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Experiments near Puerto Rico around World Ionosphere Days in June 1998 and September 1999 were carried out to develop and test techniques for nowcasting and forecasting ionospheric electron density and space weather during quiet and disturbed geomagnetic conditions. We investigate the use of GPS data for this purpose. We use the Raytrace/ ICED-Bent-Gallagher (RIBG) ionospheric model, line-of-sight propagation, and the assumption of constant differential hardware biases to model two-frequency GPS data. Discrete inverse theory is used to extract model parameters from the data. We avoid the traditional simplifying approximation of a fixed-height spherical shell model for mapping slant to vertical TEC. We show that our method is practical, provides accuracy superior to the traditional methods, and is robust against geomagnetic disturbances.