Accounting for Errors when Projecting Data onto a TC-Centered Space

Much tropical cyclone (TC) research requires quantities which are defined relative to the TC center (e.g. radial and tangential wind). Given that most data is defined in Earth-relative coordinates, a transformation and/or interpolation to a TC-centered coordinate system must be done. The approximations associated with such a transformation are thus important to any results derived from such quantities.

A common approach for data points in latitude-longitude space is to compute zonal and meridional distances from the TC center, thus defining a Cartesian (x, y) space about the TC. These coordinates could then be used to calculate radii and azimuths with respect to the TC, thus forming a polar space with the TC centered at the origin. However, this transformation does not preserve angles and distances along rays extending from the TC center, thus introducing errors in procedures that composite or compute TC-relative quantities.

An Azimuthal Equidistant projection (Snyder 1987) centered on the TC will correct these errors, allowing local radial and azimuthal directions relative to the TC to be true. For vectors, an additional transform must be applied in order to properly orient the vectors within the projected space. This more appropriately defined TC-centered polar space facilitates accurate calculation of radial and tangential wind, and any quantities derived therefrom.

This poster presentation provides examples of real-world fields mapped to this projection, along with errors in various quantities that can result from using less exact transformations.