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Chris J. Theisen, Paul A. Kucera, and Michael R. Poellot


Tropical thunderstorms produce large amounts of cirrus anvil clouds, which have a large effect on the climate system. Modeling of the cirrus anvil is a very important factor in the driving processes in atmospheric, climate, and radiation budget models. The current research project is focused on determining the relationships between the thunderstorm intensity and cirrus anvil characteristics of storms during the Cirrus Regional Study of Tropical Anvils and Cirrus Layers–Florida Area Cirrus Experiment (CRYSTAL-FACE). During July 2002, 19 different storms were selected for analysis. A vertical profile of reflectivity was extracted for each cell in which the maximum reflectivity, and maximum 10- and 40-dBZ height were identified. A majority of the thunderstorms in this study were single cells or isolated multicell clusters initiated from outflow boundaries or sea-breeze interactions. The results show that a general thunderstorm life cycle characteristic time sequence was determined, finding that the maximum reflectivity occurred on average 10 min after the cell first appeared in the base scan reflectivity image. The anvil origin and maximum height were found to occur approximately 10 and 25 min after maximum reflectivity, respectively. The anvil’s mean particle size was found to increase with time and decrease with altitude. The opposite relationship holds true for the particle concentration. Contour analysis has shown that the particle size increased with increased thunderstorm intensity and time after maximum reflectivity. An increase in convective core intensity corresponds to increased anvil particle concentrations early after maximum reflectivity, as was observed.

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Mark A. Askelson, Chris J. Theisen, and Randall S. Johnson


Owing to their ease of use, “simplified” propagation models, like the equivalent Earth model, are commonly employed to determine radar data locations. With the assumption that electromagnetic rays follow paths of constant curvature, which is a fundamental assumption in the equivalent Earth model, propagation equations that do not depend upon the spatial transformation that is utilized in the equivalent Earth model are derived. This set of equations provides the true constant curvature solution and is less complicated, conceptually, as it does not depend upon a spatial transformation. Moreover, with the assumption of constant curvature, the relations derived herein arise naturally from ray tracing relations. Tests show that this new set of equations is more accurate than the equivalent Earth equations for a “typical” propagation environment in which the index of refraction n decreases linearly at the rate dn/dh = −1/4a, where h is height above ground and a is Earth’s radius. Moreover, this new set of equations performs better than the equivalent Earth equations for an exponential reference atmosphere, which provides a very accurate representation of the average atmospheric n structure in the United States. However, with this n profile the equations derived herein, the equivalent Earth equations, and the relation associated with a flat Earth constant curvature model produce relatively large height errors at low elevations and large ranges. Taylor series approximations of the new equations are examined. While a second-order Taylor series approximation for height performs well under “typical” propagation conditions, a convenient Taylor series approximation for great circle distance was not obtained.

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