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.

Sequence analysis and distribution of an IS3-like insertion element isolated from Salmonella enteritidis

The nucleotide sequence of a 3 kb region immediately upstream of the sef operon operon of Salmonella enteritidis was determined. A 1230 base pair insertion sequence which shared sequence identity (> 75%) with members of the IS3 family was revealed. This element, designated IS1230, had almost identical (90% identity) terminal inverted repeats to Escherichia coli IS3 but unlike other IS3-like sequences lacked the two characteristic open reading frames which encode the putative transposase. S. enteritidis possessed only one copy of this insertion sequence although Southern hybridisation analysis of restriction digests of genomic DNA revealed another fragment located in a region different from the sef operon which hybridised weakly which suggested the presence of an IS1230 homologue. The distribution of IS1230 and IS1230-like elements was shown to be widespread amongst salmonellas and the patterns of restriction fragments which hybridised differed significantly between Salmonella serotypes and it is suggested that IS1230 has potential for development as a differential diagnostic tool.

Sequence heterogeneity of an mpb70 gene analogue in Mycobacterium kansasii

The protein antigen MPB70 is a major component of culture supernatants of Mycobacterium bovis and Is an active ingredient of bovine PPD used for skin-testing cattle for tuberculosis. we have shown that Mycobacterium kansasii possesses a similar gene that cross-reacts in a PCR test for M. bovis. Single strand conformational polymorphism analysis, and the DNA sequence of the PCR product, shows differences between M. kansasii strains, supporting the suggestion that M. kansasii is not a homogeneous species.

On the solvability of second kind integral equations on the real line

This paper considers general second kind integral equations of the form(in operator form φ − kφ = ψ), where the functions k and ψ are assumed known, with ψ ∈ Y, the space of bounded continuous functions on R, and k such that the mapping s → k(s, · ), from R to L1(R), is bounded and continuous. The function φ ∈ Y is the solution to be determined. Conditions on a set W ⊂ BC(R, L1(R)) are obtained such that a generalised Fredholm alternative holds: If W satisfies these conditions and I − k is injective for all k ∈ W then I − k is also surjective for all k ∈ W and, moreover, the inverse operators (I − k) − 1 on Y are uniformly bounded for k ∈ W. The approximation of the kernel in the integral equation by a sequence (kn) converging in a weak sense to k is also considered and results on stability and convergence are obtained. These general theorems are used to establish results for two special classes of kernels: k(s, t) = κ(s − t)z(t) and k(s, t) = κ(s − t)λ(s − t, t), where κ ∈ L1(R), z ∈ L∞(R), and λ ∈ BC((R\{0}) × R). Kernels of both classes arise in problems of time harmonic wave scattering by unbounded surfaces. The general integral equation results are here applied to prove the existence of a solution for a boundary integral equation formulation of scattering by an infinite rough surface and to consider the stability and convergence of approximation of the rough surface problem by a sequence of diffraction grating problems of increasingly large period.

Discovery of a mammalian splice variant of myostatin that stimulates myogenesis

Myostatin plays a fundamental role in regulating the size of skeletal muscles. To date, only a single myostatin gene and no splice variants have been identified in mammals. Here we describe the splicing of a cryptic intron that removes the coding sequence for the receptor binding moiety of sheep myostatin. The deduced polypeptide sequence of the myostatin splice variant (MSV) contains a 256 amino acid N-terminal domain, which is common to myostatin, and a unique C-terminus of 65 amino acids. Western immunoblotting demonstrated that MSV mRNA is translated into protein, which is present in skeletal muscles. To determine the biological role of MSV, we developed an MSV over-expressing C2C12 myoblast line and showed that it proliferated faster than that of the control line in association with an increased abundance of the CDK2/Cyclin E complex in the nucleus. Recombinant protein made for the novel C-terminus of MSV also stimulated myoblast proliferation and bound to myostatin with high affinity as determined by surface plasmon resonance assay. Therefore, we postulated that MSV functions as a binding protein and antagonist of myostatin. Consistent with our postulate, myostatin protein was co-immunoprecipitated from skeletal muscle extracts with an MSV-specific antibody. MSV over-expression in C2C12 myoblasts blocked myostatin-induced Smad2/3-dependent signaling, thereby confirming that MSV antagonizes the canonical myostatin pathway. Furthermore, MSV over expression increased the abundance of MyoD, Myogenin and MRF4 proteins (P,0.05), which indicates that MSV stimulates myogenesis through the induction of myogenic regulatory factors. To help elucidate a possible role in vivo, we observed that MSV protein was more abundant during early post-natal muscle development, while myostatin remained unchanged, which suggests that MSV may promote the growth of skeletal muscles. We conclude that MSV represents a unique example of intra-genic regulation in which a splice variant directly antagonizes the biological activity of the canonical gene product.

Location and characteristics of the reconnection X line deduced from low-altitude satellite and ground-based observations: 1. Theory

A method for estimating both the Alfvén speed and the field-aligned flow of the magnetosheath at the magnetopause reconnection site is presented. The method employs low-altitude cusp ion observations and requires the identification of a feature in the cusp ion spectra near the low-energy cutoff which will often be present for a low-latitude dayside reconnection site. The appearance of these features in data of limited temporal, energy, and pitch angle resolution is illustrated by using model calculations of cusp ion distribution functions. These are based on the theory of ion acceleration at the dayside magnetopause and allow for the effects on the spectrum of flight times of ions precipitating down newly opened field lines. In addition, the variation of the reconnection rate can be evaluated, and comparison with ground-based observations of the corresponding sequence of transient events allows the field-aligned distance from the ionosphere to the reconnection site to be estimated.

Conditioning and preconditioning of the optimal state estimation problem

Optimal state estimation is a method that requires minimising a weighted, nonlinear, least-squares objective function in order to obtain the best estimate of the current state of a dynamical system. Often the minimisation is non-trivial due to the large scale of the problem, the relative sparsity of the observations and the nonlinearity of the objective function. To simplify the problem the solution is often found via a sequence of linearised objective functions. The condition number of the Hessian of the linearised problem is an important indicator of the convergence rate of the minimisation and the expected accuracy of the solution. In the standard formulation the convergence is slow, indicating an ill-conditioned objective function. A transformation to different variables is often used to ameliorate the conditioning of the Hessian by changing, or preconditioning, the Hessian. There is only sparse information in the literature for describing the causes of ill-conditioning of the optimal state estimation problem and explaining the effect of preconditioning on the condition number. This paper derives descriptive theoretical bounds on the condition number of both the unpreconditioned and preconditioned system in order to better understand the conditioning of the problem. We use these bounds to explain why the standard objective function is often ill-conditioned and why a standard preconditioning reduces the condition number. We also use the bounds on the preconditioned Hessian to understand the main factors that affect the conditioning of the system. We illustrate the results with simple numerical experiments.

Pose Refinement of Active Models using Forces in 3D

A new algorithm is described for refining the pose of a model of a rigid object, to conform more accurately to the image structure. Elemental 3D forces are considered to act on the model. These are derived from directional derivatives of the image local to the projected model features. The convergence properties of the algorithm is investigated and compared to a previous technique. Its use in a video sequence of a cluttered outdoor traffic scene is also illustrated and assessed.

Impact of Tibetan Orography and Heating on the Summer Flow over Asia

The influence on the summer flow over Asia of both the orographic and thermal forcing of the Tibetan Plateau is investigated using a sequence of idealised experiments with a global primitive equation model. The zonally averaged flow is prescribed and both realistic and idealised orography and heating are used. There is some similarity between the responses to the two forcings when applied separately. The upper tropospheric Tibetan anticyclone is predominantly forced by the heating but also weakly by the orography. Below this, both forcings tend to give air descending in an equatorward anticyclonic circulation down the isentropes to the west and rising in a similar poleward circulation to the east. However the heating-only response has a strong ascending southwesterly flow that is guided around the south and south-east of the orography when it is included. On the northern side, the westerly flow over the orography gives ascent on the upslope and descent on the downslope. It is found that heating over the Plateau leads to a potential vorticity (PV) minimum and that if it is sufficiently strong the flow is unstable, producing a quasi-biweekly oscillation. During this oscillation the Tibetan anticyclone changes between a single centre over the southwestern side of the Plateau and a split/double structure with centres over China and the Middle East. These characteristics are similar to observed variability in the region. Associated with this quasi-biweekly oscillation are significant variations in the strength of the ascent over the Plateau and the Rossby wave pattern over the North Pacific. The origin of the variability is instability associated with the zonally extended potential vorticity PV minimum on a θ-surface, as proposed by Hsu and Plumb (2000). This minimum is due to the tendency to reduce the PV above the heating over the Plateau and to advection by the consequent anticyclone of high PV around from the east and low PV to the west. The deep convection to the south and southeast of the Plateau tends to suppress the quasi-biweekly oscillation because the low PV produced above it acts to reduce the meridional PV gradient reversal. The occurrence of the oscillation depends on the relative magnitude of the heating in the two regions.

Croft Moraig and the chronology of stone circles

The Perthshire stone circle of Croft Moraig was excavated 40 years ago and is usually taken to illustrate the classic sequence at such monuments in Britain. A timber setting, accompanied by a shallow ditch, was replaced by two successive stone settings. The pottery associated with the earliest construction was dated to the Neolithic period. A new analysis of the excavated material suggests that, in fact, the ceramics are Middle or Late Bronze Age. They provide a terminus post quem for at least one of the stone settings on the site. Further study of the evidence suggests an alternative sequence of construction at Croft Moraig, involving a change in the axis of the monument. It seems possible that other stone and timber circles were equally late in date and that their period of use in Britain and Ireland may have been longer than is generally supposed.

Seasonal deposition of Holocene banded sediments in the Severn Estuary Levels (southwest Britain): palynological and sedimentological evidence

Banded sediments outcrop widely in the intertidal zone of the Severn Estuary and have been suggested, on the basis of textural analysis, to have formed in response to seasonal variations in sea temperature and windiness (Holocene, 14 (2004) 536). Here palynological and sedimentological analyses of banded sediments of mid-Holocene date from Gold Cliff, on the Welsh side of the Severn Estuary, are combined to test and further develop the hypothesis of seasonal deposition. Pollen percentage and concentration data are presented from a short sequence of bands to establish whether textural variations in the bands coincide with variations in pollen content reflecting seasonal flowering patterns. It is shown that fine-grained band parts contain higher total pollen concentrations, and a higher proportion of pollen from late spring- to summer-flowering plants, than coarse-grained band parts. Pollen in the coarser deposits appears primarily to reflect deposition from the buffering `reservoir' of suspended pollen in the estuarine water-body and from rivers, when there is little pollen in the air in winter, while the finer sediments contain pollen deposited from the atmosphere during the flowering season, superimposed on these `background' sources. The potential of such deposits for refining chronologies and identifying seasonality of coastal processes is noted, and the results of charcoal particle analysis of the bands presented as an example of how they have the potential to shed light on seasonal and annual patterns of human activity. (C) 2004 Elsevier Ltd. All rights reserved.

A dendrochemical study of Pinus sylvestris from Siljansfors Experimental Forest, central Sweden

Inductively coupled plasma mass spectrometry (ICP-MS) was used to investigate changes in trace element concentration in two high resolution sequences of tree rings from central Sweden. Individual annual growth increments from 18002002 to 1930-2002 were sampled from two Scots pine (Pinus sylvestris) trees from the Siljansfors Experimental Forest. The aims of the study were: to test the viability of conventional solution induction ICP-MS as a technique for investigating the multi-elemental chemistry of long tree ring sequences at annual resolution, and, to test this specifically with a view to detecting changes in elemental concentrations of Swedish tree rings contemporary with the major (and relatively proximal) Icelandic eruption of Askja (1875). It was found that despite a time consuming sample preparation process, it was possible to use conventional ICP-MS for multi-elemental analysis of a long sequence of tree rings at annual resolution. Although promising data were produced, no truly conclusive concentration anomaly could be detected in the sequence to indicate the impact of the Askja eruption on environmental chemistry. Overall findings underlined the complexity of the tree/environment interaction and the cautious approach to data interpretation essential for any dendrochemical study. (c) 2006 Elsevier Ltd. All rights reserved.

Changing state disruption of lip-reading by irrelevant sound in perceptual and memory tasks

Three experiments investigated irrelevant sound interference of lip-read lists. In Experiment 1, an acoustically changing sequence of nine irrelevant utterances was more disruptive to spoken immediate identification of lists of nine lip-read digits than nine repetitions of the same utterances (the changing-state effect; Jones, Madden, & Miles, 1992). Experiment 2 replicated this finding when lip-read items were sampled with replacement from the nine digits to form the lip-read lists. In Experiment 3, when the irrelevant sound was confined to the retention interval of a delayed recall task, a changing-state pattern of disruption also occurred. Results confirm a changing-state effect in memory for lip-read items but also point to the possibility that, for lip-reading, changing-state effects may occur at an earlier, perceptual stage.

A singular vector perspective of 4D-Var: Filtering and interpolation

Four-dimensional variational data assimilation (4D-Var) combines the information from a time sequence of observations with the model dynamics and a background state to produce an analysis. In this paper, a new mathematical insight into the behaviour of 4D-Var is gained from an extension of concepts that are used to assess the qualitative information content of observations in satellite retrievals. It is shown that the 4D-Var analysis increments can be written as a linear combination of the singular vectors of a matrix which is a function of both the observational and the forecast model systems. This formulation is used to consider the filtering and interpolating aspects of 4D-Var using idealized case-studies based on a simple model of baroclinic instability. The results of the 4D-Var case-studies exhibit the reconstruction of the state in unobserved regions as a consequence of the interpolation of observations through time. The results also exhibit the filtering of components with small spatial scales that correspond to noise, and the filtering of structures in unobserved regions. The singular vector perspective gives a very clear view of this filtering and interpolating by the 4D-Var algorithm and shows that the appropriate specification of the a priori statistics is vital to extract the largest possible amount of useful information from the observations. Copyright © 2005 Royal Meteorological Society