A note on an integration by parts formula for the generators of uniform translations on configuration space

An integration by parts formula is derived for the first order differential operator corresponding to the action of translations on the space of locally finite simple configurations of infinitely many points on Rd. As reference measures, tempered grand canonical Gibbs measures are considered corresponding to a non-constant non-smooth intensity (one-body potential) and translation invariant potentials fulfilling the usual conditions. It is proven that such Gibbs measures fulfill the intuitive integration by parts formula if and only if the action of the translation is not broken for this particular measure. The latter is automatically fulfilled in the high temperature and low intensity regime.

On the entrainment assumption in Schatzmann's integral plume model

The behaviour of stationary, non-passive plumes can be simulated in a reasonably simple and accurate way by integral models. One of the key requirements of these models, but also one of their less well-founded aspects, is the entrainment assumption, which parameterizes turbulent mixing between the plume and the environment. The entrainment assumption developed by Schatzmann and adjusted to a set of experimental results requires four constants and an ad hoc hypothesis to eliminate undesirable terms. With this assumption, Schatzmann’s model exhibits numerical instability for certain cases of plumes with small velocity excesses, due to very fast radius growth. The purpose of this paper is to present an alternative entrainment assumption based on a first-order turbulence closure, which only requires two adjustable constants and seems to solve this problem. The asymptotic behaviour of the new formulation is studied and compared to previous ones. The validation tests presented by Schatzmann are repeated and it is found that the new formulation not only eliminates numerical instability but also predicts more plausible growth rates for jets in co-flowing streams.

Pollen-based continental climate reconstructions at 6 and 21 ka: a global synthesis

Subfossil pollen and plant macrofossil data derived from 14C-dated sediment profiles can provide quantitative information on glacial and interglacial climates. The data allow climate variables related to growing season warmth, winter cold, and plant-available moisture to be reconstructed. Continental-scale reconstructions have been made for the mid-Holocene (MH, around 6 ka) and Last Glacial Maximum (LGM, around 21 ka), allowing comparison with palaeoclimate simulations currently being carried out as part of the fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change. The synthesis of the available MH and LGM climate reconstructions and their uncertainties, obtained using modern analogue, regression and model-inversion techniques, is presented for four temperature variables and two moisture variables. Reconstructions of the same variables based on surface-pollen assemblages are shown to be accurate and unbiased. Reconstructed LGM and MH climate anomaly patterns are coherent, consistent between variables, and robust with respect to the choice of technique. They support a conceptual model of the controls of Late Quaternary climate change whereby the first-order effects of orbital variations and greenhouse forcing on the seasonal cycle of temperature are predictably modified by responses of the atmospheric circulation and surface energy balance.

On the statistical modeling of persistence in total ozone anomalies

Geophysical time series sometimes exhibit serial correlations that are stronger than can be captured by the commonly used first‐order autoregressive model. In this study we demonstrate that a power law statistical model serves as a useful upper bound for the persistence of total ozone anomalies on monthly to interannual timescales. Such a model is usually characterized by the Hurst exponent. We show that the estimation of the Hurst exponent in time series of total ozone is sensitive to various choices made in the statistical analysis, especially whether and how the deterministic (including periodic) signals are filtered from the time series, and the frequency range over which the estimation is made. In particular, care must be taken to ensure that the estimate of the Hurst exponent accurately represents the low‐frequency limit of the spectrum, which is the part that is relevant to long‐term correlations and the uncertainty of estimated trends. Otherwise, spurious results can be obtained. Based on this analysis, and using an updated equivalent effective stratospheric chlorine (EESC) function, we predict that an increase in total ozone attributable to EESC should be detectable at the 95% confidence level by 2015 at the latest in southern midlatitudes, and by 2020–2025 at the latest over 30°–45°N, with the time to detection increasing rapidly with latitude north of this range.

Dynamics, stratospheric ozone, and climate change

Dynamics affects the distribution and abundance of stratospheric ozone directly through transport of ozone itself and indirectly through its effect on ozone chemistry via temperature and transport of other chemical species. Dynamical processes must be considered in order to understand past ozone changes, especially in the northern hemisphere where there appears to be significant low-frequency variability which can look “trend-like” on decadal time scales. A major challenge is to quantify the predictable, or deterministic, component of past ozone changes. Over the coming century, changes in climate will affect the expected recovery of ozone. For policy reasons it is important to be able to distinguish and separately attribute the effects of ozone-depleting substances and greenhouse gases on both ozone and climate. While the radiative-chemical effects can be relatively easily identified, this is not so evident for dynamics — yet dynamical changes (e.g., changes in the Brewer-Dobson circulation) could have a first-order effect on ozone over particular regions. Understanding the predictability and robustness of such dynamical changes represents another major challenge. Chemistry-climate models have recently emerged as useful tools for addressing these questions, as they provide a self-consistent representation of dynamical aspects of climate and their coupling to ozone chemistry. We can expect such models to play an increasingly central role in the study of ozone and climate in the future, analogous to the central role of global climate models in the study of tropospheric climate change.

On the attribution of stratospheric ozone and temperature changes to changes in ozone-depleting substances and well-mixed greenhouse gases

The vertical profile of global-mean stratospheric temperature changes has traditionally represented an important diagnostic for the attribution of the cooling effects of stratospheric ozone depletion and CO2 increases. However, CO2-induced cooling alters ozone abundance by perturbing ozone chemistry, thereby coupling the stratospheric ozone and temperature responses to changes in CO2 and ozone-depleting substances (ODSs). Here we untangle the ozone-temperature coupling and show that the attribution of global-mean stratospheric temperature changes to CO2 and ODS changes (which are the true anthropogenic forcing agents) can be quite different from the traditional attribution to CO2 and ozone changes. The significance of these effects is quantified empirically using simulations from a three-dimensional chemistry-climate model. The results confirm the essential validity of the traditional approach in attributing changes during the past period of rapid ODS increases, although we find that about 10% of the upper stratospheric ozone decrease from ODS increases over the period 1975–1995 was offset by the increase in CO2, and the CO2-induced cooling in the upper stratosphere has been somewhat overestimated. When considering ozone recovery, however, the ozone-temperature coupling is a first-order effect; fully 2/5 of the upper stratospheric ozone increase projected to occur from 2010–2040 is attributable to CO2 increases. Thus, it has now become necessary to base attribution of global-mean stratospheric temperature changes on CO2 and ODS changes rather than on CO2 and ozone changes.

Impact of long-range correlations on trend detection in total ozone

Total ozone trends are typically studied using linear regression models that assume a first-order autoregression of the residuals [so-called AR(1) models]. We consider total ozone time series over 60°S–60°N from 1979 to 2005 and show that most latitude bands exhibit long-range correlated (LRC) behavior, meaning that ozone autocorrelation functions decay by a power law rather than exponentially as in AR(1). At such latitudes the uncertainties of total ozone trends are greater than those obtained from AR(1) models and the expected time required to detect ozone recovery correspondingly longer. We find no evidence of LRC behavior in southern middle-and high-subpolar latitudes (45°–60°S), where the long-term ozone decline attributable to anthropogenic chlorine is the greatest. We thus confirm an earlier prediction based on an AR(1) analysis that this region (especially the highest latitudes, and especially the South Atlantic) is the optimal location for the detection of ozone recovery, with a statistically significant ozone increase attributable to chlorine likely to be detectable by the end of the next decade. In northern middle and high latitudes, on the other hand, there is clear evidence of LRC behavior. This increases the uncertainties on the long-term trend attributable to anthropogenic chlorine by about a factor of 1.5 and lengthens the expected time to detect ozone recovery by a similar amount (from ∼2030 to ∼2045). If the long-term changes in ozone are instead fit by a piecewise-linear trend rather than by stratospheric chlorine loading, then the strong decrease of northern middle- and high-latitude ozone during the first half of the 1990s and its subsequent increase in the second half of the 1990s projects more strongly on the trend and makes a smaller contribution to the noise. This both increases the trend and weakens the LRC behavior at these latitudes, to the extent that ozone recovery (according to this model, and in the sense of a statistically significant ozone increase) is already on the verge of being detected. The implications of this rather controversial interpretation are discussed.

The reaction between silylene and ammonia: some gas-phase kinetic and quantum chemical studies

Time-resolved kinetic studies of the reaction of silylene, SiH2, generated by 193 nm laser flash photolysis of silacyclopent-3-ene, have been carried out in the presence of ammonia, NH3. Second order kinetics were observed. The reaction was studied in the gas phase at 10 Torr total pressure in SF6 bath gas at each of the three temperatures, 299, 340 and 400 K. The second order rate constants (laser pulse energy of 60 mJ/pulse) fitted the Arrhenius equation: log(k/cm3 molecule-1 s-1) = (-10.37 ± 0.17) + (0.36 ± 1.12 kJ mol-1)/RTln10 Experiments at other pressures showed that these rate constants were unaffected by pressure in the range 10-100 Torr, but showed small decreases in value at 3 and 1 Torr. There was also a weak intensity dependence, with rate constants decreasing at laser pulse energies of 30 mJ/pulse. Ab initio calculations at the G3 level of theory, show that SiH2 + NH3 should form an initial adduct (donor-acceptor complex), but that energy barriers are too great for further reaction of the adduct. This implies that SiH2 + NH3 should be a pressure dependent association reaction. The experimental data are inconsistent with this and we conclude that SiH2 decays are better explained by reaction of SiH2 with the amino radical, NH2, formed by photodissociation of NH3 at 193 nm. The mechanism of this previously unstudied reaction is discussed.

Runge-Kutta IMEX schemes for the Horizontally Explicit/Vertically Implicit (HEVI) solution of wave equations

Many operational weather forecasting centres use semi-implicit time-stepping schemes because of their good efficiency. However, as computers become ever more parallel, horizontally explicit solutions of the equations of atmospheric motion might become an attractive alternative due to the additional inter-processor communication of implicit methods. Implicit and explicit (IMEX) time-stepping schemes have long been combined in models of the atmosphere using semi-implicit, split-explicit or HEVI splitting. However, most studies of the accuracy and stability of IMEX schemes have been limited to the parabolic case of advection–diffusion equations. We demonstrate how a number of Runge–Kutta IMEX schemes can be used to solve hyperbolic wave equations either semi-implicitly or HEVI. A new form of HEVI splitting is proposed, UfPreb, which dramatically improves accuracy and stability of simulations of gravity waves in stratified flow. As a consequence it is found that there are HEVI schemes that do not lose accuracy in comparison to semi-implicit ones. The stability limits of a number of variations of trapezoidal implicit and some Runge–Kutta IMEX schemes are found and the schemes are tested on two vertical slice cases using the compressible Boussinesq equations split into various combinations of implicit and explicit terms. Some of the Runge–Kutta schemes are found to be beneficial over trapezoidal, especially since they damp high frequencies without dropping to first-order accuracy. We test schemes that are not formally accurate for stiff systems but in stiff limits (nearly incompressible) and find that they can perform well. The scheme ARK2(2,3,2) performs the best in the tests.

The structure of paranoia in the general population

Background: Psychotic phenomena appear to form a continuum with normal experience and beliefs, and may build on common emotional interpersonal concerns. Aims: We tested predictions that paranoid ideation is exponentially distributed and hierarchically arranged in the general population, and that persecutory ideas build on more common cognitions of mistrust, interpersonal sensitivity and ideas of reference. Method: Items were chosen from the Structured Clinical Interview for DSM-IV Axis II Disorders (SCID-II) questionnaire and the Psychosis Screening Questionnaire in the second British National Survey of Psychiatric Morbidity (n = 8580), to test a putative hierarchy of paranoid development using confirmatory factor analysis, latent class analysis and factor mixture modelling analysis. Results: Different types of paranoid ideation ranged in frequency from less than 2% to nearly 30%. Total scores on these items followed an almost perfect exponential distribution (r = 0.99). Our four a priori first-order factors were corroborated (interpersonal sensitivity; mistrust; ideas of reference; ideas of persecution). These mapped onto four classes of individual respondents: a rare, severe, persecutory class with high endorsement of all item factors, including persecutory ideation; a quasi-normal class with infrequent endorsement of interpersonal sensitivity, mistrust and ideas of reference, and no ideas of persecution; and two intermediate classes, characterised respectively by relatively high endorsement of items relating to mistrust and to ideas of reference. Conclusions: The paranoia continuum has implications for the aetiology, mechanisms and treatment of psychotic disorders, while confirming the lack of a clear distinction from normal experiences and processes.

Identification of micro-scale anthropogenic CO2, heat and moisture sources – processing eddy covariance fluxes for a dense urban environment

Anthropogenic emissions of heat and exhaust gases play an important role in the atmospheric boundary layer, altering air quality, greenhouse gas concentrations and the transport of heat and moisture at various scales. This is particularly evident in urban areas where emission sources are integrated in the highly heterogeneous urban canopy layer and directly linked to human activities which exhibit significant temporal variability. It is common practice to use eddy covariance observations to estimate turbulent surface fluxes of latent heat, sensible heat and carbon dioxide, which can be attributed to a local scale source area. This study provides a method to assess the influence of micro-scale anthropogenic emissions on heat, moisture and carbon dioxide exchange in a highly urbanized environment for two sites in central London, UK. A new algorithm for the Identification of Micro-scale Anthropogenic Sources (IMAS) is presented, with two aims. Firstly, IMAS filters out the influence of micro-scale emissions and allows for the analysis of the turbulent fluxes representative of the local scale source area. Secondly, it is used to give a first order estimate of anthropogenic heat flux and carbon dioxide flux representative of the building scale. The algorithm is evaluated using directional and temporal analysis. The algorithm is then used at a second site which was not incorporated in its development. The spatial and temporal local scale patterns, as well as micro-scale fluxes, appear physically reasonable and can be incorporated in the analysis of long-term eddy covariance measurements at the sites in central London. In addition to the new IMAS-technique, further steps in quality control and quality assurance used for the flux processing are presented. The methods and results have implications for urban flux measurements in dense urbanised settings with significant sources of heat and greenhouse gases.

Coupled subdaily and multiweek cycles during the lava dome erupt of Soufriere Hills Volcano, Montserrat

Observations of volcanoes extruding andesitic lava to produce lava domes often reveal cyclic behaviour. At Soufriere Hills Volcano, Montserrat, cycles with sub-daily and multi-week periods have been recognised on many occasions. These two types of cycle have been modelled separately as stick-slip magma flow at the junction between a dyke and an overlying cylindrical conduit (Costa et al. 2012), and as the filling and discharge of magma through the elastic-walled dyke (Costa et al., 2007a) respectively. Here, we couple these two models to simulate the behaviour over a period of well-observed multi-week cycles, with accompanying sub-daily cycles, from 13 May to 21 September 1997. The coupled model captures well the asymmetrical first-order behaviour: the first 40% of the multi-week cycle consists of high rates of lava extrusion during short period/high amplitude sub-daily cycles as the dyke reservoir discharges itself. The remainder of the cycle involves increasing pressurization as more magma is stored, and extrusion rate falls, followed by a gradual increase in the period of the sub-daily cycles.

The linearly modulated IRSL red emission from feldspars

This paper uses the linear modulation technique to study red IRSL emission of potassium feldspars. Sub-samples were subjected to various pre-treatment and measurement conditions in an attempt to understand the relevant mechanisms of charge transfer. The linear modulation curves fitted most successfully to a sum of three first order components and we present supporting empirical evidence for the presence of three separate signal components. Additionally, the form of the red emission was observed to closely resemble the UV emission, implying the same donor charge concentrations may supply different recombination centres (assuming emission wavelength depends on centre type).

A rate and state friction law for saline ice

Sea ice friction models are necessary to predict the nature of interactions between sea ice floes. These interactions are of interest on a range of scales, for example, to predict loads on engineering structures in icy waters or to understand the basin-scale motion of sea ice. Many models use Amonton's friction law due to its simplicity. More advanced models allow for hydrodynamic lubrication and refreezing of asperities; however, modeling these processes leads to greatly increased complexity. In this paper we propose, by analogy with rock physics, that a rate- and state-dependent friction law allows us to incorporate memory (and thus the effects of lubrication and bonding) into ice friction models without a great increase in complexity. We support this proposal with experimental data on both the laboratory (∼0.1 m) and ice tank (∼1 m) scale. These experiments show that the effects of static contact under normal load can be incorporated into a friction model. We find the parameters for a first-order rate and state model to be A = 0.310, B = 0.382, and μ0 = 0.872. Such a model then allows us to make predictions about the nature of memory effects in moving ice-ice contacts.

Temperature trends at the Mauna Loa observatory, Hawaii

Observations at the Mauna Loa Observatory, Hawaii, established the systematic increase of anthropogenic CO2 in the atmosphere. For the same reasons that this site provides excellent globally averaged CO2 data, it may provide temperature data with global significance. Here, we examine hourly temperature records, averaged annually for 1977–2006, to determine linear trends as a function of time of day. For night-time data (22:00 to 06:00 LST (local standard time)) there is a near-uniform warming of 0.040 °C yr−1. During the day, the linear trend shows a slight cooling of −0.014 °C yr−1 at 12:00 LST (noon). Overall, at Mauna Loa Observatory, there is a mean warming trend of 0.021 °C yr−1. The dominance of night-time warming results in a relatively large annual decrease in the diurnal temperature range (DTR) of −0.050 °C yr−1 over the period 1977–2006. These trends are consistent with the observed increases in the concentrations of CO2 and its role as a greenhouse gas (demonstrated here by first-order radiative forcing calculations), and indicate the possible relevance of the Mauna Loa temperature measurements to global warming.