As the GPS signals propagate from the GPS satellites to the receivers on the ground, they are delayed by the atmosphere. There is a dispersive effect of the ionosphere and a non-dispersive effect of the troposphere. This allows the ionospheric effects to be largely removed by a linear combination of dual frequency data, but not the tropospheric effects.
Once the ionospheric delay has been removed, the remaining atmospheric delay is due to the electrically neutral atmosphere which is non-dispersive to GPS frequencies. The neutral atmosphere consists of the stratosphere and the troposphere. Because the troposphere constitutes most of the neutral atmosphere, the neutral atmosphere is often referred to as the troposphere. The tropospheric delay consists of two components. The hydrostatic (or "dry") component that is dependent on the dry air gasses in the atmosphere and accounts for approximately 90% of the delay. And the "wet" component that depends on the moisture content of the atmosphere and accounts for the remaining effect of the delay. Although the dry component has the larger effect, the errors in the models for the wet component are larger than the errors in the models for the dry because the wet component is more spatially and temporally varying.
The dry component is not actually the true dry correction because it depends on the total pressure of the atmosphere which includes the partial pressure of the dry gasses and the partial pressure of the water vapor. Assuming static equilibrium and the ideal gas law, the hydrostatic delay is a linear function of total surface barometric pressure and can be modeled to millimeter level accuracy [Bevis et al., 1992].
In order to obtain accurate tropospheric corrections from a filter without aliasing other errors into the delay requires using precise orbits and accurate station positions and clocks. Typically the station positions have been solved for either through independent means or from GPS using independent troposphere data (such as radiometer). Multipath and tropospheric ray bending can be mitigated by employing a minimum elevation cut-off.
Because the effects of water vapor can be indistinguishable from the effects of background variations in temperature and pressure, the Total Zenith Delay (TZD) will be estimated and the wet component extracted later. TZD is estimated as a first order Gauss-Markov process or a random walk process (first order Gauss-Markov process with infinite correlation time) characterized by the process noise. See Bierman  for more information on Gauss-Markov processes in filters and Tralli and Lichten  for more information on estimating TZD.
Although the GPS satellites are rarely at zenith with respect to the receivers, the delay can be transformed by use of a mapping function from whatever direction the GPS signal is originating to zenith. Commonly this mapping function is inversely proportional to the sine of the elevation angle.
The Zenith Hydrostatic Delay (ZHD) can be calculated from the local surface pressure
where Ps is the surface pressure in millibars and f(lamda,H) is a factor accounting for the variation in gravitational acceleration with latitude and height. The ZHD subtracted from TZD yields the Zenith Wet Delay (ZWD).
Integrated Water Vapor (IWV) gives the total amount of water vapor that a signal from the zenith direction would encounter. Precipitable Water Vapor (PWV) is the IWV scaled by the density of water. IWV can be calculated from the ZWD by
where kappa is from
Rv is the specific gas constant and Tm is the integrated mean temperature given by:
Because the integrated mean temperature, Tm, is not known exactly, it can be related to the surface temperature linearly by the empirically derived formula:
using this relation yields an average error in PWV of less than 4% (which is still a conservative error estimate) [Yuan et al., 1993].
The horizontal resolution of the water vapor estimates is limited only by placement of GPS receivers. The vertical resolution is poor since only integrated column water vapor values are estimated. The current configuration of NOAA Environmental Research Lab's GPS-IPW network [Gutman, 1997]:
The data from these sites are processed and the products distributed. This picture shows a summary of the NOAA/ERL GPS-IPW Network Data Flow including data acquisition and data/products distribution [Gutman, 1997]:
The following 30 day time series comparison of GPS-IPW with radiosondes and a radiometer for Lamont, OK, shows the power of the GPS technique. The blue spike represents when the radiometer data was contaminated by rain. The GPS technique is still consistent with the radiosondes [Environmental Technology Laboratory Web Site].
At an instant in time, the data over a region can be presented as a contour plot of PWV over the region. The following contour is for Lamont, OK, on 11/1/95 [Gutman, 1997]:
Processing the GPS-IPW data in real-time could be accomplished by using the following process and dataflow summary. For adequate real-time coverage of the continental United States, approximately 800 sites would be required (100 km spacing) [Gutman, 1997].
NOAA Environmental Research
Forecast Systems Laboratory
UNAVCO's Real Time Water Vapor
Return to Water Vapor from GPS ReceiversThis page created for Remote Sensing course at the University of Texas at Austin.