Advances in sequential data assimilation and numerical weather forecasting: an Ensemble Transform Kalman-Bucy Filter, a study on clustering in deterministic Ensemble Square Root Filters, and a test of a new time stepping scheme in an atmospheric model

This dissertation deals with aspects of sequential data assimilation (in particular ensemble Kalman filtering) and numerical weather forecasting. In the first part, the recently formulated Ensemble Kalman-Bucy (EnKBF) filter is revisited. It is shown that the previously used numerical integration scheme fails when the magnitude of the background error covariance grows beyond that of the observational error covariance in the forecast window. Therefore, we present a suitable integration scheme that handles the stiffening of the differential equations involved and doesn’t represent further computational expense. Moreover, a transform-based alternative to the EnKBF is developed: under this scheme, the operations are performed in the ensemble space instead of in the state space. Advantages of this formulation are explained. For the first time, the EnKBF is implemented in an atmospheric model. The second part of this work deals with ensemble clustering, a phenomenon that arises when performing data assimilation using of deterministic ensemble square root filters in highly nonlinear forecast models. Namely, an M-member ensemble detaches into an outlier and a cluster of M-1 members. Previous works may suggest that this issue represents a failure of EnSRFs; this work dispels that notion. It is shown that ensemble clustering can be reverted also due to nonlinear processes, in particular the alternation between nonlinear expansion and compression of the ensemble for different regions of the attractor. Some EnSRFs that use random rotations have been developed to overcome this issue; these formulations are analyzed and their advantages and disadvantages with respect to common EnSRFs are discussed. The third and last part contains the implementation of the Robert-Asselin-Williams (RAW) filter in an atmospheric model. The RAW filter is an improvement to the widely popular Robert-Asselin filter that successfully suppresses spurious computational waves while avoiding any distortion in the mean value of the function. Using statistical significance tests both at the local and field level, it is shown that the climatology of the SPEEDY model is not modified by the changed time stepping scheme; hence, no retuning of the parameterizations is required. It is found the accuracy of the medium-term forecasts is increased by using the RAW filter.

Chitosan-based mucoadhesive tablets for oral delivery of ibuprofen

Chitosan and its half-acetylated derivative have been compared as excipients in mucoadhesive tablets containing ibuprofen. Initially the powder formulations containing the polymers and the drug were prepared by either co-spray drying or physical co-grinding. Polymer–drug interactions and the degree of drug crystallinity in these formulations were assessed by infrared spectroscopy and differential scanning calorimetry. Tablets were prepared and their swelling and dissolution properties were studied in media of various pHs. Mucoadhesive properties of ibuprofen-loaded and drug-free tablets were evaluated by analysing their detachment from pig gastric mucosa over a range of pHs. Greater polymer–drug interactions were seen for spray-dried particles compared to co-ground samples and drug loading into chitosan-based microparticles (41%) was greater than the corresponding half-acetylated samples (32%). Swelling and drug release was greater with the half-acetylated chitosan tablets than tablets containing the parent polymer and both tablets were mucoadhesive, the extent of which was dependent on substrate pH. The results illustrate the potential sustained drug delivery benefits of both chitosan and its half-acetylated derivative as mucoadhesive tablet excipients.

Novel polyvinylpyrrolidones to improve delivery of poorly-water soluble drugs; from design to synthesis and evaluation

Polyvinylpyrrolidone is a widely used in tablet formulations with the linear form acting as a wetting agent and disintegrant whereas the cross-linked form is a super-disintegrant. We have previously reported that simply mixing the commercial cross-linked polymer with ibuprofen disrupted drug crystallinity with consequent improvements in drug dissolution behavior. In this study, we have designed and synthesized novel cross-linking agents containing a range of oligoether moieties which have then be polymerized with vinylpyrrolidone to generate a suite of novel excipients with enhanced hydrogen-bonding capabilities. The polymers have a porous surface and swell in most common solvents and in water; properties which suggest their value as disintegrants. The polymers were evaluated in simple physical mixtures with ibuprofen as a model poorly-water soluble drug. The results show that the novel PVPs induce the drug to become “X-ray amorphous”, which increased dissolution to a greater extent than that seen with commercial cross-linked PVP. The polymers stabilize the amorphous drug with no evidence for recrystallization seen after 20 weeks storage.

Available potential energy and exergy in stratified fluids

Lorenz’s theory of available p otential energy (APE) remains the main framework for studying the atmospheric and oceanic energy cycles. Because the APE generation rate is the volume integral of a thermodynamic efficiency times the local diabatic heating/cooling rate, APE theory is often regarded as an extension of the theory of heat engines. Available energetics in classical thermodynamics, however, usually relies on the concept of exergy, and is usually measured relative to a reference state maximising entropy at constant energy, whereas APE’s reference state minimises p otential energy at constant entropy. This review seeks to shed light on the two concepts; it covers local formulations of available energetics, alternative views of the dynamics/thermodynamics coupling, APE theory and the second law, APE production/dissipation, extensions to binary fluids, mean/eddy decomp ositions, APE in incompressible fluids, APE and irreversible turbulent mixing, and the role of mechanical forcing on APE production.

CLSM method for the dynamic observation of pH change within polymer matrices for oral delivery

If acid-sensitive drugs or cells are administered orally, there is often a reduction in efficacy associated with gastric passage. Formulation into a polymer matrix is a potential method to improve their stability. The visualization of pH within these materials may help better understand the action of these polymer systems and allow comparison of different formulations. We herein describe the development of a novel confocal laser-scanning microscopy (CLSM) method for visualizing pH changes within polymer matrices and demonstrate its applicability to an enteric formulation based on chitosan-coated alginate gels. The system in question is first shown to protect an acid-sensitive bacterial strain to low pH, before being studied by our technique. Prior to this study, it has been claimed that protection by these materials is a result of buffering, but this has not been demonstrated. The visualization of pH within these matrices during exposure to a pH 2.0 simulated gastric solution showed an encroachment of acid from the periphery of the capsule, and a persistence of pHs above 2.0 within the matrix. This implies that the protective effect of the alginate-chitosan matrices is most likely due to a combination of buffering of acid as it enters the polymer matrix and the slowing of acid penetration.

Cyclodextrin-mediated enhancement of riboflavin solubility and corneal permeability

Cyclodextrins are water-soluble cyclic oligosaccharides consisting of six, seven, and eight α-(1,4)-linked glucopyranose subunits. This study reports the use of different cyclodextrins in eye drop formulations to improve the aqueous solubility and corneal permeability of riboflavin. Riboflavin is a poorly soluble drug with a solubility up to 0.08 mg mL–1 in deionized water. It is used as a drug topically administered to the eye to mediate UV-induced corneal cross-linking in the treatment of keratoconus. Aqueous solutions of β-cyclodextrin (10–30 mg mL–1) can enhance the solubility of riboflavin up to 0.12–0.19 mg mL–1, whereas the higher concentration of α-cyclodextrin (100 mg mL–1) achieved a lower level of enhancement of 0.11 mg mL–1. The other oligosaccharides were found to be inefficient for this purpose. In vitro diffusion experiments performed with fresh and cryopreserved bovine cornea have demonstrated that β-cyclodextrin enhances riboflavin permeability. The mechanism of this enhancement was examined through microscopic histological analysis of the cornea and is discussed in this paper.

Predictability and uncertainty in a regional climate model

The evaluation of the quality and usefulness of climate modeling systems is dependent upon an assessment of both the limited predictability of the climate system and the uncertainties stemming from model formulation. In this study a methodology is presented that is suited to assess the performance of a regional climate model (RCM), based on its ability to represent the natural interannual variability on monthly and seasonal timescales. The methodology involves carrying out multiyear ensemble simulations (to assess the predictability bounds within which the model can be evaluated against observations) and multiyear sensitivity experiments using different model formulations (to assess the model uncertainty). As an example application, experiments driven by assimilated lateral boundary conditions and sea surface temperatures from the ECMWF Reanalysis Project (ERA-15, 1979–1993) were conducted. While the ensemble experiment demonstrates that the predictability of the regional climate varies strongly between different seasons and regions, being weakest during the summer and over continental regions, important sensitivities of the modeling system to parameterization choices are uncovered. In particular, compensating mechanisms related to the long-term representation of the water cycle are revealed, in which summer dry and hot conditions at the surface, resulting from insufficient evaporation, can persist despite insufficient net solar radiation (a result of unrealistic cloud-radiative feedbacks).

Review of the formulation of present‐generation stratospheric chemistry‐climate models and associated external forcings

The goal of the Chemistry‐Climate Model Validation (CCMVal) activity is to improve understanding of chemistry‐climate models (CCMs) through process‐oriented evaluation and to provide reliable projections of stratospheric ozone and its impact on climate. An appreciation of the details of model formulations is essential for understanding how models respond to the changing external forcings of greenhouse gases and ozonedepleting substances, and hence for understanding the ozone and climate forecasts produced by the models participating in this activity. Here we introduce and review the models used for the second round (CCMVal‐2) of this intercomparison, regarding the implementation of chemical, transport, radiative, and dynamical processes in these models. In particular, we review the advantages and problems associated with approaches used to model processes of relevance to stratospheric dynamics and chemistry. Furthermore, we state the definitions of the reference simulations performed, and describe the forcing data used in these simulations. We identify some developments in chemistry‐climate modeling that make models more physically based or more comprehensive, including the introduction of an interactive ocean, online photolysis, troposphere‐stratosphere chemistry, and non‐orographic gravity‐wave deposition as linked to tropospheric convection. The relatively new developments indicate that stratospheric CCM modeling is becoming more consistent with our physically based understanding of the atmosphere.

Contribution of non-volatile and volatile compounds to the umami taste and overall flavour of shiitake mushroom extracts and their application as flavour enhancers in cooked minced meat

Aqueous extracts of dried shiitake mushrooms (Lentinus edodes) were prepared as taste and flavour enhancers for meat formulations. Effects of time and temperature on the chemical and sensory properties of the extracts were examined. Extracts prepared at 70 °C had significantly higher concentrations (p<0.001) of the savoury tasting 5’-ribonucleotides than those prepared at 22 °C but increasing the extraction time from 30 to 360 mins only increased their recovery slightly (p=0.053). In contrast, higher temperature extracts had considerably smaller concentrations of the major volatile compounds, such as lenthionine, 1-octen-3-ol, 1,3-dithiethane and dimethyl disulfide, because of loss through volatilisation. A sensory discrimination test showed that the lower temperature extract was perceived to have less umami taste than the higher temperature extract (p=0.048). Incorporating the 70 °C shiitake extract into minced meat formulations led to significantly higher levels of savoury tasting 5’-ribonucleotides in the cooked meat but no significant difference in umami perception.

Efficient calculation of the green function for acoustic propagation above a homogeneous impedance plane

This paper is concerned with the problem of propagation from a monofrequency coherent line source above a plane of homogeneous surface impedance. The solution of this problem occurs in the kernel of certain boundary integral equation formulations of acoustic propagation above an impedance boundary, and the discussion of the paper is motivated by this application. The paper starts by deriving representations, as Laplace-type integrals, of the solution and its first partial derivatives. The evaluation of these integral representations by Gauss-Laguerre quadrature is discussed, and theoretical bounds on the truncation error are obtained. Specific approximations are proposed which are shown to be accurate except in the very near field, for all angles of incidence and a wide range of values of surface impedance. The paper finishes with derivations of partial results and analogous Laplace-type integral representations for the case of a point source.

Through Jewish eyes: polemical literature and the medieval papacy

Although the medieval papacy's stance towards the Jews is a well-established area of research, Jewish ideas about the papacy remain a surprisingly underdeveloped historical topic. This article explores such ideas through the genre of polemic and disputational literature. Jewish writers were keen to ensure the safety of their communities in western Europe and grateful for statements of papal protection. They fully acknowledged that popes had always played and would continue to play an important role in safeguarding their well-being and determining their future. Yet although contemporary and later writers often valued papal protection more highly than that of monarchs, emperors or clergy, they also knew that it had its carefully circumscribed limits. Furthermore, although they were respectful of the papacy's power, both spiritual and temporal, they were dismissive of the scriptural and theological formulations on which Christian claims for apostolic authority rested and highly critical of Christian beliefs about the papacy, in particular that of apostolic succession. Jewish ideas about both individual popes and the medieval papacy as an institution are therefore nuanced and complex; they deserve rigorous and wide-ranging investigation and it is hoped that this article will contribute to their better understanding.

A dynamical systems framework for intermittent data assimilation

We consider the problem of discrete time filtering (intermittent data assimilation) for differential equation models and discuss methods for its numerical approximation. The focus is on methods based on ensemble/particle techniques and on the ensemble Kalman filter technique in particular. We summarize as well as extend recent work on continuous ensemble Kalman filter formulations, which provide a concise dynamical systems formulation of the combined dynamics-assimilation problem. Possible extensions to fully nonlinear ensemble/particle based filters are also outlined using the framework of optimal transportation theory.

Ensemble transform Kalman-Bucy filters

Two recent works have adapted the Kalman–Bucy filter into an ensemble setting. In the first formulation, the ensemble of perturbations is updated by the solution of an ordinary differential equation (ODE) in pseudo-time, while the mean is updated as in the standard Kalman filter. In the second formulation, the full ensemble is updated in the analysis step as the solution of single set of ODEs in pseudo-time. Neither requires matrix inversions except for the frequently diagonal observation error covariance. We analyse the behaviour of the ODEs involved in these formulations. We demonstrate that they stiffen for large magnitudes of the ratio of background error to observational error variance, and that using the integration scheme proposed in both formulations can lead to failure. A numerical integration scheme that is both stable and is not computationally expensive is proposed. We develop transform-based alternatives for these Bucy-type approaches so that the integrations are computed in ensemble space where the variables are weights (of dimension equal to the ensemble size) rather than model variables. Finally, the performance of our ensemble transform Kalman–Bucy implementations is evaluated using three models: the 3-variable Lorenz 1963 model, the 40-variable Lorenz 1996 model, and a medium complexity atmospheric general circulation model known as SPEEDY. The results from all three models are encouraging and warrant further exploration of these assimilation techniques.

Is the Helmholtz equation really sign-indefinite?

The usual variational (or weak) formulations of the Helmholtz equation are sign-indefinite in the sense that the bilinear forms cannot be bounded below by a positive multiple of the appropriate norm squared. This is often for a good reason, since in bounded domains under certain boundary conditions the solution of the Helmholtz equation is not unique at wavenumbers that correspond to eigenvalues of the Laplacian, and thus the variational problem cannot be sign-definite. However, even in cases where the solution is unique for all wavenumbers, the standard variational formulations of the Helmholtz equation are still indefinite when the wavenumber is large. This indefiniteness has implications for both the analysis and the practical implementation of finite element methods. In this paper we introduce new sign-definite (also called coercive or elliptic) formulations of the Helmholtz equation posed in either the interior of a star-shaped domain with impedance boundary conditions, or the exterior of a star-shaped domain with Dirichlet boundary conditions. Like the standard variational formulations, these new formulations arise just by multiplying the Helmholtz equation by particular test functions and integrating by parts.

Dynamic group communication for large-scale parallel data mining

Exascale systems are the next frontier in high-performance computing and are expected to deliver a performance of the order of 10^18 operations per second using massive multicore processors. Very large- and extreme-scale parallel systems pose critical algorithmic challenges, especially related to concurrency, locality and the need to avoid global communication patterns. This work investigates a novel protocol for dynamic group communication that can be used to remove the global communication requirement and to reduce the communication cost in parallel formulations of iterative data mining algorithms. The protocol is used to provide a communication-efficient parallel formulation of the k-means algorithm for cluster analysis. The approach is based on a collective communication operation for dynamic groups of processes and exploits non-uniform data distributions. Non-uniform data distributions can be either found in real-world distributed applications or induced by means of multidimensional binary search trees. The analysis of the proposed dynamic group communication protocol has shown that it does not introduce significant communication overhead. The parallel clustering algorithm has also been extended to accommodate an approximation error, which allows a further reduction of the communication costs. The effectiveness of the exact and approximate methods has been tested in a parallel computing system with 64 processors and in simulations with 1024 processing elements.