GPS-RO
5 Atmospheric profile retrieval
6 Multipath propagation in the troposphere
The GPS (Global Positioning System) consists of 25 satellites, distributed in 6 orbital planes about the globe. Each satellite is circular orbit, with an inclinaition of about 55°, a period of 12 hours and an altitude of 20,231 km. The atmospheric scientists have taken advantage of the capabilities of GPS and now Atmospheric Radio Occultation is a potentially valuable new application of the GPS.
The current development of small, high-performance instrumentation to receive GPS signals create an opportunity for active remote sounding of the earth’s atmosphere by radio occultation at comparatively low cost.
A schematic representation of atmospheric profiling by GPS Radio Occultation, using a
receiver in LEO (Low Earth Orbit), is given in the following figure
From the standpoint of the receiver, an occultation occurs whenever a GPS satellite rises
or sets and the ray path from its transmitter traverses the Earth's atmospheric limb. When
this signal passes through the Earth’s atmosphere, it is refracted and delayed by
variations in the index of refraction, producing distinctive variations in the amplitude
and the phase of the received signal. As the geometry changes, the radio waves sample
successively deeper and thus denser layers of the atmosphere. From the variation in
amplitude and phase of the signal, these limb sounding measurements are used to retrieve a
vertical profile of the index of refraction. From this significant profile parameters like
density, pressure, temperature, water-vapour, and electron density may be derived.
Radio occultation measurement represent a nearly instantaneous representation of the atmospheric state, in that such a measurement takes the order of one or two minutes for one profile, compared with a radiosonde ascent of 90 minutes. A radiosonde measurement usually end between 20 and 30 km, whereas Radio occultation measurement allow retievals up to 40 km.
A Low Earth Orbit (LEO) receiver orbiting in a near polar orbit at about 800 km.
Using the 25 GPS satellites, will observe over 500 occultation per day and this number
can be doubled if the receiver is also capable of receiving signals from the Russian
GLONASS constellation. The folloowing figure shows an exemple of radio occultation for one
day.
from Kursinski et al., 1996
To extract atmospheric information from the receiver (Meteorological receiver on LEO satelite) data, first the position of the LEO on its orbit must be determinated. This task can be achieved using several other GPS satellites and ground stations The principe to determine this position is shown on the figure below.
Once the LEO-GPS configuration is known accurately, the GPS measurements of an occulting LEO can be interpreted in terms of atmospheric delay. This delay is, in part, caused by the neutral atmosphere and in part by the ionosphere. The ionospheric delay must be corrected. The effect of the ionosphere on the GPS signal is larger and far more variable than the effect of the neutral atmosphere. To correct it, one exploits the dual frequency signals transmitted by the GPS satellite. We expect that this ionospheric correction can be carried out without significant additional error for low occultation paths, and therefore we will not describe it in detail.
In the geometrical optics approximation, a ray passing through the atmosphere is refracted according to Snell’s law (Descartes’law) due to the vertical gradient of refractive index. The overall effect of the atmosphere can be characterized by a total bending angle a , an impact parameter a, and a tangent radius rt defined innext figure depicting the instantaneous GPS-LEO occultation geometry.
Durinng an occultation, the variation of a with a depends primarily on the vertical profile of atmospheric refractive index. This profile can be retrieved from measurements of a as a function of a. during the occultation, subject to the assumption of local spherical symmetry.
The time dependence of both a and a during an occultation can be derived from accurate measurement of the Doppler-shifted frequency of the transmitter signal at the receiver.
The Doppler-shift is determined by the projection of spacecraft velocities onto the ray paths at the transmitter and receiver, so that atmospheric bending contributes to the measured Doppler shift.
The Doppler frequency shift fd is related to the phase j
= RLG + D j .
This Doppler frequency is obtained from the derivative with respect to time of the phase j . So we have :
This is the data observable.
Data from several GPS transmitters and post-processing ground stations can be used to establish the precise positions and velocities of the GPS transmitters and LEO satellites. These derived positions are used to calculate the Doppler shift expected in the absence of atmospheric bending.
The atmospheric contribution to Doppler shift, derived by substracting the expected shift from the measured shift, it is called the excess Doppler shift and is the type of data provided by the GPS/MET (UCAR GPS meteorological mision). These data can then be combined with satellite position and velocity knowledge to give an estimate of a and a.
The profile of atmospheric refractive index can be retrieved from measurements of a . Since the refractive index of the media contains information about temperature, pressure and water vapour, we could retrieve these profiles making several assumption, from a profile of atmospheric refractive index.
For each observational epochs , a bending angle a is calculated from the excess phase derived from the phase observations and expected Phase calculated from the GPS LEO geometry.
Here the refractive index within each layer is assumed to be constant. To retrieve the refractive index for the layer i, the bending angle associated with all the upper layers from i to the first one is required. It is the principe of the oinion pealing as shown in next figure. In this figure you can see how the profile of refractivity is calculate from the set of bending angles.
5 Atmospheric profile retrieval
In the atmosphere, refractivity is given by the relation:
N : refractivity
P : atmospheric pressure [mbar]
Pw : water vapor [mbar]
ne : electron number density per cubic meter [number of electron/m3]
f : transmitter frequency [Hz]
w : liquid water content [g/m3]
We can neglect the liquid water content and after correcting for the ionosphere, only the dry and moist atmospheric contributions to refractivity remain. The correction for the ionosphere allows to estimate the electron density.
In this case the refractivity is
In regions where the atmosphere is drier than a volume mixing ratio of 10-4, the moist term can be negled and N begin :
In this case we can get density, pressure and temperature profile from refractivity.
The relation between virtual temperature Tv and temperature T is :
= 0.622
Rd = 287 J deg-1 kg-1 : Gas constant for 1 kg dry air.
With a dry atmosphere, we have Pw = 0 so that Tv = T, thus
then as 
we have 
and finally we get the air density 
from
the refractivity
N is derived from the occultation measurement as described in previous section.
Now we will retrieve the pressure profile from the density profile. Pressure can be obtain
from density by integrating the equation of hydrostatic equilibrium:
g = 9.81 m s-2
For the simple model of atmosphere : 
:
, 
or 
In theory, the upper integration limits of this hydrostatic integral extend to an
infinite altitude whereas the occultation observations do not. This limitation introduce
error in refractivity, density, pressure and temperature at altitudes below zu The
relative error decrease with decreasing altitude. It is therefore desirable to have zu
as high as possible.
From the pressure profile, it is now possible to retrieve the temperature profile. we can
either use the refractivity and pressure profile : 
or we can use the density and pressure profile : 
The presence of significant tropospheric water vapor complicates the interpretation of refractivity. However, in the colder tropospheric regions, where water vapor concentrations are small, accurate profiles of density, pressure, and temperature can be retrieved, given an estimate of humidity.
6 Multipath propagation in the troposphere
The first result from the GPS/MET program of radio sounding of the Earth’s atmosphere indicates that the interpretation of the phase measurements encounters difficulties in the lowest 5 km of the atmosphere. The complicated structure of atmospheric refractivity in the lower troposphere, especially in tropical regions, results not only in degrading of the accuracy of the reconstruction of refractivity due to insufficient horizontal resolution but may also result in multipath propagation, i.e., the situation when several different rays arrive at the receiver simultaneously. Analysis of the GPS/MET radio occultations indicates that this situation is a rule rather than an exception.
Multipath occurs when strong refractivity gradient are present. During multipath, you have more than one signal arriving at the receiver. Since these signals come from different directions as seen by the receiver and have traveled paths of different lenghts, their phase are different.
The signal input to the receiver is the superposition of the different signals which contains different phases and amplitudes. This signal contaminated with strong oscillations of the phase and amplitude, impedes tracking of the signal and can result in the receiver losing the signal. Indeed the PLL (Phase Lock Loop, which is used in the receiver to perform carrier acquisition) will attempt to track the strongest signal, i.e. the signal with the largest amplitude but, if the signals are close in amplitude and frequency, the PLL will have trouble detecting a single peak in the correlator and will lose lock (see annex 5).
One issue to improve this problem is to have the receiver track in open loop mode, In this mode which is included in the GRAS receiver, the receiver delivers the output raw correlator. From these time series which include the superimposed multipath signal, one can reconstruct the refractivity profiles, in the ideal scenario. However this scenario requires the elaboration of special method in order to have correct interpretation of the measurements of the signal in the multipath area.
A paper (Algorithm of inversion of Microlab-1 satellite data including effects of multipath propagation : M. E. Gorbunov and A. S. Gurvich : Int. J. Rmote Sensing, 1998, vol. 19, No. 12, 2283-2300) propose an algorithm of processing of radio occultation data, based on the theory of diffraction using data recorded in Open loop mode.
Page last modified 26 aout-1999
Mail to jh@acri.fr