Incorporation of a physically based melt pond scheme into the sea ice component of a climate model

The extent and thickness of the Arctic sea ice cover has decreased dramatically in the past few decades with minima in sea ice extent in September 2005 and 2007. These minima have not been predicted in the IPCC AR4 report, suggesting that the sea ice component of climate models should more realistically represent the processes controlling the sea ice mass balance. One of the processes poorly represented in sea ice models is the formation and evolution of melt ponds. Melt ponds accumulate on the surface of sea ice from snow and sea ice melt and their presence reduces the albedo of the ice cover, leading to further melt. Toward the end of the melt season, melt ponds cover up to 50% of the sea ice surface. We have developed a melt pond evolution theory. Here, we have incorporated this melt pond theory into the Los Alamos CICE sea ice model, which has required us to include the refreezing of melt ponds. We present results showing that the presence, or otherwise, of a representation of melt ponds has a significant effect on the predicted sea ice thickness and extent. We also present a sensitivity study to uncertainty in the sea ice permeability, number of thickness categories in the model representation, meltwater redistribution scheme, and pond albedo. We conclude with a recommendation that our melt pond scheme is included in sea ice models, and the number of thickness categories should be increased and concentrated at lower thicknesses.

Structure, conduct and the stochastic volatility of food markets: theory and empirics

The relationship between price volatility and competition is examined. Atheoretic, vector auto regressions on farm prices of wheat and retail prices of derivatives (flour, bread, pasta, bulgur and cookies) are compared to results from a dynamic, simultaneous-equations model with theory-based farm-to-retail linkages. Analytical results yield insights about numbers of firms and their impacts on demand- and supply-side multipliers, but the applications to Turkish time series (1988:1-1996:12) yield mixed results.

Modelling QoS of a pervasive MVNO/M2M using semi-group theory

This paper aims to develop a mathematical model based on semi-group theory, which allows to improve quality of service (QoS), including the reduction of the carbon path, in a pervasive environment of a Mobile Virtual Network Operator (MVNO). This paper generalise an interrelationship Machine to Machine (M2M) mathematical model, based on semi-group theory. This paper demonstrates that using available technology and with a solid mathematical model, is possible to streamline relationships between building agents, to control pervasive spaces so as to reduce the impact in carbon footprint through the reduction of GHG.

Bifurcations and state changes in the human alpha rhythm: Theory and experiment

Despite many decades investigating scalp recordable 8–13-Hz (alpha) electroencephalographic activity, no consensus has yet emerged regarding its physiological origins nor its functional role in cognition. Here we outline a detailed, physiologically meaningful, theory for the genesis of this rhythm that may provide important clues to its functional role. In particular we find that electroencephalographically plausible model dynamics, obtained with physiological admissible parameterisations, reveals a cortex perched on the brink of stability, which when perturbed gives rise to a range of unanticipated complex dynamics that include 40-Hz (gamma) activity. Preliminary experimental evidence, involving the detection of weak nonlinearity in resting EEG using an extension of the well-known surrogate data method, suggests that nonlinear (deterministic) dynamics are more likely to be associated with weakly damped alpha activity. Thus rather than the “alpha rhythm” being an idling rhythm it may be more profitable to conceive it as a readiness rhythm.

Dynamical complexity in a mean-field model of human EEG

A recently proposed mean-field theory of mammalian cortex rhythmogenesis describes the salient features of electrical activity in the cerebral macrocolumn, with the use of inhibitory and excitatory neuronal populations (Liley et al 2002). This model is capable of producing a range of important human EEG (electroencephalogram) features such as the alpha rhythm, the 40 Hz activity thought to be associated with conscious awareness (Bojak & Liley 2007) and the changes in EEG spectral power associated with general anesthetic effect (Bojak & Liley 2005). From the point of view of nonlinear dynamics, the model entails a vast parameter space within which multistability, pseudoperiodic regimes, various routes to chaos, fat fractals and rich bifurcation scenarios occur for physiologically relevant parameter values (van Veen & Liley 2006). The origin and the character of this complex behaviour, and its relevance for EEG activity will be illustrated. The existence of short-lived unstable brain states will also be discussed in terms of the available theoretical and experimental results. A perspective on future analysis will conclude the presentation.

Self-organized 40Hz synchronization in a physiological theory of EEG

We present evidence that large-scale spatial coherence of 40 Hz oscillations can emerge dynamically in a cortical mean field theory. The simulated synchronization time scale is about 150 ms, which compares well with experimental data on large-scale integration during cognitive tasks. The same model has previously provided consistent descriptions of the human EEG at rest, with tranquilizers, under anesthesia, and during anesthetic-induced epileptic seizures. The emergence of coherent gamma band activity is brought about by changing just one physiological parameter until cortex becomes marginally unstable for a small range of wavelengths. This suggests for future study a model of dynamic computation at the edge of cortical stability.

Understanding the effects of anesthetic agents on the EEG through neural field theory

Anesthetic and analgesic agents act through a diverse range of pharmacological mechanisms. Existing empirical data clearly shows that such "microscopic" pharmacological diversity is reflected in their "macroscopic" effects on the human electroencephalogram (EEG). Based on a detailed mesoscopic neural field model we theoretically posit that anesthetic induced EEG activity is due to selective parametric changes in synaptic efficacy and dynamics. Specifically, on the basis of physiologically constrained modeling, it is speculated that the selective modification of inhibitory or excitatory synaptic activity may differentially effect the EEG spectrum. Such results emphasize the importance of neural field theories of brain electrical activity for elucidating the principles whereby pharmacological agents effect the EEG. Such insights will contribute to improved methods for monitoring depth of anesthesia using the EEG.

Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics: part 2. pseudoenergy-based theory

This paper represents the second part of a study of semi-geostrophic (SG) geophysical fluid dynamics. SG dynamics shares certain attractive properties with the better known and more widely used quasi-geostrophic (QG) model, but is also a good prototype for balanced models that are more accurate than QG dynamics. The development of such balanced models is an area of great current interest. The goal of the present work is to extend a central body of QG theory, concerning the evolution of disturbances to prescribed basic states, to SG dynamics. Part 1 was based on the pseudomomentum; Part 2 is based on the pseudoenergy. A pseudoenergy invariant is a conserved quantity, of second order in disturbance amplitude relative to a prescribed steady basic state, which is related to the time symmetry of the system. We derive such an invariant for the semi-geostrophic equations, and use it to obtain: (i) a linear stability theorem analogous to Arnol'd's ‘first theorem’; and (ii) a small-amplitude local conservation law for the invariant, obeying the group-velocity property in the WKB limit. The results are analogous to their quasi-geostrophic forms, and reduce to those forms in the limit of small Rossby number. The results are derived for both the f-plane Boussinesq form of semi-geostrophic dynamics, and its extension to β-plane compressible flow by Magnusdottir & Schubert. Novel features particular to semi-geostrophic dynamics include apparently unnoticed lateral boundary stability criteria. Unlike the boundary stability criteria found in the first part of this study, however, these boundary criteria do not necessarily preclude the construction of provably stable basic states. The interior semi-geostrophic dynamics has an underlying Hamiltonian structure, which guarantees that symmetries in the system correspond naturally to the system's invariants. This is an important motivation for the theoretical approach used in this study. The connection between symmetries and conservation laws is made explicit using Noether's theorem applied to the Eulerian form of the Hamiltonian description of the interior dynamics.

Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics: part 1. pseudomomentum-based theory

There exists a well-developed body of theory based on quasi-geostrophic (QG) dynamics that is central to our present understanding of large-scale atmospheric and oceanic dynamics. An important question is the extent to which this body of theory may generalize to more accurate dynamical models. As a first step in this process, we here generalize a set of theoretical results, concerning the evolution of disturbances to prescribed basic states, to semi-geostrophic (SG) dynamics. SG dynamics, like QG dynamics, is a Hamiltonian balanced model whose evolution is described by the material conservation of potential vorticity, together with an invertibility principle relating the potential vorticity to the advecting fields. SG dynamics has features that make it a good prototype for balanced models that are more accurate than QG dynamics. In the first part of this two-part study, we derive a pseudomomentum invariant for the SG equations, and use it to obtain: (i) linear and nonlinear generalized Charney–Stern theorems for disturbances to parallel flows; (ii) a finite-amplitude local conservation law for the invariant, obeying the group-velocity property in the WKB limit; and (iii) a wave-mean-flow interaction theorem consisting of generalized Eliassen–Palm flux diagnostics, an elliptic equation for the stream-function tendency, and a non-acceleration theorem. All these results are analogous to their QG forms. The pseudomomentum invariant – a conserved second-order disturbance quantity that is associated with zonal symmetry – is constructed using a variational principle in a similar manner to the QG calculations. Such an approach is possible when the equations of motion under the geostrophic momentum approximation are transformed to isentropic and geostrophic coordinates, in which the ageostrophic advection terms are no longer explicit. Symmetry-related wave-activity invariants such as the pseudomomentum then arise naturally from the Hamiltonian structure of the SG equations. We avoid use of the so-called ‘massless layer’ approach to the modelling of isentropic gradients at the lower boundary, preferring instead to incorporate explicitly those boundary contributions into the wave-activity and stability results. This makes the analogy with QG dynamics most transparent. This paper treats the f-plane Boussinesq form of SG dynamics, and its recent extension to β-plane, compressible flow by Magnusdottir & Schubert. In the limit of small Rossby number, the results reduce to their respective QG forms. Novel features particular to SG dynamics include apparently unnoticed lateral boundary stability criteria in (i), and the necessity of including additional zonal-mean eddy correlation terms besides the zonal-mean potential vorticity fluxes in the wave-mean-flow balance in (iii). In the companion paper, wave-activity conservation laws and stability theorems based on the SG form of the pseudoenergy are presented.

Nonlinear saturation of baroclinic instability: part I: the two-layer model

A rigorous bound is derived which limits the finite-amplitude growth of arbitrary nonzonal disturbances to an unstable baroclinic zonal flow within the context of the two-layer model. The bound is valid for conservative (unforced) flow, as well as for forced-dissipative flow that when the dissipation is proportional to the potential vorticity. The method used to derive the bound relies on the existence of a nonlinear Liapunov (normed) stability theorem for subcritical flows, which is a finite-amplitude generalization of the Charney-Stern theorem. For the special case of the Philips model of baroclinic instability, and in the limit of infinitesimal initial nonzonal disturbance amplitude, an improved form of the bound is possible which states that the potential enstrophy of the nonzonal flow cannot exceed ϵβ2, where ϵ = (U − Ucrit)/Ucrit is the (relative) supereriticality. This upper bound turns out to be extremely similar to the maximum predicted by the weakly nonlinear theory. For unforced flow with ϵ < 1, the bound demonstrates that the nonzonal flow cannot contain all of the potential enstrophy in the system; hence in this range of initial supercriticality the total flow must remain, in a certain sense, “close” to a zonal state.

Home, meaning and identity: learning from the English model of shared ownership

This article explores the problematic nature of the label “home ownership” through a case study of the English model of shared ownership, one of the methods used by the UK government to make home ownership affordable. Adopting a legal and socio-legal analysis, the article considers whether shared ownership is capable of fulfilling the aspirations households have for home ownership. To do so, the article considers the financial and nonfinancial meanings attached to home ownership and suggests that the core expectation lies in ownership of the value. The article demonstrates that the rights and responsibilities of shared owners are different in many respects from those of traditional home owners, including their rights as regards ownership of the value. By examining home ownership through the lens of shared ownership the article draws out lessons of broader significance to housing studies. In particular, it is argued that shared ownership shows the limitations of two dichotomies commonly used in housing discourse: that between private and social housing; and the classification of tenure between owner-occupiers and renters. The article concludes that a much more nuanced way of referring to home ownership is required, and that there is a need for a change of expectations amongst consumers as to what sharing ownership means.

Interpersonal interaction and economic theory: the case of public goods

Interpersonal interaction in public goods contexts is very different in character to its depiction in economic theory, despite the fact that the standard model is based on a small number of apparently plausible assumptions. Approaches to the problem are reviewed both from within and outside economics. It is argued that quick fixes such as a taste for giving do not provide a way forward. An improved understanding of why people contribute to such goods seems to require a different picture of the relationships between individuals than obtains in standard microeconomic theory, where they are usually depicted as asocial. No single economic model at present is consistent with all the relevant field and laboratory data. It is argued that there are defensible ideas from outside the discipline which ought to be explored, relying on different conceptions of rationality and/or more radically social agents. Three such suggestions are considered, one concerning the expressive/communicative aspect of behaviour, a second the possibility of a part-whole relationship between interacting agents and the third a version of conformism.

Theory and generalization of Monte Carlo models of the BOLD signal source

The dependency of the blood oxygenation level dependent (BOLD) signal on underlying hemodynamics is not well understood. Building a forward biophysical model of this relationship is important for the quantitative estimation of the hemodynamic changes and neural activity underlying functional magnetic resonance imaging (fMRI) signals. We have developed a general model of the BOLD signal which can model both intra- and extravascular signals for an arbitrary tissue model across a wide range of imaging parameters. The model of the BOLD signal was instantiated as a look-up-table (LuT), and was verified against concurrent fMRI and optical imaging measurements of activation induced hemodynamics. Magn Reson Med, 2008. © 2008 Wiley-Liss, Inc.

Retrieval of phytoplankton size from bio-optical measurements: theory and applications

The absorption coefficient of a substance distributed as discrete particles in suspension is less than that of the same material dissolved uniformly in a medium—a phenomenon commonly referred to as the flattening effect. The decrease in the absorption coefficient owing to flattening effect depends on the concentration of the absorbing pigment inside the particle, the specific absorption coefficient of the pigment within the particle, and on the diameter of the particle, if the particles are assumed to be spherical. For phytoplankton cells in the ocean, with diameters ranging from less than 1 µm to more than 100 µm, the flattening effect is variable, and sometimes pronounced, as has been well documented in the literature. Here, we demonstrate how the in vivo absorption coefficient of phytoplankton cells per unit concentration of its major pigment, chlorophyll a, can be used to determine the average cell size of the phytoplankton population. Sensitivity analyses are carried out to evaluate the errors in the estimated diameter owing to potential errors in the model assumptions. Cell sizes computed for field samples using the model are compared qualitatively with indirect estimates of size classes derived from high performance liquid chromatography data. Also, the results are compared quantitatively against measurements of cell size in laboratory cultures. The method developed is easy-to-apply as an operational tool for in situ observations, and has the potential for application to remote sensing of ocean colour data.

What should we expect of a liberal explanatory theory?

One of the most problematic aspects of the ‘Harvard School’ of liberal international theory is its failure to fulfil its own methodological ideals. Although Harvard School liberals subscribe to a nomothetic model of explanation, in practice they employ their theories as heuristic resources. Given this practice, we should expect them neither to develop candidate causal generalizations nor to be value-neutral: their explanatory insights are underpinned by value-laden choices about which questions to address and what concepts to employ. A key question for liberal theorists, therefore, is how a theory may be simultaneously explanatory and value-oriented. The difficulties inherent in resolving this problem are manifested in Ikenberry’s writing: whilst his work on constitutionalism in international politics partially fulfils the requirements of a more satisfactory liberal explanatory theory, his recent attempts to develop prescriptions for US foreign policy reproduce, in a new form, key failings of Harvard School realism.