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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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Melissa Wagner, Robert K. Doe, Aaron Johnson, Zhiang Chen, Jnaneshwar Das, and Randall S. Cerveny
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Christopher S. Ruf, Robert Atlas, Paul S. Chang, Maria Paola Clarizia, James L. Garrison, Scott Gleason, Stephen J. Katzberg, Zorana Jelenak, Joel T. Johnson, Sharanya J. Majumdar, Andrew O’brien, Derek J. Posselt, Aaron J. Ridley, Randall J. Rose, and Valery U. Zavorotny


The Cyclone Global Navigation Satellite System (CYGNSS) is a new NASA earth science mission scheduled to be launched in 2016 that focuses on tropical cyclones (TCs) and tropical convection. The mission’s two primary objectives are the measurement of ocean surface wind speed with sufficient temporal resolution to resolve short-time-scale processes such as the rapid intensification phase of TC development and the ability of the surface measurements to penetrate through the extremely high precipitation rates typically encountered in the TC inner core. The mission’s goal is to support significant improvements in our ability to forecast TC track, intensity, and storm surge through better observations and, ultimately, better understanding of inner-core processes. CYGNSS meets its temporal sampling objective by deploying a constellation of eight satellites. Its ability to see through heavy precipitation is enabled by its operation as a bistatic radar using low-frequency GPS signals. The mission will deploy an eight-spacecraft constellation in a low-inclination (35°) circular orbit to maximize coverage and sampling in the tropics. Each CYGNSS spacecraft carries a four-channel radar receiver that measures GPS navigation signals scattered by the ocean surface. The mission will measure inner-core surface winds with high temporal resolution and spatial coverage, under all precipitating conditions, and over the full dynamic range of TC wind speeds.

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