Stability results for the time-harmonic Maxwell equations with impedance boundary conditions

We consider the time-harmonic Maxwell equations with constant coefficients in a bounded, uniformly star-shaped polyhedron. We prove wavenumber-explicit norm bounds for weak solutions. This result is pivotal for convergence proofs in numerical analysis and may be a tool in the analysis of electromagnetic boundary integral operators.

Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations

In this paper, we extend to the time-harmonic Maxwell equations the p-version analysis technique developed in [R. Hiptmair, A. Moiola and I. Perugia, Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the p-version, SIAM J. Numer. Anal., 49 (2011), 264-284] for Trefftz-discontinuous Galerkin approximations of the Helmholtz problem. While error estimates in a mesh-skeleton norm are derived parallel to the Helmholtz case, the derivation of estimates in a mesh-independent norm requires new twists in the duality argument. The particular case where the local Trefftz approximation spaces are built of vector-valued plane wave functions is considered, and convergence rates are derived.

Comment on “A modified leapfrog scheme for shallow water equations” by Wen-Yih Sun and Oliver M.T. Sun

A recent paper published in this journal considers the numerical integration of the shallow-water equations using the leapfrog time-stepping scheme [Sun Wen-Yih, Sun Oliver MT. A modified leapfrog scheme for shallow water equations. Comput Fluids 2011;52:69–72]. The authors of that paper propose using the time-averaged height in the numerical calculation of the pressure-gradient force, instead of the instantaneous height at the middle time step. The authors show that this modification doubles the maximum Courant number (and hence the maximum time step) at which the integrations are stable, doubling the computational efficiency. Unfortunately, the pressure-averaging technique proposed by the authors is not original. It was devised and published by Shuman [5] and has been widely used in the atmosphere and ocean modelling community for over 40 years.

The prediction of nutrients into estuaries and their subsequent behaviour: application to the Tamar and comparison with the Tweed, U.K.

Some of the techniques used to model nitrogen (N) and phosphorus (P) discharges from a terrestrial catchment to an estuary are discussed and applied to the River Tamar and Tamar Estuary system in Southwest England, U.K. Data are presented for dissolved inorganic nutrient concentrations in the Tamar Estuary and compared with those from the contrasting, low turbidity and rapidly flushed Tweed Estuary in Northeast England. In the Tamar catchment, simulations showed that effluent nitrate loads for typical freshwater flows contributed less than 1% of the total N load. The effect of effluent inputs on ammonium loads was more significant (∼10%). Cattle, sheep and permanent grassland dominated the N catchment export, with diffuse-source N export greatly dominating that due to point sources. Cattle, sheep, permanent grassland and cereal crops generated the greatest rates of diffuse-source P export. This reflected the higher rates of P fertiliser applications to arable land and the susceptibility of bare, arable land to P export in wetter winter months. N and P export to the Tamar Estuary from human sewage was insignificant. Non-conservative behaviour of phosphate was particularly marked in the Tamar Estuary. Silicate concentrations were slightly less than conservative levels, whereas nitrate was essentially conservative. The coastal sea acted as a sink for these terrestrially derived nutrients. A pronounced sag in dissolved oxygen that was associated with strong nitrite and ammonium peaks occurred in the turbidity maximum region of the Tamar Estuary. Nutrient behaviour within the Tweed was very different. The low turbidity and rapid flushing ensured that nutrients there were essentially conservative, so that flushing of nutrients to the coastal zone from the river occurred with little estuarine modification.

Strategies: Revolution in climate prediction is both necessary and possible: A declaration at the World Modelling Summit for Climate Prediction

The impending threat of global climate change and its regional manifestations is among the most important and urgent problems facing humanity. Society needs accurate and reliable estimates of changes in the probability of regional weather variations to develop science-based adaptation and mitigation strategies. Recent advances in weather prediction and in our understanding and ability to model the climate system suggest that it is both necessary and possible to revolutionize climate prediction to meet these societal needs. However, the scientific workforce and the computational capability required to bring about such a revolution is not available in any single nation. Motivated by the success of internationally funded infrastructure in other areas of science, this paper argues that, because of the complexity of the climate system, and because the regional manifestations of climate change are mainly through changes in the statistics of regional weather variations, the scientific and computational requirements to predict its behavior reliably are so enormous that the nations of the world should create a small number of multinational high-performance computing facilities dedicated to the grand challenges of developing the capabilities to predict climate variability and change on both global and regional scales over the coming decades. Such facilities will play a key role in the development of next-generation climate models, build global capacity in climate research, nurture a highly trained workforce, and engage the global user community, policy-makers, and stakeholders. We recommend the creation of a small number of multinational facilities with computer capability at each facility of about 20 peta-flops in the near term, about 200 petaflops within five years, and 1 exaflop by the end of the next decade. Each facility should have sufficient scientific workforce to develop and maintain the software and data analysis infrastructure. Such facilities will enable questions of what resolution, both horizontal and vertical, in atmospheric and ocean models, is necessary for more confident predictions at the regional and local level. Current limitations in computing power have placed severe limitations on such an investigation, which is now badly needed. These facilities will also provide the world's scientists with the computational laboratories for fundamental research on weather–climate interactions using 1-km resolution models and on atmospheric, terrestrial, cryospheric, and oceanic processes at even finer scales. Each facility should have enabling infrastructure including hardware, software, and data analysis support, and scientific capacity to interact with the national centers and other visitors. This will accelerate our understanding of how the climate system works and how to model it. It will ultimately enable the climate community to provide society with climate predictions, which are based on our best knowledge of science and the most advanced technology.

Collaboration of the weather and climate communities to advance subseasonal-to-seasonal prediction

The World Weather Research Programme (WWRP) and the World Climate Research Programme (WCRP) have identified collaborations and scientific priorities to accelerate advances in analysis and prediction at subseasonal-to-seasonal time scales, which include i) advancing knowledge of mesoscale–planetary-scale interactions and their prediction; ii) developing high-resolution global–regional climate simulations, with advanced representation of physical processes, to improve the predictive skill of subseasonal and seasonal variability of high-impact events, such as seasonal droughts and floods, blocking, and tropical and extratropical cyclones; iii) contributing to the improvement of data assimilation methods for monitoring and predicting used in coupled ocean–atmosphere–land and Earth system models; and iv) developing and transferring diagnostic and prognostic information tailored to socioeconomic decision making. The document puts forward specific underpinning research, linkage, and requirements necessary to achieve the goals of the proposed collaboration.

An earth-system prediction initiative for the twenty-first century

The necessity and benefits for establishing the international Earth-system Prediction Initiative (EPI) are discussed by scientists associated with the World Meteorological Organization (WMO) World Weather Research Programme (WWRP), World Climate Research Programme (WCRP), International Geosphere–Biosphere Programme (IGBP), Global Climate Observing System (GCOS), and natural-hazards and socioeconomic communities. The proposed initiative will provide research and services to accelerate advances in weather, climate, and Earth system prediction and the use of this information by global societies. It will build upon the WMO, the Group on Earth Observations (GEO), the Global Earth Observation System of Systems (GEOSS) and the International Council for Science (ICSU) to coordinate the effort across the weather, climate, Earth system, natural-hazards, and socioeconomic disciplines. It will require (i) advanced high-performance computing facilities, supporting a worldwide network of research and operational modeling centers, and early warning systems; (ii) science, technology, and education projects to enhance knowledge, awareness, and utilization of weather, climate, environmental, and socioeconomic information; (iii) investments in maintaining existing and developing new observational capabilities; and (iv) infrastructure to transition achievements into operational products and services.

The potential for skill across the range of the seamless weather-climate prediction problem: a stimulus for our science

Predictability is considered in the context of the seamless weather-climate prediction problem, and the notion is developed that there can be predictive power on all time-scales. On all scales there are phenomena that occur as well as longer time-scales and external conditions that should combine to give some predictability. To what extent this theoretical predictability may actually be realised and, further, to what extent it may be useful is not clear. However the potential should provide a stimulus to, and high profile for, our science and its application for many years.