Estimation of Hidden Markov Models parameters using differential evolution

Hidden Markov Models (HMMs) have been successfully applied to different modelling and classification problems from different areas over the recent years. An important step in using HMMs is the initialisation of the parameters of the model as the subsequent learning of HMM’s parameters will be dependent on these values. This initialisation should take into account the knowledge about the addressed problem and also optimisation techniques to estimate the best initial parameters given a cost function, and consequently, to estimate the best log-likelihood. This paper proposes the initialisation of Hidden Markov Models parameters using the optimisation algorithm Differential Evolution with the aim to obtain the best log-likelihood.

An empirical study of process-related attributes in segmented software cost-estimation relationships

Parametric software effort estimation models consisting on a single mathematical relationship suffer from poor adjustment and predictive characteristics in cases in which the historical database considered contains data coming from projects of a heterogeneous nature. The segmentation of the input domain according to clusters obtained from the database of historical projects serves as a tool for more realistic models that use several local estimation relationships. Nonetheless, it may be hypothesized that using clustering algorithms without previous consideration of the influence of well-known project attributes misses the opportunity to obtain more realistic segments. In this paper, we describe the results of an empirical study using the ISBSG-8 database and the EM clustering algorithm that studies the influence of the consideration of two process-related attributes as drivers of the clustering process: the use of engineering methodologies and the use of CASE tools. The results provide evidence that such consideration conditions significantly the final model obtained, even though the resulting predictive quality is of a similar magnitude.

Porcine models for the metabolic syndrome, digestive and bone disorders: a general overview

The aim of this review article is to provide an overview of the role of pigs as a biomedical model for humans. The usefulness and limitations of porcine models have been discussed in terms of metabolic, cardiovascular, digestive and bone diseases in humans. Domestic pigs and minipigs are the main categories of pigs used as biomedical models. One drawback of minipigs is that they are in short supply and expensive compared with domestic pigs, which in contrast cost more to house, feed and medicate. Different porcine breeds show different responses to the induction of specific diseases. For example, ossabaw minipigs provide a better model than Yucatan for the metabolic syndrome as they exhibit obesity, insulin resistance and hypertension, all of which are absent in the Yucatan. Similar metabolic/physiological differences exist between domestic breeds (e.g. Meishan v. Pietrain). The modern commercial (e.g. Large White) domestic pig has been the preferred model for developmental programming due to the 2- to 3-fold variation in body weight among littermates providing a natural form of foetal growth retardation not observed in ancient (e.g. Meishan) domestic breeds. Pigs have been increasingly used to study chronic ischaemia, therapeutic angiogenesis, hypertrophic cardiomyopathy and abdominal aortic aneurysm as their coronary anatomy and physiology are similar to humans. Type 1 and II diabetes can be induced in swine using dietary regimes and/or administration of streptozotocin. Pigs are a good and extensively used model for specific nutritional studies as their protein and lipid metabolism is comparable with humans, although pigs are not as sensitive to protein restriction as rodents. Neonatal and weanling pigs have been used to examine the pathophysiology and prevention/treatment of microbial-associated diseases and immune system disorders. A porcine model mimicking various degrees of prematurity in infants receiving total parenteral nutrition has been established to investigate gut development, amino acid metabolism and non-alcoholic fatty liver disease. Endoscopic therapeutic methods for upper gastrointestinal tract bleeding are being developed. Bone remodelling cycle in pigs is histologically more similar to humans than that of rats or mice, and is used to examine the relationship between menopause and osteoporosis. Work has also been conducted on dental implants in pigs to consider loading; however with caution as porcine bone remodels slightly faster than human bone. We conclude that pigs are a valuable translational model to bridge the gap between classical rodent models and humans in developing new therapies to aid human health.

Predicting microbial pollution concentrations in UK rivers in response to land use change

The Water Framework Directive has caused a paradigm shift towards the integrated management of recreational water quality through the development of drainage basin-wide programmes of measures. This has increased the need for a cost-effective diagnostic tool capable of accurately predicting riverine faecal indicator organism (FIO) concentrations. This paper outlines the application of models developed to fulfil this need, which represent the first transferrable generic FIO models to be developed for the UK to incorporate direct measures of key FIO sources (namely human and livestock population data) as predictor variables. We apply a recently developed transfer methodology, which enables the quantification of geometric mean presumptive faecal coliforms and presumptive intestinal enterococci concentrations for base- and high-flow during the summer bathing season in unmonitored UK watercourses, to predict FIO concentrations in the Humber river basin district. Because the FIO models incorporate explanatory variables which allow the effects of policy measures which influence livestock stocking rates to be assessed, we carry out empirical analysis of the differential effects of seven land use management and policy instruments (fiscal constraint, production constraint, cost intervention, area intervention, demand-side constraint, input constraint, and micro-level land use management) all of which can be used to reduce riverine FIO concentrations. This research provides insights into FIO source apportionment, explores a selection of pollution remediation strategies and the spatial differentiation of land use policies which could be implemented to deliver river quality improvements. All of the policy tools we model reduce FIO concentrations in rivers but our research suggests that the installation of streamside fencing in intensive milk producing areas may be the single most effective land management strategy to reduce riverine microbial pollution.

Non-intrusive monitoring of atmospheric CO2 in analogue models of terrestrial carbon cycle

1. Closed Ecological Systems (CES) are small manmade ecosystems which do not have any material exchange with the surrounding environment. Recent ecological and technological advances enable successful establishment and maintenance of CES, making them a suitable tool for detecting and measuring subtle feedbacks and mechanisms. 2. As a part of an analogue (physical) C cycle modelling experiment, we developed a non-intrusive methodology to control the internal environment and to monitor atmospheric CO2 concentration inside 16 replicated CES. Whilst maintaining an air-tight seal of all CES, this approach allowed for access to the CO2 measuring equipment for periodic re-calibration and repairs. 3. To ensure reliable cross-comparison of CO2 observations between individual CES units and to minimise the cost of the system, only one CO2 sampling unit was used. An ADC BioScientific OP-2 (open-path) analyser mounted on a swinging arm was passing over a set of 16 measuring cells. Each cell was connected to an individual CES with air continuously circulating between them. 4. Using this setup, we were able to continuously measure several environmental variables and CO2 concentration within each closed system, allowing us to study minute effects of changing temperature on C fluxes within each CES. The CES and the measuring cells showed minimal air leakage during an experimental run lasting, on average, 3 months. The CO2 analyser assembly performed reliably for over 2 years, however an early iteration of the present design proved to be sensitive to positioning errors. 5. We indicate how the methodology can be further improved and suggest possible avenues where future CES based research could be applied.

Dynamic stall for a Vertical Axis Wind Turbine in a two-dimensional study

The last few years have proved that Vertical Axis Wind Turbines (VAWTs) are more suitable for urban areas than Horizontal Axis Wind Turbines (HAWTs). To date, very little has been published in this area to assess good performance and lifetime of VAWTs either in open or urban areas. At low tip speed ratios (TSRs<5), VAWTs are subjected to a phenomenon called 'dynamic stall'. This can really affect the fatigue life of a VAWT if it is not well understood. The purpose of this paper is to investigate how CFD is able to simulate the dynamic stall for 2-D flow around VAWT blades. During the numerical simulations different turbulence models were used and compared with the data available on the subject. In this numerical analysis the Shear Stress Transport (SST) turbulence model seems to predict the dynamic stall better than the other turbulence models available. The limitations of the study are that the simulations are based on a 2-D case with constant wind and rotational speeds instead of considering a 3-D case with variable wind speeds. This approach was necessary for having a numerical analysis at low computational cost and time. Consequently, in the future it is strongly suggested to develop a more sophisticated model that is a more realistic simulation of a dynamic stall in a three-dimensional VAWT.

Demand response experience in Europe: policies, programmes and implementation

Over the last few years, load growth, increases in intermittent generation, declining technology costs and increasing recognition of the importance of customer behaviour in energy markets have brought about a change in the focus of Demand Response (DR) in Europe. The long standing programmes involving large industries, through interruptible tariffs and time of day pricing, have been increasingly complemented by programmes aimed at commercial and residential customer groups. Developments in DR vary substantially across Europe reflecting national conditions and triggered by different sets of policies, programmes and implementation schemes. This paper examines experiences within European countries as well as at European Union (EU) level, with the aim of understanding which factors have facilitated or impeded advances in DR. It describes initiatives, studies and policies of various European countries, with in-depth case studies of the UK, Italy and Spain. It is concluded that while business programmes, technical and economic potentials vary across Europe, there are common reasons as to why coordinated DR policies have been slow to emerge. This is because of the limited knowledge on DR energy saving capacities; high cost estimates for DR technologies and infrastructures; and policies focused on creating the conditions for liberalising the EU energy markets.

Assessment of evaluations made to healthy eating policies in Europe: a review within the EATWELL Project

Objective: To identify and assess healthy eating policies at national level which have been evaluated in terms of their impact on awareness of healthy eating, food consumption, health outcome or cost/benefit. Design: Review of policy documents and their evaluations when available. Setting: European Member States. Subjects: One hundred and twenty-one policy documents revised, 107 retained. Results: Of the 107 selected interventions, twenty-two had been evaluated for their impact on awareness or knowledge and twenty-seven for their impact on consumption. Furthermore sixteen interventions provided an evaluation of health impact, while three actions specifically measured any cost/benefit ratio. The indicators used in these evaluations were in most cases not comparable. Evaluation was more often found for public information campaigns, regulation of meals at schools/canteens and nutrition education programmes. Conclusions: The study highlights the need not only to develop harmonized and verifiable procedures but also indicators for measuring effectiveness and success and for comparing between interventions and countries. EU policies are recommended to provide a set of indicators that may be measured consistently and regularly in all countries. Furthermore, public information campaigns should be accompanied by other interventions, as evaluations may show an impact on awareness and intention, but rarely on consumption patterns and health outcome.

An overview of domestic energy models and a new approach with agent based modelling

Government targets for CO2 reductions are being progressively tightened, the Climate Change Act set the UK target as an 80% reduction by 2050 on 1990 figures. The residential sector accounts for about 30% of emissions. This paper discusses current modelling techniques in the residential sector: principally top-down and bottom-up. Top-down models work on a macro-economic basis and can be used to consider large scale economic changes; bottom-up models are detail rich to model technological changes. Bottom-up models demonstrate what is technically possible. However, there are differences between the technical potential and what is likely given the limited economic rationality of the typical householder. This paper recommends research to better understand individuals’ behaviour. Such research needs to include actual choices, stated preferences and opinion research to allow a detailed understanding of the individual end user. This increased understanding can then be used in an agent based model (ABM). In an ABM, agents are used to model real world actors and can be given a rule set intended to emulate the actions and behaviours of real people. This can help in understanding how new technologies diffuse. In this way a degree of micro-economic realism can be added to domestic carbon modelling. Such a model should then be of use for both forward projections of CO2 and to analyse the cost effectiveness of various policy measures.

Determining the cost of in-field mitigation options to reduce sediment and phosphorus loss

The Mitigation Options for Phosphorus and Sediment (MOPS) project investigated the effectiveness of within-field control measures (tramline management, straw residue management, type of cultivation and direction, and vegetative buffers) in terms of mitigating sediment and phosphorus loss from winter-sown combinable cereal crops using three case study sites. To determine the cost of the approaches, simple financial spreadsheet models were constructed at both farm and regional levels. Taking into account crop areas, crop rotation margins per hectare were calculated to reflect the costs of crop establishment, fertiliser and agro-chemical applications, harvesting, and the associated labour and machinery costs. Variable and operating costs associated with each mitigation option were then incorporated to demonstrate the impact on the relevant crop enterprise and crop rotation margins. These costs were then compared to runoff, sediment and phosphorus loss data obtained from monitoring hillslope-length scale field plots. Each of the mitigation options explored in this study had potential for reducing sediment and phosphorus losses from arable land under cereal crops. Sediment losses were reduced from between 9 kg ha−1 to as much as 4780 kg ha−1 with a corresponding reduction in phosphorus loss from 0.03 kg ha−1 to 2.89 kg ha−1. In percentage terms reductions of phosphorus were between 9% and 99%. Impacts on crop rotation margins also varied. Minimum tillage resulted in cost savings (up to £50 ha−1) whilst other options showed increased costs (up to £19 ha−1 for straw residue incorporation). Overall, the results indicate that each of the options has potential for on-farm implementation. However, tramline management appeared to have the greatest potential for reducing runoff, sediment, and phosphorus losses from arable land (between 69% and 99%) and is likely to be considered cost-effective with only a small additional cost of £2–4 ha−1, although further work is needed to evaluate alternative tramline management methods. Tramline management is also the only option not incorporated within current policy mechanisms associated with reducing soil erosion and phosphorus loss and in light of its potential is an approach that should be encouraged once further evidence is available.

Design and management of sustainable built environments

The United Nation Intergovernmental Panel on Climate Change (IPCC) makes it clear that climate change is due to human activities and it recognises buildings as a distinct sector among the seven analysed in its 2007 Fourth Assessment Report. Global concerns have escalated regarding carbon emissions and sustainability in the built environment. The built environment is a human-made setting to accommodate human activities, including building and transport, which covers an interdisciplinary field addressing design, construction, operation and management. Specifically, Sustainable Buildings are expected to achieve high performance throughout the life-cycle of siting, design, construction, operation, maintenance and demolition, in the following areas: • energy and resource efficiency; • cost effectiveness; • minimisation of emissions that negatively impact global warming, indoor air quality and acid rain; • minimisation of waste discharges; and • maximisation of fulfilling the requirements of occupants’ health and wellbeing. Professionals in the built environment sector, for example, urban planners, architects, building scientists, engineers, facilities managers, performance assessors and policy makers, will play a significant role in delivering a sustainable built environment. Delivering a sustainable built environment needs an integrated approach and so it is essential for built environment professionals to have interdisciplinary knowledge in building design and management . Building and urban designers need to have a good understanding of the planning, design and management of the buildings in terms of low carbon and energy efficiency. There are a limited number of traditional engineers who know how to design environmental systems (services engineer) in great detail. Yet there is a very large market for technologists with multi-disciplinary skills who are able to identify the need for, envision and manage the deployment of a wide range of sustainable technologies, both passive (architectural) and active (engineering system),, and select the appropriate approach. Employers seek applicants with skills in analysis, decision-making/assessment, computer simulation and project implementation. An integrated approach is expected in practice, which encourages built environment professionals to think ‘out of the box’ and learn to analyse real problems using the most relevant approach, irrespective of discipline. The Design and Management of Sustainable Built Environment book aims to produce readers able to apply fundamental scientific research to solve real-world problems in the general area of sustainability in the built environment. The book contains twenty chapters covering climate change and sustainability, urban design and assessment (planning, travel systems, urban environment), urban management (drainage and waste), buildings (indoor environment, architectural design and renewable energy), simulation techniques (energy and airflow), management (end-user behaviour, facilities and information), assessment (materials and tools), procurement, and cases studies ( BRE Science Park). Chapters one and two present general global issues of climate change and sustainability in the built environment. Chapter one illustrates that applying the concepts of sustainability to the urban environment (buildings, infrastructure, transport) raises some key issues for tackling climate change, resource depletion and energy supply. Buildings, and the way we operate them, play a vital role in tackling global greenhouse gas emissions. Holistic thinking and an integrated approach in delivering a sustainable built environment is highlighted. Chapter two demonstrates the important role that buildings (their services and appliances) and building energy policies play in this area. Substantial investment is required to implement such policies, much of which will earn a good return. Chapters three and four discuss urban planning and transport. Chapter three stresses the importance of using modelling techniques at the early stage for strategic master-planning of a new development and a retrofit programme. A general framework for sustainable urban-scale master planning is introduced. This chapter also addressed the needs for the development of a more holistic and pragmatic view of how the built environment performs, , in order to produce tools to help design for a higher level of sustainability and, in particular, how people plan, design and use it. Chapter four discusses microcirculation, which is an emerging and challenging area which relates to changing travel behaviour in the quest for urban sustainability. The chapter outlines the main drivers for travel behaviour and choices, the workings of the transport system and its interaction with urban land use. It also covers the new approach to managing urban traffic to maximise economic, social and environmental benefits. Chapters five and six present topics related to urban microclimates including thermal and acoustic issues. Chapter five discusses urban microclimates and urban heat island, as well as the interrelationship of urban design (urban forms and textures) with energy consumption and urban thermal comfort. It introduces models that can be used to analyse microclimates for a careful and considered approach for planning sustainable cities. Chapter six discusses urban acoustics, focusing on urban noise evaluation and mitigation. Various prediction and simulation methods for sound propagation in micro-scale urban areas, as well as techniques for large scale urban noise-mapping, are presented. Chapters seven and eight discuss urban drainage and waste management. The growing demand for housing and commercial developments in the 21st century, as well as the environmental pressure caused by climate change, has increased the focus on sustainable urban drainage systems (SUDS). Chapter seven discusses the SUDS concept which is an integrated approach to surface water management. It takes into consideration quality, quantity and amenity aspects to provide a more pleasant habitat for people as well as increasing the biodiversity value of the local environment. Chapter eight discusses the main issues in urban waste management. It points out that population increases, land use pressures, technical and socio-economic influences have become inextricably interwoven and how ensuring a safe means of dealing with humanity’s waste becomes more challenging. Sustainable building design needs to consider healthy indoor environments, minimising energy for heating, cooling and lighting, and maximising the utilisation of renewable energy. Chapter nine considers how people respond to the physical environment and how that is used in the design of indoor environments. It considers environmental components such as thermal, acoustic, visual, air quality and vibration and their interaction and integration. Chapter ten introduces the concept of passive building design and its relevant strategies, including passive solar heating, shading, natural ventilation, daylighting and thermal mass, in order to minimise heating and cooling load as well as energy consumption for artificial lighting. Chapter eleven discusses the growing importance of integrating Renewable Energy Technologies (RETs) into buildings, the range of technologies currently available and what to consider during technology selection processes in order to minimise carbon emissions from burning fossil fuels. The chapter draws to a close by highlighting the issues concerning system design and the need for careful integration and management of RETs once installed; and for home owners and operators to understand the characteristics of the technology in their building. Computer simulation tools play a significant role in sustainable building design because, as the modern built environment design (building and systems) becomes more complex, it requires tools to assist in the design process. Chapter twelve gives an overview of the primary benefits and users of simulation programs, the role of simulation in the construction process and examines the validity and interpretation of simulation results. Chapter thirteen particularly focuses on the Computational Fluid Dynamics (CFD) simulation method used for optimisation and performance assessment of technologies and solutions for sustainable building design and its application through a series of cases studies. People and building performance are intimately linked. A better understanding of occupants’ interaction with the indoor environment is essential to building energy and facilities management. Chapter fourteen focuses on the issue of occupant behaviour; principally, its impact, and the influence of building performance on them. Chapter fifteen explores the discipline of facilities management and the contribution that this emerging profession makes to securing sustainable building performance. The chapter highlights a much greater diversity of opportunities in sustainable building design that extends well into the operational life. Chapter sixteen reviews the concepts of modelling information flows and the use of Building Information Modelling (BIM), describing these techniques and how these aspects of information management can help drive sustainability. An explanation is offered concerning why information management is the key to ‘life-cycle’ thinking in sustainable building and construction. Measurement of building performance and sustainability is a key issue in delivering a sustainable built environment. Chapter seventeen identifies the means by which construction materials can be evaluated with respect to their sustainability. It identifies the key issues that impact the sustainability of construction materials and the methodologies commonly used to assess them. Chapter eighteen focuses on the topics of green building assessment, green building materials, sustainable construction and operation. Commonly-used assessment tools such as BRE Environmental Assessment Method (BREEAM), Leadership in Energy and Environmental Design ( LEED) and others are introduced. Chapter nineteen discusses sustainable procurement which is one of the areas to have naturally emerged from the overall sustainable development agenda. It aims to ensure that current use of resources does not compromise the ability of future generations to meet their own needs. Chapter twenty is a best-practice exemplar - the BRE Innovation Park which features a number of demonstration buildings that have been built to the UK Government’s Code for Sustainable Homes. It showcases the very latest innovative methods of construction, and cutting edge technology for sustainable buildings. In summary, Design and Management of Sustainable Built Environment book is the result of co-operation and dedication of individual chapter authors. We hope readers benefit from gaining a broad interdisciplinary knowledge of design and management in the built environment in the context of sustainability. We believe that the knowledge and insights of our academics and professional colleagues from different institutions and disciplines illuminate a way of delivering sustainable built environment through holistic integrated design and management approaches. Last, but not least, I would like to take this opportunity to thank all the chapter authors for their contribution. I would like to thank David Lim for his assistance in the editorial work and proofreading.

Fit for policy? Some evidence on the application of development viability models in the UK planning system

This paper investigates the application and use of development viability models in the formation of planning policies in the UK. Particular attention is paid to three key areas; the assumed development scheme in development viability models, the use of forecasts and the debate concerning Threshold Land Value. The empirical section reports on the results of an interview survey involving the main producers of development viability models and appraisals. It is concluded that, although development viability models have intrinsic limitations associated with model composition and input uncertainties, the most significant limitations are related to the ways that they have been adapted for use in the planning system. In addition, it is suggested that the contested nature of Threshold Land Value is an example of calculative practices providing a façade of technocratic rationality in the planning system.

Estimation of optimal gravity wave parameters for climate models using data assimilation

There is a current need to constrain the parameters of gravity wave drag (GWD) schemes in climate models using observational information instead of tuning them subjectively. In this work, an inverse technique is developed using data assimilation principles to estimate gravity wave parameters. Because mostGWDschemes assume instantaneous vertical propagation of gravity waves within a column, observations in a single column can be used to formulate a one-dimensional assimilation problem to estimate the unknown parameters. We define a cost function that measures the differences between the unresolved drag inferred from observations (referred to here as the ‘observed’ GWD) and the GWD calculated with a parametrisation scheme. The geometry of the cost function presents some difficulties, including multiple minima and ill-conditioning because of the non-independence of the gravity wave parameters. To overcome these difficulties we propose a genetic algorithm to minimize the cost function, which provides a robust parameter estimation over a broad range of prescribed ‘true’ parameters. When real experiments using an independent estimate of the ‘observed’ GWD are performed, physically unrealistic values of the parameters can result due to the non-independence of the parameters. However, by constraining one of the parameters to lie within a physically realistic range, this degeneracy is broken and the other parameters are also found to lie within physically realistic ranges. This argues for the essential physical self-consistency of the gravity wave scheme. A much better fit to the observed GWD at high latitudes is obtained when the parameters are allowed to vary with latitude. However, a close fit can be obtained either in the upper or the lower part of the profiles, but not in both at the same time. This result is a consequence of assuming an isotropic launch spectrum. The changes of sign in theGWDfound in the tropical lower stratosphere, which are associated with part of the quasi-biennial oscillation forcing, cannot be captured by the parametrisation with optimal parameters.

Broker use and the cost of liquidity in commercial real estate investment

Purpose – Commercial real estate is a highly specific asset: heterogeneous, indivisible and with less information transparency than most other commonly held investment assets. These attributes encourage the use of intermediaries during asset acquisition and disposal. However, there are few attempts to explain the use of different brokerage models (with differing costs) in different markets. This study aims to address this gap. Design/methodology/approach – The study analyses 9,338 real estate transactions in London and New York City from 2001 to 2011. Data are provided by Real Capital Analytics and cover over $450 billion of investments in this period. Brokerage trends in the two cities are compared and probit regressions are used to test whether the decision to transact with broker representation varies with investor or asset characteristics. Findings – Results indicate greater use of brokerage in London, especially by purchasers. This persists when data are disaggregated by sector, time or investor type, pointing to the role of local market culture and institutions in shaping brokerage models and transaction costs. Within each city, the nature of the investors involved seems to be a more significant influence on broker use than the characteristics of the assets being traded. Originality/value – Brokerage costs are the single largest non-tax charge to an investor when trading commercial real estate, yet there is little research in this area. This study examines the role of brokers and provides empirical evidence on factors that influence the use and mode of brokerage in two major investment destinations.

Numerical analyses of Runge–Kutta implicit–explicit schemes for horizontally explicit, vertically implicit solutions of atmospheric models

With the prospect of exascale computing, computational methods requiring only local data become especially attractive. Consequently, the typical domain decomposition of atmospheric models means horizontally-explicit vertically-implicit (HEVI) time-stepping schemes warrant further attention. In this analysis, Runge-Kutta implicit-explicit schemes from the literature are analysed for their stability and accuracy using a von Neumann stability analysis of two linear systems. Attention is paid to the numerical phase to indicate the behaviour of phase and group velocities. Where the analysis is tractable, analytically derived expressions are considered. For more complicated cases, amplification factors have been numerically generated and the associated amplitudes and phase diagnosed. Analysis of a system describing acoustic waves has necessitated attributing the three resultant eigenvalues to the three physical modes of the system. To do so, a series of algorithms has been devised to track the eigenvalues across the frequency space. The result enables analysis of whether the schemes exactly preserve the non-divergent mode; and whether there is evidence of spurious reversal in the direction of group velocities or asymmetry in the damping for the pair of acoustic modes. Frequency ranges that span next-generation high-resolution weather models to coarse-resolution climate models are considered; and a comparison is made of errors accumulated from multiple stability-constrained shorter time-steps from the HEVI scheme with a single integration from a fully implicit scheme over the same time interval. Two schemes, “Trap2(2,3,2)” and “UJ3(1,3,2)”, both already used in atmospheric models, are identified as offering consistently good stability and representation of phase across all the analyses. Furthermore, according to a simple measure of computational cost, “Trap2(2,3,2)” is the least expensive.