Confidence Intervals and Significance Tests for Spherical Data Derived from Feature Tracking

Abstract

A methodology is described that improves the efficiency with which statistical estimates of the distribution and mean attributes of dynamical weather systems, such as extratropical cyclones and tropical easterly waves, are derived from ensembles of the system trajectories using spherical kernel estimators. The improvement in the application of the spherical kernel estimators facilitates the use of the resampling methodology to estimate confidence intervals for weather system climatologies and to perform significance tests for the comparison between estimates derived from separate samples, for example, when the track data are partitioned with respect to teleconnection indices. The improvement in the statistical estimation makes use of spherical quad tree data structures based on a hierarchical decomposition of the sphere into spherical triangles into which the data and estimation points are partitioned. Examples are shown of the application of the new methodology to extratropical cyclones identified in reanalysis data of confidence intervals for the climatology and significance tests for differences between the positive and negative phases of the North Atlantic Oscillation teleconnection.