Improving a global model from the boundary layer: total turbulent energy and the neutral limit Prandtl number

Model intercomparisons have identified important deficits in the representation of the stable boundary layer by turbulence parametrizations used in current weather and climate models. However, detrimental impacts of more realistic schemes on the large-scale flow have hindered progress in this area. Here we implement a total turbulent energy scheme into the climate model ECHAM6. The total turbulent energy scheme considers the effects of Earth’s rotation and static stability on the turbulence length scale. In contrast to the previously used turbulence scheme, the TTE scheme also implicitly represents entrainment flux in a dry convective boundary layer. Reducing the previously exaggerated surface drag in stable boundary layers indeed causes an increase in southern hemispheric zonal winds and large-scale pressure gradients beyond observed values. These biases can be largely removed by increasing the parametrized orographic drag. Reducing the neutral limit turbulent Prandtl number warms and moistens low-latitude boundary layers and acts to reduce longstanding radiation biases in the stratocumulus regions, the Southern Ocean and the equatorial cold tongue that are common to many climate models.

Resting-state functional connectivity following a single dose treatment with CB1 neutral antagonist tetrahydrocannabivarin (THCv) in healthy volunteers

BACKGROUND: The cannabinoid cannabinoid type 1 (CB1) neutral antagonist tetrahydrocannabivarin (THCv) has been suggested as a possible treatment for obesity, but without the depressogenic side-effects of inverse antagonists such as Rimonabant. However, how THCv might affect the resting state functional connectivity of the human brain is as yet unknown. METHOD: We examined the effects of a single 10mg oral dose of THCv and placebo in 20 healthy volunteers in a randomized, within-subject, double-blind design. Using resting state functional magnetic resonance imaging and seed-based connectivity analyses, we selected the amygdala, insula, orbitofrontal cortex, and dorsal medial prefrontal cortex (dmPFC) as regions of interest. Mood and subjective experience were also measured before and after drug administration using self-report scales. RESULTS: Our results revealed, as expected, no significant differences in the subjective experience with a single dose of THCv. However, we found reduced resting state functional connectivity between the amygdala seed region and the default mode network and increased resting state functional connectivity between the amygdala seed region and the dorsal anterior cingulate cortex and between the dmPFC seed region and the inferior frontal gyrus/medial frontal gyrus. We also found a positive correlation under placebo for the amygdala-precuneus connectivity with the body mass index, although this correlation was not apparent under THCv. CONCLUSION: Our findings are the first to show that treatment with the CB1 neutral antagonist THCv decreases resting state functional connectivity in the default mode network and increases connectivity in the cognitive control network and dorsal visual stream network. This effect profile suggests possible therapeutic activity of THCv for obesity, where functional connectivity has been found to be altered in these regions.

Mesh adaptation on the sphere using optimal transport and the numerical solution of a Monge-Ampère type equation

An equation of Monge-Ampère type has, for the first time, been solved numerically on the surface of the sphere in order to generate optimally transported (OT) meshes, equidistributed with respect to a monitor function. Optimal transport generates meshes that keep the same connectivity as the original mesh, making them suitable for r-adaptive simulations, in which the equations of motion can be solved in a moving frame of reference in order to avoid mapping the solution between old and new meshes and to avoid load balancing problems on parallel computers. The semi-implicit solution of the Monge-Ampère type equation involves a new linearisation of the Hessian term, and exponential maps are used to map from old to new meshes on the sphere. The determinant of the Hessian is evaluated as the change in volume between old and new mesh cells, rather than using numerical approximations to the gradients. OT meshes are generated to compare with centroidal Voronoi tesselations on the sphere and are found to have advantages and disadvantages; OT equidistribution is more accurate, the number of iterations to convergence is independent of the mesh size, face skewness is reduced and the connectivity does not change. However anisotropy is higher and the OT meshes are non-orthogonal. It is shown that optimal transport on the sphere leads to meshes that do not tangle. However, tangling can be introduced by numerical errors in calculating the gradient of the mesh potential. Methods for alleviating this problem are explored. Finally, OT meshes are generated using observed precipitation as a monitor function, in order to demonstrate the potential power of the technique.

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