The authors thank Mark Bourassa and Vasubandhu Misra of The Florida State University for their feedback on the thesis on which this work was based. Additionally, the authors thank two anonymous reviewers for their helpful comments on this manuscript. Data support for the PREDICT field experiment is provided by NCAR/EOL under sponsorship of the National Science Foundation. This work was funded through NASA Genesis and Rapid Intensification Processes (GRIP) Grant NNX09AC43G.
Bellamy, J. C., 1949: Objective calculations of divergence, vertical velocity, and vorticity. Bull. Amer. Meteor. Soc., 30, 45–49.
Bourassa, M. A., , and K. M. Ford, 2010: Uncertainty in scatterometer-derived vorticity. J. Atmos. Oceanic Technol., 27, 594–603.
Davies-Jones, R., 1993: Useful formulas for computing divergence, vorticity, and their errors from three or more stations. Mon. Wea. Rev., 121, 713–725.
Helms, C. N., , and R. E. Hart, 2012: The evolution of dropsonde-derived vorticity in developing and nondeveloping tropical convective systems. Preprints, 30th Conf. on Hurricanes and Tropical Meteorology, Ponte Vedra, FL, Amer. Meteor. Soc., 10A.2. [Available online at https://ams.confex.com/ams/30Hurricane/webprogram/Paper205957.html.]
Lee, D. T., , and B. J. Schachter, 1980: Two algorithms for constructing a Delaunay triangulation. Int. J. Comput. Info. Sci., 9, 219–241.
Lloyd, E. L., 1977: On triangulation of a set of points in the plane. MIT Laboratory for Computer Science Tech. Rep. MIT/LCS/TM-88, 13 pp.
Montgomery, M. T., and Coauthors, 2012: The Pre-Depression Investigation of Cloud Systems in the Tropics (PREDICT): Scientific basis, new analysis tools, and some first results. Bull. Amer. Meteor. Soc., 93, 153–172.
Spencer, P. L., , and C. A. Doswell, 2001: A quantitative comparison between traditional and line integral methods of derivative estimation. Mon. Wea. Rev., 129, 2538–2554.
By maximizing the minimum angle, the total of the other angles must see a corresponding decrease. This results in the angles and edge lengths becoming closer in size to one another. There are two possible methods by which this can occur: the short edges can grow or the longer edges can shrink. Increasing the length of the short edges requires constructing a larger triangle that will have data points located within its bounds. As a Delaunay triangulation is constructed such that no point may lie within a circle that circumscribes a triangle in the tessellation, the first method is not a viable solution. Hence, the longer edges must shrink, resulting in smaller triangle sizes in general (but not necessarily for each individual triangle).