Determining Geometry for Common Comparison Radar Space

As part of the Meteorological Service of Canada's intention for weather radar network stabilization and renewal, it is required to determine the consistency of our adjacent measurements and spatial coverage. A condition for the successful inter-radar comparison between two radars is the time-space synchronization in the middle region where the comparison is the most effective. We present a description of the theoretical basis for the geometrical evaluation of a common inter-radar space.

Since the radar locates the target volume in reference to the local reference system, it was necessary to convert local coordinates to a common “fixed” frame of reference. A geocentric coordinate system (GCS), in which the Earth is modeled as an oblate spheroid, was chosen as the prime framework with zero coordinates at the center of the Earth.

The position vector of a common target point of two radars relative to the GCS is the composition of the three vectors: a position vector from the geocentric origin to the surface of the oblate geoid at the geographical latitude and longitude of a radar location, an altitude vector that is normal to the oblate spheroid surface at the point of the radar location and which represents the height of the radar antenna above mean sea level, and at third vector is a local position vector of a common target point measured from the radar. Similarly, the location of the same target point from the second radar in reference to the GCS is given as a composition of the corresponding three vectors. Since the two sets of three vectors describe the position of same target with respect to the Earth centre, equating them results in three scalar equations. Our problem in turn has three unknowns.

We wish to define a target point at equal distance from both radars with a specified local azimuth and elevation in reference to each of the radars. Using the three scalar equations it is possible to obtain the local azimuth and elevation from the second radar as well as the equal distance, assuming the geographical coordinates and antenna heights are known. In the paper it is explicitly described how a set of these points was derived which identify theoretical geometrical center points of the radar pulse volume for a common inter-radar space between two neighboring radars.