Solutions of a two-dimensional dam-break problem

Solutions of a two-dimensional dam break problem are presented for two tailwater/reservoir height ratios. The numerical scheme used is an extension of one previously given by the author [J. Hyd. Res. 26(3), 293–306 (1988)], and is based on numerical characteristic decomposition. Thus approximate solutions are obtained via linearised problems, and the method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids non-physical, spurious oscillations.

Prediction of supercritical flow in open channels

A finite difference scheme based on flux difference splitting is presented for the solution of the one-dimensional shallow water equations in open channels. A linearised problem, analogous to that of Riemann for gas dynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearised problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids non-physical, spurious oscillations. The scheme is applied to a problem of flow in a river whose geometry induces a region of supercritical flow.

Flux difference splitting for open channel flows

A finite difference scheme based on flux difference splitting is presented for the solution of the one-dimensional shallow-water equations in open channels, together with an extension to two-dimensional flows. A linearized problem, analogous to that of Riemann for gas dynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearized problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second-order scheme which avoids non-physical, spurious oscillations. The scheme is applied to a one-dimensional dam-break problem, and to a problem of flow in a river whose geometry induces a region of supercritical flow. The scheme is also applied to a two-dimensional dam-break problem. The numerical results are compared with the exact solution, or other numerical results, where available.

On a class of non-self-adjoint periodic eigenproblems with boundary and interior singularities

We prove that all the eigenvalues of a certain highly non-self-adjoint Sturm–Liouville differential operator are real. The results presented are motivated by and extend those recently found by various authors (Benilov et al. (2003) [3], Davies (2007) [7] and Weir (2008) [18]) on the stability of a model describing small oscillations of a thin layer of fluid inside a rotating cylinder.

How predation and landscape fragmentation affect vole population dynamics

Background: Microtine species in Fennoscandia display a distinct north-south gradient from regular cycles to stable populations. The gradient has often been attributed to changes in the interactions between microtines and their predators. Although the spatial structure of the environment is known to influence predator-prey dynamics of a wide range of species, it has scarcely been considered in relation to the Fennoscandian gradient. Furthermore, the length of microtine breeding season also displays a north-south gradient. However, little consideration has been given to its role in shaping or generating population cycles. Because these factors covary along the gradient it is difficult to distinguish their effects experimentally in the field. The distinction is here attempted using realistic agent-based modelling. Methodology/Principal Findings: By using a spatially explicit computer simulation model based on behavioural and ecological data from the field vole (Microtus agrestis), we generated a number of repeated time series of vole densities whose mean population size and amplitude were measured. Subsequently, these time series were subjected to statistical autoregressive modelling, to investigate the effects on vole population dynamics of making predators more specialised, of altering the breeding season, and increasing the level of habitat fragmentation. We found that fragmentation as well as the presence of specialist predators are necessary for the occurrence of population cycles. Habitat fragmentation and predator assembly jointly determined cycle length and amplitude. Length of vole breeding season had little impact on the oscillations. Significance: There is good agreement between our results and the experimental work from Fennoscandia, but our results allow distinction of causation that is hard to unravel in field experiments. We hope our results will help understand the reasons for cycle gradients observed in other areas. Our results clearly demonstrate the importance of landscape fragmentation for population cycling and we recommend that the degree of fragmentation be more fully considered in future analyses of vole dynamics.

Nitric oxide suppresses cerebral vasomotion by sGC-independent effects on ryanodine receptors and voltage-gated calcium channels

Background/Aims: In cerebral arteries, nitric oxide (NO) release plays a key role in suppressing vasomotion. Our aim was to establish the pathways affected by NO in rat middle cerebral arteries. Methods: In isolated segments of artery, isometric tension and simultaneous measurements of either smooth muscle membrane potential or intracellular [Ca 2+ ] ([Ca 2+ ] SMC ) changes were recorded. Results: In the absence of L -NAME, asynchronous propagating Ca 2+ waves were recorded that were sensitive to block with ryanodine, but not nifedipine. L -NAME stimulated pronounced vasomotion and synchronous Ca 2+ oscillations with close temporal coupling between membrane potential, tone and [Ca 2+ ] SMC . If nifedipine was applied together with L -NAME, [Ca 2+ ] SMC decreased and synchronous Ca 2+ oscillations were lost, but asynchronous propagating Ca 2+ waves persisted. Vasomotion was similarly evoked by either iberiotoxin, or by ryanodine, and to a lesser extent by ODQ. Exogenous application of NONOate stimulated endothelium-independent hyperpolarization and relaxation of either L -NAME-induced or spontaneous arterial tone. NO-evoked hyperpolarization involved activation of BK Ca channels via ryanodine receptors (RYRs), with little involvement of sGC. Further, in whole cell mode, NO inhibited current through L-type voltage-gated Ca 2+ channels (VGCC), which was independent of both voltage and sGC. Conclusion: NO exerts sGC-independent actions at RYRs and at VGCC, both of which normally suppress cerebral artery myogenic tone.

Evidence both L-type and non-L-type voltage-dependent calcium channels contribute to cerebral artery vasospasm following loss of NO in the rat

We recently found block of NO synthase in rat middle cerebral artery caused spasm, associated with depolarizing oscillations in membrane potential (Em) similar in form but faster in frequency (circa 1 Hz) to vasomotion. T-type voltage-gated Ca2+ channels contribute to cerebral myogenic tone and vasomotion, so we investigated the significance of T-type and other ion channels for membrane potential oscillations underlying arterial spasm. Smooth muscle cell membrane potential (Em) and tension were measured simultaneously in rat middle cerebral artery. NO synthase blockade caused temporally coupled depolarizing oscillations in cerebrovascular Em with associated vasoconstriction. Both events were accentuated by block of smooth muscle BKCa. Block of T-type channels or inhibition of Na+/K+-ATPase abolished the oscillations in Em and reduced vasoconstriction. Oscillations in Em were either attenuated or accentuated by reducing [Ca2+]o or block of KV, respectively. TRAM-34 attenuated oscillations in both Em and tone, apparently independent of effects against KCa3.1. Thus, rapid depolarizing oscillations in Em and tone observed after endothelial function has been disrupted reflect input from T-type calcium channels in addition to L-type channels, while other depolarizing currents appear to be unimportant. These data suggest that combined block of T and L-type channels may represent an effective approach to reverse cerebral vasospasm.

The last glacial cycle: transient simulations with an AOGCM

A number of transient climate runs simulating the last 120kyr have been carried out using FAMOUS, a fast atmosphere-ocean general circulation model (AOGCM). This is the first time such experiments have been done with a full AOGCM, providing a three-dimensional simulation of both atmosphere and ocean over this period. Our simulation thus includes internally generated temporal variability over periods from days to millennia, and physical, detailed representations of important processes such as clouds and precipitation. Although the model is fast, computational restrictions mean that the rate of change of the forcings has been increased by a factor of 10, making each experiment 12kyr long. Atmospheric greenhouse gases (GHGs), northern hemisphere ice sheets and variations in solar radiation arising from changes in the Earth's orbit are treated as forcing factors, and are applied either separately or combined in different experiments. The long-term temperature changes on Antarctica match well with reconstructions derived from ice-core data, as does variability on timescales longer than 10 kyr. Last Glacial Maximum (LGM) cooling on Greenland is reasonably well simulated, although our simulations, which lack ice-sheet meltwater forcing, do not reproduce the abrupt, millennial scale climate shifts seen in northern hemisphere climate proxies or their slower southern hemisphere counterparts. The spatial pattern of sea surface cooling at the LGM matches proxy reconstructions reasonably well. There is significant anti-correlated variability in the strengths of the Atlantic Meridional Overturning Circulation (AMOC) and the Antarctic Circumpolar Current (ACC) on timescales greater than 10kyr in our experiments. We find that GHG forcing weakens the AMOC and strengthens the ACC, whilst the presence of northern hemisphere ice-sheets strengthens the AMOC and weakens the ACC. The structure of the AMOC at the LGM is found to be sensitive to the details of the ice-sheet reconstruction used. The precessional component of the orbital forcing induces ~20kyr oscillations in the AMOC and ACC, whose amplitude is mediated by changes in the eccentricity of the Earth's orbit. These forcing influences combine, to first order, in a linear fashion to produce the mean climate and ocean variability seen in the run with all forcings.

Computational modes and grid imprinting on five quasi-uniform spherical C-grids

Currently, most operational forecasting models use latitude-longitude grids, whose convergence of meridians towards the poles limits parallel scaling. Quasi-uniform grids might avoid this limitation. Thuburn et al, JCP, 2009 and Ringler et al, JCP, 2010 have developed a method for arbitrarily-structured, orthogonal C-grids (TRiSK), which has many of the desirable properties of the C-grid on latitude-longitude grids but which works on a variety of quasi-uniform grids. Here, five quasi-uniform, orthogonal grids of the sphere are investigated using TRiSK to solve the shallow-water equations. We demonstrate some of the advantages and disadvantages of the hexagonal and triangular icosahedra, a Voronoi-ised cubed sphere, a Voronoi-ised skipped latitude-longitude grid and a grid of kites in comparison to a full latitude-longitude grid. We will show that the hexagonal-icosahedron gives the most accurate results (for least computational cost). All of the grids suffer from spurious computational modes; this is especially true of the kite grid, despite it having exactly twice as many velocity degrees of freedom as height degrees of freedom. However, the computational modes are easiest to control on the hexagonal icosahedron since they consist of vorticity oscillations on the dual grid which can be controlled using a diffusive advection scheme for potential vorticity.

Asymmetric space market adjustment in the London office market

Models of the City of London office market are extended by considering a longer time series of data, covering two cycles, and by explicit modeling of asymmetric rental response to supply and demand model. A long run structural model linking demand for office space, real rental levels and office-based employment is estimated and then rental adjustment processes are modeled using an error correction model framework. Adjustment processes are seen to be asymmetric, dependent both on the direction of the supply and demand shock and on the state of the rental market at the time of the shock. A complete system of equations is estimated: unit shocks produce oscillations but there is a return to a steady equilibrium state in the long run.

Controlling the computational modes of the arbitrarily structured C-grid

The arbitrarily structured C-grid, TRiSK (Thuburn, Ringler, Skamarock and Klemp, 2009, 2010) is being used in the ``Model for Prediction Across Scales'' (MPAS) and is being considered by the UK Met Office for their next dynamical core. However the hexagonal C-grid supports a branch of spurious Rossby modes which lead to erroneous grid-scale oscillations of potential vorticity (PV). It is shown how these modes can be harmlessly controlled by using upwind-biased interpolation schemes for PV. A number of existing advection schemes for PV are tested, including that used in MPAS, and none are found to give adequate results for all grids and all cases. Therefore a new scheme is proposed; continuous, linear-upwind stabilised transport (CLUST), a blend between centred and linear-upwind with the blend dependent on the flow direction with respect to the cell edge. A diagnostic of grid-scale oscillations is proposed which gives further discrimination between schemes than using potential enstrophy alone and indeed some schemes are found to destroy potential enstrophy while grid-scale oscillations grow. CLUST performs well on hexagonal-icosahedral grids and unrotated skipped latitude-longitude grids of the sphere for various shallow water test cases. Despite the computational modes, the hexagonal icosahedral grid performs well since these modes are easy and harmless to filter. As a result TRiSK appears to perform better than a spectral shallow water model.

Changing climate and the Irish landscape

The impacts of current and future changes in climate have been investigated for Irish vegetation. Warming has been observed over the last two decades, with impacts that are also strongly influenced by natural oscillations of the surrounding ocean, seen as fluctuations in the North Atlantic Oscillation and the Atlantic Multidecadal Oscillation. Satellite observations show that vegetation greenness increases in warmer years, a feature mirrored by increases in net ecosystem production observed for a grassland and a plantation forest. An ensemble of general circulation model simulations of future climates indicate temperature rises over the twenty-first century ranging from 1°C to 7°C, depending on future scenarios of greenhouse gas emissions. Net primary production is simulated to increase under all scenarios, due to the positive impacts of rising temperature, a modest rise of precipitation and rising carbon dioxide concentrations. In an optimistic scenario of reducing future emissions, CO2 concentration is simulated to flatten from about 2070, although temperatures continue to increase. Under this scenario Ireland could become a source of carbon, whereas under all other emission scenarios Ireland is a sink for carbon that may increase by up to three-fold over the twenty-first century. A likely and unavoidable impact of changing climate is the arrival of alien plant species, which may disrupt ecosystems and exert negative impacts on native biodiversity. Alien species arrive continually, with about 250 dated arrivals in the twentieth century. A simulation model indicates that this rate of alien arrival may increase by anything between two and ten times, dependent on the future climatic scenario, by 2050. Which alien species may become severely disruptive is, however, not known.

Pedosedimentary, cultural and environmental significance of palaeosols within Pre-Hispanic agricultural terraces in the southern Peruvian Andes

Paleosols were exposed in sections through four abandoned pre-Hispanic agricultural terraces surrounding an infilled mire basin in the southern Peruvian Andes. The two paleosols beneath the Tocotoccasa terrace represent the original ‘natural’ solum and a later soil formed after construction of the agricultural terrace, probably during the early Middle Horizon cultural period (615–695 AD). The soil at the current surface developed subsequent to the building up and reconstruction of the terrace, possibly during the late Late Intermediate period (1200–1400 AD). Micromorphology revealed an unexpected abundance of clay coatings within the upper terrace paleosol and surface terrace soil, a phenonemon attributed to the migration and/or accumulation of neoformed clay produced from the weathering of very unstable volcanic clasts, perhaps fuelled by arid/humid climatic oscillations and/or seasonal input of irrigation waters. The paleosols at Tocotoccasa could not be correlated with any degree of confidence with those beneath the other three terraces due to differences in pedosedimentary properties and uncertainties over chronological controls. Thus, it seems likely that either the terraces were (re)constructed and utilised over different cultural periods or that there is significant variation in the extent of weathering of material used for reconstruction of the terraces. Unfortunately, it cannot be ascertained from the data available whether the terraces were abandoned for any significant period of time prior to reconstruction and, if so, whether this was a regional phenomenon related to climate, social, or economic changes.

Bridging a yawning chasm: EEG investigations into the debate concerning the role of the human mirror neuron system in contagious yawning

Ongoing debate in the literature concerns whether there is a link between contagious yawning and the human mirror neuron system (hMNS). One way of examining this issue is with the use of the electroencephalogram (EEG) to measure changes in mu activation during the observation of yawns. Mu oscillations are seen in the alpha bandwidth of the EEG (8–12 Hz) over sensorimotor areas. Previous work has shown that mu suppression is a useful index of hMNS activation and is sensitive to individual differences in empathy. In two experiments, we presented participants with videos of either people yawning or control stimuli. We found greater mu suppression for yawns than for controls over right motor and premotor areas, particularly for those scoring higher on traits of empathy. In a third experiment, auditory recordings of yawns were compared against electronically scrambled versions of the same yawns. We observed greater mu suppression for yawns than for the controls over right lateral premotor areas. Again, these findings were driven by those scoring highly on empathy. The results from these experiments support the notion that the hMNS is involved in contagious yawning, emphasise the link between contagious yawning and empathy, and stress the importance of good control stimuli.

Probabilistic evaluation of time series models : a comparison of several approaches

Several methods are examined which allow to produce forecasts for time series in the form of probability assignments. The necessary concepts are presented, addressing questions such as how to assess the performance of a probabilistic forecast. A particular class of models, cluster weighted models (CWMs), is given particular attention. CWMs, originally proposed for deterministic forecasts, can be employed for probabilistic forecasting with little modification. Two examples are presented. The first involves estimating the state of (numerically simulated) dynamical systems from noise corrupted measurements, a problem also known as filtering. There is an optimal solution to this problem, called the optimal filter, to which the considered time series models are compared. (The optimal filter requires the dynamical equations to be known.) In the second example, we aim at forecasting the chaotic oscillations of an experimental bronze spring system. Both examples demonstrate that the considered time series models, and especially the CWMs, provide useful probabilistic information about the underlying dynamical relations. In particular, they provide more than just an approximation to the conditional mean.