An evaluation of a Procrustes shape analysis verification tool using idealized cases

A recently developed verification tool developed by the Department of Statistics at the University of Missouri-Columbia will be evaluated utilizing several idealized cases. The verification methodology utilizes a Procrustes fit for shape analysis of individual cells. The scheme also includes statistics based on intensity parameters for a complete verification solution. The information on the error based on size, translation, and rotation are combined with error based on intensity values via a penalty function. As the errors are residual sum of squares they are open-ended and this testing procedure allows the assessment of the scale such that (1) different forecast situations can be compared, (2) comparability can be achieved between the different components that make up the total error, and (3) suitable normalization factors can be found that take the previous issues into account to create a robust and practical verification scheme.

The idealized cases are a series of simple geometric objects, such as ellipsoids, and vary in intensity, intensity distribution within the cell, as well as orientation, size, and translation. These idealized cases highlight the usefulness of the new Procrustes verification scheme as it is able to decompose the error contribution of various attributes combined in the penalty function. Results will also be shown for a few real cases for completeness.