Atmospheric limitations to clock synchronization at microwave frequencies

Clock synchronization schemes utilizing microwave signals that pass through the Earth's atmosphere are ultimately limited by our ability to correct for the variable delay imposed by the atmosphere. The atmosphere is non-dispersive at microwave frequencies and imposes a delay of roughly 8 nanosec times the cosecant of the elevation angle. This delay is composed of two parts, the delay due to water vapor molecules (i.e., the wet delay), and the delay due to all other atmospheric constituents (i.e., the dry delay). Water vapor contributes approximately 5 to 10% of the total atmospheric delay but is highly variable, not well mixed, and difficult to estimate from surface air measurements. However, the techniques of passive remote sensing using microwave radiometry can be used to estimate the line of sight delay due to water vapor with potential accuracies of 10 to 20 picosec. The devices that are used are called water vapor radiometers and simply measure the power emitted by the water vapor molecule at the 22.2 GHz spectral line. An additional power measurement is usually included at 31.4 GHz in order to compensate for the effect of liquid water (e.g., clouds). The dry atmosphere is generally in something close to hydrostatic equilibrium and its delay contribution at zenith can be estimated quite well from a simple barometric measurement. At low elevation angles one must compensate for refractive bending and possible variations in the vertical refractivity profile. With care these effects can be estimated with accuracies on the order of 30 picosec down to elevation angles of 10 degree.