Sparse space-time boundary element methods for the heat equation

The goal of this work is the efficient solution of the heat equation with Dirichlet or Neumann boundary conditions using the Boundary Elements Method (BEM). Efficiently solving the heat equation is useful, as it is a simple model problem for other types of parabolic problems. In complicated spatial domains as often found in engineering, BEM can be beneficial since only the boundary of the domain has to be discretised. This makes BEM easier than domain methods such as finite elements and finite differences, conventionally combined with time-stepping schemes to solve this problem. The contribution of this work is to further decrease the complexity of solving the heat equation, leading both to speed gains (in CPU time) as well as requiring smaller amounts of memory to solve the same problem. To do this we will combine the complexity gains of boundary reduction by integral equation formulations with a discretisation using wavelet bases. This reduces the total work to O(h

Impact of Laptev Sea flaw polynyas on the atmospheric boundary layer and ice production using idealized mesoscale simulations

The interaction between polynyas and the atmospheric boundary layer is examined in the Laptev Sea using the regional, non-hydrostatic Consortium for Small-scale Modelling (COSMO) atmosphere model. A thermodynamic sea-ice model is used to consider the response of sea-ice surface temperature to idealized atmospheric forcing. The idealized regimes represent atmospheric conditions that are typical for the Laptev Sea region. Cold wintertime conditions are investigated with sea-ice–ocean temperature differences of up to 40 K. The Laptev Sea flaw polynyas strongly modify the atmospheric boundary layer. Convectively mixed layers reach heights of up to 1200 m above the polynyas with temperature anomalies of more than 5 K. Horizontal transport of heat expands to areas more than 500 km downstream of the polynyas. Strong wind regimes lead to a more shallow mixed layer with strong near-surface modifications, while weaker wind regimes show a deeper, well-mixed convective boundary layer. Shallow mesoscale circulations occur in the vicinity of ice-free and thin-ice covered polynyas. They are forced by large turbulent and radiative heat fluxes from the surface of up to 789 W m−2, strong low-level thermally induced convergence and cold air flow from the orographic structure of the Taimyr Peninsula in the western Laptev Sea region. Based on the surface energy balance we derive potential sea-ice production rates between 8 and 25 cm d−1. These production rates are mainly determined by whether the polynyas are ice-free or covered by thin ice and by the wind strength.

The BALTIMOS (BALTEX Integrated Model System) fi eld experiments: A comprehensive atmospheric boundary layer data set for model validation over the open and ice- covered Baltic Sea

A comprehensive atmospheric boundary layer (ABL) data set was collected in eight fi eld experiments (two during each season) over open water and sea ice in the Baltic Sea during 1998–2001 with the primary objective to validate the coupled atmospheric- ice-ocean-land surface model BALTIMOS (BALTEX Integrated Model System). Measurements were taken by aircraft, ships and surface stations and cover the mean and turbulent structure of the ABL including turbulent fl uxes, radiation fl uxes, and cloud conditions. Measurement examples of the spatial variability of the ABL over the ice edge zone and of the stable ABL over open water demonstrate the wide range of ABL conditions collected and the strength of the data set which can also be used to validate other regional models.

The role of evaporating showers in the transfer of sting-jet momentum to the surface

The most damaging winds in a severe extratropical cyclone often occur just ahead of the evaporating ends of cloud filaments emanating from the so-called cloud head. These winds are associated with low-level jets (LLJs), sometimes occurring just above the boundary layer. The question then arises as to how the high momentum is transferred to the surface. An opportunity to address this question arose when the severe ‘St Jude's Day’ windstorm travelled across southern England on 28 October 2013. We have carried out a mesoanalysis of a network of 1 min resolution automatic weather stations and high-resolution Doppler radar scans from the sensitive S-band Chilbolton Advanced Meteorological Radar (CAMRa), along with satellite and radar network imagery and numerical weather prediction products. We show that, although the damaging winds occurred in a relatively dry region of the cyclone, there was evidence within the LLJ of abundant precipitation residues from shallow convective clouds that were evaporating in a localized region of descent. We find that pockets of high momentum were transported towards the surface by the few remaining actively precipitating convective clouds within the LLJ and also by precipitation-free convection in the boundary layer that was able to entrain evaporatively cooled air from the LLJ. The boundary-layer convection was organized in along-wind rolls separated by 500 to about 3000 m, the spacing varying according to the vertical extent of the convection. The spacing was greatest where the strongest winds penetrated to the surface. A run with a medium-resolution version of the Weather Research and Forecasting (WRF) model was able to reproduce the properties of the observed LLJ. It confirmed the LLJ to be a sting jet, which descended over the leading edge of a weaker cold-conveyor-belt jet.

Late Quaternary environmental change in the interior South American tropics: new insight from leaf wax stable isotopes

Stable isotope analysis of leaf waxes in a sediment core from Laguna La Gaiba, a shallow lake located at the Bolivian margin of the Pantanal wetlands, provides new perspective on vegetation and climate change in the lowland interior tropics of South America over the past 40,000 years. The carbon isotopic compositions (δ13C) of long-chain n-alkanes reveal large shifts between C3-and C4-dominated vegetation communities since the last glacial period, consistent with landscape reconstructions generated with pollen data from the same sediment core. Leaf wax δ13C values during the last glacial period reflect an open landscape composed of C4grasses and C3herbs from 41–20ka. A peak in C4abundance during the Last Glacial Maximum (LGM, ∼21ka) suggests drier or more seasonal conditions relative to the earlier glacial period, while the development of a C3-dominated forest community after 20 ka points to increased humidity during the last deglaciation. Within the Holocene, large changes in the abundance of C4 vegetation indicate a transition from drier or more seasonal conditions during the early/mid-Holocene to wetter conditions in the late Holocene coincident with increasing austral summer insolation. Strong negative correlations between leaf wax δ13C and δD values over the entire record indicate that the majority of variability in leaf wax δD at this site can be explained by variability in the magnitude of biosynthetic fractionation by different vegetation types rather than changes in meteoric water δD signatures. However, positive δD deviations from the observed δ13C–δD trends are consistent with more enriched source water and drier or more seasonal conditions during the early/mid-Holocene and LGM. Overall, our record adds to evidence of varying influence of glacial boundary conditions and orbital forcing on South American Summer Monsoon precipitation in different regions of the South American tropics. Moreover, the relationships between leaf wax stable isotopes and pollen data observed at this site underscore the complementary nature of pollen and leaf wax δ13C data for reconstructing past vegetation changes and the potentially large effects of such changes on leaf wax δD signatures.

The longitudinal variation of equatorial waves due to propagation on a varying zonal flow

The general 1-D theory of waves propagating on a zonally varying flow is developed from basic wave theory, and equations are derived for the variation of wavenumber and energy along ray paths. Different categories of behaviour are found, depending on the sign of the group velocity (cg) and a wave property, B. For B positive the wave energy and the wave number vary in the same sense, with maxima in relative easterlies or westerlies, depending on the sign of cg. Also the wave accumulation of Webster and Chang (1988) occurs where cg goes to zero. However for B negative they behave in opposite senses and wave accumulation does not occur. The zonal propagation of the gravest equatorial waves is analysed in detail using the theory. For non-dispersive Kelvin waves, B reduces to 2, and analytic solution is possible. B is positive for all the waves considered, except for the westward moving mixed Rossby-gravity (WMRG) wave which can have negative as well as positive B. Comparison is made between the observed climatologies of the individual equatorial waves and the result of pure propagation on the climatological upper tropospheric flow. The Kelvin wave distribution is in remarkable agreement, considering the approximations made. Some aspects of the WMRG and Rossby wave distributions are also in qualitative agreement. However the observed maxima in these waves in the winter westerlies in the eastern Pacific and Atlantic are not consistent with the theory. This is consistent with the importance of the sources of equatorial waves in these westerly duct regions due to higher latitude wave activity.

Seasonality of submesoscale flows in the ocean surface boundary layer

A signature of submesoscale flows in the upper ocean is skewness in the distribution of relative vorticity. Expected to result for high Rossby-number flows, such skewness has implications for mixing, dissipation and stratification within the upper ocean. An array of moorings deployed in the Northeast Atlantic for one year as part of the OSMOSIS experiment reveals that relative vorticity is positively skewed during winter even though the scale of the Rossby number is less than 0.5. Furthermore, this skewness is reduced to zero during spring and autumn. There is also evidence of modest seasonal variations in the gradient Rossby number. The proposed mechanism by which relative vorticity is skewed is that the ratio of lateral to vertical buoyancy gradients, as summarized by the inverse gradient Richardson number, restricts its range during winter but less so at other times of the year. These results support recent observations and model simulations suggesting the upper ocean is host to a seasonal cycle in submesoscale turbulence.

Langmuir turbulence and surface heating in the ocean surface boundary layer

This study uses large-eddy simulation to investigate the structure of the ocean surface boundary layer (OSBL) in the presence of Langmuir turbulence and stabilizing surface heat fluxes. The OSBL consists of a weakly stratified layer, despite a surface heat flux, above a stratified thermocline. The weakly stratified (mixed) layer is maintained by a combination of a turbulent heat flux produced by the wave-driven Stokes drift and downgradient turbulent diffusion. The scaling of turbulence statistics, such as dissipation and vertical velocity variance, is only affected by the surface heat flux through changes in the mixed layer depth. Diagnostic models are proposed for the equilibrium boundary layer and mixed layer depths in the presence of surface heating. The models are a function of the initial mixed layer depth before heating is imposed and the Langmuir stability length. In the presence of radiative heating, the models are extended to account for the depth profile of the heating.

Geography, skills and careers patterns at the boundary of creativity & innovation: digital technology and creative arts graduates in the UK

In the last decades, research on knowledge economies has taken central stage. Within this broader research field, research on the role of digital technologies and the creative industries has become increasingly important for researchers, academics and policy makers with particular focus on their development, supply-chains and models of production. Furthermore, many have recognised that, despite the important role played by digital technologies and innovation in the development of the creative industries, these dynamics are hard to capture and quantify. Digital technologies are embedded in the production and market structures of the creative industries and are also partially distinct and discernible from it. They also seem to play a key role in innovation of access and delivery of creative content. This chapter tries to assess the role played by digital technologies focusing on a key element of their implementation and application: human capital. Using student micro-data collected by the Higher Education Statistical Agency (HESA) in the United Kingdom, we explore the characteristics and location patterns of graduates who entered the creative industries, specifically comparing graduates in the creative arts and graduates from digital technology subjects. We highlight patterns of geographical specialisation but also how different context are able to better integrate creativity and innovation in their workforce. The chapter deals specifically with understanding whether these skills are uniformly embedded across the creative sector or are concentrated in specific sub-sectors of the creative industries. Furthermore, it explores the role that these graduates play in different sub-sector of the creative economy, their economic rewards and their geographical determinants.