Variational Principles on Geometric Rough Paths and the L\'{e}vy Area Correction

In this paper, we describe two effects of the L\'evy area correction on the invariant measure of stochastic rigid body dynamics on geometric rough paths. From the viewpoint of dynamics, the L\'evy area correction introduces an additional deterministic torque into the rigid body motion equation on geometric rough paths. When the dynamics is driven by coloured noise, and for rigid body dynamics with double-bracket dissipation, theoretical and numerical results show that this additional deterministic torque shifts the centre of the probability distribution function by shifting the Hamiltonian function in the exponent of the Gibbsian invariant measure.Comment: 39 pages, 9 figures, 3rd version, comments welcom

Improving the inter-hemispheric gradient of total column atmospheric CO₂ and CH₄ in simulations with the ECMWF semi-Lagrangian atmospheric global model

It is a widely established fact that standard semi-Lagrangian advection schemes are highly efficient numerical techniques for simulating the transport of atmospheric tracers. However, as they are not formally mass conserving, it is essential to use some method for restoring mass conservation in long time range forecasts. A common approach is to use global mass fixers. This is the case of the semi-Lagrangian advection scheme in the Integrated Forecasting System (IFS) model used by the Copernicus Atmosphere Monitoring Service (CAMS) at the European Centre for Medium-Range Weather Forecasts (ECMWF). Mass fixers are algorithms with substantial differences in complexity and sophistication but in general of low computational cost. This paper shows the positive impact mass fixers have on the inter-hemispheric gradient of total atmospheric column-averaged CO₂ and CH₄, a crucial feature of their spatial distribution. Two algorithms are compared: the simple "proportional" and the more complex Bermejo-Conde schemes. The former is widely used by several Earth system climate models as well the CAMS global forecasts and analysis of atmospheric composition, while the latter has been recently implemented in IFS. Comparisons against total column observations demonstrate that the proportional mass fixer is shown to be suitable for the low-resolution simulations, but for the high-resolution simulations the Bermejo-Conde scheme clearly gives better results. These results have potential repercussions for climate Earth system models using proportional mass fixers as their resolution increases. It also emphasises the importance of benchmarking the tracer mass fixers with the inter-hemispheric gradient of long-lived greenhouse gases using observations

Improving the inter-hemispheric gradient of total column atmospheric CO2 and CH4 in simulations with the ECMWF semi-Lagrangian atmospheric global model

It is a widely established fact that standard semi-Lagrangian advection schemes are highly efficient numerical techniques for simulating the transport of atmospheric tracers. However, as they are not formally mass conserving, it is essential to use some method for restoring mass conservation in long time range forecasts. A common approach is to use global mass fixers. This is the case of the semi-Lagrangian advection scheme in the Integrated Forecasting System (IFS) model used by the Copernicus Atmosphere Monitoring Service (CAMS) at the European Centre for Medium-Range Weather Forecasts (ECMWF). Mass fixers are algorithms with substantial differences in complexity and sophistication but in general of low computational cost. This paper shows the positive impact mass fixers have on the inter-hemispheric gradient of total atmospheric column-averaged CO2 and CH4, a crucial feature of their spatial distribution. Two algorithms are compared: the simple "proportional" and the more complex Bermejo-Conde schemes. The former is widely used by several Earth system climate models as well the CAMS global forecasts and analysis of atmospheric composition, while the latter has been recently implemented in IFS. Comparisons against total column observations demonstrate that the proportional mass fixer is shown to be suitable for the low-resolution simulations, but for the high-resolution simulations the Bermejo-Conde scheme clearly gives better results. These results have potential repercussions for climate Earth system models using proportional mass fixers as their resolution increases. It also emphasises the importance of benchmarking the tracer mass fixers with the inter-hemispheric gradient of long-lived greenhouse gases using observations

Variational principles on geometric rough paths and the Lévy area correction

In this paper, we describe two effects of the Lévy area correction on the invariant measure of stochastic rigid body dynamics on geometric rough paths. From the viewpoint of dynamics, the Lévy area correction introduces an additional deterministic torque into the rigid body motion equation on geometric rough paths. When the rigid body dynamics is driven by colored noise, and damped by double-bracket dissipation, our theoretical and numerical results show that the additional deterministic torque due to the the Lévy area correction shifts the center of the probability distribution function by shifting the Hamiltonian function in the exponent of the Gibbsian invariant measure

Incorporating bio-physical sciences into a decision support tool for sustainable urban planning

Deciding upon optimum planning actions in terms of sustainable urban planning involves the consideration of multiple environmental and socio-economic criteria. The transformation of natural landscapes to urban areas affects energy and material fluxes. An important aspect of the urban environment is the urban metabolism, and changes in such metabolism need to be considered for sustainable planning decisions. A spatial Decision Support System (DSS) prototyped within the European FP7-funded project BRIDGE (sustainaBle uRban plannIng Decision support accountinG for urban mEtabolism), enables accounting for the urban metabolism of planning actions, by exploiting the current knowledge and technology of biophysical sciences. The main aim of the BRIDGE project was to bridge the knowledge and communication gap between urban planners and environmental scientists and to illustrate the advantages of considering detailed environmental information in urban planning processes. The developed DSS prototype integrates biophysical observations and simulation techniques with socio-economic aspects in fiveEuropean cities, selected as case studies for the pilot application of the tool. This paper describes the design and implementation of the BRIDGE DSS prototype, illustrates some examples of use, and highlights the need for further research and development in the field

R : Regio- and Enantioselective asymmetric transfer hydrogenation of one Carbonyl group in a diketone through steric hindrance

On the basis of steric hindrance, one carbonyl group in a diketone can be reduced in a regioselective manner, with high enantioselectivity. The methodology can be extended to ketones with varied length of hydrocarbon chain spacing, and the products can be converted by oxidation to hydroxy esters or lactones without loss of enantiopurity