Estimation of the friction velocity in stably stratified boundary-layer flows over hills

A method is suggested for the calculation of the friction velocity for stable turbulent boundary-layer flow over hills. The method is tested using a continuous upstream mean velocity profile compatible with the propagation of gravity waves, and is incorporated into the linear model of Hunt, Leibovich and Richards with the modification proposed by Hunt, Richards and Brighton to include the effects of stability, and the reformulated solution of Weng for the near-surface region. Those theoretical results are compared with results from simulations using a non-hydrostatic microscale-mesoscale two-dimensional numerical model, and with field observations for different values of stability. These comparisons show a considerable improvement in the behaviour of the theoretical model when the friction velocity is calculated using the method proposed here, leading to a consistent variation of the boundary-layer structure with stability, and better agreement with observational and numerical data.

Lateral boundary contributions to wave-activity invariants and nonlinear stability theorems for balanced dynamics

The slow advective-timescale dynamics of the atmosphere and oceans is referred to as balanced dynamics. An extensive body of theory for disturbances to basic flows exists for the quasi-geostrophic (QG) model of balanced dynamics, based on wave-activity invariants and nonlinear stability theorems associated with exact symmetry-based conservation laws. In attempting to extend this theory to the semi-geostrophic (SG) model of balanced dynamics, Kushner & Shepherd discovered lateral boundary contributions to the SG wave-activity invariants which are not present in the QG theory, and which affect the stability theorems. However, because of technical difficulties associated with the SG model, the analysis of Kushner & Shepherd was not fully nonlinear. This paper examines the issue of lateral boundary contributions to wave-activity invariants for balanced dynamics in the context of Salmon's nearly geostrophic model of rotating shallow-water flow. Salmon's model has certain similarities with the SG model, but also has important differences that allow the present analysis to be carried to finite amplitude. In the process, the way in which constraints produce boundary contributions to wave-activity invariants, and additional conditions in the associated stability theorems, is clarified. It is shown that Salmon's model possesses two kinds of stability theorems: an analogue of Ripa's small-amplitude stability theorem for shallow-water flow, and a finite-amplitude analogue of Kushner & Shepherd's SG stability theorem in which the ‘subsonic’ condition of Ripa's theorem is replaced by a condition that the flow be cyclonic along lateral boundaries. As with the SG theorem, this last condition has a simple physical interpretation involving the coastal Kelvin waves that exist in both models. Salmon's model has recently emerged as an important prototype for constrained Hamiltonian balanced models. The extent to which the present analysis applies to this general class of models is discussed.

Late Quaternary fire regimes of Australasia

We have compiled 223 sedimentary charcoal records from Australasia in order to examine the temporal and spatial variability of fire regimes during the Late Quaternary. While some of these records cover more than a full glacial cycle, here we focus on the last 70,000 years when the number of individual records in the compilation allows more robust conclusions. On orbital time scales, fire in Australasia predominantly reflects climate, with colder periods characterized by less and warmer intervals by more biomass burning. The composite record for the region also shows considerable millennial-scale variability during the last glacial interval (73.5–14.7 ka). Within the limits of the dating uncertainties of individual records, the variability shown by the composite charcoal record is more similar to the form, number and timing of Dansgaard–Oeschger cycles as observed in Greenland ice cores than to the variability expressed in the Antarctic ice-core record. The composite charcoal record suggests increased biomass burning in the Australasian region during Greenland Interstadials and reduced burning during Greenland Stadials. Millennial-scale variability is characteristic of the composite record of the sub-tropical high pressure belt during the past 21 ka, but the tropics show a somewhat simpler pattern of variability with major peaks in biomass burning around 15 ka and 8 ka. There is no distinct change in fire regime corresponding to the arrival of humans in Australia at 50 ± 10 ka and no correlation between archaeological evidence of increased human activity during the past 40 ka and the history of biomass burning. However, changes in biomass burning in the last 200 years may have been exacerbated or influenced by humans.

Applying Jackson’s methodological ideal-types: problems of differentiation and classification

In The Conduct of Inquiry in International Relations, Patrick Jackson situates methodologies in International Relations in relation to their underlying philosophical assumptions. One of his aims is to map International Relations debates in a way that ‘capture[s] current controversies’ (p. 40). This ambition is overstated: whilst Jackson’s typology is useful as a clarificatory tool, (re)classifying existing scholarship in International Relations is more problematic. One problem with Jackson’s approach is that he tends to run together the philosophical assumptions which decisively differentiate his methodologies (by stipulating a distinctive warrant for knowledge claims) and the explanatory strategies that are employed to generate such knowledge claims, suggesting that the latter are entailed by the former. In fact, the explanatory strategies which Jackson associates with each methodology reflect conventional practice in International Relations just as much as they reflect philosophical assumptions. This makes it more difficult to identify each methodology at work than Jackson implies. I illustrate this point through a critical analysis of Jackson’s controversial reclassification of Waltz as an analyticist, showing that whilst Jackson’s typology helps to expose inconsistencies in Waltz’s approach, it does not fully support the proposed reclassification. The conventional aspect of methodologies in International Relations also raises questions about the limits of Jackson’s ‘engaged pluralism’.

On the difficulties of present theoretical models to predict the oxidation state of atomic Au adsorbed on regular sites of CeO2(111)

The electronic structure and oxidation state of atomic Au adsorbed on a perfect CeO2(111) surface have been investigated in detail by means of periodic density functional theory-based calculations, using the LDA+U and GGA+U potentials for a broad range of U values, complemented with calculations employing the HSE06 hybrid functional. In addition, the effects of the lattice parameter a0 and of the starting point for the geometry optimization have also been analyzed. From the present results we suggest that the oxidation state of single Au atoms on CeO2(111) predicted by LDA+U, GGA+U, and HSE06 density functional calculations is not conclusive and that the final picture strongly depends on the method chosen and on the construction of the surface model. In some cases we have been able to locate two well-defined states which are close in energy but with very different electronic structure and local geometries, one with Au fully oxidized and one with neutral Au. The energy difference between the two states is typically within the limits of the accuracy of the present exchange-correlation potentials, and therefore, a clear lowest-energy state cannot be identified. These results suggest the possibility of a dynamic distribution of Au0 and Au+ atomic species at the regular sites of the CeO2(111) surface.

New age estimates for the Palaeolithic assemblages and Pleistocene succession of Casablanca, Morocco

Marine and aeolian Quaternary sediments from Casablanca, Morocco were dated using the optically stimulated luminescence (OSL) signal of quartz grains. These sediments form part of an extensive succession spanning the Pleistocene, and contain a rich faunal and archaeological record, including an Acheulian lithic assemblage from before the Brunhes–Matayama boundary, and a Homo erectus jaw from younger cave deposits. Sediment samples from the sites of Reddad Ben Ali, Oulad J’mel, Sidi Abderhamane and Thomas Quarries have been dated, in order to assess the upper limits of OSL. The revision of previously measured mammalian tooth enamel electron spin resonance (ESR) dates from the Grotte des Rhinocéros, Oulad Hamida Quarry 1, incorporating updated environmental dose rate measurements and attenuation calculations, also provide chronological constraint for the archaeological material preserved at Thomas Quarries. Several OSL age estimates extend back to around 500,000 years, with a single sample providing an OSL age close to 1 Ma in magnetically reversed sediments. These luminescence dates are some of the oldest determined, and their reliability is assessed using both internal criteria based on stratigraphic consistency, and external lithostratigraphic, morphostratigraphic and independent chronological constraints. For most samples, good internal agreement is observed using single aliquot regenerative-dose OSL measurements, while multiple aliquot additive-dose measurements generally have poorer resolution and consistency. Novel slow-component and component-resolved OSL approaches applied to four samples provide significantly enhanced dating precision, and an examination of the degree of signal zeroing at deposition. A comparison of the OSL age estimates with the updated ESR dates and one U-series date demonstrate that this method has great potential for providing reliable age estimates for sediments of this antiquity. We consider the cause of some slight age inversion observed at Thomas Quarries, and provide recommendations for further luminescence dating within this succession.

Acts of estrangement: reading the psoriatic-skin

I am continually surprised by the acts of estrangement in which my body engages. All bodies do this to some extent – lungs breathe, hearts beat and so on, but with psoriasis, which my article is concerned with, these processes are highly visible. As a condition of the skin, it is a pathology which is enacted both within and without, visible to the social world as well emerging from some little understood inflammatory source within the body. This article will undertake a phenomenological exploration of my own skin and how my experience of my body is affected by its lack of compliance with medicine, cosmetics etc. By some unknown causation it flakes, breaks, itches constantly drawing attention to bodily limits and the limits of medical knowledge. I want to think through the meanings we ascribe to such inflammatory conditions in Western society, how my skin materialises at the nexus of industrialisation, medicine, class and capital. This investigation will emerge at the limit point, the thin skin between the subjective and objective, observing and theorising my skin in ways which dissolve disciplinary boundaries, to comprehend the cultural, biological and environmental forces that work upon my body, estranging it from me.

Travelling waves in a model of species migration

A model of species migration is presented which takes the form of a reaction-diffusion system. We consider special limits of this model in which we demonstrate the existence of travelling wave solutions. These solutions can be used to describe the migration of cells, bacteria, and some organisms. © 2000 Elsevier Science Ltd. All rights reserved.

Global patterns of vegetation response to millennial-scale variability and rapid climate change during the last glacial period

Ninety-four sites worldwide have sufficient resolution and dating to document the impact of millennial-scale climate variability on vegetation and fire regimes during the last glacial period. Although Dansgaard–Oeschger (D–O) cycles all show a basically similar gross structure, they vary in the magnitude and the length of the warm and cool intervals. We illustrate the geographic patterns in the climate-induced changes in vegetation by comparing D–O 6, D–O 8 and D–O 19. There is a strong response to both D–O warming events and subsequent cooling, most marked in the northern extratropics. Pollen records from marine cores from the northern extratropics confirm that there is no lag between the change in climate and the vegetation response, within the limits of the dating resolution (50–100 years). However, the magnitude of the change in vegetation is regionally specific and is not a simple function of either the magnitude or the duration of the change in climate as registered in Greenland ice cores. Fire regimes also show an initial immediate response to climate changes, but during cooling intervals there is a slow recovery of biomass burning after the initial reduction, suggesting a secondary control through the recovery of vegetation productivity. In the extratropics, vegetation changes are largely determined by winter temperatures while in the tropics they are largely determined by changes in plant-available water. Tropical vegetation records show changes corresponding to Heinrich Stadials but the response to D–O warming events is less marked than in the northern extratropics. There are very few high-resolution records from the Southern Hemisphere extratropics, but these records also show both a vegetation and fire response to millennial-scale climate variability. It is not yet possible to determine unequivocally whether terrestrial records reflect the asynchroneity apparent in the ice-core records.

Pollen-based reconstructions of Japanese biomes at 0, 6000 and 18,000 14C yr bp

A biomization method, which objectively assigns individual pollen assemblages to biomes ( Prentice et al., 1996 ), was tested using modern pollen data from Japan and applied to fossil pollen data to reconstruct palaeovegetation patterns 6000 and 18,000 14C yr bp Biomization started with the assignment of 135 pollen taxa to plant functional types (PFTs), and nine possible biomes were defined by specific combinations of PFTs. Biomes were correctly assigned to 54% of the 94 modern sites. Incorrect assignments occur near the altitudinal limits of individual biomes, where pollen transport from lower altitudes blurs the local pollen signals or continuous changes in species composition characterizes the range limits of biomes. As a result, the reconstructed changes in the altitudinal limits of biomes at 6000 and 18,000 14C yr bp are likely to be conservative estimates of the actual changes. The biome distribution at 6000 14C yr bp was rather similar to today, suggesting that changes in the bioclimate of Japan have been small since the mid-Holocene. At 18,000 14C yr bp the Japanese lowlands were covered by taiga and cool mixed forests. The southward expansion of these forests and the absence of broadleaved evergreen/warm mixed forests reflect a pronounced year-round cooling.

Transreal limits expose category errors in IEEE 754 floating-point arithmetic and in mathematics

The IEEE 754 standard for oating-point arithmetic is widely used in computing. It is based on real arithmetic and is made total by adding both a positive and a negative infinity, a negative zero, and many Not-a-Number (NaN) states. The IEEE infinities are said to have the behaviour of limits. Transreal arithmetic is total. It also has a positive and a negative infinity but no negative zero, and it has a single, unordered number, nullity. We elucidate the transreal tangent and extend real limits to transreal limits. Arguing from this firm foundation, we maintain that there are three category errors in the IEEE 754 standard. Firstly the claim that IEEE infinities are limits of real arithmetic confuses limiting processes with arithmetic. Secondly a defence of IEEE negative zero confuses the limit of a function with the value of a function. Thirdly the definition of IEEE NaNs confuses undefined with unordered. Furthermore we prove that the tangent function, with the infinities given by geometrical con- struction, has a period of an entire rotation, not half a rotation as is commonly understood. This illustrates a category error, confusing the limit with the value of a function, in an important area of applied mathe- matics { trigonometry. We brie y consider the wider implications of this category error. Another paper proposes transreal arithmetic as a basis for floating- point arithmetic; here we take the profound step of proposing transreal arithmetic as a replacement for real arithmetic to remove the possibility of certain category errors in mathematics. Thus we propose both theo- retical and practical advantages of transmathematics. In particular we argue that implementing transreal analysis in trans- floating-point arith- metic would extend the coverage, accuracy and reliability of almost all computer programs that exploit real analysis { essentially all programs in science and engineering and many in finance, medicine and other socially beneficial applications.

Structure of the planetary boundary layer over southeast England: modeling and measurements

The Weather Research and Forecasting model was applied to analyze variations in the planetary boundary layer (PBL) structure over Southeast England including central and suburban London. The parameterizations and predictive skills of two nonlocal mixing PBL schemes, YSU and ACM2, and two local mixing PBL schemes, MYJ and MYNN2, were evaluated over a variety of stability conditions, with model predictions at a 3 km grid spacing. The PBL height predictions, which are critical for scaling turbulence and diffusion in meteorological and air quality models, show significant intra-scheme variance (> 20%), and the reasons are presented. ACM2 diagnoses the PBL height thermodynamically using the bulk Richardson number method, which leads to a good agreement with the lidar data for both unstable and stable conditions. The modeled vertical profiles in the PBL, such as wind speed, turbulent kinetic energy (TKE), and heat flux, exhibit large spreads across the PBL schemes. The TKE predicted by MYJ were found to be too small and show much less diurnal variation as compared with observations over London. MYNN2 produces better TKE predictions at low levels than MYJ, but its turbulent length scale increases with height in the upper part of the strongly convective PBL, where it should decrease. The local PBL schemes considerably underestimate the entrainment heat fluxes for convective cases. The nonlocal PBL schemes exhibit stronger mixing in the mean wind fields under convective conditions than the local PBL schemes and agree better with large-eddy simulation (LES) studies.

Explaining patterns of avian diversity and endemicity: climate and biomes of southern Africa over the last 140,000 years

Aim Test hypotheses that present biodiversity and endemic species richness are related to climatic stability and/or biome persistence.Location Africa south of 15° S. Methods Seventy eight HadCM3 general circulation model palaeoclimate experiments spanning the last 140,000 years, plus a pre-industrial experiment,were used to calculate measures of climatic variability for 0.5° grid cells. Models were fitted relating distributions of the nine biomes of South Africa,Lesotho and Swaziland to present climate. These models were used to simulate potential past biome distribution and extent for the 78 palaeoclimate experiments, and three measures of biome persistence. Climatic response surfaces were fitted for 690 bird species regularly breeding in the region and used to simulate present species richness for cells of the 0.5° grid. Species richness was evaluated for residents, mobile species (nomadic or partially/altitudinally migrant within the region), and intra-African migrants, and also separately for endemic/near-endemic (hereafter ‘endemic’) species as a whole and those associated with each biome. Our hypotheses were tested by analysing correlations between species richness and climatic variability or biome persistence. Results The magnitude of climatic variability showed clear spatial patterns. Marked changes in biome distributions and extents were projected, although limited areas of persistence were projected for some biomes. Overall species richness was not correlated with climatic variability, although richness of mobile species showed a weak negative correlation. Endemic species richness was significantly negatively correlated with climatic variability. Strongest correlations, however, were positive correlations between biome persistence and richness of endemics associated with individual biomes. Main conclusions Low climatic variability, and especially a degree of stability enabling biome persistence, is strongly correlated with species richness of birds endemic to southern Africa. This probably principally reflects reduced extinction risk for these species where the biome to which they are adapted persisted