### One can estimate the local refractivity of the atmosphere as a function of altitude.

A method of determining the radio refractivity of the atmosphere as a function of altitude involves processing of data acquired by airborne or mountain-top Global Positioning System (GPS) receivers from particular GPS satellites as those satellites rise above or fall below the horizon. Previously, data of this type ("GPS occultation data" for short) have been gathered from outside the atmosphere by GPS receivers in low orbits around the Earth and used to generate global refractivity profiles. With the help of temperature data from weather analysis, the refractivity profiles can be converted to water-vapor profiles. In contrast, the present method of utilizing data from GPS receivers located within the atmosphere (see figure) makes it possible to obtain refractivity profiles, and thus water-vapor profiles, that are not global averages and, instead, are averaged over smaller geographic regions wherein the GPS receivers are located. Such higher-resolution water-vapor profiles can be used in studies of regional weather.

For a GPS receiver and a GPS transmitter of interest, the raw GPS data used in the method include the phase delays of the L1 and L2 GPS signals, which are at wavelengths of 19.0 and 24.4 cm, respectively. Other GPS data that are needed in this method include the position of the transmitter of interest, the position of the receiver, and the clock data of the receiver and the transmitter of interest as determined partly from data received simultaneously from other GPS satellites.

By a mathematical derivation that greatly exceeds the scope of this article and that involves a ray-tracing model of propagation of GPS signals through a spherically symmetrical atmosphere, one can find the relationships among the data and other variables. Of particular relevance are the following:

- The relationship between the total bending angle (
*a*) of a GPS ray and the L1 and L2 phase delays;

- The index of refraction (
*n*) of the atmosphere as a function of radius (*r*) from the center of the Earth [*n*(*r*) is the desired information)];

- The parameter
*a*in the equation obtained by applying Snell's law of refraction to a ray propagating through a spherically symmetrical atmosphere [this equation is*nr*sin(*f*) =*a*, where*f*is the local angle between the direction of propagation and the radius vector]; and - An equation, derived from the preceding equation, that expresses the bending as an integral function of
*n*,*r*, and*a*:

In this method, the refractivity of the atmosphere is modeled as piecewise exponential with a scale height that changes from one atmospheric layer to the next. The scale heights and a normalizing value of refractivity are retrieved by minimizing, in a least-square sense, differences between (1) bending angles and refractivity determined from GPS data and (2) corresponding quantities obtained from the exponential model and ray-tracing.

The method has been tested by computational simulation for the case of a GPS receiver at an altitude of 5 km. The results of the test have been interpreted as suggesting that the method yields accurate profiles of refractivity at heights ranging from ground level to slightly above the receiver.

*This work was done by Cinzia Zuffada, George Hajj, and Robert Kursinski of Caltech for *NASA's Jet Propulsion Laboratory*. For further information, access the Technical Support Package (TSP) *free on-line at www.techbriefs.com/tsp* under the Physical Sciences category.*

*NPO-20704 *

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