Fundamentally, the technique relies on the simple fact that a planet's atmosphere acts much like a spherical lens, bending and slowing the propagation of microwave signals passing through it tangent to the surface. The lens effect results from decreasing atmospheric density with altitude. If the positions of transmitting and receiving satellites are precisely known, the "atmosphere delay" can be measured precisely, the time derivative of which (Doppler) can be inverted to give atmospheric density vs. altitude.
For an Earth observing system based on the radio occultation technique, the cost of maintaining a constellation of Earth orbiting satellites transmitting on appropriate frequencies would be dominant. In contrast, the receiving satellites would be relatively inexpensive. It so happens that the GPS exists, is free of charge, and already has 24 satellites transmitting on frequencies suitable for occultation observations. Moreover, by using the GPS to derive the precise satellite positions, overall system complexity (and cost) are further reduced. Thus, there is a strong economic incentive to base an Earth radio occultation observing system on GPS.
The GPS satellites transmit on two L-band carrier frequencies: 1575.42 MHz (L1) and 1227.6 MHz (L2). Each carrier is phase modulated by a precise ranging code (P code) consisting of pseudo random bit sequences at 10.23 Mb/s. In addition, the L1 carrier is modulated in quadrature with a 1.023 Mb/s pseudo random bit sequence used for the coarse (or clear) acquisition code (C/A code). The transmit time, as kept by the clock onboard each GPS satellite, is precisely known for each bit in the sequence. A GPS receiver identifies the incoming code bits and measures their arrival time, as kept by the receiver clock, with a precision of better than 1% of a bit length (about 1 nsec or 30 cm for the P code). A priori GPS orbital positions and clock offsets between GPS satellites are broadcast to the user along with other information on a 50 bps data message superimposed on the L1 and L2 carriers. The difference between the known transmit time and observed arrival time is a measure of the distance between the satellite and receiver, plus the clock offset between transmitter and receiver clocks, a quantity referred to as "pseudorange." A receiver simultaneously measuring pseudorange to four satellites can instantaneously determine its three components of position and its time offset from GPS time, typically with an accuracy of 10-15 m and <1 microsecond respectively. Modern receivers can also measure and keep continuous count of carrier phase with a precision of better than .5% of a wavelength (~ 1 mm). Continuous phase can then be used to construct a record of position change with millimeter precision.
For reasons of national security, current U S Government policy calls for limiting access to the Precision Positioning Service (PPS), and the accuracy of the Standard Positioning Service (SPS). Two techniques are used to limit the access and the accuracy of GPS: Selective Availability (S/A) and/or Anti Spoofing (A/S). A/S is a process used to deny users access to the full capabilities of the system by encryption of the high rate P code normally required for high precision measurements. When so encrypted, the high rate code is referred to as the "Y code". Unless the user has the required "encryption key" to track the Y code, the user will not have access to the PPS. S/A is believed to involve the deliberate introduction of small, random errors in the satellite ephemeris data broadcast in the almanac, and in the carrier and/or clock frequency transmitted. Uncorrected, S/A can result in position errors on the order of 100 m.
For GPS/MET, access to the highest precision available from GPS is required. However, "Y Code receivers" and encryption keys are not needed. Instead, a "codeless receiver", capable of tracking the L2 carrier phase without explicit knowledge of the Y Code, is used. With respect to S/A, a UNAVCO study has shown that when Double Differencing (described below) is used in conjunction with synchronized receiver clocks, S/A is effectively canceled, just as normal clock and orbit errors are canceled.[12] Therefore, A/S and S/A do not impose any insurmountable limitation on the use of the GPS for occultation measurements.
In GPS precision geodesy, "Double Differencing" (DD) is employed to effectively cancel nearly all errors resulting from transmitter clock uncertainty and receiver clock biases. As illustrated in Figure 2 below, the DD technique starts by forming a "DD observable" from the linear combination of 4 observables, each with certain common errors. By differencing observations of a given GPS satellite at 2 receivers, clock errors and S/A dithering for that satellite are canceled. This is referred to as a Single Difference (SD). If SDs are formed for a second GPS satellite and differenced with the first SD, a DD is formed canceling errors common to the receiver clocks. For GPS/MET, a network of ground based receivers, located at precisely known fiducial sites, will be used in conjunction with the data collected from the GPS/MET LEO receiver to implement the DD technique.
TDL1 = 1.5336 *T (1)
T is the measurable difference in
delay between L1 and L2. The Doppler frequency offset, also affected by the
ionosphere, can be modeled with a similar linear correction:
fL2 - fL1) is the measurable
Doppler difference.[15]
Correcting for these ionospheric effects completes the first step in the
recovery of meteorological data from the observables.[16]The method described above provides a simple first order correction for ionospheric effects. In most ground based applications, where the L1 and L2 rays follow substantially identical paths, it is sufficient. And for GPS/MET, it will provide sufficient accuracy for soundings below 30 km. However, for profiles above 30 km, a more sophisticated ionospheric correction scheme is required. To meet the requirement, an advanced technique which takes into account the separation of the L1 and L2 rays is under development by the GPS/MET team.
, as shown in Figure 3 below.
The variation of with experiment geometry can be characterized
through use of an "impact parameter", a, defined as the perpendicular
distance between the center of the planet and the straight line followed by the
ray approaching the atmosphere. When combined with a precise knowledge of the
geometry (obtained concurrently from other GPS satellites), each sample of
phase data (corrected for ionospheric effects) can be converted to the
corresponding values for and a. This step is
straightforward and involves simple geometrical considerations, basic laws of
geometrical optics, and relativistic formulas for Doppler shifts.
For an atmosphere with local spherical symmetry (i.e., no significant
asymmetric horizontal variations in temperature or moisture), there is
a unique relationship between (a) and µ(r), the
atmospheric refractive index as a function of radius (r). The
refractive index profile µ(r) is then derived through an Abel transform
of the measurements of (a) obtained over the complete
occultation, as given in Eq. (3).
(3)
The assumption of spherical symmetry, required for the classical retrieval method, is a limitation which may need to be overcome to achieve the generality desired for an operational system. However, the error introduced by using the assumption of spherical symmetry may not be the dominant error source, and therefor may be acceptable for operational systems. A recent paper by Russian scientists Sokolovskiy and Gorbonov tend to support this possibility.[18] It should be noted that some state-of-the-art ray tracing algorithms developed for seismology do not depend on the assumption of spherical symmetry. We plan to explore the incorporation of these advanced algorithms in our refractivity retrieval approach.
N = (µ-1) * 106 (4)
N = 77.60 * (P/T) (5)
= 0.3484 * (P/T) (6)
is the air density in kg m-3. Equations (5) and (6)
show that is directly proportional to N for dry air, so
that (r) can be obtained easily from µ(r). Next, P(r)
can be obtained from (r) by integrating the equation of
hydrostatic equilibrium:dP/dh = -g
using Eq. (6). In summary, vertical profiles of , P, and
T can be obtained from µ(r) in a direct and simple manner.
The total refractive bending angle, , shown in
Figure 3 is greatly exaggerated. For the Earth's atmosphere, the
maximum bending angle is on the order of 0.02 radians ( 1deg. ). To place this
in perspective, the phase shift measurements made with the Voyager spacecraft
demonstrated that could be measured with an accuracy
approaching 10-8 radians. With comparable performance from a
space-borne GPS receiver, the refractive bending caused by the terrestrial
atmosphere could be resolved to about 1 ppm. It is this type of precision
in the radio measurements that leads to the expectation of obtaining high
precision vertical profiles of N, , P, and T
in regions of the atmosphere where the air is dry.
N = 77.60 * (P/T) + 3.730 * 105 * (Pw/T2) (8) (DRY TERM) (WET TERM)
, P, and T; the
effects of water vapor at variable and uncertain concentrations are
indistinguishable from the effects of background variations in temperature and
pressure.At altitudes above 8-10 km, this ambiguity is not a significant problem as the contribution to the refractive index by water vapor is usually much less than 2%. Similarly, the contribution of moisture to refractive index is negligible throughout the polar atmosphere during winter. In the lower troposphere, the water vapor limitations can be overcome by one of several means, such as use of auxiliary methods for estimation of water vapor content (e.g., through microwave radiometry or ground-based GPS measurements)[20] and use of independent temperature measurements at known locations (e.g., radiosondes, aircraft). For example, if the temperature profile in the troposphere was known from model calculations, then moisture profiles could be retrieved from the measurements. This approach will work best in tropical regions where the temperature profiles exhibit relatively small changes, but moisture fields change significantly in space and time. It should be emphasized that µ and N can still be determined accurately regardless of the abundance of water vapor.