Conditioning of incremental variational data assimilation, with application to the Met Office system

Implementations of incremental variational data assimilation require the iterative minimization of a series of linear least-squares cost functions. The accuracy and speed with which these linear minimization problems can be solved is determined by the condition number of the Hessian of the problem. In this study, we examine how different components of the assimilation system influence this condition number. Theoretical bounds on the condition number for a single parameter system are presented and used to predict how the condition number is affected by the observation distribution and accuracy and by the specified lengthscales in the background error covariance matrix. The theoretical results are verified in the Met Office variational data assimilation system, using both pseudo-observations and real data.

Conditioning and preconditioning of the variational data assimilation problem

Numerical weather prediction (NWP) centres use numerical models of the atmospheric flow to forecast future weather states from an estimate of the current state. Variational data assimilation (VAR) is used commonly to determine an optimal state estimate that miminizes the errors between observations of the dynamical system and model predictions of the flow. The rate of convergence of the VAR scheme and the sensitivity of the solution to errors in the data are dependent on the condition number of the Hessian of the variational least-squares objective function. The traditional formulation of VAR is ill-conditioned and hence leads to slow convergence and an inaccurate solution. In practice, operational NWP centres precondition the system via a control variable transform to reduce the condition number of the Hessian. In this paper we investigate the conditioning of VAR for a single, periodic, spatially-distributed state variable. We present theoretical bounds on the condition number of the original and preconditioned Hessians and hence demonstrate the improvement produced by the preconditioning. We also investigate theoretically the effect of observation position and error variance on the preconditioned system and show that the problem becomes more ill-conditioned with increasingly dense and accurate observations. Finally, we confirm the theoretical results in an operational setting by giving experimental results from the Met Office variational system.

A metabolic system-wide characterisation of the pig: a model for human physiology

The pig is a single-stomached omnivorous mammal and is an important model of human disease and nutrition. As such, it is necessary to establish a metabolic framework from which pathology-based variation can be compared. Here, a combination of one and two-dimensional (1)H and (13)C nuclear magnetic resonance spectroscopy (NMR) and high-resolution magic angle spinning (HR-MAS) NMR was used to provide a systems overview of porcine metabolism via characterisation of the urine, serum, liver and kidney metabolomes. The metabolites observed in each of these biological compartments were found to be qualitatively comparable to the metabolic signature of the same biological matrices in humans and rodents. The data were modelled using a combination of principal components analysis and Venn diagram mapping. Urine represented the most metabolically distinct biological compartment studied, with a relatively greater number of NMR detectable metabolites present, many of which are implicated in gut-microbial co-metabolic processes. The major inter-species differences observed were in the phase II conjugation of extra-genomic metabolites; the pig was observed to conjugate p-cresol, a gut microbial metabolite of tyrosine, with glucuronide rather than sulfate as seen in man. These observations are important to note when considering the translatability of experimental data derived from porcine models.

L1-regularisation for ill-posed problems in variational data assimilation

We consider four-dimensional variational data assimilation (4DVar) and show that it can be interpreted as Tikhonov or L2-regularisation, a widely used method for solving ill-posed inverse problems. It is known from image restoration and geophysical problems that an alternative regularisation, namely L1-norm regularisation, recovers sharp edges better than L2-norm regularisation. We apply this idea to 4DVar for problems where shocks and model error are present and give two examples which show that L1-norm regularisation performs much better than the standard L2-norm regularisation in 4DVar.

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.

Random-walk-based characterisation of multiple access interference in a DS/SSMA system

The problem of calculating the probability of error in a DS/SSMA system has been extensively studied for more than two decades. When random sequences are employed some conditioning must be done before the application of the central limit theorem is attempted, leading to a Gaussian distribution. The authors seek to characterise the multiple access interference as a random-walk with a random number of steps, for random and deterministic sequences. Using results from random-walk theory, they model the interference as a K-distributed random variable and use it to calculate the probability of error in the form of a series, for a DS/SSMA system with a coherent correlation receiver and BPSK modulation under Gaussian noise. The asymptotic properties of the proposed distribution agree with other analyses. This is, to the best of the authors' knowledge, the first attempt to propose a non-Gaussian distribution for the interference. The modelling can be extended to consider multipath fading and general modulation

Chemical characterisation and determination of sensory attributes of hydrolysates produced by enzymatic hydrolysis of whey proteins following a novel integrative process

The overall aim of this work was to characterize the major angiotensin converting enzyme (ACE) inhibitory peptides produced by enzymatic hydrolysis of whey proteins, through the application of a novel integrative process. This process consisted of the combination of adsorption and microfiltration within a stirred cell unit for the selective immobilization of β-lactoglobulin and casein derived peptides (CDP) from whey. The adsorbed proteins were hydrolyzed in-situ which resulted in the separation of peptide products from the substrate and fractionation of peptides. Two different hydrolysates were produced: (i) from CDP (IC50 =287μg/mL) and (ii) from β-lactoglobulin (IC50=128μg/mL). IC50 is the concentration of inhibitor needed to inhibit ACE by half. The well known antihypertensive peptide IPP and several novel peptides that have structural similarities with reported ACE inhibitory peptides were identified and characterized in both hydrolysates. Furthermore, the hydrolysates were assessed for bitterness. No significant difference was found between the control (milk with no hydrolysate) and hydrolysate samples at different concentrations (at, below and above the IC50).

Characterisation of connective tissue from the hypertrophic skeletal muscle of myostatin null mice

Myostatin is a potent inhibitor of muscle development. Genetic deletion of myostatin in mice results in muscle mass increase, with muscles often weighing three times their normal values. Contracting muscle transfers tension to skeletal elements through an elaborate connective tissue network. Therefore, the connective tissue of skeletal muscle is an integral component of the contractile apparatus. Here we examine the connective tissue architecture in myostatin null muscle. We show that the hypertrophic muscle has decreased connective tissue content compared with wild-type muscle. Secondly, we show that the hypertrophic muscle fails to show the normal increase in muscle connective tissue content during ageing. Therefore, genetic deletion of myostatin results in an increase in contractile elements but a decrease in connective tissue content. We propose a model based on the contractile profile of muscle fibres that reconciles this apparent incompatible tissue composition phenotype.

Integration of a 3D Variational data assimilation scheme with a coastal area morphodynamic model of Morecambe Bay

This paper describes the implementation of a 3D variational (3D-Var) data assimilation scheme for a morphodynamic model applied to Morecambe Bay, UK. A simple decoupled hydrodynamic and sediment transport model is combined with a data assimilation scheme to investigate the ability of such methods to improve the accuracy of the predicted bathymetry. The inverse forecast error covariance matrix is modelled using a Laplacian approximation which is calibrated for the length scale parameter required. Calibration is also performed for the Soulsby-van Rijn sediment transport equations. The data used for assimilation purposes comprises waterlines derived from SAR imagery covering the entire period of the model run, and swath bathymetry data collected by a ship-borne survey for one date towards the end of the model run. A LiDAR survey of the entire bay carried out in November 2005 is used for validation purposes. The comparison of the predictive ability of the model alone with the model-forecast-assimilation system demonstrates that using data assimilation significantly improves the forecast skill. An investigation of the assimilation of the swath bathymetry as well as the waterlines demonstrates that the overall improvement is initially large, but decreases over time as the bathymetry evolves away from that observed by the survey. The result of combining the calibration runs into a pseudo-ensemble provides a higher skill score than for a single optimized model run. A brief comparison of the Optimal Interpolation assimilation method with the 3D-Var method shows that the two schemes give similar results.

Phenotype MicroArray (TM) in the metabolic characterisation of Salmonella serotypes Agona, Enteritidis, Give, Hvittingfoss, Infantis, Newport and Typhimurium

The Phenotype MicroArray (TM) (PM) technology was used to study the metabolic characteristics of 29 Salmonella strains belonging to seven serotypes of S. enterica spp. enterica. Strains of serotypes Typhimurium (six strains among definite phage types DTs 1, 40 and 104) and Agona (two strains) were tested for 949 substrates, Enteritidis (six strains of phage type PT1), Give, Hvittingfoss, Infantis and Newport strains (two of each) were tested for 190 substrates and seven other Agona strains for 95 substrates. The strains represented 18 genotypes in pulsed-field gel electrophoresis (PFGE). Among 949 substrates, 18 were identified that could be used to differentiate between the strains of those seven serotypes or within a single serotype. Unique metabolic differences between the Finnish endemic Typhimurium DT1 and Agona strains were detected, for example, in the metabolism of d-tagatose, d-galactonic acid gamma-lactone and l-proline as a carbon source. Thus, the PM technique is a useful tool for identifying potential differential markers on a metabolic basis that could be used for epidemiological surveillance.

Characterisation of Escherichia fergusonii isolates from farm animals using an Escherichia coli virulence gene array and tissue culture adherence assays

Escherichia fergusonii has been associated with a wide variety of intestinal and extra-intestinal infections in both humans and animals but, despite strong circumstantial evidence, the degree to which the organism is responsible for the pathologies identified remains uncertain. Thirty isolates of E fergusonii collected between 2003 and 2004 were screened using an Escherichia coli virulence gene array to test for the presence of homologous virulence genes in E. fergusonii. The iss (increased serum survival) gene was present in 13/30 (43%) of the test strains and the prfB (P-related fimbriae regulatory) and ireA (siderophore receptor IreA) genes were also detected jointly in 3/30 (10%) strains. No known virulence genes were detected in 14/30 (47%) of strains. Following confirmatory PCR and sequence analysis, the E. fergusonii prfB, iss and ireA genes shared a high degree of sequence similarity to their counterparts in E. coli, and a particular resemblance was noted with the E. coli strain APEC O1 pathogenicity island. In tissue culture adherence assays, nine E. fergusonii isolates associated with HEp-2 cells with a 'localised adherence' or 'diffuse adherence' phenotype, and they proved to be moderately invasive. The E fergusonii isolates in this study possess both some phenotypic and genotypic features linked to known pathotypes of E coli, and support existing evidence that strains of E fergusonii may act as an opportunistic pathogens, although their specific virulence factors may need to be explored. Crown Copyright (c) 2008 Published by Elsevier Ltd. All rights reserved.

A variational method to retrieve the extinction profile in liquid clouds using multiple field-of-view lidar

Liquid clouds play a profound role in the global radiation budget but it is difficult to remotely retrieve their vertical profile. Ordinary narrow field-of-view (FOV) lidars receive a strong return from such clouds but the information is limited to the first few optical depths. Wideangle multiple-FOV lidars can isolate radiation scattered multiple times before returning to the instrument, often penetrating much deeper into the cloud than the singly-scattered signal. These returns potentially contain information on the vertical profile of extinction coefficient, but are challenging to interpret due to the lack of a fast radiative transfer model for simulating them. This paper describes a variational algorithm that incorporates a fast forward model based on the time-dependent two-stream approximation, and its adjoint. Application of the algorithm to simulated data from a hypothetical airborne three-FOV lidar with a maximum footprint width of 600m suggests that this approach should be able to retrieve the extinction structure down to an optical depth of around 6, and total opticaldepth up to at least 35, depending on the maximum lidar FOV. The convergence behavior of Gauss-Newton and quasi-Newton optimization schemes are compared. We then present results from an application of the algorithm to observations of stratocumulus by the 8-FOV airborne “THOR” lidar. It is demonstrated how the averaging kernel can be used to diagnose the effective vertical resolution of the retrieved profile, and therefore the depth to which information on the vertical structure can be recovered. This work enables exploitation of returns from spaceborne lidar and radar subject to multiple scattering more rigorously than previously possible.

Characterisation of the intracellular-glutamate decarboxylase system (GAD): analysis of its function, transcription and role in the acid resistance of various strains of Listeria monocytogenes

The glutamate decarboxylase (GAD) system is important for the acid resistance of Listeria monocytogenes. We previously showed that under acidic conditions, glutamate (Glt)/γ-aminobutyrate (GABA) antiport is impaired in minimal media but not in rich ones, like brain heart infusion. Here we demonstrate that this behavior is more complex and it is subject to strain and medium variation. Despite the impaired Glt/GABA antiport, cells accumulate intracellular GABA (GABA(i)) as a standard response against acid in any medium, and this occurs in all strains tested. Since these systems can occur independently of one another, we refer to them as the extracellular (GAD(e)) and intracellular (GAD(i)) systems. We show here that GAD(i) contributes to acid resistance since in a ΔgadD1D2 mutant, reduced GABA(i) accumulation coincided with a 3.2-log-unit reduction in survival at pH 3.0 compared to that of wild-type strain LO28. Among 20 different strains, the GAD(i) system was found to remove 23.11% ± 18.87% of the protons removed by the overall GAD system. Furthermore, the GAD(i) system is activated at milder pH values (4.5 to 5.0) than the GAD(e) system (pH 4.0 to 4.5), suggesting that GAD(i) is the more responsive of the two and the first line of defense against acid. Through functional genomics, we found a major role for GadD2 in the function of GAD(i), while that of GadD1 was minor. Furthermore, the transcription of the gad genes in three common reference strains (10403S, LO28, and EGD-e) during an acid challenge correlated well with their relative acid sensitivity. No transcriptional upregulation of the gadT2D2 operon, which is the most important component of the GAD system, was observed, while gadD3 transcription was the highest among all gad genes in all strains. In this study, we present a revised model for the function of the GAD system and highlight the important role of GAD(i) in the acid resistance of L. monocytogenes.