Feature tracking on the hierarchical equal area triangular mesh

A novel scheme is presented to enable the identification of weather-like features in meteorological data along with a method to track the features across timesteps. The scheme defines a hierarchical triangular mesh produced by repeatedly subdividing an icosahedron. The surface area of each triangle in the mesh is equalised by an iterative application of vertex repulsion, analogous to Coulomb's law. The scheme regrids meteorological data to the triangular mesh via a point inclusion test and area-weighted averaging. Weather-like feature points are detected in the regridded data via a search for extrema in adjacent triangles. These feature points are transformed into objects, such as a low pressure system, by growing the feature point into an area where the sign of the second derivative of the data remains unchanged. The centre points of these objects are tracked across timesteps by the application of a cost minimising algorithm which guarantees locally optimal tracks. By using this suite of methods, weather-like features are identified consistently at high and low latitudes, all weather-like features remain on the same scale and the tracking of features at high latitudes and across the Poles is enabled. These properties are demonstrated by test cases using synthetic data.

► An hierarchical triangular mesh is created by subdivision of an icosahedron.
► The area of the triangles in the mesh are equalised by vertex repulsion.
► Regridding of data from regularly spaced grids performed by area weighted averaging.
► Detection of weather-like features by adjacent triangle search for extrema.
► Locally optimal tracking of features by minimisation of a cost function.