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.

The influence of the QBO on the propagation of equatorial waves into the stratosphere

The variation of stratospheric equatorial wave characteristics with the phase of the quasi-biennial oscillation (QBO) is investigated using ECMWF Re-Analysis and NOAA outgoing longwave radiation (OLR) data. The impact of the QBO phases on the upward propagation of equatorial waves is found to be consistent and significant. In the easterly phase, there is larger Kelvin wave amplitude but smaller westward-moving mixed Rossby–gravity (WMRG) and n = 1 Rossby (R1) wave amplitude due to reduced propagation from the upper troposphere into the lower stratosphere, compared with the westerly phase. Differences in the wave amplitude exist in a deeper layer in summer than in winter, consistent with the seasonality of ambient zonal winds. There is a strong evidence of Kelvin wave amplitude peaking just below the descending westerly phase, suggesting that Kelvin waves act to bring the westerly phase downward. However, the corresponding evidence for WMRG and R1 waves is less clear. In the lower stratosphere there is zonal variation in equatorial waves. This reflects the zonal asymmetry of wave amplitudes in the upper troposphere, the source for the lower-stratospheric waves. In easterly winters the upper-tropospheric WMRG and R1 waves over the eastern Pacific region appear to be somewhat stronger compared to climatology, perhaps because of the accumulation of waves that are unable to propagate upward into the lower stratosphere. Vertical propagation features of these waves are generally consistent with theory and suggest a mixture of Doppler shifting by ambient flows and filtering. Some lower-stratosphere equatorial waves have a connection with preceding tropical convection, especially for Kelvin and R1 waves in winter.

Multispacecraft observation of magnetic cloud erosion by magnetic reconnection during propagation

During propagation, Magnetic Clouds (MC) interact with their environment and, in particular, may reconnect with the solar wind around it, eroding away part of its initial magnetic flux. Here we quantitatively analyze such an interaction using combined, multipoint observations of the same MC flux rope by STEREO A, B, ACE, WIND and THEMIS on November 19–20, 2007. Observation of azimuthal magnetic flux imbalance inside a MC flux rope has been argued to stem from erosion due to magnetic reconnection at its front boundary. The present study adds to such analysis a large set of signatures expected from this erosion process. (1) Comparison of azimuthal flux imbalance for the same MC at widely separated points precludes the crossing of the MC leg as a source of bias in flux imbalance estimates. (2) The use of different methods, associated errors and parametric analyses show that only an unexpectedly large error in MC axis orientation could explain the azimuthal flux imbalance. (3) Reconnection signatures are observed at the MC front at all spacecraft, consistent with an ongoing erosion process. (4) Signatures in suprathermal electrons suggest that the trailing part of the MC has a different large-scale magnetic topology, as expected. The azimuthal magnetic flux erosion estimated at ACE and STEREO A corresponds respectively to 44% and 49% of the inferred initial azimuthal magnetic flux before MC erosion upon propagation. The corresponding average reconnection rate during transit is estimated to be in the range 0.12–0.22 mV/m, suggesting most of the erosion occurs in the inner parts of the heliosphere. Future studies ought to quantify the influence of such an erosion process on geo-effectiveness.

Landscape, regional and global estimates of nitrogen flux from land to sea: errors and uncertainties

Regional to global scale modelling of N flux from land to ocean has progressed to date through the development of simple empirical models representing bulk N flux rates from large watersheds, regions, or continents on the basis of a limited selection of model parameters. Watershed scale N flux modelling has developed a range of physically-based approaches ranging from models where N flux rates are predicted through a physical representation of the processes involved, through to catchment scale models which provide a simplified representation of true systems behaviour. Generally, these watershed scale models describe within their structure the dominant process controls on N flux at the catchment or watershed scale, and take into account variations in the extent to which these processes control N flux rates as a function of landscape sensitivity to N cycling and export. This paper addresses the nature of the errors and uncertainties inherent in existing regional to global scale models, and the nature of error propagation associated with upscaling from small catchment to regional scale through a suite of spatial aggregation and conceptual lumping experiments conducted on a validated watershed scale model, the export coefficient model. Results from the analysis support the findings of other researchers developing macroscale models in allied research fields. Conclusions from the study confirm that reliable and accurate regional scale N flux modelling needs to take account of the heterogeneity of landscapes and the impact that this has on N cycling processes within homogenous landscape units.

Importance of oceanic resolution and mean state on the extra-tropical response to El Niño in a matrix of coupled models

The extra-tropical response to El Niño in configurations of a coupled model with increased horizontal resolution in the oceanic component is shown to be more realistic than in configurations with a low resolution oceanic component. This general conclusion is independent of the atmospheric resolution. Resolving small-scale processes in the ocean produces a more realistic oceanic mean state, with a reduced cold tongue bias, which in turn allows the atmospheric model component to be forced more realistically. A realistic atmospheric basic state is critical in order to represent Rossby wave propagation in response to El Niño, and hence the extra-tropical response to El Niño. Through the use of high and low resolution configurations of the forced atmospheric-only model component we show that, in isolation, atmospheric resolution does not significantly affect the simulation of the extra-tropical response to El Niño. It is demonstrated, through perturbations to the SST forcing of the atmospheric model component, that biases in the climatological SST field typical of coupled model configurations with low oceanic resolution can account for the erroneous atmospheric basic state seen in these coupled model configurations. These results highlight the importance of resolving small-scale oceanic processes in producing a realistic large-scale mean climate in coupled models, and suggest that it might may be possible to “squeeze out” valuable extra performance from coupled models through increases to oceanic resolution alone.

Creative participation in construction firms: bridging creativity and innovation

An intricate evolution of mainstream theories follows the growing need to explain employees’ commitment and engagement. Our understanding of these work-related phenomena and behaviour has improved but creativity and innovation as desired indicators are still often treated as coexisting constructs with very little attention given to a state of willingness of an individual to even consider contributing ideas. In this research we investigate the influence of knowledge and understanding, perceived radicality, personality dimensions, and favouring of ideas on employee willingness to creatively participate in order to trace its existence in propagation of ideas. A total of 76 construction and non-construction professionals participated in between-subject quasi-experiments. We also proposed IPO-based radicality of ideas construct from the viewpoint of employees involved in the processes of transformation. The research findings show that experts with deep understanding of the work are more likely to contribute highly radical ideas to decision-makers than less knowledgeable employees. Furthermore, personal factors that impact employee willingness to creatively participate have been valued higher than organisational factors. Personality dimensions by The BigFive Inventory have shown no effect on willingness to contribute ideas, while favouring of ideas showed a significant effect. In general, the findings show similarities with some studies of consumer willingness to participate in co-creation processes and thus indicate that firms may be studied as dynamic internal markets of ideas.

On the seasonal onset of polar mesospheric clouds and the breakdown of the stratospheric polar vortex in the Southern Hemisphere

Southern Hemisphere (SH) polar mesospheric clouds (PMCs), also known as noctilucent clouds, have been observed to be more variable and, in general, dimmer than their Northern Hemisphere (NH) counterparts. The precise cause of these hemispheric differences is not well understood. This paper focuses on one aspect of the hemispheric differences: the timing of the PMC season onset. Observations from the Aeronomy of Ice in the Mesosphere satellite indicate that in recent years the date on which the PMC season begins varies much more in the SH than in the NH. Using the Canadian Middle Atmosphere Model, we show that the generation of sufficiently low temperatures necessary for cloud formation in the SH summer polar mesosphere is perturbed by year‐to‐year variations in the timing of the late‐spring breakdown of the SH stratospheric polar vortex. These stratospheric variations, which persist until the end of December, influence the propagation of gravity waves up to the mesosphere. This adds a stratospheric control to the temperatures in the polar mesopause region during early summer, which causes the onset of PMCs to vary from one year to another. This effect is much stronger in the SH than in the NH because the breakdown of the polar vortex occurs much later in the SH, closer in time to the PMC season.

Climatology and Forcing of the Quasi-Biennial Oscillation in the MAECHAM5 Model

The quasi-biennial oscillation (QBO) in the equatorial zonal wind is an outstanding phenomenon of the atmosphere. The QBO is driven by a broad spectrum of waves excited in the tropical troposphere and modulates transport and mixing of chemical compounds in the whole middle atmosphere. Therefore, the simulation of the QBO in general circulation models and chemistry climate models is an important issue. Here, aspects of the climatology and forcing of a spontaneously occurring QBO in a middle-atmosphere model are evaluated, and its influence on the climate and variability of the tropical middle atmosphere is investigated. Westerly and easterly phases are considered separately, and 40-yr ECMWF Re-Analysis (ERA-40) data are used as a reference where appropriate. It is found that the simulated QBO is realistic in many details. Resolved large-scale waves are particularly important for the westerly phase, while parameterized gravity wave drag is more important for the easterly phase. Advective zonal wind tendencies are important for asymmetries between westerly and easterly phases, as found for the suppression of the easterly phase downward propagation. The simulation of the QBO improves the tropical upwelling and the atmospheric tape recorder compared to a model without a QBO. The semiannual oscillation is simulated realistically only if the QBO is represented. In sensitivity tests, it is found that the simulated QBO is strongly sensitive to changes in the gravity wave sources. The sensitivity to the tested range of horizontal resolutions is small. The stratospheric vertical resolution must be better than 1 km to simulate a realistic QBO.

Wave-activity conservation laws for the three-dimensional anelastic and Boussinesq equations with a horizontally homogeneous background flow

Wave-activity conservation laws are key to understanding wave propagation in inhomogeneous environments. Their most general formulation follows from the Hamiltonian structure of geophysical fluid dynamics. For large-scale atmospheric dynamics, the Eliassen–Palm wave activity is a well-known example and is central to theoretical analysis. On the mesoscale, while such conservation laws have been worked out in two dimensions, their application to a horizontally homogeneous background flow in three dimensions fails because of a degeneracy created by the absence of a background potential vorticity gradient. Earlier three-dimensional results based on linear WKB theory considered only Doppler-shifted gravity waves, not waves in a stratified shear flow. Consideration of a background flow depending only on altitude is motivated by the parameterization of subgrid-scales in climate models where there is an imposed separation of horizontal length and time scales, but vertical coupling within each column. Here we show how this degeneracy can be overcome and wave-activity conservation laws derived for three-dimensional disturbances to a horizontally homogeneous background flow. Explicit expressions for pseudoenergy and pseudomomentum in the anelastic and Boussinesq models are derived, and it is shown how the previously derived relations for the two-dimensional problem can be treated as a limiting case of the three-dimensional problem. The results also generalize earlier three-dimensional results in that there is no slowly varying WKB-type requirement on the background flow, and the results are extendable to finite amplitude. The relationship A E =cA P between pseudoenergy A E and pseudomomentum A P, where c is the horizontal phase speed in the direction of symmetry associated with A P, has important applications to gravity-wave parameterization and provides a generalized statement of the first Eliassen–Palm theorem.

Assessment of temperature, trace species, and ozone in chemistry-climate model simulations of the recent past

Simulations of the stratosphere from thirteen coupled chemistry-climate models (CCMs) are evaluated to provide guidance for the interpretation of ozone predictions made by the same CCMs. The focus of the evaluation is on how well the fields and processes that are important for determining the ozone distribution are represented in the simulations of the recent past. The core period of the evaluation is from 1980 to 1999 but long-term trends are compared for an extended period (1960–2004). Comparisons of polar high-latitude temperatures show that most CCMs have only small biases in the Northern Hemisphere in winter and spring, but still have cold biases in the Southern Hemisphere spring below 10 hPa. Most CCMs display the correct stratospheric response of polar temperatures to wave forcing in the Northern, but not in the Southern Hemisphere. Global long-term stratospheric temperature trends are in reasonable agreement with satellite and radiosonde observations. Comparisons of simulations of methane, mean age of air, and propagation of the annual cycle in water vapor show a wide spread in the results, indicating differences in transport. However, for around half the models there is reasonable agreement with observations. In these models the mean age of air and the water vapor tape recorder signal are generally better than reported in previous model intercomparisons. Comparisons of the water vapor and inorganic chlorine (Cly) fields also show a large intermodel spread. Differences in tropical water vapor mixing ratios in the lower stratosphere are primarily related to biases in the simulated tropical tropopause temperatures and not transport. The spread in Cly, which is largest in the polar lower stratosphere, appears to be primarily related to transport differences. In general the amplitude and phase of the annual cycle in total ozone is well simulated apart from the southern high latitudes. Most CCMs show reasonable agreement with observed total ozone trends and variability on a global scale, but a greater spread in the ozone trends in polar regions in spring, especially in the Arctic. In conclusion, despite the wide range of skills in representing different processes assessed here, there is sufficient agreement between the majority of the CCMs and the observations that some confidence can be placed in their predictions.

The angular momentum constraint on climate sensitivity and downward influence in the middle atmosphere

It is shown that under reasonable assumptions, conservation of angular momentum provides a strong constraint on gravity wave drag feedbacks to radiative perturbations in the middle atmosphere. In the time mean, radiatively induced temperature perturbations above a given altitude z cannot induce changes in zonal mean wind and temperature below z through feedbacks in gravity wave drag alone (assuming an unchanged gravity wave source spectrum). Thus, despite the many uncertainties in the parameterization of gravity wave drag, the role of gravity wave drag in middle-atmosphere climate perturbations may be much more limited than its role in climate itself. This constraint limits the possibilities for downward influence from the mesosphere. In order for a gravity wave drag parameterization to respect the momentum constraint and avoid spurious downward influence, any nonzero parameterized momentum flux at a model lid must be deposited within the model domain, and there must be no zonal mean sponge layer. Examples are provided of how violation of these conditions leads to spurious downward influence. For planetary waves, the momentum constraint does not prohibit downward influence, but it limits the mechanisms by which it can occur: in the time mean, downward influence from a radiative perturbation can only arise through changes in reflection and meridional propagation properties of planetary waves.

Uncertainties and assessments of chemistry-climate models of the stratosphere

In recent years a number of chemistry-climate models have been developed with an emphasis on the stratosphere. Such models cover a wide range of time scales of integration and vary considerably in complexity. The results of specific diagnostics are here analysed to examine the differences amongst individual models and observations, to assess the consistency of model predictions, with a particular focus on polar ozone. For example, many models indicate a significant cold bias in high latitudes, the “cold pole problem”, particularly in the southern hemisphere during winter and spring. This is related to wave propagation from the troposphere which can be improved by improving model horizontal resolution and with the use of non-orographic gravity wave drag. As a result of the widely differing modelled polar temperatures, different amounts of polar stratospheric clouds are simulated which in turn result in varying ozone values in the models. The results are also compared to determine the possible future behaviour of ozone, with an emphasis on the polar regions and mid-latitudes. All models predict eventual ozone recovery, but give a range of results concerning its timing and extent. Differences in the simulation of gravity waves and planetary waves as well as model resolution are likely major sources of uncertainty for this issue. In the Antarctic, the ozone hole has probably reached almost its deepest although the vertical and horizontal extent of depletion may increase slightly further over the next few years. According to the model results, Antarctic ozone recovery could begin any year within the range 2001 to 2008. The limited number of models which have been integrated sufficiently far indicate that full recovery of ozone to 1980 levels may not occur in the Antarctic until about the year 2050. For the Arctic, most models indicate that small ozone losses may continue for a few more years and that recovery could begin any year within the range 2004 to 2019. The start of ozone recovery in the Arctic is therefore expected to appear later than in the Antarctic.

Efficient calculation of two-dimensional periodic and waveguide acoustic Green’s functions

New representations and efficient calculation methods are derived for the problem of propagation from an infinite regularly spaced array of coherent line sources above a homogeneous impedance plane, and for the Green's function for sound propagation in the canyon formed by two infinitely high, parallel rigid or sound soft walls and an impedance ground surface. The infinite sum of source contributions is replaced by a finite sum and the remainder is expressed as a Laplace-type integral. A pole subtraction technique is used to remove poles in the integrand which lie near the path of integration, obtaining a smooth integrand, more suitable for numerical integration, and a specific numerical integration method is proposed. Numerical experiments show highly accurate results across the frequency spectrum for a range of ground surface types. It is expected that the methods proposed will prove useful in boundary element modeling of noise propagation in canyon streets and in ducts, and for problems of scattering by periodic surfaces.

A uniformly valid far field asymptotic expansion of the green function for two-dimensional propagation above a homogeneous impedance plane

A generalized asymptotic expansion in the far field for the problem of cylindrical wave reflection at a homogeneous impedance plane is derived. The expansion is shown to be uniformly valid over all angles of incidence and values of surface impedance, including the limiting cases of zero and infinite impedance. The technique used is a rigorous application of the modified steepest descent method of Ot

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.