## 2 Principles of GNSS Remote Sensing Technique  
### Gnss Ro  
When a low LEO satellite equipped with an RO receiver ascends or descends, the receiver intercepts electromagnetic waves emitted by GNSS satellites that have undergone atmospheric refraction, which constitutes an occultation event [15]. If the atmosphere were a vacuum, the propagation path of the radio signals from the GNSS satellite to the LEOsatellite receiver would be a straight line connecting the two satellites. However, in the real atmosphere, the radio signals bend toward the region of higher atmospheric refractivity, creating a curved path. Due to the density of the atmosphere, the atmospheric refractivity decreases exponentially with altitude, with the refractivity gradient being strongest in the vertical direction. This gradient is primarily influenced by local weather systems, particularly by the water vapor field in the lower troposphere. Consequently, the radio signal path in an occultation event generally bends toward the Earth's surface, with the maximum bending occurring near the point where the path is closest to the Earth's surface. Figure 2 illustrates the principle of RO.  
The initial data of RO observation are the variation in optical path lengths at two L band frequencies. Firstly, based on precise orbital positioning and stable atomic clocks, the variation in the optical path length can be used to determine the excess optical path length. The excess optical path length is the difference between the optical path length in the real atmosphere and the vacuum atmosphere, representing the effect of the actual atmosphere on the optical path. Then, under the assumption of spherical symmetry, the excess optical path length can be used in conjunction with satellite geometry to determine the bending angle. After that, through Abel integral inversion (1), the atmospheric refractivity in the vertical can be derived as Equation (1)  
\[n(r)=exp\left(-\frac{1}{\pi}\int_{r}^{\infty}\frac{d\alpha}{dr^{\prime}}\frac {dr^{\prime}}{\sqrt{r^{\prime 2}-r^{2}}}\right) \tag{1}\]  
where \(n(r)\) is the refractivity with \(r\), \(r\) is the distance between the Earth's center and observation, and \(\alpha\) is the bending angle, which will change by broadcasting through the atmosphere.  
If the influence of atmospheric moisture is neglected, the refractivity can be used to calculate the temperature in dry atmospheric conditions using the hydrostatic Equations (2) and (3)  
\[\frac{dp}{dh}=-\rho g \tag{2}\]  
Figure 2: The geometric relations of RO and GNSS-R.  
where \(p\) is the atmospheric pressure, \(h\) is height, \(\rho\) is the density of the atmosphere, and \(g\) is gravitational acceleration;  
\[N=n\times 10^{6}=77.6\frac{p}{T} \tag{3}\]  
where \(N\) is the refractivity index, \(n\) is the atmospheric refractivity at a certain height, \(p\) is atmospheric pressure in mbar, and \(T\) is the temperature in Kelvin.  
If considering the impact of water vapor, to retrieve the moisture, the relationship among the refractivity index, atmospheric pressure, temperature, and water vapor partial pressure becomes  
\[N=n\times 10^{6}=77.6\frac{p}{T}+3.37\times 10^{5}\frac{e}{T^{2}} \tag{4}\]  
where \(e\) is the water vapor partial pressure in mbar. We can analyze a priori temperature field [16] and then use a one-dimensional variational method to obtain the atmospheric profile.  
Figure 3 shows examples of GNSS RO profiles of temperature and humidity for tropical cyclones.  
Figure 3: Typhoon Hondo in 2008 best-track and co-located ROs (**a**). TD (tropical depression), TS (tropical storm), and Cat. 1–4 means 1 min maximum sustained wind speed (m/s) \(\leq\) 17, 18–32, 33–42, 43–49, 50–58, and 58–70 respectively. From the surface to 25 km altitude temperature (**b**) and specific humidity (**c**) profiles in the storm [17].