The full-spectrum correlated-k method for longwave atmospheric radiative transfer using an effective Planck function

The correlated k-distribution (CKD) method is widely used in the radiative transfer schemes of atmospheric models and involves dividing the spectrum into a number of bands and then reordering the gaseous absorption coefficients within each one. The fluxes and heating rates for each band may then be computed by discretizing the reordered spectrum into of order 10 quadrature points per major gas and performing a monochromatic radiation calculation for each point. In this presentation it is shown that for clear-sky longwave calculations, sufficient accuracy for most applications can be achieved without the need for bands: reordering may be performed on the entire longwave spectrum. The resulting full-spectrum correlated k (FSCK) method requires significantly fewer monochromatic calculations than standard CKD to achieve a given accuracy. The concept is first demonstrated by comparing with line-by-line calculations for an atmosphere containing only water vapor, in which it is shown that the accuracy of heating-rate calculations improves approximately in proportion to the square of the number of quadrature points. For more than around 20 points, the root-mean-squared error flattens out at around 0.015 K/day due to the imperfect rank correlation of absorption spectra at different pressures in the profile. The spectral overlap of m different gases is treated by considering an m-dimensional hypercube where each axis corresponds to the reordered spectrum of one of the gases. This hypercube is then divided up into a number of volumes, each approximated by a single quadrature point, such that the total number of quadrature points is slightly fewer than the sum of the number that would be required to treat each of the gases separately. The gaseous absorptions for each quadrature point are optimized such that they minimize a cost function expressing the deviation of the heating rates and fluxes calculated by the FSCK method from line-by-line calculations for a number of training profiles. This approach is validated for atmospheres containing water vapor, carbon dioxide, and ozone, in which it is found that in the troposphere and most of the stratosphere, heating-rate errors of less than 0.2 K/day can be achieved using a total of 23 quadrature points, decreasing to less than 0.1 K/day for 32 quadrature points. It would be relatively straightforward to extend the method to include other gases.

The full-spectrum correlated k method for longwave atmospheric radiative transfer: treatment of gaseous overlap

The correlated k-distribution (CKD) method is widely used in the radiative transfer schemes of atmospheric models, and involves dividing the spectrum into a number of bands and then reordering the gaseous absorption coefficients within each one. The fluxes and heating rates for each band may then be computed by discretizing the reordered spectrum into of order 10 quadrature points per major gas, and performing a pseudo-monochromatic radiation calculation for each point. In this paper it is first argued that for clear-sky longwave calculations, sufficient accuracy for most applications can be achieved without the need for bands: reordering may be performed on the entire longwave spectrum. The resulting full-spectrum correlated k (FSCK) method requires significantly fewer pseudo-monochromatic calculations than standard CKD to achieve a given accuracy. The concept is first demonstrated by comparing with line-by-line calculations for an atmosphere containing only water vapor, in which it is shown that the accuracy of heating-rate calculations improves approximately in proportion to the square of the number of quadrature points. For more than around 20 points, the root-mean-squared error flattens out at around 0.015 K d−1 due to the imperfect rank correlation of absorption spectra at different pressures in the profile. The spectral overlap of m different gases is treated by considering an m-dimensional hypercube where each axis corresponds to the reordered spectrum of one of the gases. This hypercube is then divided up into a number of volumes, each approximated by a single quadrature point, such that the total number of quadrature points is slightly fewer than the sum of the number that would be required to treat each of the gases separately. The gaseous absorptions for each quadrature point are optimized such they minimize a cost function expressing the deviation of the heating rates and fluxes calculated by the FSCK method from line-by-line calculations for a number of training profiles. This approach is validated for atmospheres containing water vapor, carbon dioxide and ozone, in which it is found that in the troposphere and most of the stratosphere, heating-rate errors of less than 0.2 K d−1 can be achieved using a total of 23 quadrature points, decreasing to less than 0.1 K d−1 for 32 quadrature points. It would be relatively straightforward to extend the method to include other gases.

Optimizing the number of stations in arrays measurements: experimental outcomes for different array geometries and the f-k method

Array measurements have become a valuable tool for site response characterization in a non-invasive way. The array design, i.e. size, geometry and number of stations, has a great influence in the quality of the obtained results. From the previous parameters, the number of available stations uses to be the main limitation for the field experiments, because of the economical and logistical constraints that it involves. Sometimes, from the initially planned array layout, carefully designed before the fieldwork campaign, one or more stations do not work properly, modifying the prearranged geometry. Whereas other times, there is not possible to set up the desired array layout, because of the lack of stations. Therefore, for a planned array layout, the number of operative stations and their arrangement in the array become a crucial point in the acquisition stage and subsequently in the dispersion curve estimation. In this paper we carry out an experimental work to analyze which is the minimum number of stations that would provide reliable dispersion curves for three prearranged array configurations (triangular, circular with central station and polygonal geometries). For the optimization study, we analyze together the theoretical array responses and the experimental dispersion curves obtained through the f-k method. In the case of the f-k method, we compare the dispersion curves obtained for the original or prearranged arrays with the ones obtained for the modified arrays, i.e. the dispersion curves obtained when a certain number of stations n is removed, each time, from the original layout of X geophones. The comparison is evaluated by means of a misfit function, which helps us to determine how constrained are the studied geometries by stations removing and which station or combination of stations affect more to the array capability when they are not available. All this information might be crucial to improve future array designs, determining when it is possible to optimize the number of arranged stations without losing the reliability of the obtained results.

Pitfalls on computing liquid-liquid phase equilibria using the k-value method

Poster presented in the 11th Mediterranean Congress of Chemical Engineering, Barcelona, October 21-24, 2008.

Two fast radiative transfer methods to improve the temporal sampling of clouds in numerical weather prediction and climate models

The high computational cost of calculating the radiative heating rates in numerical weather prediction (NWP) and climate models requires that calculations are made infrequently, leading to poor sampling of the fast-changing cloud field and a poor representation of the feedback that would occur. This paper presents two related schemes for improving the temporal sampling of the cloud field. Firstly, the ‘split time-stepping’ scheme takes advantage of the independent nature of the monochromatic calculations of the ‘correlated-k’ method to split the calculation into gaseous absorption terms that are highly dependent on changes in cloud (the optically thin terms) and those that are not (optically thick). The small number of optically thin terms can then be calculated more often to capture changes in the grey absorption and scattering associated with cloud droplets and ice crystals. Secondly, the ‘incremental time-stepping’ scheme uses a simple radiative transfer calculation using only one or two monochromatic calculations representing the optically thin part of the atmospheric spectrum. These are found to be sufficient to represent the heating rate increments caused by changes in the cloud field, which can then be added to the last full calculation of the radiation code. We test these schemes in an operational forecast model configuration and find a significant improvement is achieved, for a small computational cost, over the current scheme employed at the Met Office. The ‘incremental time-stepping’ scheme is recommended for operational use, along with a new scheme to correct the surface fluxes for the change in solar zenith angle between radiation calculations.

Friction losses in valves and fittings for liquid food products

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Friction losses in valves and fittings for power-law fluids

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Friction losses in valves and fittings for viscoplastic fluids

Data on pressure drop were obtained in stainless steel, sanitary fittings and valves during laminar and turbulent flow of aqueous suspensions of sucrose and bentonite. The rheological properties of these suspensions were determined and the Bingham model provided the best fitting with the experimental data. Friction losses were measured in fully- and partially-open butterfly and plug valves, bends and union. Values of loss coefficients (k(f)) were calculated and correlated as functions of the classical Reynolds number and the Reynolds number proposed by Govier and Aziz (1972) for viscoplastic fluids. The two-k method and a new proposed model presented the best adjustments for the Govier and Aziz Reynolds number, and Hedstrom and classical Reynolds numbers, respectively.

High-throughput sequencing of black pepper root transcriptome

Background: Black pepper (Piper nigrum L.) is one of the most popular spices in the world. It is used in cooking and the preservation of food and even has medicinal properties. Losses in production from disease are a major limitation in the culture of this crop. The major diseases are root rot and foot rot, which are results of root infection by Fusarium solani and Phytophtora capsici, respectively. Understanding the molecular interaction between the pathogens and the host's root region is important for obtaining resistant cultivars by biotechnological breeding. Genetic and molecular data for this species, though, are limited. In this paper, RNA-Seq technology has been employed, for the first time, to describe the root transcriptome of black pepper. Results: The root transcriptome of black pepper was sequenced by the NGS SOLiD platform and assembled using the multiple-k method. Blast2Go and orthoMCL methods were used to annotate 10338 unigenes. The 4472 predicted proteins showed about 52% homology with the Arabidopsis proteome. Two root proteomes identified 615 proteins, which seem to define the plant's root pattern. Simple-sequence repeats were identified that may be useful in studies of genetic diversity and may have applications in biotechnology and ecology. Conclusions: This dataset of 10338 unigenes is crucially important for the biotechnological breeding of black pepper and the ecogenomics of the Magnoliids, a major group of basal angiosperms.

Effect of precracking method on K(Ic) results for medium-density polyethylene tested under cryogenic condition

The effect of different precracking methods on the results of linear elastic K(Ic) fracture toughness testing with medium-density polyethylene (MDPE) was investigated. Cryogenic conditions were imposed in order to obtain valid K(Ic) values from specimens of suitable size. Most conservative K(Ic) values were obtained by slow pressing a fresh razor blade at the notch root of the specimen. Due to the low deformation level imposed on the crack tip region, the slow pressing razor blade technique also produced less scatter in fracture toughness results. It has been shown that the slow stable crack growth preceding catastrophic brittle failure during K(Ic) tests in MOPE under cryogenic conditions should not be disregarded as it has relevant physical meaning and may affect the fracture toughness results. (C) 2010 Elsevier Ltd. All rights reserved.

The differentiation of character state relationships by binary coding and the monothetic subset method / Hymen Marx, George B. Rabb and Harold K. Voris.

v.72:no.1(1977)

Potentiometric titration as a method of determining the stoichiometric dissociation constants of weak acids from the thermodynamic dissociation constants of aqueous solutions at 298.15 K

The simple single-ion activity coefficient equation originating from the Debye-Hückel theory was used to determine the thermodynamic and stoichiometric dissociation constants of weak acids from data concerning galvanic cells. Electromotive force data from galvanic cells without liquid junctions, which was obtained from literature, was studied in conjuction with the potentiometric titration data relating to aqueous solutions at 298.15 K. The dissociation constants of weak acids could be determined by the presented techniques and almost all the experimental data studied could be interpreted within the range of experimental error. Potentiometric titration has been used here and the calculation methods were developed to obtain the thermodynamic and stoichiometric dissociation constants of some weak acids in aqueous solutions at 298.15 K. The ionic strength of titrated solutions were adjusted using an inert electrolyte, namely, sodium or potassium chloride. Salt content alonedetermines the ionic strength. The ionic strength of the solutions studied varied from 0.059 mol kg-1 to 0.37 mol kg-1, and in some cases up to 1.0 mol kg-1. The following substances were investigated using potentiometric titration: aceticacid, propionic acid, L-aspartic acid, L-glutamic acid and bis(2,2-dimethyl-3-oxopropanol) amine.

The Li+, Na+ and K+ ion exchange reaction process on the surface of mixed oxide SiO2/TiO2/Sb2O5 surface prepared by the sol-gel processing method

The porous mixed oxide SiO2/TiO2/Sb2O5 obtained by the sol-gel processing method presented a good ion exchange property and a high exchange capacity towards the Li+, Na+ and K+ ions. In the H+/M+ ion exchange process, the H+ / Na+ could be described as presenting an ideal character. The ion exchange equilibria of Li+ and K+ were quantitatively described with the help of the model of fixed tetradentate centers. The results of simulation evidence that for the H+ / Li+ exchange the usual situation takes place: the affinity of the material to the Li+ ions is decreased with increasing the degree of ion exchange. On the contrary, for K+ the effects of positive cooperativity, that facilitate the H+ / K+ exchange, were revealed.

Physical characterization of K-doped 0.9PMN-0.1PT synthesized by an association of the columbite route and the polymeric precursor method

The solid solution 0.9PbMg 1/3Nb 2/3O 3-0.1PbTiO 3 is one of the most widely investigated relaxor ceramic, because of its high dielectric constant and low sintering temperatures. PMN-PT powders containing single perovskite phase were prepared by using a Timodified columbite precursor obtained by the polymeric precursor method. Such precursor reacts directly with stoichiometric amount of PbO to obtain pyrochlore-free PMN-PT powders. The structural effects of K additive included in the columbite precursor and 0.9PMN-0.1PT powders were also studied. The phase formation at each processing step was verified by XRD analysis, being these results used for the structural refinement by the Rietveld method. It was verified the addition of K in the columbite precursor promotes a slight increasing in the powder crystallinity. There was not a decrease in the amount of perovskite phase PMN-PT for 1mol% of K, and the particle and grain size were reduced, making this additive a powerful tool for grain size control.