## Constraining the Abel Bending Angle Integral

In the middle atmosphere where water concentrations are low, radio occultations profile temperature, pressure, and density by determining density versus altitude and combining that with a boundary condition on the hydrostatic integral. Density is derived from refractivity which is derived from bending angle derived in turn from the atmospheric Doppler shift. Maximizing the upper altitude of the bending angle profile requires minimizing errors in the atmospheric Doppler profile. Minimization is achieved via a combination of much higher frequencies to reduce ionospheric sensitivity, use of excellent reference oscillators in combination with GPS to further calibrate the oscillator errors, maximizing the signal-to-noise ratio (SNR) and very accurate reconstruction of the orbits.

A key question is at what altitude in an occultation does observational noise become sufficiently smaller than the atmospheric Doppler signature that accurate profiling of the atmosphere can begin. Frequency variations of a 10-13 ultra stable oscillator (USO) are approximately 10 times less than the atmospheric Doppler near 85 km altitude (Kursinski et al. 1997). GPS measurements made during the occultations can be used to estimate and remove USO frequency variations at time scales of several seconds or longer (limited by the GPS SNR). Such an error reduction can extend a low vertical resolution bending angle profile higher by a scale height or more and extend the Abel integral that derives refractivity. Conceivably, if every ATOMMS instrument in orbit were to radiate occultation signals such that occultation signals travel in both directions, the USO errors can be cancelled as is done on GRACE (e.g., Dunn et al.2003). This approach will be used in the ATOMMS aircraft to aircraft occultation demonstration.

Orbital inaccuracy is an important source of error. To be 10% of the atmospheric Doppler at 85 km, the velocity error along the occultation path direction must be 0.03 mm/s or less. A beauty of the occultations is that any slowly varying error such as that due to a bias in the orbital velocity will be evident as a non-zero signal frequency (after orbital motion has been removed) at altitudes above the detectable atmosphere. Any such non-zero frequency and slow variation above the detectable atmosphere can be fitted and extrapolated down through altitudes where the atmosphere is detectable to reduce the errors due to orbit and other sources below those of the reference oscillator. Such an approach has been used in planetary occultations where the orbit reconstructions are less accurate.

We estimate that ATOMMS will derive accurate, high vertical resolution bending angle profiles to at least 80 km altitude, approximately consistent with Kursinski et al. (2002).

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