Space weather driven changes in lower atmosphere phenomena

During a period of heliospheric disturbance in 2007-9 associated with a co-rotating interaction region (CIR), a characteristic periodic variation becomes apparent in neutron monitor data. This variation is phase locked to periodic heliospheric current sheet crossings. Phase-locked electrical variations are also seen in the terrestrial lower atmosphere in the southern UK, including an increase in the vertical conduction current density of fair weather atmospheric electricity during increases in the neutron monitor count rate and energetic proton count rates measured by spacecraft. At the same time as the conduction current increases, changes in the cloud microphysical properties lead to an increase in the detected height of the cloud base at Lerwick Observatory, Shetland, with associated changes in surface meteorological quantities. As electrification is expected at the base of layer clouds, which can influence droplet properties, these observations of phase-locked thermodynamic, cloud, atmospheric electricity and solar sector changes are not inconsistent with a heliospheric disturbance driving lower troposphere changes.

A generalized collectively compact operator theory with an application to integral equations on unbounded domains

In this paper a generalization of collectively compact operator theory in Banach spaces is developed. A feature of the new theory is that the operators involved are no longer required to be compact in the norm topology. Instead it is required that the image of a bounded set under the operator family is sequentially compact in a weaker topology. As an application, the theory developed is used to establish solvability results for a class of systems of second kind integral equations on unbounded domains, this class including in particular systems of Wiener-Hopf integral equations with L1 convolutions kernels

Modeling requirement driven architecture of adaptive healthcare system based on semiotics

In order to improve the quality of healthcare services, the integrated large-scale medical information system is needed to adapt to the changing medical environment. In this paper, we propose a requirement driven architecture of healthcare information system with hierarchical architecture. The system operates through the mapping mechanism between these layers and thus can organize functions dynamically adapting to user’s requirement. Furthermore, we introduce the organizational semiotics methods to capture and analyze user’s requirement through ontology chart and norms. Based on these results, the structure of user’s requirement pattern (URP) is established as the driven factor of our system. Our research makes a contribution to design architecture of healthcare system which can adapt to the changing medical environment.

Scenario and modelling uncertainty in global mean temperature change derived from emission-driven global climate models

We compare future changes in global mean temperature in response to different future scenarios which, for the first time, arise from emission-driven rather than concentration-driven perturbed parameter ensemble of a global climate model (GCM). These new GCM simulations sample uncertainties in atmospheric feedbacks, land carbon cycle, ocean physics and aerosol sulphur cycle processes. We find broader ranges of projected temperature responses arising when considering emission rather than concentration-driven simulations (with 10–90th percentile ranges of 1.7 K for the aggressive mitigation scenario, up to 3.9 K for the high-end, business as usual scenario). A small minority of simulations resulting from combinations of strong atmospheric feedbacks and carbon cycle responses show temperature increases in excess of 9 K (RCP8.5) and even under aggressive mitigation (RCP2.6) temperatures in excess of 4 K. While the simulations point to much larger temperature ranges for emission-driven experiments, they do not change existing expectations (based on previous concentration-driven experiments) on the timescales over which different sources of uncertainty are important. The new simulations sample a range of future atmospheric concentrations for each emission scenario. Both in the case of SRES A1B and the Representative Concentration Pathways (RCPs), the concentration scenarios used to drive GCM ensembles, lies towards the lower end of our simulated distribution. This design decision (a legacy of previous assessments) is likely to lead concentration-driven experiments to under-sample strong feedback responses in future projections. Our ensemble of emission-driven simulations span the global temperature response of the CMIP5 emission-driven simulations, except at the low end. Combinations of low climate sensitivity and low carbon cycle feedbacks lead to a number of CMIP5 responses to lie below our ensemble range. The ensemble simulates a number of high-end responses which lie above the CMIP5 carbon cycle range. These high-end simulations can be linked to sampling a number of stronger carbon cycle feedbacks and to sampling climate sensitivities above 4.5 K. This latter aspect highlights the priority in identifying real-world climate-sensitivity constraints which, if achieved, would lead to reductions on the upper bound of projected global mean temperature change. The ensembles of simulations presented here provides a framework to explore relationships between present-day observables and future changes, while the large spread of future-projected changes highlights the ongoing need for such work.

First order k-th moment finite element analysis of nonlinear operator equations with stochastic data

We develop and analyze a class of efficient Galerkin approximation methods for uncertainty quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin discretizations of tensorized linearizations at nominal parameters. Specifically, we consider abstract, nonlinear, parametric operator equations J(\alpha ,u)=0 for random input \alpha (\omega ) with almost sure realizations in a neighborhood of a nominal input parameter \alpha _0. Under some structural assumptions on the parameter dependence, we prove existence and uniqueness of a random solution, u(\omega ) = S(\alpha (\omega )). We derive a multilinear, tensorized operator equation for the deterministic computation of k-th order statistical moments of the random solution's fluctuations u(\omega ) - S(\alpha _0). We introduce and analyse sparse tensor Galerkin discretization schemes for the efficient, deterministic computation of the k-th statistical moment equation. We prove a shift theorem for the k-point correlation equation in anisotropic smoothness scales and deduce that sparse tensor Galerkin discretizations of this equation converge in accuracy vs. complexity which equals, up to logarithmic terms, that of the Galerkin discretization of a single instance of the mean field problem. We illustrate the abstract theory for nonstationary diffusion problems in random domains.

Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

A statistical model for sea surface diurnal warming driven by numercial weather predictions fluxes and winds

A statistical model is derived relating the diurnal variation of sea surface temperature (SST) to the net surface heat flux and surface wind speed from a numerical weather prediction (NWP) model. The model is derived using fluxes and winds from the European Centre for Medium-Range Weather Forecasting (ECMWF) NWP model and SSTs from the Spinning Enhanced Visible and Infrared Imager (SEVIRI). In the model, diurnal warming has a linear dependence on the net surface heat flux integrated since (approximately) dawn and an inverse quadratic dependence on the maximum of the surface wind speed in the same period. The model coefficients are found by matching, for a given integrated heat flux, the frequency distributions of the maximum wind speed and the observed warming. Diurnal cooling, where it occurs, is modelled as proportional to the integrated heat flux divided by the heat capacity of the seasonal mixed layer. The model reproduces the statistics (mean, standard deviation, and 95-percentile) of the diurnal variation of SST seen by SEVIRI and reproduces the geographical pattern of mean warming seen by the Advanced Microwave Scanning Radiometer (AMSR-E). We use the functional dependencies in the statistical model to test the behaviour of two physical model of diurnal warming that display contrasting systematic errors.

A benchmark-driven modelling approach for evaluating deployment choices on a multicore architecture

The complexity of current and emerging high performance architectures provides users with options about how best to use the available resources, but makes predicting performance challenging. In this work a benchmark-driven performance modelling approach is outlined that is appro- priate for modern multicore architectures. The approach is demonstrated by constructing a model of a simple shallow water code on a Cray XE6 system, from application-specific benchmarks that illustrate precisely how architectural char- acteristics impact performance. The model is found to recre- ate observed scaling behaviour up to 16K cores, and used to predict optimal rank-core affinity strategies, exemplifying the type of problem such a model can be used for.

The end of the opportunism vs trust debate: bounded reliability as a new envelope concept in research on MNE governance

Modern transaction cost economics (TCE) thinking has developed into a key intellectual foundation of international business (IB) research, but the Williamsonian version has faced substantial criticism for adopting the behavioral assumption of opportunism. In this paper we assess both the opportunism concept and existing alternatives such as trust within the context of IB research, especially work on multinational enterprise (MNE) governance. Case analyses of nine global MNEs illustrate an alternative to the opportunism assumption that captures more fully the mechanisms underlying failed commitments inside the MNE. As a substitute for the often-criticized assumption of opportunism, we propose the envelope concept of bounded reliability (BRel), an assumption that represents more accurately and more completely the reasons for failed commitments, without invalidating the other critical assumption in conventional TCE (and internalization theory) thinking, namely the widely accepted envelope concept of bounded rationality (BRat). Bounded reliability as an envelope concept includes two main components, within the context of global MNE management: opportunism as intentional deceit, and benevolent preference reversal. The implications for IB research of adopting the bounded reliability concept are far reaching, as this concept may increase the legitimacy of comparative institutional analysis in the social sciences.

Eddy-driven exchange between the open ocean and a sub-ice shelf cavity

The exchange between the open ocean and sub-ice shelf cavities is important to both water mass transformations and ice shelf melting. Here we use a high-resolution (500 m) numerical model to investigate to which degree eddies produced by frontal instability at the edge of a polynya are capable of transporting dense High Salinity Shelf Water (HSSW) underneath an ice shelf. The applied surface buoyancy flux and ice shelf geometry is based on Ronne Ice Shelf in the southern Weddell Sea, an area of intense wintertime sea ice production where a flow of HSSW into the cavity has been observed. Results show that eddies are able to enter the cavity at the southwestern corner of the polynya where an anticyclonic rim current intersects the ice shelf front. The size and time scale of simulated eddies are in agreement with observations close to the Ronne Ice Front. The properties and strength of the inflow are sensitive to the prescribed total ice production, flushing the ice shelf cavity at a rate of 0.2–0.4 × 106 m3 s−1 depending on polynya size and magnitude of surface buoyancy flux. Eddy-driven HSSW transport into the cavity is reduced by about 50% if the model grid resolution is decreased to 2-5 km and eddies are not properly resolved.

Generation of a buoyancy-driven coastal current by an Antarctic Polynya

Descent and spreading of high salinity water generated by salt rejection during sea ice formation in an Antarctic coastal polynya is studied using a hydrostatic, primitive equation three-dimensional ocean model called the Proudman Oceanographic Laboratory Coastal Ocean Modeling System (POLCOMS). The shape of the polynya is assumed to be a rectangle 100 km long and 30 km wide, and the salinity flux into the polynya at its surface is constant. The model has been run at high horizontal spatial resolution (500 m), and numerical simulations reveal a buoyancy-driven coastal current. The coastal current is a robust feature and appears in a range of simulations designed to investigate the influence of a sloping bottom, variable bottom drag, variable vertical turbulent diffusivities, higher salinity flux, and an offshore position of the polynya. It is shown that bottom drag is the main factor determining the current width. This coastal current has not been produced with other numerical models of polynyas, which may be because these models were run at coarser resolutions. The coastal current becomes unstable upstream of its front when the polynya is adjacent to the coast. When the polynya is situated offshore, an unstable current is produced from its outset owing to the capture of cyclonic eddies. The effect of a coastal protrusion and a canyon on the current motion is investigated. In particular, due to the convex shape of the coastal protrusion, the current sheds a dipolar eddy.

Examining reliability of seasonal to decadal sea surface temperature forecasts: the role of ensemble dispersion

Useful probabilistic climate forecasts on decadal timescales should be reliable (i.e. forecast probabilities match the observed relative frequencies) but this is seldom examined. This paper assesses a necessary condition for reliability, that the ratio of ensemble spread to forecast error being close to one, for seasonal to decadal sea surface temperature retrospective forecasts from the Met Office Decadal Prediction System (DePreSys). Factors which may affect reliability are diagnosed by comparing this spread-error ratio for an initial condition ensemble and two perturbed physics ensembles for initialized and uninitialized predictions. At lead times less than 2 years, the initialized ensembles tend to be under-dispersed, and hence produce overconfident and hence unreliable forecasts. For longer lead times, all three ensembles are predominantly over-dispersed. Such over-dispersion is primarily related to excessive inter-annual variability in the climate model. These findings highlight the need to carefully evaluate simulated variability in seasonal and decadal prediction systems.Useful probabilistic climate forecasts on decadal timescales should be reliable (i.e. forecast probabilities match the observed relative frequencies) but this is seldom examined. This paper assesses a necessary condition for reliability, that the ratio of ensemble spread to forecast error being close to one, for seasonal to decadal sea surface temperature retrospective forecasts from the Met Office Decadal Prediction System (DePreSys). Factors which may affect reliability are diagnosed by comparing this spread-error ratio for an initial condition ensemble and two perturbed physics ensembles for initialized and uninitialized predictions. At lead times less than 2 years, the initialized ensembles tend to be under-dispersed, and hence produce overconfident and hence unreliable forecasts. For longer lead times, all three ensembles are predominantly over-dispersed. Such over-dispersion is primarily related to excessive inter-annual variability in the climate model. These findings highlight the need to carefully evaluate simulated variability in seasonal and decadal prediction systems.

Evolutionary and revolutionary effects of transcomputation

Mathematics in Defence 2011 Abstract. We review transreal arithmetic and present transcomplex arithmetic. These arithmetics have no exceptions. This leads to incremental improvements in computer hardware and software. For example, the range of real numbers, encoded by floating-point bits, is doubled when all of the Not-a-Number(NaN) states, in IEEE 754 arithmetic, are replaced with real numbers. The task of programming such systems is simplified and made safer by discarding the unordered relational operator,leaving only the operators less-than, equal-to, and greater than. The advantages of using a transarithmetic in a computation, or transcomputation as we prefer to call it, may be had by making small changes to compilers and processor designs. However, radical change is possible by exploiting the reliability of transcomputations to make pipelined dataflow machines with a large number of cores. Our initial designs are for a machine with order one million cores. Such a machine can complete the execution of multiple in-line programs each clock tick

Spectral asymmetry of the massless Dirac operator on a 3-torus

Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double eigenvalue. The aim of the paper is to develop a perturbation theory for the eigenvalue with smallest modulus with respect to perturbations of the metric. Here the application of perturbation techniques is hindered by the fact that eigenvalues of the massless Dirac operator have even multiplicity, which is a consequence of this operator commuting with the antilinear operator of charge conjugation (a peculiar feature of dimension 3). We derive an asymptotic formula for the eigenvalue with smallest modulus for arbitrary perturbations of the metric and present two particular families of Riemannian metrics for which the eigenvalue with smallest modulus can be evaluated explicitly. We also establish a relation between our asymptotic formula and the eta invariant.

Eigenvalues of a one-dimensional Dirac operator pencil

We study the spectrum of a one-dimensional Dirac operator pencil, with a coupling constant in front of the potential considered as the spectral parameter. Motivated by recent investigations of graphene waveguides, we focus on the values of the coupling constant for which the kernel of the Dirac operator contains a square integrable function. In physics literature such a function is called a confined zero mode. Several results on the asymptotic distribution of coupling constants giving rise to zero modes are obtained. In particular, we show that this distribution depends in a subtle way on the sign variation and the presence of gaps in the potential. Surprisingly, it also depends on the arithmetic properties of certain quantities determined by the potential. We further observe that variable sign potentials may produce complex eigenvalues of the operator pencil. Some examples and numerical calculations illustrating these phenomena are presented.