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.

Evaluation of Fracture Parameters by Double-G, Double-K Models and Crack Extension Resistance for High Strength and Ultra High Strength Concrete Beams

This paper presents the advanced analytical methodologies such as Double- G and Double - K models for fracture analysis of concrete specimens made up of high strength concrete (HSC, HSC1) and ultra high strength concrete. Brief details about characterization and experimentation of HSC, HSC1 and UHSC have been provided. Double-G model is based on energy concept and couples the Griffith's brittle fracture theory with the bridging softening property of concrete. The double-K fracture model is based on stress intensity factor approach. Various fracture parameters such as cohesive fracture toughness (4), unstable fracture toughness (K-Ic(c)), unstable fracture toughness (K-Ic(un)) and initiation fracture toughness (K-Ic(ini)) have been evaluated based on linear elastic fracture mechanics and nonlinear fracture mechanics principles. Double-G and double-K method uses the secant compliance at the peak point of measured P-CMOD curves for determining the effective crack length. Bi-linear tension softening model has been employed to account for cohesive stresses ahead of the crack tip. From the studies, it is observed that the fracture parameters obtained by using double - G and double - K models are in good agreement with each other. Crack extension resistance has been estimated by using the fracture parameters obtained through double - K model. It is observed that the values of the crack extension resistance at the critical unstable point are almost equal to the values of the unstable fracture toughness K-Ic(un) of the materials. The computed fracture parameters will be useful for crack growth study, remaining life and residual strength evaluation of concrete structural components.

A high order accurate difference scheme for complex flow fields

A high order accurate finite difference method for direct numerical simulation of coherent structure in the mixing layers is presented. The reason for oscillation production in numerical solutions is analyzed, It is caused by a nonuniform group velocity of wavepackets. A method of group velocity control for the improvement of the shock resolution is presented. In numerical simulation the fifth-order accurate upwind compact difference relation is used to approximate the derivatives in the convection terms of the compressible N-S equations, a sixth-order accurate symmetric compact difference relation is used to approximate the viscous terms, and a three-stage R-K method is used to advance in time. In order to improve the shock resolution the scheme is reconstructed with the method of diffusion analogy which is used to control the group velocity of wavepackets. (C) 1997 Academic Press.

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.

Continuous-cooling method of specific heat measurement in the temperature range 100-300 K

The authors have developed a simple continuous-cooling method to determine specific heat of liquids and solids in the temperature range 100-300 K. The technique employs very simple instrumentation and continuously records the sample temperature as it cools to the bath temperature through a calibrated heat link. They have obtained specific heat values which agree with the reported data to within 3% for the samples investigated. This method also facilitates easy detection of abrupt changes in specific heat, as demonstrated in the observation of glass transition in some organic glass-forming systems. The method is sensitive to the study of relaxing heat capacity in supercooled liquids.