A unified theory of balance in the extratropics

Many physical systems exhibit dynamics with vastly different time scales. Often the different motions interact only weakly and the slow dynamics is naturally constrained to a subspace of phase space, in the vicinity of a slow manifold. In geophysical fluid dynamics this reduction in phase space is called balance. Classically, balance is understood by way of the Rossby number R or the Froude number F; either R ≪ 1 or F ≪ 1. We examined the shallow-water equations and Boussinesq equations on an f -plane and determined a dimensionless parameter _, small values of which imply a time-scale separation. In terms of R and F, ∈= RF/√(R^2+R^2 ) We then developed a unified theory of (extratropical) balance based on _ that includes all cases of small R and/or small F. The leading-order systems are ensured to be Hamiltonian and turn out to be governed by the quasi-geostrophic potential-vorticity equation. However, the height field is not necessarily in geostrophic balance, so the leading-order dynamics are more general than in quasi-geostrophy. Thus the quasi-geostrophic potential-vorticity equation (as distinct from the quasi-geostrophic dynamics) is valid more generally than its traditional derivation would suggest. In the case of the Boussinesq equations, we have found that balanced dynamics generally implies hydrostatic balance without any assumption on the aspect ratio; only when the Froude number is not small and it is the Rossby number that guarantees a timescale separation must we impose the requirement of a small aspect ratio to ensure hydrostatic balance.

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.

Optimising the FAMOUS climate model: inclusion of global carbon cycling

FAMOUS fills an important role in the hierarchy of climate models, both explicitly resolving atmospheric and oceanic dynamics yet being sufficiently computationally efficient that either very long simulations or large ensembles are possible. An improved set of carbon cycle parameters for this model has been found using a perturbed physics ensemble technique. This is an important step towards building the "Earth System" modelling capability of FAMOUS, which is a reduced resolution, and hence faster running, version of the Hadley Centre Climate model, HadCM3. Two separate 100 member perturbed parameter ensembles were performed; one for the land surface and one for the ocean. The land surface scheme was tested against present-day and past representations of vegetation and the ocean ensemble was tested against observations of nitrate. An advantage of using a relatively fast climate model is that a large number of simulations can be run and hence the model parameter space (a large source of climate model uncertainty) can be more thoroughly sampled. This has the associated benefit of being able to assess the sensitivity of model results to changes in each parameter. The climatologies of surface and tropospheric air temperature and precipitation are improved relative to previous versions of FAMOUS. The improved representation of upper atmosphere temperatures is driven by improved ozone concentrations near the tropopause and better upper level winds.

Assessing the reliability of probabilistic flood inundation model predictions

An ability to quantify the reliability of probabilistic flood inundation predictions is a requirement not only for guiding model development but also for their successful application. Probabilistic flood inundation predictions are usually produced by choosing a method of weighting the model parameter space, but previous study suggests that this choice leads to clear differences in inundation probabilities. This study aims to address the evaluation of the reliability of these probabilistic predictions. However, a lack of an adequate number of observations of flood inundation for a catchment limits the application of conventional methods of evaluating predictive reliability. Consequently, attempts have been made to assess the reliability of probabilistic predictions using multiple observations from a single flood event. Here, a LISFLOOD-FP hydraulic model of an extreme (>1 in 1000 years) flood event in Cockermouth, UK, is constructed and calibrated using multiple performance measures from both peak flood wrack mark data and aerial photography captured post-peak. These measures are used in weighting the parameter space to produce multiple probabilistic predictions for the event. Two methods of assessing the reliability of these probabilistic predictions using limited observations are utilized; an existing method assessing the binary pattern of flooding, and a method developed in this paper to assess predictions of water surface elevation. This study finds that the water surface elevation method has both a better diagnostic and discriminatory ability, but this result is likely to be sensitive to the unknown uncertainties in the upstream boundary condition

Evaluation of two hybrid metric-conceptual models, for simulating phosphorus transfer from agricultural land in the river enborne, a lowland UK catchment

Across Europe, elevated phosphorus (P) concentrations in lowland rivers have made them particularly susceptible to eutrophication. This is compounded in southern and central UK by increasing pressures on water resources, which may be further enhanced by the potential effects of climate change. The EU Water Framework Directive requires an integrated approach to water resources management at the catchment scale and highlights the need for modelling tools that can distinguish relative contributions from multiple nutrient sources and are consistent with the information content of the available data. Two such models are introduced and evaluated within a stochastic framework using daily flow and total phosphorus concentrations recorded in a clay catchment typical of many areas of the lowland UK. Both models disaggregate empirical annual load estimates, derived from land use data, as a function of surface/near surface runoff, generated using a simple conceptual rainfall-runoff model. Estimates of the daily load from agricultural land, together with those from baseflow and point sources, feed into an in-stream routing algorithm. The first model assumes constant concentrations in runoff via surface/near surface pathways and incorporates an additional P store in the river-bed sediments, depleted above a critical discharge, to explicitly simulate resuspension. The second model, which is simpler, simulates P concentrations as a function of surface/near surface runoff, thus emphasising the influence of non-point source loads during flow peaks and mixing of baseflow and point sources during low flows. The temporal consistency of parameter estimates and thus the suitability of each approach is assessed dynamically following a new approach based on Monte-Carlo analysis. (c) 2004 Elsevier B.V. All rights reserved.

Global scale water stages from SAR imagery (GlosSARi) to support global flood forecasting

Despite the success of studies attempting to integrate remotely sensed data and flood modelling and the need to provide near-real time data routinely on a global scale as well as setting up online data archives, there is to date a lack of spatially and temporally distributed hydraulic parameters to support ongoing efforts in modelling. Therefore, the objective of this project is to provide a global evaluation and benchmark data set of floodplain water stages with uncertainties and assimilation in a large scale flood model using space-borne radar imagery. An algorithm is developed for automated retrieval of water stages with uncertainties from a sequence of radar imagery and data are assimilated in a flood model using the Tewkesbury 2007 flood event as a feasibility study. The retrieval method that we employ is based on possibility theory which is an extension of fuzzy sets and that encompasses probability theory. In our case we first attempt to identify main sources of uncertainty in the retrieval of water stages from radar imagery for which we define physically meaningful ranges of parameter values. Possibilities of values are then computed for each parameter using a triangular ‘membership’ function. This procedure allows the computation of possible values of water stages at maximum flood extents along a river at many different locations. At a later stage in the project these data are then used in assimilation, calibration or validation of a flood model. The application is subsequently extended to a global scale using wide swath radar imagery and a simple global flood forecasting model thereby providing improved river discharge estimates to update the latter.

Framing the local and the global in the anti-nuclear movement: Law and the politics of place

This article examines the politics of place in relation to legal mobilization by the anti-nuclear movement. It examines two case examples - citizens' weapons inspections and civil disobedience strategies - which have involved the movement drawing upon the law in particular spatial contexts. The article begins by examining a number of factors which have been employed in recent social movement literature to explain strategy choice, including ideology, resources, political and legal opportunity, and framing. It then proceeds to argue that the issues of scale, space, and place play an important role in relation to framing by the movement in the two case examples. Both can be seen to involve scalar reframing, with the movement attempting to resist localizing tendencies and to replace them with a global frame. Both also involve an attempt to reframe the issue of nuclear weapons away from the contested frame of the past (unilateral disarmament) towards the more universal and widely accepted frame of international law.

Instability of surface-temperature filaments in strain and shear

The effects of uniform straining and shearing on the stability of a surface quasi-geostrophic temperature filament are investigated. Straining is shown to stabilize perturbations for wide filaments but only for a finite time until the filament thins to a critical width, after which some perturbations can grow. No filament can be stabilized in practice, since there are perturbations that can grow large for any strain rate. The optimally growing perturbations, defined as solutions that reach a certain threshold amplitude first, are found numerically for a wide range of parameter values. The radii of the vortices formed through nonlinear roll-up are found to be proportional to θ/s, where θ is the temperature anomaly of the filament and s the strain rate, and are not dependent on the initial size of the filament. Shearing is shown to reduce the normal-mode growth rates, but it cannot stabilize them completely when there are temperature discontinuities in the basic state; smooth filaments can be stabilized completely by shearing and a simple scaling argument provides the shear rate required. Copyright © 2010 Royal Meteorological Society

Initial results from Phase 2 of the international urban energy balance model comparison

Urban land surface schemes have been developed to model the distinct features of the urban surface and the associated energy exchange processes. These models have been developed for a range of purposes and make different assumptions related to the inclusion and representation of the relevant processes. Here, the first results of Phase 2 from an international comparison project to evaluate 32 urban land surface schemes are presented. This is the first large-scale systematic evaluation of these models. In four stages, participants were given increasingly detailed information about an urban site for which urban fluxes were directly observed. At each stage, each group returned their models' calculated surface energy balance fluxes. Wide variations are evident in the performance of the models for individual fluxes. No individual model performs best for all fluxes. Providing additional information about the surface generally results in better performance. However, there is clear evidence that poor choice of parameter values can cause a large drop in performance for models that otherwise perform well. As many models do not perform well across all fluxes, there is need for caution in their application, and users should be aware of the implications for applications and decision making.

Design and analysis of climate model experiments for the efficient estimation of anthropogenic signals

Presented herein is an experimental design that allows the effects of several radiative forcing factors on climate to be estimated as precisely as possible from a limited suite of atmosphere-only general circulation model (GCM) integrations. The forcings include the combined effect of observed changes in sea surface temperatures, sea ice extent, stratospheric (volcanic) aerosols, and solar output, plus the individual effects of several anthropogenic forcings. A single linear statistical model is used to estimate the forcing effects, each of which is represented by its global mean radiative forcing. The strong colinearity in time between the various anthropogenic forcings provides a technical problem that is overcome through the design of the experiment. This design uses every combination of anthropogenic forcing rather than having a few highly replicated ensembles, which is more commonly used in climate studies. Not only is this design highly efficient for a given number of integrations, but it also allows the estimation of (nonadditive) interactions between pairs of anthropogenic forcings. The simulated land surface air temperature changes since 1871 have been analyzed. The changes in natural and oceanic forcing, which itself contains some forcing from anthropogenic and natural influences, have the most influence. For the global mean, increasing greenhouse gases and the indirect aerosol effect had the largest anthropogenic effects. It was also found that an interaction between these two anthropogenic effects in the atmosphere-only GCM exists. This interaction is similar in magnitude to the individual effects of changing tropospheric and stratospheric ozone concentrations or to the direct (sulfate) aerosol effect. Various diagnostics are used to evaluate the fit of the statistical model. For the global mean, this shows that the land temperature response is proportional to the global mean radiative forcing, reinforcing the use of radiative forcing as a measure of climate change. The diagnostic tests also show that the linear model was suitable for analyses of land surface air temperature at each GCM grid point. Therefore, the linear model provides precise estimates of the space time signals for all forcing factors under consideration. For simulated 50-hPa temperatures, results show that tropospheric ozone increases have contributed to stratospheric cooling over the twentieth century almost as much as changes in well-mixed greenhouse gases.

Systematic distortions of perceptual stability investigated using immersive virtual reality

Using an immersive virtual reality system, we measured the ability of observers to detect the rotation of an object when its movement was yoked to the observer's own translation. Most subjects had a large bias such that a static object appeared to rotate away from them as they moved. Thresholds for detecting target rotation were similar to those for an equivalent speed discrimination task carried out by static observers, suggesting that visual discrimination is the predominant limiting factor in detecting target rotation. Adding a stable visual reference frame almost eliminated the bias. Varying the viewing distance of the target had little effect, consistent with observers underestimating distance walked. However, accuracy of walking to a briefly presented visual target was high and not consistent with an underestimation of distance walked. We discuss implications for theories of a task-independent representation of visual space. © 2005 Elsevier Ltd. All rights reserved.

Hemispace differences in the visual perception of size in left hemi-Parkinson's disease

The visual perception of size in different regions of external space was studied in Parkinson's disease (PD). A group of patients with worse left-sided symptoms (LPD) was compared with a group with worse right-sided symptoms (RPD) and with a group of age-matched controls on judgements of the relative height or width of two rectangles presented in different regions of external space. The relevant dimension of one rectangle (the 'standard') was held constant, while that of the other (the 'variable') was varied in a method of constant stimuli. The point of subjective equality (PSE) of rectangle width or height was obtained by probit analysis as the mean of the resulting psychometric function. When the standard was in left space, the PSE of the LPD group occurred when the variable was smaller, and when the standard was in right space, when the variable was larger. Similarly, when the standard rectangle was presented in upper space, and the variable in lower space, the PSE occurred when the variable was smaller, an effect which was similar in both left and right spaces. In all these experiments, the PSEs for both the controls and the RPD group did not differ significantly, and were close to a physical match, and the slopes of the psychometric functions were steeper in the controls than the patients, though not significantly so. The data suggest that objects appear smaller in the left and upper visual spaces in LPD, probably because of right hemisphere impairment. (C) 2002 Elsevier Science Ltd. All rights reserved.

Subspace system identification framework for the analysis of multimoded propagation of THz-transient signals

We provide a system identification framework for the analysis of THz-transient data. The subspace identification algorithm for both deterministic and stochastic systems is used to model the time-domain responses of structures under broadband excitation. Structures with additional time delays can be modelled within the state-space framework using additional state variables. We compare the numerical stability of the commonly used least-squares ARX models to that of the subspace N4SID algorithm by using examples of fourth-order and eighth-order systems under pulse and chirp excitation conditions. These models correspond to structures having two and four modes simultaneously propagating respectively. We show that chirp excitation combined with the subspace identification algorithm can provide a better identification of the underlying mode dynamics than the ARX model does as the complexity of the system increases. The use of an identified state-space model for mode demixing, upon transformation to a decoupled realization form is illustrated. Applications of state-space models and the N4SID algorithm to THz transient spectroscopy as well as to optical systems are highlighted.

Orthogonal space-time block codes for free-space IM/DD optical links

Use of orthogonal space-time block codes (STBCs) with multiple transmitters and receivers can improve signal quality. However, in optical intensity modulated signals, output of the transmitter is non-negative and hence standard orthogonal STBC schemes need to be modified. A generalised framework for applying orthogonal STBCs for free-space IM/DD optical links is presented.