Spatial analysis of the error in a model of soil nitrogen

Models of the dynamics of nitrogen in soil (soil-N) can be used to aid the fertilizer management of a crop. The predictions of soil-N models can be validated by comparison with observed data. Validation generally involves calculating non-spatial statistics of the observations and predictions, such as their means, their mean squared-difference, and their correlation. However, when the model predictions are spatially distributed across a landscape the model requires validation with spatial statistics. There are three reasons for this: (i) the model may be more or less successful at reproducing the variance of the observations at different spatial scales; (ii) the correlation of the predictions with the observations may be different at different spatial scales; (iii) the spatial pattern of model error may be informative. In this study we used a model, parameterized with spatially variable input information about the soil, to predict the mineral-N content of soil in an arable field, and compared the results with observed data. We validated the performance of the N model spatially with a linear mixed model of the observations and model predictions, estimated by residual maximum likelihood. This novel approach allowed us to describe the joint variation of the observations and predictions as: (i) independent random variation that occurred at a fine spatial scale; (ii) correlated random variation that occurred at a coarse spatial scale; (iii) systematic variation associated with a spatial trend. The linear mixed model revealed that, in general, the performance of the N model changed depending on the spatial scale of interest. At the scales associated with random variation, the N model underestimated the variance of the observations, and the predictions were correlated poorly with the observations. At the scale of the trend, the predictions and observations shared a common surface. The spatial pattern of the error of the N model suggested that the observations were affected by the local soil condition, but this was not accounted for by the N model. In summary, the N model would be well-suited to field-scale management of soil nitrogen, but suited poorly to management at finer spatial scales. This information was not apparent with a non-spatial validation. (c),2007 Elsevier B.V. All rights reserved.

Dissolution of phosphorus from animal bone char in 12 soils

Heat-treated animal bone char (ABC) has not previously been evaluated for its potential as a phosphorus (P) fertilizer. ABC, Gafsa phosphate rock (GPR) and triple superphosphate fertilizer (TSP) were incubated in 12 soils. Dissolved-P was assessed by extraction with NaOH and bioavailability with the Olsen extractant. The rate of P dissolution from ABC was described almost equally well by the Elovich and Power equations. After 145 days, the fraction of P dissolved ranged from 0 to 73% and to 56% for ABC and GPR, respectively. The most important soil properties determining P dissolution from ABC were pH and P sorption. P dissolution was not significant at soil pH > 6.1 (ABC) and > 5 (GPR) and the lower the pH, the greater the Dissolved-P. Dissolved-P also correlated positively and significantly with inorganic P sorption, measured by the Freundlich isotherm and the P sorption index of Bache and Williams (1971). Soil pH and P sorption index could be combined in multiple regression equations that use readily measured soil properties to predict the potential for ABC dissolution in a soil. Dissolution of P from GPR correlated with soil pH and exchangeable acidity. In comparison with GPR, ABC was a better source of available P, assessed by Olsen-P. In most soils, ABC increased Olsen-P immediately after application, including soils of relatively high pH in which GPR was ineffective. ABC is a P fertilizer of solubility intermediate between GPR and TSP.

On the initiation of surface waves by turbulent shear flow

An analytical model is developed for the initial stage of surface wave generation at an air-water interface by a turbulent shear flow in either the air or in the water. The model treats the problem of wave growth departing from a flat interface and is relevant for small waves whose forcing is dominated by turbulent pressure fluctuations. The wave growth is predicted using the linearised and inviscid equations of motion, essentially following Phillips [Phillips, O.M., 1957. On the generation of waves by turbulent wind. J. Fluid Mech. 2, 417-445], but the pressure fluctuations that generate the waves are treated as unsteady and related to the turbulent velocity field using the rapid-distortion treatment of Durbin [Durbin, P.A., 1978. Rapid distortion theory of turbulent flows. PhD thesis, University of Cambridge]. This model, which assumes a constant mean shear rate F, can be viewed as the simplest representation of an oceanic or atmospheric boundary layer. For turbulent flows in the air and in the water producing pressure fluctuations of similar magnitude, the waves generated by turbulence in the water are found to be considerably steeper than those generated by turbulence in the air. For resonant waves, this is shown to be due to the shorter decorrelation time of turbulent pressure in the air (estimated as proportional to 1/Gamma), because of the higher shear rate existing in the air flow, and due to the smaller length scale of the turbulence in the water. Non-resonant waves generated by turbulence in the water, although being somewhat gentler, are still steeper than resonant waves generated by turbulence in the air. Hence, it is suggested that turbulence in the water may have a more important role than previously thought in the initiation of the surface waves that are subsequently amplified by feedback instability mechanisms.

Moving boundary value problems for the wave equation

We study certain boundary value problems for the one-dimensional wave equation posed in a time-dependent domain. The approach we propose is based on a general transform method for solving boundary value problems for integrable nonlinear PDE in two variables, that has been applied extensively to the study of linear parabolic and elliptic equations. Here we analyse the wave equation as a simple illustrative example to discuss the particular features of this method in the context of linear hyperbolic PDEs, which have not been studied before in this framework.

Systemic gut microbial modulation of bile acid metabolism in host tissue compartments

We elucidate the detailed effects of gut microbial depletion on the bile acid sub-metabolome of multiple body compartments (liver, kidney, heart, and blood plasma) in rats. We use a targeted ultraperformance liquid chromatography with time of flight mass-spectrometry assay to characterize the differential primary and secondary bile acid profiles in each tissue and show a major increase in the proportion of taurine-conjugated bile acids in germ-free (GF) and antibiotic (streptomycin/penicillin)-treated rats.Although conjugated bile acids dominate the hepatic profile (97.0 ± 1.5%) of conventional animals, unconjugated bile acids comprise the largest proportion of the total measured bile acid profile in kidney (60.0±10.4%) andheart (53.0 ± 18.5%) tissues. In contrast, in the GF animal, taurine-conjugated bile acids (especially taurocholic acid and tauro-β-muricholic acid) dominated the bile acid profiles (liver: 96.0 ± 14.5%; kidney: 96 ± 1%; heart: 93 ± 1%; plasma: 93.0 ± 2.3%), with unconjugated and glycine-conjugated species representing a small proportion of the profile. Higher free taurine levels were found in GF livers compared with the conventional liver (5.1-fold; P < 0.001). Bile acid diversity was also lower in GF and antibiotic-treated tissues compared with conventional animals. Because bile acids perform important signaling functions, it is clear that these chemical communication networks are strongly influencedbymicrobial activitiesormodulation, as evidenced by farnesoid X receptor-regulated pathway transcripts. The presence of specific microbial bile acid co-metabolite patterns in peripheral tissues (including heart and kidney) implies a broader signaling role for these compounds and emphasizes the extent of symbiotic microbial influences in mammalian homeostasis.

Proteomic analysis of plasma membrane vesicles isolated from the rat renal cortex

Polarized epithelial cells are responsible for the vectorial transport of solutes and have a key role in maintaining body fluid and electrolyte homeostasis. Such cells contain structurally and functionally distinct plasma membrane domains. Brush border and basolateral membranes of renal and intestinal epithelial cells can be separated using a number of different separation techniques, which allow their different transport functions and receptor expressions to be studied. In this communication, we report a proteomic analysis of these two membrane segments, apical and basolateral, obtained from the rat renal cortex isolated by two different methods: differential centrifugation and free-flow electrophoresis. The study was aimed at assessing the nature of the major proteins isolated by these two separation techniques. Two analytical strategies were used: separation by sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) at the protein level or by cation-exchange high-performance liquid chromatography (HPLC) after proteolysis (i.e., at the peptide level). Proteolytic peptides derived from the proteins present in gel pieces or from HPLC fractions after proteolysis were sequenced by on-line liquid chromatography-tandem mass spectrometry (LC-MS/MS). Several hundred proteins were identified in each membrane section. In addition to proteins known to be located at the apical and basolateral membranes, several novel proteins were also identified. In particular, a number of proteins with putative roles in signal transduction were identified in both membranes. To our knowledge, this is the first reported study to try and characterize the membrane proteome of polarized epithelial cells and to provide a data set of the most abundant proteins present in renal proximal tubule cell membranes.

Proteomic analysis of plasma membrane vesicles isolated from the rat renal cortex

Polarized epithelial cells are responsible for the vectorial transport of solutes and have a key role in maintaining body fluid and electrolyte homeostasis. Such cells contain structurally and functionally distinct plasma membrane domains. Brush border and basolateral membranes of renal and intestinal epithelial cells can be separated using a number of different separation techniques, which allow their different transport functions and receptor expressions to be studied. In this communication, we report a proteomic analysis of these two membrane segments, apical and basolateral, obtained from the rat renal cortex isolated by two different methods: differential centrifugation and free-flow electrophoresis. The study was aimed at assessing the nature of the major proteins isolated by these two separation techniques. Two analytical strategies were used: separation by sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) at the protein level or by cation-exchange high-performance liquid chromatography (HPLC) after proteolysis (i.e., at the peptide level). Proteolytic peptides derived from the proteins present in gel pieces or from HPLC fractions after proteolysis were sequenced by on-line liquid chromatography-tandem mass spectrometry (LC-MS/MS). Several hundred proteins were identified in each membrane section. In addition to proteins known to be located at the apical and basolateral membranes, several novel proteins were also identified. In particular, a number of proteins with putative roles in signal transduction were identified in both membranes. To our knowledge, this is the first reported study to try and characterize the membrane proteome of polarized epithelial cells and to provide a data set of the most abundant proteins present in renal proximal tubule cell membranes.

Kinetics of high pressure facilitated starch gelatinisation in Thai glutinous rice

The combined effect of pressure and temperature on the rate of gelatinisation of starch present in Thai glutinous rice was investigated. Pressure was found to initiate gelatinisation when its value exceeded 200 MPa at ambient temperature. On the other hand, complete gelatinisation was observed at 500 and 600 MPa at 70 degrees C, when the rice was soaked in water under these conditions for 120 min. A first-order kinetic model describing the rate of gelatinisation was developed to estimate the values of the rate constants as a function of pressure and temperature in the range: 0.1-600 MPa and 20-70 degrees C. The model, based on the well-known Arrhenius and Eyring equations, assumed the form [GRAPHICS] The constants k(0), E-a, and Delta V were found to take values: 31.19 s(-1), 37.89 kJ mol(-1) and -9.98 cm(3) mol(-1), respectively. It was further noted that the extent of gelatinisation occurring at any time, temperature and pressure, could be exclusively correlated with the grain moisture content. (c) 2006 Elsevier Ltd. All rights reserved.

Optimal observers for ARMA models

A polynomial-based ARMA model, when posed in a state-space framework can be regarded in many different ways. In this paper two particular state-space forms of the ARMA model are considered, and although both are canonical in structure they differ in respect of the mode in which disturbances are fed into the state and output equations. For both forms a solution is found to the optimal discrete-time observer problem and algebraic connections between the two optimal observers are shown. The purpose of the paper is to highlight the fact that the optimal observer obtained from the first state-space form, commonly known as the innovations form, is not that employed in an optimal controller, in the minimum-output variance sense, whereas the optimal observer obtained from the second form is. Hence the second form is a much more appropriate state-space description to use for controller design, particularly when employed in self-tuning control schemes.

Dispersion of a point-source release of a passive scalar through an urban-like array for different wind directions

The dispersion of a point-source release of a passive scalar in a regular array of cubical, urban-like, obstacles is investigated by means of direct numerical simulations. The simulations are conducted under conditions of neutral stability and fully rough turbulent flow, at a roughness Reynolds number of Reτ = 500. The Navier–Stokes and scalar equations are integrated assuming a constant rate release from a point source close to the ground within the array. We focus on short-range dispersion, when most of the material is still within the building canopy. Mean and fluctuating concentrations are computed for three different pressure gradient directions (0◦ , 30◦ , 45◦). The results agree well with available experimental data measured in a water channel for a flow angle of 0◦ . Profiles of mean concentration and the three-dimensional structure of the dispersion pattern are compared for the different forcing angles. A number of processes affecting the plume structure are identified and discussed, including: (i) advection or channelling of scalar down ‘streets’, (ii) lateral dispersion by turbulent fluctuations and topological dispersion induced by dividing streamlines around buildings, (iii) skewing of the plume due to flow turning with height, (iv) detrainment by turbulent dispersion or mean recirculation, (v) entrainment and release of scalar in building wakes, giving rise to ‘secondary sources’, (vi) plume meandering due to unsteady turbulent fluctuations. Finally, results on relative concentration fluctuations are presented and compared with the literature for point source dispersion over flat terrain and urban arrays. Keywords Direct numerical simulation · Dispersion modelling · Urban array

Radar scattering from ice aggregates using the horizontally aligned oblate spheroid approximation

The assumed relationship between ice particle mass and size is profoundly important in radar retrievals of ice clouds, but, for millimeter-wave radars, shape and preferred orientation are important as well. In this paper the authors first examine the consequences of the fact that the widely used ‘‘Brown and Francis’’ mass–size relationship has often been applied to maximumparticle dimension observed by aircraftDmax rather than to the mean of the particle dimensions in two orthogonal directions Dmean, which was originally used by Brown and Francis. Analysis of particle images reveals that Dmax ’ 1.25Dmean, and therefore, for clouds for which this mass–size relationship holds, the consequences are overestimates of ice water content by around 53% and of Rayleigh-scattering radar reflectivity factor by 3.7 dB. Simultaneous radar and aircraft measurements demonstrate that much better agreement in reflectivity factor is provided by using this mass–size relationship with Dmean. The authors then examine the importance of particle shape and fall orientation for millimeter-wave radars. Simultaneous radar measurements and aircraft calculations of differential reflectivity and dual-wavelength ratio are presented to demonstrate that ice particles may usually be treated as horizontally aligned oblate spheroids with an axial ratio of 0.6, consistent with them being aggregates. An accurate formula is presented for the backscatter cross section apparent to a vertically pointing millimeter-wave radar on the basis of a modified version of Rayleigh–Gans theory. It is then shown that the consequence of treating ice particles as Mie-scattering spheres is to substantially underestimate millimeter-wave reflectivity factor when millimeter-sized particles are present, which can lead to retrieved ice water content being overestimated by a factor of 4.h

A unified theory of balance in the extratropics

Many physical systems exhibit dynamics with vastly different time scales. Often the different motions interact only weakly and the slow dynamics is naturally constrained to a subspace of phase space, in the vicinity of a slow manifold. In geophysical fluid dynamics this reduction in phase space is called balance. Classically, balance is understood by way of the Rossby number R or the Froude number F; either R ≪ 1 or F ≪ 1. We examined the shallow-water equations and Boussinesq equations on an f -plane and determined a dimensionless parameter _, small values of which imply a time-scale separation. In terms of R and F, ∈= RF/√(R^2+R^2 ) We then developed a unified theory of (extratropical) balance based on _ that includes all cases of small R and/or small F. The leading-order systems are ensured to be Hamiltonian and turn out to be governed by the quasi-geostrophic potential-vorticity equation. However, the height field is not necessarily in geostrophic balance, so the leading-order dynamics are more general than in quasi-geostrophy. Thus the quasi-geostrophic potential-vorticity equation (as distinct from the quasi-geostrophic dynamics) is valid more generally than its traditional derivation would suggest. In the case of the Boussinesq equations, we have found that balanced dynamics generally implies hydrostatic balance without any assumption on the aspect ratio; only when the Froude number is not small and it is the Rossby number that guarantees a timescale separation must we impose the requirement of a small aspect ratio to ensure hydrostatic balance.

Hamiltonian geophysical fluid dynamics

Hamiltonian dynamics describes the evolution of conservative physical systems. Originally developed as a generalization of Newtonian mechanics, describing gravitationally driven motion from the simple pendulum to celestial mechanics, it also applies to such diverse areas of physics as quantum mechanics, quantum field theory, statistical mechanics, electromagnetism, and optics – in short, to any physical system for which dissipation is negligible. Dynamical meteorology consists of the fundamental laws of physics, including Newton’s second law. For many purposes, diabatic and viscous processes can be neglected and the equations are then conservative. (For example, in idealized modeling studies, dissipation is often only present for numerical reasons and is kept as small as possible.) In such cases dynamical meteorology obeys Hamiltonian dynamics. Even when nonconservative processes are not negligible, it often turns out that separate analysis of the conservative dynamics, which fully describes the nonlinear interactions, is essential for an understanding of the complete system, and the Hamiltonian description can play a useful role in this respect. Energy budgets and momentum transfer by waves are but two examples.