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.

Climatology of polar lows over the Sea of Japan using the JRA-55 reanalysis

Polar lows are intense meso- a -scale cyclones that develop over the oceans poleward of the main baroclinic zone. A number of previous studies have reported polar low formation over the Sea of Japan within the East Asian winter monsoon. To understand the climatology of polar lows over the Sea of Japan, a tracking al- gorithm for polar lows is applied to the recent JRA-55 reanalysis. The polar low tracking is applied to 36 cold seasons (October–March) from October 1979 to March 2015. The polar lows over the Sea of Japan reach their maximum intensity on the southeastern side of the midline between the Japanese islands and the Asian continent. Consistent with previous case studies, composite analysis demonstrates that the polar low devel- opment is associated with the enhanced northerly flow on the western side of a synoptic-scale extratropical cyclone, with the cold trough in the midtroposphere and with increased heat fluxes from the sea surface. Furthermore, the present climatological study has revealed two dominant directions of motion of the polar lows: southward and eastward. Southward-moving polar lows are steered by a strong northerly flow in the lower troposphere, which is enhanced on the western side of synoptic-scale extratropical cyclones, while the eastward-moving polar lows occur within a planetary-scale westerly flow in the midlatitudes. Thus, the di- rection of polar low motion reflects the difference in planetary- and synoptic-scale conditions.