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I In his account of predominantly Scottish eighteenth-century migrs, Robert Crawford uncovers a fractured "English" identity, curiously amenable to British influences, while at the same time never completely assimilating them. Tolerance of all non-provincial accents or traditions gave the impression of a permeability that was far from universal (see Robert Crawford 45-110). This symbiotic relationship bears upon the oppositional minorities with especial force, causing them often, as Terry Eagleton has recognized, to "move under the sign of irony, knowing themselves ineluctably parasitic on their antagonists," a realization felt with differing stresses and foci by Irish visitors such as Swift, Congreve, Burke, and Berkeley as well as Goldsmith (7). For the latter, the culture clash was jarring, as Edmond Malone described: when Goldsmith arrived in London in 1756 as an "entire stranger" to pursue a career as an apothecary's assistant, "his broad Irish accent, and the uncouthness of his appearance" met with initial refusal (Poems and Plays v). (1) If he temporarily forgot his roots, it was inevitable that there would be someone by to remind him. Goldsmith has been, on the other hand, a character that the Irish are apt to distrust. Yeats caught this mood of liminality in "The Seven Sages": Oliver Goldsmith sang what he had seen, Roads full of beggars, cattle in the fields, But never saw the trefoil stained with blood, The avenging leaf those fields raised up against it. (lines 17-20) (2) This line of argument spies the pastoral and elegiac, the pity rather than the outrage. When the "rural virtues leave the land" in "The Deserted Village," it may refer to Lissoy from his native childhood, but, then, why did he preface his survey with a digression on "a time ... ere England's griefs began"? (398, 57). What is certainly suspect is that the Goldsmith who reported back home in the early years might be directly confessional; the letter to his brother, the Rev. Henry Goldsmith (January 1759), is only a startling variation on a common theme, where he traces in himself, a "settled melancholy and an utter disgust of all that life brings with it. Whence the romantic turn that all our family are possessed with, whence this love for every place and every country but that in which we reside?" (Collected Letters 58). For himself the result was a "hesitating disagreeable manner of speaking" (58). This provokes a significant crux for the biographer, for how might we discern the genuine cry of pain from the staged melancholia? Or the canny manipulation of convention from the true confession? A third alternative is always available: that Goldsmith found that conventions were expressive opportunities, not obstacles. Eagleton's view sets an agenda that could apply to many exiles at this time, but it bears upon Goldsmith most significantly. The same letter to his brother quoted above introduces linked but still distinct personae in addition to the confirmed depressive: the man of the world, the unbookish savant, and the unwisely generous benefactor ("In general [says Goldsmith] take the word of a man who has seen the world, and studied human nature more by experience than precept, take my word for it I say that books teach us very little of the world"), plus the philosopher rendered by his reliance on learning as vulnerable to "cunning" and ridicule, especially as regards misplaced charity (Collected Letters 60-61). The decision to assimilate or not--or the degree of such negotiation--faces all exiles, yet the evidence of these early letters is not as revealing as it seems. Ralph M. Wardle's survey of them leads to a view that is shared by other biographers: "Goldsmith's character does not appear to its best advantage in these letters: his shifts from extravagant flattery to the business at hand, from joviality to grief, sometimes ring false and leave one questioning the man's sincerity" (85). …

A quartic spline based remapping algorithm is developed and illustrative tests of it are presented herein. To ensure mass conservation, the scheme solves an integral form of the transport equation rather than the differential form. The integrals are computed from reconstructed quartic splines with mass conservation constraints. For higher dimensions, this remapping can be used within a standard directional splitting methodology or within the flow-dependent cascade splitting approach. A high-order grid and sub-grid based monotonic filter is also incorporated into the overall scheme. This filter is independent of the underlying spline representation adopted here, and is of more general application.

Application of the semi-Lagrangian method to the vector momentum equation in orthogonal curvilinear systems is considered, with emphasis on spherical and spheroidal coordinates for deep-atmosphere models (in which the shallow-atmosphere approximation is not made). In spherical coordinates, a certain rotation matrix allows vector components at semi-Lagrangian departure points to be expressed in the required component forms at the corresponding arrival points. This rotation matrix also allows the unit vector triad at the arrival point to be expressed in terms of the unit vector triad at the departure point. The resulting formalisation of the momentum equation applies to timesteps of arbitrary length, and in the limit of infinitesimal timestep it delivers the familiar Eulerian components. Extension of the rotation matrix technique to more general orthogonal curvilinear systems is remarkably straightforward, thus demonstrating the versatility of the semi-Lagrangian method. Explicit forms are given for systems having longitude as one coordinate and general orthogonal coordinates in the meridional plane, and in particular these forms are applicable to both confocal oblate spheroidal and similar oblate spheroidal systems. A specific factorisation of the rotation matrix in the spherical polar case involves three matrices, one of which represents rotation of the unit vector triad along a great circle arc; the non-Euclidean, shallow-atmosphere approximation of the total rotation matrix results when the great circle rotation matrix is replaced by the identity matrix (but the other two matrices involved in the factorisation are kept intact). This shallow-atmosphere rotation matrix agrees with that used by ECMWF and Meteo-France. © Crown Copyright 2010. Published by John Wiley & Sons, Ltd.

In a recent paper, a conservative semi-Lagrangian mass transport scheme SLICE has been coupled to a semi-implicit semi-Lagrangian scheme for the shallow-water equations. The algorithm involves the solution at each timestep of a nonlinear Helmholtz problem, which is achieved by iterative solution of a linear ‘inner’ Helmholtz problem; this framework, as well as the linear Helmholtz operator itself, are the same as would be used with a non-conservative interpolating semi-Lagrangian scheme for mass transport. However, in order to do this, a reference value of geopotential was introduced into the discretization. It is shown here that this results in a weak dependence of the results on that reference value. An alternative coupling is therefore proposed that preserves the same solution framework and linear Helmholtz operator but, at convergence of the nonlinear solver, has no dependence on the reference value. However, in order to maintain accuracy at large timesteps, this approach requires a modification to how SLICE performs its remapping. An advantage of removing the dependence on the reference value is that the scheme then gives consistent tracer transport. Copyright © 2010 Royal Meteorological Society and Crown Copyright. Published by John Wiley & Sons, Ltd.

AFFILIATIONS: Weller—National Centre for Atmospheric Science, University of Reading, Reading, United Kingdom; ringler—Climate, Ocean, and Sea Ice Modeling Group, Los Alamos National Laboratory, Los Alamos, New Mexico; PiggoTT— Grantham Institute for Climate Change, Imperial College London, London, United Kingdom; Wood—Met Office, Exeter, United Kingdom CORRESPONDENCE AUTHOR: Hilary Weller, Department of Meteorology, University of Reading, Earley Gate, Reading RG6 6BB, United Kingdom E-mail: h.weller@reading.ac.uk

When the trajectory equation is discretised in semi-Lagrangian models, the departure points can be spuriously located outside the model domain. Historically this has been addressed in an ad hoc manner by relocating any such departure point to the domain boundary. This procedure, whilst convenient, is not physically justified and is inaccurate. It is of particular concern for mass-conserving, finite-volume, semi-Lagrangian schemes that use the locations of departure points to determine upstream volumes, since it can lead to spuriously massless or near-massless volumes, and large errors in mass transport. This weakness of current discretisations is discussed. An improved near-boundary discretisation of the trajectory equation is then proposed and analysed via an example. Crown Copyright © 2009. Reproduced with the permission of HMSO. Published by John Wiley & Sons Ltd.

For the shallow-water equations on the sphere, an inherently mass-conserving semi-Lagrangian discretisation (SLICE) of the continuity equation is coupled with a semi-implicit semi-Lagrangian discretisation of the momentum equations. Various tests from the literature (two with analytical nonlinear solutions) are used to assess the model's performance and also to compare it with that of a variant model that instead employs a standard non-conserving semi-implicit semi-Lagrangian discretisation of the continuity equation. The mass-conserving version gives results that are overall somewhat better than the non-conserving one.

This Note presents some further developments to the Semi-Lagrangian Inherently Conservative and Efficient (SLICE) scheme. The revised scheme, termed C-SLICE, is designed to exploit the good dispersion properties of a C-grid staggering of mass and momentum variables in atmospheric models. Furthermore, several simplifications are made to the SLICE scheme, leading to improved computational efficiency without loss of accuracy. The revised scheme is evaluated using some standard tests from the literature. © Crown Copyright 2009. Reproduced with the permission of the Controller of HMSO. Published by John Wiley & Sons, Ltd.

In meteorological dynamics it is common practice to represent the potential surfaces of apparent gravity (the geopotentials) as spheres, and consequently the use of spherical polar coordinates in models of the global atmosphere is widespread. Several writers have considered how oblate spheroidal coordinates might be used instead, thus enabling the Figure of the Earth to be better represented. It is observed here that oblate spheroidal coordinate systems are conventionally defined using confocal oblate spheroids, and that such spheroids are inappropriate representations of the geopotentials because they imply the wrong sign for the latitudinal variation of apparent gravity. Re-examination of a classical problem of Newtonian gravitation shows that, near the Earth, the geopotentials are to a very good approximation spheroids, but not spheroids of an analytically simple type. However, similar oblate spheroids are a qualitatively correct model of the near-Earth geopotentials, and are a quantitatively good approximation in so far as Newton's uniform-density model adequately describes the real Earth. An orthogonal curvilinear coordinate system based on similar oblate spheroids is proposed and examined.

The relation between order of accuracy and convergence rate for simple linear finite difference schemes for differentiation and advection is examined theoretically and empirically. For sufficiently smooth functions, i.e. those with sufficiently steep spectral slope, the convergence rate is given by the order of accuracy. For less smooth functions, with shallower spectral slope, differentiation and advection behave slightly differently: the convergence rate of a finite difference derivative is determined entirely by the spectral slope, while the convergence rate of a finite difference advection scheme is determined by an interaction between the spectral slope and the order of accuracy.

Eight sherds of 9th -10th century AD Abbasid blue-and-white glazed earthenware, excavated in 1931 at Hira in western Iraq, were analysed using, variously, quantitative wavelength dispersive spectrometry (WDS) and energy dispersive spectrometry (EDS) in association with scanning electron microscopes (SEM), and semi-quantitative x-ray fluorescence spectrometry (XRF). In order to compare the compositions of the cobalt pigments used, the glazes of seven complete vessels of 8th century AD Chinese Tang blue-and-white sancai were also analysed semi-quantitatively using XRF. The Abbasid wares were shown to have used traditional Mesopotamian alkali-lime glazes applied to calcareous clay bodies. However, about half the glazes examined were opacified with tin oxide. The three types of blue decoration (ie raised; spreading; and flat, non-spreading) were produced using a variety of glaze formulations including a mixture of cobalt pigment with lead oxide. The sources of the ores used for the cobalt pigments have not been identified. However, the analytical data showed that the cobalt ore used for the Abbasid blue-and-white ware could be distinguished from that used for the Tang blue-and-white sancai by its higher iron content and by the presence of a significant amount of zinc. The use of cobalt blue decoration on the 9th – 10th century AD Abbasid ware was anticipated in China by 8th century AD Tang blue-and-white sancai wares. However, whether its introduction by the Abbasid potters should be seen as an independent invention that followed the introduction of tin-opacified glazes in Iraq, or whether it was influenced in some way by Chinese originals is still a problem.

The recently devised one-dimensional parabolic spline method (PSM) for efficient, conservative, and monotonic remapping is introduced into the semi-Lagrangian inherently-conserving and efficient (SLICE) scheme for transport problems in multi-dimensions. To ensure mass conservation, an integral form of the transport equation is used rather than the differential form of classical semi-Lagrangian schemes. Integrals within the SLICE scheme are computed using multiple sweeps of PSM along flow-dependent cascade directions to avoid the large timestep-dependent splitting errors associated with traditional fixed-direction splitting. Accuracy of the overall scheme, including at large timestep, is demonstrated using two-dimensional test problems in both Cartesian and spherical geometries and compared with that of the piecewise parabolic method (PPM) applied within the same SLICE framework.

We present a new two-step temporal discretization of the diffusion equation, which is formally second-order-accurate and unconditionally stable. A novel aspect of the scheme is that it is monotonically damping: the damping rate is a monotonically-increasing function of the diffusion coefficient, independent of the size of the time step, when the diffusion coefficient is independent of the variable being diffused. Furthermore, the damping rate increases without bound as the diffusion coefficient similarly increases. We discuss the nonlinear behaviour of the scheme when the diffusion coefficient is a function of the diffused variable. The scheme is designed to maintain any steady-state solution. We present examples of the performance of the scheme. © Crown Copyright 2007. Reproduced with the permission of the Controller of HMSO. Published by John Wiley & Sons, Ltd.

A predictor–corrector time-stepping algorithm is used by the Met Office's semi-implicit semi-Lagrangian non-hydrostatic Unified Model. This scheme is here extended to include an iterative option, improving performance when large time steps are used in highly nonlinear situations. The scheme is described, and results from global model tests, which show improvements in forecast accuracy, are presented. Copyright © 2007 Royal Meteorological Society

A regularized time-staggered discretization of the shallow-water equations has recently been proposed. The form of the regularization operator is chosen such that linear equivalence with the semi-implicit method can be achieved. Here, we present a further generalization of the regularization that also takes into account nonlinear balance. The performance of the improved regularization procedure is demonstrated for a simple nonlinear test problem. © Crown Copyright 2007. Reproduced with the permission of the Controller of HMSO. Published by John Wiley & Sons, Ltd.

There is a reassuring motive for choosing to translate a famous author in that you are servant to the master voice, relaying as innocently and accurately as you can past sentiments and tropes. In the wake of this irreproachable impulse, on the other hand, one might discover less obedient traces, not quite graffiti, but — because not announced — perhaps more insidious projections of the self; the ‘strong’ authors need to be misprized in order that their complex literariness might survive, but also that the imitator is no plagiarist. Interpretation has to intervene and not only at the micro level, but also in constructing the wider perspective, where the source text does not fit and, issuing from that dissonance, a cross-cultural dialogue emerges. In Wolfgang Iser’s phrase, ‘translatability is motivated by the need to cope with a crisis that can no longer be alleviated by the mere assimilation or appropriation of other cultures’. This gesture could be a form of ‘therapy for a growing awareness of cultural pathology’.1 The spectrum of cross-cultural adherence embraces imitation as well as academic translation, and the effect of ‘coping’ and negotiating is only a difference of degree. Pope’s Imitations of Horace offer us some material for reassurance in that the ethics of retirement and its apparently apolitical consequences are very much part of what is overt about the very form of the literary choice: the inclusion of the Horace text interleaved with Pope’s own and the adoption of Horace’s own conversational register.

Nigel Wood assesses the contemporary institutional status of English and English Studies, addressing three areas of concern: the relevance of tertiary level study, changing definitions of knowledge and the connection of higher education to the ‘public sphere’. Not all present influences are unwelcome, he argues. The new investigations possible in a digital economy — mining large volumes of data and contextualizing individual items with more precision — are progressive. Accountability and transparency in promoting the public good’, however, incorporate limiting levels of scrutiny and self-censorship, inviting the academy to conform to external pressures. Truly democratic humanistic enquiry should aim at as free and engaged an exchange of ideas as possible, bringing a truly critical and ‘oppositional’ perspective to bear on the present and the past.

A recently proposed time-staggered semi-Lagrangian discretization of the unforced rotating shallow-water equations is extended to include orographic forcing. Linear analysis shows that, as for traditional semi-implicit semi-Lagrangian schemes, it is also susceptible to spurious orographic resonance for large Courant numbers. A solution is proposed which, as shown by further linear analysis, addresses spurious orographic resonance whilst also maintaining computational stability. © Crown copyright, 2006. Royal Meteorological Society

A time-staggered semi-Lagrangian discretization of the rotating shallow-water equations is proposed and analysed. Application of regularization to the geopotential field used in the momentum equations leads to an unconditionally stable scheme. The analysis, together with a fully nonlinear example application, suggests that this approach is a promising, efficient, and accurate alternative to traditional schemes. © Royal Meteorological Society, 2006. A. Staniforth's and N. Wood's contributions are Crown copyright material, reproduced with the permission of the Controller of Her Majesty's Stationery Office.

At the present time there exist a number of different approaches to the problem of coupling parametrized physical processes to the dynamical core in operational numerical weather-prediction (NWP) and climate models. Motivated by the various strategies in use, some idealized representative coupling schemes are constructed and subsequently analysed using a methodology in which the physics and dynamics terms are represented in a simplified way. Particular numerical properties of the idealized schemes which are of interest are the ability to capture correct steady-state solutions and to be second-order accurate in time. In general, the schemes require specific choices for the time-differencing of certain coupled processes if correct steady-state solutions are to be obtained. This has implications for the overall numerical stability of a coupling strategy. An alternative physics–dynamics coupling approach is then described and analysed. A multiple-sweep predictor–corrector coupling scheme is shown to capture the correct steady-state solution and to allow for second-order accuracy, provided that the convective process is coupled explicitly. This approach has a number of advantages over those currently used in operational NWP models. Copyright © 2006 Crown copyright

A new and efficient parabolic spline based remapping algorithm is developed and tested herein. To ensure mass conservation, the scheme solves an integral form of the transport equation rather than the differential form. The integrals are computed from reconstructed parabolic splines with mass conservation constraints. For higher dimensions, this remapping can be used within a standard directional splitting methodology or within the flow-dependent cascade splitting approach. A grid and sub-grid based monotonic filter is also incorporated into the overall scheme. A truncation error analysis of the scheme is presented and discussed in terms of results from test cases. The analysis shows that although it has a similar truncation error in the converged limit as that of the widely used Piecewise Parabolic Method (PPM) for infinitely differentiable functions, PSM is more accurate than PPM for problems with slow spectral decay. Additionally, an operation count of the scheme is given which demonstrates the computational advantage of PSM compared to PPM. © Crown copyright 2005. Reproduced with the permission of Her Majesty's Stationery Office. Published by John Wiley & Sons, Ltd.

A regularized and time-staggered discretization of the two-dimensional, vertical slice Euler equation set is described and analysed. A linear normal mode analysis of the time-discrete system indicates that unconditional stability is obtained, for appropriate values of the regularization parameters, for both the hydrostatic and non-hydrostatic cases. Furthermore, when these parameters take their optimal values, the stability behaviour of the normal modes is identical to that obtained from a semi-implicit discretization of the unregularized equations. © Crown Copyright 2006. Reproduced with the permission of the Controller of HMSO. Published by John Wiley & Sons, Ltd.

A new monotonic and positive–definite filter is incorporated into an existing Semi-Lagrangian Inherently Conserving and Efficient (SLICE) scheme for transport problems in both Cartesian and spherical geometry. The SLICE scheme is based on a control-volume approach that uses multiple sweeps of a one-dimensional O (Δx4) conservation remapping algorithm along predetermined cascade directions. The new filter combines a selective detection algorithm, to pinpoint regions of non-monotonic behaviour, with a hierarchical reduction of the degree of the piecewise reconstruction in such regions, to re-establish monotonicity. The enhanced, monotonic and positive–definite, SLICE scheme is tested in one dimension, and then applied to standard two-dimensional test problems in both Cartesian and spherical geometries. Comparisons with published results of other conservative semi-Lagrangian schemes show that it performs well. © Crown copyright, 2005.

Split schemes for time-stepping physical parameterizations in numerical weather prediction and climate models are investigated within the context of simplified model equations. A symmetrized-splitting technique is applied to various parameterized systems containing fast and slow physics processes. The physics processes are represented by time-dependent forcing terms and linear damping/oscillatory terms. Finite-difference schemes, obtained from the splitting procedures, are examined to determine their stability properties, degree of splitting error, and truncation error. This analysis provides insight into the advantages and disadvantages of different splitting procedures across a range of possible parameterization scenarios. Many schemes obtained via splitting have time-step-dependent splitting errors, which can lead to inaccurate solutions when fast processes are present and the time step is large. Some splitting combinations, however, are more useful than others. The symmetrized-splitting procedure considered in this paper can produce stable first- and second-order accurate schemes, which have either no significant splitting errors or acceptably small errors relative to a steady-state solution. The consequences of this analysis for physics coupling strategies in realistic numerical weather prediction and climate models are noted.

A computational scheme suitable for numerical weather prediction and climate modelling over a wide range of length scales is described. Its formulation is non-hydrostatic and fully compressible, and shallow atmosphere approximations are not made. Semi-implicit, semi-Lagrangian time-integration methods are used. The scheme forms the dynamical core of the unified model used at the Met Office for all its operational numerical weather prediction and in its climate studies. © Crown copyright, 2005. Royal Meteorological Society

The use of near infrared spectroscopy (NIRS) was investigated in the context of an efficient high cell density fed-batch industrial Pichia pastoris bioprocess for the production of a therapeutic mammalian protein. This process represented a considerable challenge from the viewpoint of using NIRS to model key analytes because it involved two carbon sources (glycerol and methanol) added at differing rates and times, used a chemically complex medium, and showed a change in liquid phase behaviour due to cell growth. Models for biomass, glycerol, methanol and product were constructed. Different methods of spectral collection and mathematical procedures were used relative to which analyte in the fermentation matrix was being modelled and the rationale behind the model building is clearly described. Regardless of the mode of spectral collection it was essential to consider the changes in modelled analyte concentration relative to changes in other spectral contributors (analytes). The study considerably extends the use of NIRS in fermentation processes to high cell density complex industrial production processes, and comments on how this further developments the technology towards routine in situ NIRS monitoring of bioprocesses.

Chinese celadon shards of the Longquan type, believed to date from the Southern Song dynasty (1127–1279 AD), were excavated in 1934 on Mapungubwe Hill, a 13th century Iron Age site in the Limpopo valley, South Africa. We studied the shards with Raman spectroscopy, x-ray fluorescence (XRF) spectroscopy and x-ray diffraction (XRD). The Raman polymerization index (Ip), calculated from the spectra of the glaze of the shards, indicated a higher firing temperature than expected for the relatively calcium-rich Longquan glazes of the Southern Song dynasty. XRF analysis of the glaze and XRD measurements of the bulk of the shards supported this view and date the shards to possibly the Yuan (1279–1368 AD) or even early Ming (1368–1644 AD) dynasties. These results have an impact on the chronology of the history of the region and therefore call for further research of a comparative nature of other Chinese celadon shards excavated on archaeological sites in Africa, in addition to additional carbon dates of Mapungubwe hill. Copyright © 2005 John Wiley & Sons, Ltd.

A key aspect of the recently proposed Hamiltonian particle-mesh (HPM) method is its time-staggered discretization combined with a regularization of the continuous governing equations. In this article, the time discretization aspect of the HPM method is analysed for the linearized, rotating, shallow-water equations with orography, and the combined effect of time-staggering and regularization is compared analytically with the popular two-time-level semi-implicit time discretization of the unregularized equations. It is found that the two approaches are essentially equivalent, provided the regularization parameter is chosen appropriately in terms of the time step Δt. The article treats space as a continuum and, hence, its analysis is not limited to the HPM method. Copyright © 2005 Royal Meteorological Society

The impact of one- and two-term extrapolated-trajectory schemes on the stability properties of centred semi-implicit semi-Lagrangian schemes is analysed by examining the behaviour of the discrete (acoustic) normal modes of a prototypical column model. It is found that, in the absence of any controlling mechanism, both extrapolated-trajectory schemes are unstable. Additionally, they can significantly distort the vertical structure of the modes. Though not studied herein, the analogous distortion of Rossby and gravity waves could be expected to be deleterious to a forecast model. © Crown copyright, 2005. Royal Meteorological Society

The Semi-Lagrangian Inherently Conserving and Efficient (SLICE) scheme developed for Cartesian geometry is generalized to spherical geometry. The spherical version, SLICE-S, is similarly based on a Control Volume approach and multiple sweeps of a one-dimensional O(Δs4) (where s is the spherical distance) conservative remapping algorithm along Eulerian latitudes, then along Lagrangian longitudes. The resulting conservative scheme requires no restriction on either the polar meridional or zonal Courant numbers. SLICE-S is applied to the standard problems of solid-body rotation and deformational flow, and results are compared with those of a standard non-conservative and other published conservative semi-Lagrangian schemes. In addition to mass conservation, and consistent with the performance of SLICE, the present scheme is competitive in terms of accuracy and efficiency. © Crown copyright, 2004. Royal Meteorological Society

A new parametrization is presented for the representation in large-scale models of turbulent form drag due to subgrid orography with horizontal scales smaller than around 5000 m. The scheme is based on earlier work in which surface stress and its vertical distribution is formulated in terms of a slope parameter for sinusoidal hills. The new elements of the current parametrization are: (i) the spectrum of the orography is represented by a piecewise empirical power law, (ii) the turbulent form drag scheme integrates over the spectral orography to represent all the relevant scales, and (iii) the wind forcing level of the drag scheme depends on the horizontal scale of the orography, which implies that the smaller scales respond to lighter winds than do the larger scales. The scheme is controlled by a single parameter, namely the spectral density of the orography at scales of a few kilometres, as can be accurately obtained from a global 1 km data set. The empirical orographic power-law spectrum is derived by analysing fine resolution data as available for the USA. In order to be applicable in a large-scale model, simplifications are applied. Single-column simulations are performed to assess the consequences of these simplifications. Comparisons of single-column simulations with output from fine-scale simulations for sinusoidal hills show that the approximations are within the uncertainty of the fine-scale models. Furthermore, it is felt that the scheme is sufficiently accurate given the uncertainty in the characterization of the orography with current global datasets. © Royal Meteorological Society, 2004. Contributions by A. R. Brown and N. Wood are Crown copyright.

Various numerical issues concerning different approaches to the time stepping of physical parameterizations in numerical weather prediction (NWP) and climate models are examined. Parallel-split and sequential-split methods are explained and analyzed in the context of simple model equations. Terms arising from the use of splitting techniques produce erroneous solutions if the time step is large (of the size typically used in semi-implicit semi-Lagrangian models). Errors in steady-state solutions are examined in particular, as these may lead to systematic biases and climate drift. Splitting methods are then applied to a multiple timescale problem. For large time steps, a useful scheme should produce an accurate discrete representation of the reduced system, which has fast modes removed. Parallel splitting may be of limited use because only explicit versions model reduced systems without splitting errors, but such versions cannot stably integrate fast modes with acceptably large time steps. In a num...

Thiopurine-based drugs are a widely prescribed group of medications. Their tolerance and effectiveness is dependent on an individual’s ability to metabolize these compounds. An essential enzyme for the metabolism of these drugs is thiopurine S-methyltransferase (TPMT), whose activity is subject to genetic variation. Genotyping of the most frequent allelic variants in TPMTaffords an extremely accurate prediction of the three clinical phenotypes: high, intermediate, and low enzyme activity. One constraint of most genotyping methods is the inability to demonstrate physical linkage between two sequence variants that occur in different exons, e.g., c.460G4A and c.719A4G, which give rise to TPMT*3, the most common defective allele in Caucasian populations. Using mRNA/cDNA as a template enables analysis of both sequence variants in a single assay. This approach could be applicable to other genes where allelic variation (in-cis and in-trans) is due to alterations in different exons. Induced heteroduplex generator analysis has previously been shown to discriminate in-cis and has also been suitable for multiplexing. In this method we have exploited both these features and for the first time have applied them to a RT-PCR analysis. The primary reagent developed allows unequivocal resolution of TPMT*3A and the alleles carrying the c.719A4G allelic variant, TPMT*3C, as well as the silent alteration c.474T4C. The TPMT*3B variant has not been observed. A secondary reagent, which can be multiplexed, identifies the TPMT*2 allele. Hum Mutat 24:93–99, 2004. r 2004 Wiley-Liss, Inc.

Results are presented from numerical simulations of stable boundary-layer flow over low ridges. Internal gravity waves are seen within the boundary layer when a Froude number based on the wavelength of the ridges and the magnitude of the cross-ridge velocity component becomes sufficiently small. It is noted that this can always be achieved, even for short-wavelength ridges, if the ridge axis is aligned so as to be closely parallel to the wind direction. The surface pressure forces are found to be highly sensitive to the presence of gravity waves, and are also affected by the presence of critical levels within the boundary layer. © Crown copyright, 2003. Royal Meteorological Society

Previous analysis of the hydrostatic primitive equations using a generalized vertical coordinate is extended to the deep-atmosphere nonhydrostatic Euler equations, and some special vertical coordinates of interest are noted. Energy and axial angular momentum budgets are also derived. This would facilitate the development of conserving finite-difference schemes for deep-atmosphere models. It is found that the implied principles of energy and axial angular momentum conservation depend on the form of the upper boundary. In particular, for a modeled atmosphere of finite extent, global energy conservation is only obtained for a rigid lid, fixed in space and time. To additionally conserve global axial angular momentum, the height of the lid cannot vary with longitude.

Various simplifications of the fully compressible inviscid (Euler) equations have been made over the years to filter out rapidly-propagating acoustic oscillations, resulting in various anelastic, hydrostatic and pseudo-incompressible equation sets. The principal tool used to develop approximate equation sets, and to assess their validity as a function of flow regime, has been scale analysis which has proven quite subtle to apply. Here it is shown that normal-mode analysis provides a useful complementary tool for assessing the validity of the abovementioned approximate equation sets for both small- and large-scale flows, and leads to the following conclusions. Whilst of key importance for small-scale theoretical studies and process modelling, the anelastic equations are not recommended for either operational numerical weather prediction or climate simulation at any scale. The pseudo-incompressible set appears to be viable for numerical weather prediction, but only at short horizontal scales. For global non-hydrostatic modelling, only the fully compressible equations are suitable. Advances in numerical techniques in the past decade allow these to be integrated in a computationally efficient manner. © Crown copyright, 2003. Royal Meteorological Society

An important aspect of semi-Lagrangian models is the determination of departure points. This involves the calculation of particle displacements and is done by integrating a discrete form of the trajectory, or kinematic, equation. The way this equation is discretized affects the stability and accuracy of the equation set. Additionally, recent work in the context of a time-centred, semi-implicit, semi-Lagrangian scheme has shown that the form of the discrete kinematic equation reflects the preservation or violation of a dynamical equivalence between momentum and angular momentum formulations. Here that work is extended to the case of off-centred semi-implicit time weighting as used in most semi-implicit, semi-Lagrangian models. Two types of discretization of the trajectory equation are identified which preserve dynamical equivalence: some existing discretizations are found to be approximations to them. It is also shown how to incorporate physical forcings and/or predictor–corrector dynamics into the formulation. Two simple model problems (for solid-body rotation and wave motion) are used to provide some further insight into the accuracy and stability properties of various trajectory schemes, including: dynamically-equivalent schemes, approximations to these, and several existing schemes. Copyright © Crown copyright, 2003. Royal Meteorological Society

A Semi-Lagrangian Inherently Conserving and Efficient (SLICE) scheme is described for transport of passive scalars in Cartesian geometry. It is based on a Control-Volume (CV) approach and uses multiple sweeps of a one-dimensional O(Δx4) conservative remapping algorithm along pre-determined cascade directions. The scheme is applied to standard two-dimensional tests from the literature. Overall, it is found that in addition to conserving mass exactly, it is also competitive with standard non-conserving semi-Lagrangian schemes from the viewpoints of both computational efficiency and accuracy. © Crown Copyright, 2002.

A methodology for analysing the numerical properties of schemes for coupling physics parametrizations to a dynamical core is presented. As an example of its application, the methodology is used to study four coupling schemes (‘explicit’, ‘implicit’, ‘split-implicit’ and ‘symmetrized split-implicit’) in the context of a semi-implicit semi-Lagrangian dynamical core. Each coupling scheme is assessed in terms of its numerical stability and of the accuracy of both its transient and steady-state responses. Additionally, the occurrence of spurious, computational resonance is analysed and discussed. It is found that in this respect all four schemes behave similarly. In particular, in the absence of any damping mechanism to control resonance, the time-step restriction needed to avoid spurious resonance is twice as restrictive for time-dependent forcing as for stationary forcing. © Crown Copyright, 2002.

Numerical weather- and climate-prediction models have traditionally applied the hydrostatic approximation and also, in particular, the shallow-atmosphere approximation. In addition, and probably as a result, studies of the normal modes of the atmosphere too have made the shallow-atmosphere approximation. The approximation appears to be based on simple scaling arguments. Here, the forms of the unforced, linear normal modes for the deep atmosphere on a sphere are considered and compared with those of the shallow atmosphere. Also, the impact of ignoring the vertical variation of gravity is investigated. For terrestrial parameters, it is found that relaxing either or both of these approximations has very little impact on the spatial form of the energetically significant components of most normal modes. The frequencies too are only slightly changed. However, relaxing the shallow-atmosphere approximation does lead to significant changes in the tropical structure of internal acoustic modes. Relaxing the shallow-atmosphere approximation also leads to non-zero vertical-velocity and potential-temperature fields for external acoustic and Rossby modes; these fields are identically zero when the shallow-atmosphere approximation is made. For a finite-difference numerical model to be able to represent well the behaviour of the free atmosphere it must be able to capture accurately the structures of the normal modes. Therefore, the structures of normal modes can have implications for the choice of prognostic variables and grid staggering. In particular, the vertical structure of normal modes suggests that density and temperature should be analytically eliminated in favour of pressure and potential temperature as the prognostic thermodynamic variables, and that potential temperature and vertical velocity should be staggered in the vertical with respect to the other dynamic prognostic variables, the so-called Charney– Phillips grid. © Royal Meteorological Society, 2002. N. Wood's and A. Staniforth's contributions are Crown copyright.

Numerical results have shown that, for a rotating spherical atmosphere with terrestrial parameters, making the shallow-atmosphere approximation has only a very small impact on the frequency of linear, unforced normal modes, compared with those obtained from the full, unapproximated equations. In nearly all cases the normal-mode frequencies are smaller in magnitude when the shallow-atmosphere approximation is relaxed. Relaxing the approximation was also found to have only a small impact on the structures of normal modes, with the exception of long-zonal-wavelength internal acoustic modes. These results are particularly surprising in the tropics where the inclusion of the F = 2Ω cosϕ Coriolis terms (which are dropped in the shallow-atmosphere approximation) might be expected to dominate the usual f=2Ωsinϕ Coriolis terms. The complexity of the full equations, however, prevents analysis of why this insensitivity to the extra terms arises. In this paper normal modes are examined under the f–F-plane approximation and compared with those on the more usual f-plane. The resulting equations are more amenable to analysis than the full equation set, and analytic expressions for the dispersion relation and for the normal-mode structures are obtained for the particular case of an isothermal reference profile. This simplified geometry allows the effects of the F Coriolis terms to be examined while eliminating the geometrical effects of relaxing the shallow-atmosphere approximation, giving some insight into the relative importance of the two types of effect as well as the physical mechanisms at work. The F Coriolis terms are found to be responsible for the structural changes to long-zonal-wavelength internal acoustic modes, and can also affect extremely shallow and extremely deep gravity modes. However, these terms are found to have only a small effect on normal-mode frequencies, and geometrical effects, rather than these Coriolis terms, are responsible for the systematic reduction in the magnitude of normal-mode frequencies in a deep spherical atmosphere. In planar geometry the inclusion of the F terms gives rise to a new kind of normal mode in addition to the usual Rossby, gravity, and acoustic modes. The new modes are inertial in character, have frequency very close to f, and have extremely strong vertical tilt. © Royal Meteorological Society, 2002. N. Wood's and A. Staniforth's contributions are Crown copyright.