An update to the expression of atmospheric refractivity for GNSS signals

Abstract. This study revisits previous formulations of atmospheric refractivity at L-band frequencies, focusing on signals from Global Navigation Satellite Systems (GNSS). A refined model expression is proposed as a function of air density, temperature, and composition, evaluated using a comprehensive set of existing laboratory and atmospheric measurements. The key measurements that most affect the final accuracy are identified, establishing traceable error bounds and indicating where further experimental work could confirm or improve the model.

Recent studies on the use of large volumes of GNSS radio occultation (GNSSRO) observations in Numerical Weather Prediction (NWP) show that the precise formulation of refractivity becomes increasingly critical as data volumes grow. Although the revision is modest, its impact lies within the range where NWP sensitivity becomes non-negligible.

Compared to earlier work, this study (1) incorporates updated fundamental measurements, (2) accounts for the small but measurable variability in atmospheric composition, mainly increasing CO₂ and decreasing O₂, emphasizing that refractivity traceability is composition-dependent, and (3) extends the model to include hydrometeors. A simplified formulation based on hydrometeor oblateness is proposed, suitable for NWP applications where only limited hydrometeor information is available. Nonspherical hydrometeors tend to align during fall, introducing weak birefringence that can be detected during GNSS occultations with dual-polarization receivers.

The resulting refractivity expression is presented as a function of air density, temperature, moisture, and composition, and (using a simplified model of atmospheric evolution) also as a function of density, temperature, moisture, and time.