We consider a nonlocal version of the NJL model, based on a separable quark-quark interaction. The interaction is extended to include terms that bind vector and axial-vector mesons. The nonlocality means that no further regulator is required. Moreover the model is able to confine the quarks by generating a quark propagator without poles at real energies. Working in the ladder approximation, we calculate amplitudes in Euclidean space and discuss features of their continuation to Minkowski energies. Conserved currents are constructed and we demonstrate their consistency with various Ward identities. Various meson masses are calculated, along with their strong and electromagnetic decay amplitudes. We also calculate the electromagnetic form factor of the pion, as well as form factors associated with the processes γγ * → π 0and ω → π 0 γ * . The results are found to lead to a satisfactory phenomenology and lend some dynamical support to the idea of vector-meson dominance.

As part of an international intercomparison project, a set of single-column models (SCMs) and cloud-resolving models (CRMs) are run under the weak-temperature gradient (WTG) method and the damped gravity wave (DGW) method. For each model, the implementation of the WTG or DGW method involves a simulated column which is coupled to a reference state defined with profiles obtained from the same model in radiative-convective equilibrium. The simulated column has the same surface conditions as the reference state and is initialized with profiles from the reference state. We performed systematic comparison of the behavior of different models under a consistent implementation of the WTG method and the DGW method and systematic comparison of the WTG and DGW methods in models with different physics and numerics. CRMs and SCMs produce a variety of behaviors under both WTG and DGW methods. Some of the models reproduce the reference state while others sustain a large-scale circulation which results in either substantially lower or higher precipitation compared to the value of the reference state. CRMs show a fairly linear relationship between precipitation and circulation strength. SCMs display a wider range of behaviors than CRMs. Some SCMs under the WTG method produce zero precipitation. Within an individual SCM, a DGW simulation and a corresponding WTG simulation can produce different signed circulation. When initialized with a dry troposphere, DGW simulations always result in a precipitating equilibrium state. The greatest sensitivities to the initial moisture conditions occur for multiple stable equilibria in some WTG simulations, corresponding to either a dry equilibrium state when initialized as dry or a precipitating equilibrium state when initialized as moist. Multiple equilibria are seen in more WTG simulations for higher SST. In some models, the existence of multiple equilibria is sensitive to some parameters in the WTG calculations.

Convection-permitting ensembles have led to improved forecasts of many atmospheric phenomena. However, to fully utilize these forecasts the dependence of predictability on synoptic conditions needs to be understood. In this study, convective regimes are diagnosed based on a convective time scale that identifies the degree to which convection is in equilibrium with the large-scale forcing. Six convective cases are examined in a convection-permitting ensemble constructed using the Met Office Unified Model. The ensemble members were generated using small-amplitude buoyancy perturbations added into the boundary layer, which can be considered to represent turbulent fluctuations close to the grid scale. Perturbation growth is shown to occur on different scales with an order of magnitude difference between the regimes [O(1) km for cases closer to nonequilibrium convection and O(10) km for cases closer to equilibrium convection]. This difference reflects the fact that cell locations are essentially random in the equilibrium events after the first 12 h of the forecast, indicating a more rapid upscale perturbation growth compared to the nonequilibrium events. Furthermore, large temporal variability is exhibited in all perturbation growth diagnostics for the nonequilibrium regime. Two boundary condition–driven cases are also considered and show similar characteristics to the nonequilibrium cases, implying that caution is needed to interpret the time scale when initiation is not within the domain. Further understanding of perturbation growth within the different regimes could lead to a better understanding of where ensemble design improvements can be made beyond increasing the model resolution and could improve interpretation of forecasts.

Abstract. Most parameterizations for precipitating convection in use today are bulk schemes, in which an ensemble of cumulus elements with different properties is modelled as a single, representative entraining-detraining plume. We review the underpinning mathematical model for such parameterizations, in particular by comparing it with spectral models in which elements are not combined into the representative plume. The chief merit of a bulk model is that the representative plume can be described by an equation set with the same structure as that which describes each element in a spectral model. The equivalence relies on an ansatz for detrained condensate introduced by Yanai et al. (1973) and on a simplified microphysics. There are also conceptual differences in the closure of bulk and spectral parameterizations. In particular, we show that the convective quasi-equilibrium closure of Arakawa and Schubert (1974) for spectral parameterizations cannot be carried over to a bulk parameterization in a straightforward way. Quasi-equilibrium of the cloud work function assumes a timescale separation between a slow forcing process and a rapid convective response. But, for the natural bulk analogue to the cloud-work function, the relevant forcing is characterised by a different timescale, and so its quasi-equilibrium entails a different physical constraint. Closures of bulk parameterizations that use a parcel value of CAPE do not suffer from this timescale issue. However, the Yanai et al. (1973) ansatz must be invoked as a necessary ingredient of those closures.

SUMMARYA recently proposed extension to the twofold extratropical cyclogenesis classi cation scheme of Petterssen and Smebye is discussed. A third class of extratropical cyclone (type C) is described, in which initial development is controlled by a pre-existing upper-level potential vorticity (PV) anomaly. In its early stages, such a system is indistinguishable from the classical type B cyclone of the Petterssen and Smebye scheme. However, subsequent development cannot be understood in terms of a co-operative interaction of the upper-level feature with a lowlevel baroclinic zone. Rather, the cyclogenetic dynamics of type C systems are dominated by the action of strong midlevel latent heating. Such heating can generate important anomalies of PV that act to suppress the formation of a low-level thermal anomaly and that interact destructively with the pre-existing upper-level feature.Candidate type C events are identi ed using recently developed, height-attributable, quasi-geostrophic, vertical-motion diagnostics. The application of one such diagnostic to a climatology of instantaneous cyclonic features suggests that type C events may occur with reasonable frequency. The generic behaviour of system types in the proposed threefold classi cation scheme is compared with the actual dynamics of some cyclones from the Fronts and Atlantic Storm-Track EXperiment (FASTEX). The analysis is based on piecewise PV inversions and numerical simulations. This approach is able to provide a good description of a case of standard type B development, consistent with the qualitative description of Petterssen and Smebye and with the quasi-geostrophic diagnostics. Within the same framework, two systems are discussed whose behaviours do not t the simple A/B classi cation, but are consistent with the proposed type C mechanism.

This book has two central aims. The first is to give a fair, comprehensive, and analytical account of the central features of the neo‐liberal view about the role and limits of the state in the modern world. It considers important ideas such as the contrast between a state based on rules and the one based on outcomes, the implications of this contrast for the rule of law, for the ideas of freedom, social justice, and rights. It provides a full account of the neo‐liberal view of the relationship between the state and the economy and to civil society and voluntary organizations. It draws upon a wide range of works by neo‐liberal thinkers to build up the theoretical case for this conception of the role of government and politics. The thinkers at the heart of this part of the study are Hayek, Buchanan, Mises, Menger, as well as others who while not regarding themselves as neo‐liberals nevertheless have contributed to neo‐liberal ideas. These include Oakeshott, Nozick, and Rothbard. The study also looks at the public policy implications of neo‐liberal ideas in relation to the role of the welfare state and other forms of public sector provision. The second part of the book provides a detailed critical appraisal of some of the central neo‐liberal doctrines particularly in relation to the core ideas of freedom, justice, rights, the role of collective organizations in civil society, and the provision of welfare. The book argues that contrary to neo‐liberal arguments there is no coherent way of providing a sharp and categorical distinction between neo‐liberalism and Social Democracy on the one hand and libertarianism on the other.

Strong vertical gradients at the top of the atmospheric boundary layer affect the propagation of electromagnetic waves and can produce radar ducts. A three-dimensional, time-dependent, nonhydrostatic numerical model was used to simulate the propagation environment in the atmosphere over the Persian Gulf when aircraft observations of ducting had been made. A division of the observations into high-and low-wind cases was used as a framework for the simulations. Three sets of simulations were conducted with initial conditions of varying degrees of idealization and were compared with the observations taken in the Ship Antisubmarine Warfare Readiness/ Effectiveness Measuring (SHAREM-115) program. The best results occurred with the initialization based on a sounding taken over the coast modified by the inclusion of data on low-level atmospheric conditions over the Gulf waters. The development of moist, cool, stable marine internal boundary layers (MIBL) in air flowing from land over the waters of the Gulf was simulated. The MIBLs were capped by temperature inversions and associated lapses of humidity and refractivity. The low-wind MIBL was shallower and the gradients at its top were sharper than in the high-wind case, in agreement with the observations. Because it is also forced by land-sea contrasts, a sea-breeze circulation frequently occurs in association with the MIBL. The size, location, and internal structure of the sea-breeze circulation were realistically simulated. The gradients of temperature and humidity that bound the MIBL cause perturbations in the refractivity distribution that, in turn, lead to trapping layers and ducts. The existence, location, and surface character of the ducts were well captured. Horizontal variations in duct characteristics due to the sea-breeze circulation were also evident. The simulations successfully distinguished between high-and low-wind occasions, a notable feature of the SHAREM-115 observations. The modeled magnitudes of duct depth and strength, although leaving scope for improvement, were most encouraging.

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