells drilled in Morungaba Granitoids (Southern Brazil). Sampling was done monthly for little longer than 1 year. Significant disequilibrium between U-238, U-234 and Ra-226 were observed in all samples. The variation of U-238 and U-234 activity concentrations and U-234/U-238 activity ratios is related to seasonal changes. Although the distance between the two wells is short (about 900m), systematic differences of activity concentrations of U isotopes, as well as of U-234/U-238, Ra-226/U-234 and Ra-228/Ra-226 activity ratios were noticed, indicating distinct host rock-water interactions. Slightly acidic ground water percolation through heterogeneous host rock, associated with different recharge processes, may explain uranium and radium isotope behavior. (c) 2008 Elsevier Ltd. All rights reserved.

Strong quenching of chlorophyll fluorescence in the desiccated state in three poikilohydric and homoiochlorophyllous moss species indicates photo-oxidative protection on highly light-exposed rocks of a tropical inselberg

The three poikilophydric and homoiochlorophyllous moss species Campylopus savannarum (C. Muell.) Mitt., Racocarpus fontinaloides (C. Muell.) Par. and Ptychomitrium vaginatum Besch. grow on sun-exposed rocks of a tropical inselberg in Brazil subject to regular drying and wetting cycles. Effective photo-oxidative protection in the light-adapted desiccated state in all three species is achieved by a reduction of ground chlorophyll fluorescence, F, to almost zero. Upon rewatering, the kinetics of the recovery of F in air dry cushions to higher values is very fast in the first 5min, but more than 80min are needed until an equilibrium is reached gradually. The kinetics were not different between the three species. The three moss species, have a distinct niche occupation and form a characteristic zonation around soil vegetation islands on the rock outcrops, where C. savannarum and R. fontinaloides form an inner and outer belt, respectively, around vegetation islands and P vaginatum occurs as small isolated cushions on bare rock. However, they were not distinguished by the reduction of F in the dry state and the rewetting recovery kinetics and only slightly different in their photosynthetic capacity. Stable isotope ratios (delta C-13, delta N-15) indicate that liquid films of water limiting diffusion of CO2 are important in determining carbon acquisition and suggest that limitation of CO2 fixation by water films must be more pronounced over time in P vaginatum than in the latter species. This is determined by both the micro site occupied and the form of the moss cushions. (c) 2007 Elsevier GmbH. All rights reserved.

Stability and related properties of vacua and ground states

We consider the formal non-relativistic limit (nrl) of the : phi(4):(s+1) relativistic quantum field theory (rqft), where s is the space dimension. Following the work of R. Jackiw [R. Jackiw, in: A. Ali, P. Hood-bhoy (Eds.), Beg Memorial Volume, World Scientific, Singapore, 1991], we show that, for s = 2 and a given value of the ultraviolet cutoff K, there are two ways to perform the nrl: (i) fixing the renormalized mass m(2) equal to the bare mass m(0)(2); (ii) keeping the renormalized mass fixed and different from the bare mass mo. In the (infinite-volume) two-particle sector the scattering amplitude tends to zero as K -> infinity in case (i) and, in case (ii), there is a bound state, indicating that the interaction potential is attractive. As a consequence, stability of matter fails for our boson system. We discuss why both alternatives do not reproduce the low-energy behaviour of the full rqft. The singular nature of the nrl is also nicely illustrated for s = 1 by a rigorous stability/instability result of a different nature. (C) 2007 Elsevier Inc. All rights reserved.

Combined Crystallographic and Solution Molecular Dynamics Study of Allosteric Effects in Ester and Ketone p-tert-Butylcalix[4]arene Derivatives and Their Complexes with Acetonitrile, Cd(II), and Pb(II)

We describe here a procedure to bridge the gap in the field of calixarene physicochemistry between solid-state atomic-resolution structural information and the liquid-state low-resolution thermodynamics and spectroscopic data. We use MD simulations to study the kinetics and energetics involved in the complexation of lower rim calix[4]arene derivatives (L), containing bidentate ester (1) and ketone (2) pendant groups, with acetonitrile molecule (MeCN) and Cd2+ and Pb2+ ions (M2+) in acetonitrile solution. On one hand, we found that the prior inclusion of MeCN into the calix to form a L(MeCN) adduct has only a weak effect in preorganizing the hydrophilic cavity toward metal ion binding. On the other hand, the strong ion-hydrophilic cavity interaction produces a wide open calix which enhances the binding of one MeCN molecule (allosteric effect) to stabilize the whole (M2+)1(MeCN) bifunctional complex. We reach two major conclusions: (i) the MD results for the (M2+)1(MeCN) binding are in close agreement with the ""endo"", fully encapsulated, metal complex found by X-ray diffraction and in vacuo MD calculations, and (ii) the MD structure for the more flexible 2 ligand, however, differs from the also endo solid-state molecule. In fact, it shows strong solvation effects at the calixarene lower bore by competing MeCN molecules that share the metal coordination sphere with the four C=O oxygens of an ""exo"" (M2+)2(MeCN) complex.

gamma-zein secondary structure in solution by circular dichroism

The proline-rich N-terminal domain of gamma-zein has been reported in relevant process, which include its ability to cross the cell membranes. Evidences indicate that synthetic hexapeptide (PPPVHL), naturally found in N-terminal portion of gamma-zein, can adopt the polyproline II (PPII) conformation in aqueous solution. The secondary structure of gamma-zein in maize protein bodies had been analyzed by solid state Fourier transform infrared and nuclear magnetic resonance spectroscopies. However, it was not possible to measure PPII content in physiological environment since the beta-sheet and PPII signals overlap in both solid state techniques. Here, the secondary structure of gamma-zein has been analyzed by circular dichroism in SDS aqueous solution with and without ditiothreitol (DTT), and in 60% of 2-propanol and water with DTT The results show that gamma-zein has high helical content in all solutions. The PPII conformation was present at about 7% only in water/DTT solution. (c) 2007 Wiley Periodicals, Inc.

2-Aminopurine non-radiative decay and emission in aqueous solution: A theoretical study

The minimum energy path along the lowest-lying pi pi* excited state of 2-aminopurine was calculated to elucidate the mechanisms of radiationless decay and emission in water. The sequential Monte Carlo quantum mechanics approach with a multiconfigurational and perturbative description of the wave function was employed to compute the minimum, transition state, and conical intersection. It was found that the barrier in the potential energy surface to access the conical intersection funnel increases in aqueous environment, making the system prone to enlarge the emission yield. These results rationalize the observed enhancement of emission in 2-aminopurine upon increasing of the solvent polarity. (c) 2008 Elsevier B.V. All rights reserved.

Reaction of a model siderophore with Ni(II), Co(II) and Zn(II) in aqueous solution: Kinetics and spectroscopy

A spectroscopic study was performed showing that the [Fe(III)(L(2-))(2)](1-) (L(2-) = dopacatecholate) complex reacts with Ni(II), Co(II) and Zn(II) in an aqueous solution containing S(2)O(3)(2-) resulting in the soluble [M(L(1-))(3)](1-) (L(1-) = dopasemiquinone; M = Ni(II), Co(II) or Zn(II) complex species. The Raman and IR spectra of the [CTA][M(L(1-))(3)] complexes, CTA hexadecyltrimethylammonium cation, in the solid state were obtained. The kinetic constants for the metal substitution reactions were determined at four different temperatures, providing values for Delta W(not equal) Delta S(not equal) and Delta G(not equal). The reactions were slow (k = 10(-1)1 M s(-1)) and endothermic. The system investigated can be considered as a simplified model to explain some aspects of siderophore chemistry. (c) 2007 Elsevier Inc. All rights reserved.

Excited-State Dynamics in fac-[Re(CO)(3)(Me(4)phen)(L)](+)

Excited-state dynamics in fac-[Re(CO)(3)(Me(4)phen)(cis-L)](+) (Me(4)phen = 3,4,7,8-tetramethyl-1,10-phenanthroline, L = 4-styrylpyridine (stpy) or 1,2-bis(4-pyridyl)ethylene (bpe)) were investigated by steady-state and time-resolved techniques. A complex equilibrium among three closely lying excited states, 3IL(cis-L), (3)MLCT(Re -> me4phen), and (3)IL(Me4phen), has been established. Under UV irradiation, cis-to-trans isomerization of coordinated cis-L is observed with a quantum yield of 0.15 in acetonitrile solutions. This photoreaction competes with radiative decay from (3)MLCT(Re -> Me4phen) and (3)IL(Me4phen) excited states, leading to a decrease in the emission quantum yield relative to the nonisomerizable complex fac-[Re(CO)(3)(Me(4)phen)(bpa)](+) (bpa = 1,2-bis(4-pyridyl)ethane). From temperature-dependent time-resolved emission measurements in solution and in poly(methyl methacrylate) (PMMA) films, energy barriers (Delta E(a)) for interconversion between (3)MLCT(Re -> me4Phen) and (3)IL(Me4phen) emitting states were determined. For L = cis-stpy, Delta E(a) = 11 (920 cm(-1)) and 15 kJ mol(-1) (1254 cm(-1)) in 5:4 propionitrile/butyronitrile and PMMA, respectively. For L = cis-bpe, Delta E(a) = 13 kJ mol(-1) (1087 cm(-1)) in 5:4 propionitrile/butyronitrile. These energy barriers are sufficient to decrease the rate constant for internal conversion from higher-lying (3)IL(me4phen) state to (3)MLCT(Re -> Me4phen), k(i) congruent to 10(6) s(-1). The decrease in rate allows for the observation of intraligand phosphorescence, even in fluid medium at room temperature. Our results provide additional insight into the role of energy gap and excited-state dynamics on the photochemical and photophysical properties of Re(I) polypyridyl complexes.

Removal of metal ions from aqueous solution by chelating polymeric hydrogel

Polysaccharide natural seed coat from the tree Magonia pubescens, in the form of hydrogel was used to remove metals in aqueous solution. Swelling tests indicate that seed coat presents hydrogel behavior, with maximum water absorption of 292 g water/g. Adsorption experiments performed using Na(+), Mg(2+), K(+), Ca(2+), Cr(3+), Fe(3+) and Zn(2+) demonstrated that the polysaccharide structure has a high capacity to extract these ions from the aqueous solution. Scanning electron microscopy revealed significant morphological changes of the material before and after water contact. Differential scanning calorimetry measurements indicate a signal shift of the water evaporation temperature in the material with adsorbed zinc. X-ray photoelectron spectroscopy analysis combined with theoretical studies by the density functional theory and on Hartree-Fock (HF) level evidence that the metallic ions were adsorbed through coordination with hydroxyl groups of polysaccharide. In the case of Zn(2+) the lowest HF energy was observed for the tetracoordination mode, where Zn(2+) is coordinated by two hydroxyl groups and two water molecules.