Improving GNSS Tropospheric Tomography by Better Knowledge of Atmospheric Turbulence
Nilsson, T.
Chalmers University of Technology

Tomographic methods are applied to GNSS (Global Navigation Satellite System) data from a local network of GNSS receivers (baseline lengths of the order a few km) in order to estimate the 3D structure of the wet refractivity field of the troposphere. This is done by dividing the troposphere into a number of boxes (called voxels, volume pixels) and assume that the wet refractivity is constant in each voxel, thus describing the wet tropospheric path delays as linear combinations of voxel refractivities. Hence the GNSS phase observations is described by a linear system of equations in which the voxel refractivities are unknown, and solving the system gives the wet refractivity field. A problem with this technique is that the equation system will in general be ill conditioned due to weak geometry. This is especially true if the network of GNSS receivers is rather flat, i.e. the separation in height between the GNSS receivers is low. The problem is mostly in the vertical direction since the sensitivity of the GNSS observations to the vertical wet refractivity profile is rather low. Hence additional information needs to be used in order to do the tomographic inversion.

One way is to use theory of atmospheric turbulence to constrain the variations of the wet refractivity of the voxels both spatially and temporally. This can for example be implemented by using the turbulence theory to calculate the covariance matrix for the variations between the voxel refractivities and use this in a Kalman filter. One important parameter when describing the turbulence is the "wet refractivity structure constant". This parameter is varying both and as function of position and in time. To know the detailed profile at a specific time instant would require having access to measurements at that specific time. There exist methods to carry out such measurements, for example the structure constant profile could be calculated from high resolution radiosonde data. However, over a typical GNSS tomographic network such measurements may typically not be available, hence an approximate profile needs to be used. This could for example be a typical profile above the network obtained from e.g. a large number of high resolution radiosonde launches in the past. Less accurate would be to use a typical profile obtained from e.g. high resolution radiosonde launches at a site with the same climate as the region where the GNSS tomographic network is situated. This work assesses how much the accuracy of GNSS tomography will be affected by the knowledge of the structure constant. In the case statistics of the structure constant above the network from a long time period is available, it is investigated what structure constant profile which is best to use in the tomographic inversion, i.e. if it is better to use the average profile or a more extreme profile corresponding to the case when the atmosphere is more turbulent.

The investigations will be focused on using GNSS tomography for determining horizontal motions in the wet refractivity field. This is the case where GNSS tomography can be most useful. This is done by investigating how well a volume of air with e.g. higher refractivity moving over a GNSS network can be detected. It is investigated how the accuracy depend on e.g. the height of the volume and how accurately the structure constant profile is known. By using simulations we have perfect control over the fields to be estimated. It is also investigated if there is any difference between using data from both GPS and Galileo as compared to only using one GNSS, as well as the the dependence upon the size and geometry of the GNSS tomography network.