A simple column model to explore anticipated problems in variational assimilation of satellite observations

We investigate a simplified form of variational data assimilation in a fully nonlinear framework with the aim of extracting dynamical development information from a sequence of observations over time. Information on the vertical wind profile, w(z ), and profiles of temperature, T (z , t), and total water content, qt (z , t), as functions of height, z , and time, t, are converted to brightness temperatures at a single horizontal location by defining a two-dimensional (vertical and time) variational assimilation testbed. The profiles of T and qt are updated using a vertical advection scheme. A basic cloud scheme is used to obtain the fractional cloud amount and, when combined with the temperature field, this information is converted into a brightness temperature, using a simple radiative transfer scheme. It is shown that our model exhibits realistic behaviour with regard to the prediction of cloud, but the effects of nonlinearity become non-negligible in the variational data assimilation algorithm. A careful analysis of the application of the data assimilation scheme to this nonlinear problem is presented, the salient difficulties are highlighted, and suggestions for further developments are discussed.

The effect of nonlinearity on the variational assimilation of satellite observations using a simple column model

Cloud imagery is not currently used in numerical weather prediction (NWP) to extract the type of dynamical information that experienced forecasters have extracted subjectively for many years. For example, rapidly developing mid-latitude cyclones have characteristic signatures in the cloud imagery that are most fully appreciated from a sequence of images rather than from a single image. The Met Office is currently developing a technique to extract dynamical development information from satellite imagery using their full incremental 4D-Var (four-dimensional variational data assimilation) system. We investigate a simplified form of this technique in a fully nonlinear framework. We convert information on the vertical wind field, w(z), and profiles of temperature, T(z, t), and total water content, qt (z, t), as functions of height, z, and time, t, to a single brightness temperature by defining a 2D (vertical and time) variational assimilation testbed. The profiles of w, T and qt are updated using a simple vertical advection scheme. We define a basic cloud scheme to obtain the fractional cloud amount and, when combined with the temperature field, we convert this information into a brightness temperature, having developed a simple radiative transfer scheme. With the exception of some matrix inversion routines, all our code is developed from scratch. Throughout the development process we test all aspects of our 2D assimilation system, and then run identical twin experiments to try and recover information on the vertical velocity, from a sequence of observations of brightness temperature. This thesis contains a comprehensive description of our nonlinear models and assimilation system, and the first experimental results.

Deriving global flood hazard maps of fluvial floods through a physical model cascade

Global flood hazard maps can be used in the assessment of flood risk in a number of different applications, including (re)insurance and large scale flood preparedness. Such global hazard maps can be generated using large scale physically based models of rainfall-runoff and river routing, when used in conjunction with a number of post-processing methods. In this study, the European Centre for Medium Range Weather Forecasts (ECMWF) land surface model is coupled to ERA-Interim reanalysis meteorological forcing data, and resultant runoff is passed to a river routing algorithm which simulates floodplains and flood flow across the global land area. The global hazard map is based on a 30 yr (1979–2010) simulation period. A Gumbel distribution is fitted to the annual maxima flows to derive a number of flood return periods. The return periods are calculated initially for a 25×25 km grid, which is then reprojected onto a 1×1 km grid to derive maps of higher resolution and estimate flooded fractional area for the individual 25×25 km cells. Several global and regional maps of flood return periods ranging from 2 to 500 yr are presented. The results compare reasonably to a benchmark data set of global flood hazard. The developed methodology can be applied to other datasets on a global or regional scale.

Fractional order modeling of large three-dimensional RC networks

An incidence matrix analysis is used to model a three-dimensional network consisting of resistive and capacitive elements distributed across several interconnected layers. A systematic methodology for deriving a descriptor representation of the network with random allocation of the resistors and capacitors is proposed. Using a transformation of the descriptor representation into standard state-space form, amplitude and phase admittance responses of three-dimensional random RC networks are obtained. Such networks display an emergent behavior with a characteristic Jonscher-like response over a wide range of frequencies. A model approximation study of these networks is performed to infer the admittance response using integral and fractional order models. It was found that a fractional order model with only seven parameters can accurately describe the responses of networks composed of more than 70 nodes and 200 branches with 100 resistors and 100 capacitors. The proposed analysis can be used to model charge migration in amorphous materials, which may be associated to specific macroscopic or microscopic scale fractal geometrical structures in composites displaying a viscoelastic electromechanical response, as well as to model the collective responses of processes governed by random events described using statistical mechanics.

The influence of vegetation, fire spread and fire behaviour on biomass burning and trace gas emissions: results from a process-based model

A process-based fire regime model (SPITFIRE) has been developed, coupled with ecosystem dynamics in the LPJ Dynamic Global Vegetation Model, and used to explore fire regimes and the current impact of fire on the terrestrial carbon cycle and associated emissions of trace atmospheric constituents. The model estimates an average release of 2.24 Pg C yr−1 as CO2 from biomass burning during the 1980s and 1990s. Comparison with observed active fire counts shows that the model reproduces where fire occurs and can mimic broad geographic patterns in the peak fire season, although the predicted peak is 1–2 months late in some regions. Modelled fire season length is generally overestimated by about one month, but shows a realistic pattern of differences among biomes. Comparisons with remotely sensed burnt-area products indicate that the model reproduces broad geographic patterns of annual fractional burnt area over most regions, including the boreal forest, although interannual variability in the boreal zone is underestimated.

Identification of fractional-order transfer functions using a step excitation

This brief proposes a new method for the identification of fractional order transfer functions based on the time response resulting from a single step excitation. The proposed method is applied to the identification of a three-dimensional RC network, which can be tailored in terms of topology and composition to emulate real time systems governed by fractional order dynamics. The results are in excellent agreement with the actual network response, yet the identification procedure only requires a small number of coefficients to be determined, demonstrating that the fractional order modelling approach leads to very parsimonious model formulations.

Fractional quantum Hall effect in second subband of a 2DES

In the present paper we report on the experimental electron sheet density vs. magnetic field diagram for the magnetoresistance R(xx) of a two-dimensional electron system (2DES) with two occupied subbands. For magnetic fields above 9T, we found fractional quantum Hall levels centered around the filing factor v = 3/2 in both the two occupied electric subbands. We focused specially on the fractional levels of the second subband, whose experimental values of the magnetic field B of their minima do not obey a periodicity law in 1/|B-B(c)|, where B(c) is the critical field at the filling factor v = 3/2, and we explain this fact entirely in the framework of the composite fermions theory. We use a simple theoretical model to give a possible explanation for the fact. Copyright (c) EPLA, 2011

Effects of apolipoprotein B-100 on the metabolism of a lipid microemulsion model in rats

In previous studies, it was shown that lipid microemulsions resembling LDL (LDE) but not containing protein, acquire apolipoprotein E when injected into the bloodstream and bind to LDL receptors (LDLR) using this protein as ligand. Aiming to evaluate the effects of apolipoprotein (apo) B-100 on the catabolism of these microemulsions, LDE with incorporated apo B-100 (LDE-apoB) and native LDL, all labeled with radioactive lipids were studied after intraarterial injection into Wistar rats. Plasma decay curves of the labels were determined in samples collected over 10 h and tissue uptake was assayed from organs excised from the animals sacrificed 24 h after injection. LDE-apo B had a fractional clearance rate (FCR) similar to native LDL (0.40 and 0.33, respectively) but both had FCR pronouncedly smaller than LDE (0.56, P<0.01). Liver was the main uptake site for LDE, LDE-apoB, and native LDL, but LDE-apoB and native LDL had lower hepatic uptake rates than LDE. Pre-treatment of the rats with 17 alpha-ethinylestradiol, known to upregulate LDLR, accelerated the removal from plasma of both LDE and LDE-apoB, but the effect was greater upon LDE than LDE-apoB. These differences in metabolic behavior documented in vivo can be interpreted by the lower affinity of LDLR for apo B-100 than for apo E, demonstrated in in vitro studies. Therefore, our study shows in vivo that, in comparison with apo E, apo B is a less efficient ligand to remove lipid particles such as microemulsions or lipoproteins from the intravascular compartment. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Fractional polynomial response surface models

Second-order polynomial models have been used extensively to approximate the relationship between a response variable and several continuous factors. However, sometimes polynomial models do not adequately describe the important features of the response surface. This article describes the use of fractional polynomial models. It is shown how the models can be fitted, an appropriate model selected, and inference conducted. Polynomial and fractional polynomial models are fitted to two published datasets, illustrating that sometimes the fractional polynomial can give as good a fit to the data and much more plausible behavior between the design points than the polynomial model. © 2005 American Statistical Association and the International Biometric Society.

Fractional fermion charges induced by axial-vector and vector gauge potentials and parity anomaly in planar graphenelike structures

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A prelude to the fractional calculus applied to tumor dynamic

In order to refine the solution given by the classical logistic equation and extend its range of applications in the study of tumor dynamics, we propose and solve a generalization of this equation, using the so-called Fractional Calculus, i.e., we replace the ordinary derivative of order 1, in one version of the usual equation, by a non-integer derivative of order 0 < α < 1, and recover the classical solution as a particular case. Finally, we analyze the applicability of this model to describe the growth of cancer tumors.

Chronic VEGF Blockade Worsens Glomerular Injury in the Remnant Kidney Model

VEGF inhibition can promote renal vascular and parenchymal injury, causing proteinuria, hypertension and thrombotic microangiopathy. The mechanisms underlying these side effects are unclear. We investigated the renal effects of the administration, during 45 days, of sunitinib (Su), a VEGF receptor inhibitor, to rats with 5/6 renal ablation (Nx). Adult male Munich-Wistar rats were distributed among groups S+V, sham-operated rats receiving vehicle only; S+Su, S rats given Su, 4 mg/kg/day; Nx+V, Nx rats receiving V; and Nx+Su, Nx rats receiving Su. Su caused no change in Group S. Seven and 45 days after renal ablation, renal cortical interstitium was expanded, in association with rarefaction of peritubular capillaries. Su did not worsen hypertension, proteinuria or interstitial expansion, nor did it affect capillary rarefaction, suggesting little angiogenic activity in this model. Nx animals exhibited glomerulosclerosis (GS), which was aggravated by Su. This effect could not be explained by podocyte damage, nor could it be ascribed to tuft hypertrophy or hyperplasia. GS may have derived from organization of capillary microthrombi, frequently observed in Group Nx+Su. Treatment with Su did not reduce the fractional glomerular endothelial area, suggesting functional rather than structural cell injury. Chronic VEGF inhibition has little effect on normal rats, but can affect glomerular endothelium when renal damage is already present.

Alzheimer random walk model: Two previously overlooked diffusion regimes

A non-Markovian one-dimensional random walk model is studied with emphasis on the phase-diagram, showing all the diffusion regimes, along with the exactly determined critical lines. The model, known as the Alzheimer walk, is endowed with memory-controlled diffusion, responsible for the model's long-range correlations, and is characterized by a rich variety of diffusive regimes. The importance of this model is that superdiffusion arises due not to memory per se, but rather also due to loss of memory. The recently reported numerically and analytically estimated values for the Hurst exponent are hereby reviewed. We report the finding of two, previously overlooked, phases, namely, evanescent log-periodic diffusion and log-periodic diffusion with escape, both with Hurst exponent H = 1/2. In the former, the log-periodicity gets damped, whereas in the latter the first moment diverges. These phases further enrich the already intricate phase diagram. The results are discussed in the context of phase transitions, aging phenomena, and symmetry breaking.

Hyperbaric Oxygen Therapy Induces Kidney Protection in an Ischemia/Reperfusion Model in Rats

Ischemia/reperfusion (I/R) injury remains a major cause of graft dysfunction, which impacts short- and long-term follow-up. Hyperbaric oxygen therapy (HBO), through plasma oxygen transport, has been currently used as an alternative treatment for ischemic tissues. The aim of this study was to analyze the effects of HBO on kidney I/R injury model in rats, in reducing the harmful effect of I/R. The renal I/R model was obtained by occluding bilateral renal pedicles with nontraumatic vascular clamps for 45 minutes, followed by 48 hours of reperfusion. HBO therapy was delivered an hypebaric chamber (2.5 atmospheres absolute). Animals underwent two sessions of 60 minutes each at 6 hours and 20 hours after initiation of reperfusion. Male Wistar rats (n = 38) were randomized into four groups: sham, sham operated rats; Sham+HBO, sham operated rats exposed to HBO; I/R, animals submitted to I/R; and I/R+HBO, I/R rats exposed to HBO. Blood, urine, and kidney tissue were collected for biochemical, histologic, and immunohistochemical analyses. The histopathological evaluation of the ischemic injury used a grading scale of 0 to 4. HBO attenuated renal dysfunction after ischemia characterized by a significant decrease in blood urea nitrogen (BUN), serum creatinine, and proteinuria in the I/R+HBO group compared with I/R alone. In parallel, tubular function was improved resulting in significantly lower fractional excretions of sodium and potassium. Kidney sections from the I/R plus HBO group showed significantly lower acute kidney injury scores compared with the I/R group. HBO treatment significantly diminished proliferative activity in I/R (P < .05). There was no significant difference in macrophage infiltration or hemoxygenase-1 expression. In conclusion, HBO attenuated renal dysfunction in a kidney I/R injury model with a decrease in BUN, serum creatinine, proteinuria, and fractional excretion of sodium and potassium, associated with reduced histological damage.

Regional lung perfusion estimated by electrical impedance tomography in a piglet model of lung collapse

Borges JB, Suarez-Sipmann F, Bohm SH, Tusman G, Melo A, Maripuu E, Sandstrom M, Park M, Costa EL, Hedenstierna G, Amato M. Regional lung perfusion estimated by electrical impedance tomography in a piglet model of lung collapse. J Appl Physiol 112: 225-236, 2012. First published September 29, 2011; doi: 10.1152/japplphysiol.01090.2010.-The assessment of the regional match between alveolar ventilation and perfusion in critically ill patients requires simultaneous measurements of both parameters. Ideally, assessment of lung perfusion should be performed in real-time with an imaging technology that provides, through fast acquisition of sequential images, information about the regional dynamics or regional kinetics of an appropriate tracer. We present a novel electrical impedance tomography (EIT)-based method that quantitatively estimates regional lung perfusion based on first-pass kinetics of a bolus of hypertonic saline contrast. Pulmonary blood flow was measured in six piglets during control and unilateral or bilateral lung collapse conditions. The first-pass kinetics method showed good agreement with the estimates obtained by single-photon-emission computerized tomography (SPECT). The mean difference (SPECT minus EIT) between fractional blood flow to lung areas suffering atelectasis was -0.6%, with a SD of 2.9%. This method outperformed the estimates of lung perfusion based on impedance pulsatility. In conclusion, we describe a novel method based on EIT for estimating regional lung perfusion at the bedside. In both healthy and injured lung conditions, the distribution of pulmonary blood flow as assessed by EIT agreed well with the one obtained by SPECT. The method proposed in this study has the potential to contribute to a better understanding of the behavior of regional perfusion under different lung and therapeutic conditions.